Ti IW'82 14-19 JUNE, 1982 Balafonfüred, HUNGARY

mm I82 OF THE INTERNATIONAL CONFERENCE ti IW'82 14-19 JUNE, 1982 BALAfONFüRED, HUNGARY

EDITORS A. FRENKEL LJENIK

BUDAPEST, 1982 SPONSORS

European Physical Society, Central Research Institute for Physics, Hungarian Academy of Sciences, Roland Eötvös University

INTERNATIONAL ADVISORY COMMITTEE I- v C. Baltay USA V. Peterson USA A. Barkov USSR H. Pietschmann Austria A. Bunyatov USSR A. Pomansky USSR H. Faissner FRG B. Pontecorvo USSR E. Fiorini Italy F. Reines USA C. Jarlskog Norway R. Sosnovsky Poland 0. Kiss Hungary L. Suiak USA T. Kitagaki Japan M. Vivargent France K. Lanius GDR K. Winter CERN G. Marx Hungary V. Yarba USSR G. Myatt UK G. Zatsepin USSR J. Nilsson Sweden Ya.Zeidovich USSR

ORGANIZING BODIES

Central Research Institute for Physics of the Hungarian Academy of Sciences, Roland Eötvös Physical Society LOCAL ORGANIZING COMMITTEE

D. Kiss G. Marx chairman vice-chairman

Gy. Csikai E. Nagy A. Frenkel K. Nagy Livia Jenik Marta Nemènyi T. Kovács S. Szalay Edit Nagy K. Szegő Gy. Vesztergombi

TECHNICAL ASSISTANCE

Zsuzsanna Bodi Etelka Horváth G. Huba CONTENTS*

Volume I :

OPENING ADDRESS NEUTRINO OSCILLATION SEARCH FOR NEUTRINO OSCILLATIONS - A PROGRESS REPORT R.L. Mössbauer 1 SEARCH FOR NEUTRINO OSCILLATION F. Reines Suppl NEUTRINO OSCILLATION EXPERIMENTS ON AMERICAN ACCELERATORS C. Baltay Suppl PAST AND FUTURE OSCILLATION EXPERIMENTS IN CERN NEUTRINO BEAMS H. Wachsmuth 13 DETECTION OF MATTER EFFECTS ON NEUTRINO OSCILLATIONS BY DUMAND R.J. Oakes 23 LARGE AMPLITUDE NEUTRINO OSCILLATIONS WITH MAJORANA MASS EI6ENSTATES? % B. Pontecorvo 35 :; TRULY NEUTRAL MICRCOBJECTS AND OSCILLATIONS IN ' PARTICLE PHYSICS S.M. Bilenky 42 '•': A POSSIBLE TEST OF CP INVARIANCE IN NEUTRINO ''} OSCILLATIONS ^ S.M. Bilonky 46 •'

"Papers labelled "Suppl" are to be found in the Supplement to this | Proceedings. Their titles as given here are proviaional. '\ VI.

NEUTRINO MASS AN EXPERIMENT TO STUDY THE 0-DECAY OP FREE ATOMIC AND MOLECULAR TRITIUM R.G.H. Robertson 51 MEASUREMENT OF THE MASS OF THE ELECTRON NEUTRINO USING THE ELECTRON CAPTURE DECAY PROCESS OF THE NUCLEUS S. Yasumi 59 AN EXPERIMENT TO DETERMINE THE MASS OF THE ELECTRON ANTINEUTRINO R.N. Boyd 67 DETERMINATION OF AN UPPER LIMIT OF THE MASS OF THE MUONIC NEUTRINO FROM THE PION DECAY IN FLIGHT P. Le Coultre 75 ff/ RADIATIVE DECAYS OF DIRAC AND MAJORANA NEUTRINOS p (RECENT RESULTS) %\ S.T. Petcov 82

f BEAM DUMP V PROMPT NEUTRINO OSCILLATION BY 400 GeV PROTON £ INTERACTIONS ";;: R.J. Loveless 89 ÍJ A STUDY OF THE FORWARD PRODUCTION OF CHARM STATES | AND PROMPT MUONS IN 350 GeV p-Fe AND 278 GeV n"-Fe p INTERACTIONS | A. Bodek 109

I' NEW PARTICLES p NEW PARTICLES AND THEIR WEAK CHARGED-CURRENT Ç COUPLINGS !| K. Kleinknecht 115 I: NEW BEAM DUMP AND REACTOR DATA ON PENETRATING LIGHT PARTICLES H. Falssner 146 NEW BOUNDS ON HEAVY NEUTRINO MASSES AND MIXING FROM

Kjjj AND ni2 DECAYS T. Yamazaki 178 VÍI. I".

í LEPTON CONSERVATION ï. I LEPTON NUMBER CONSERVED? V I. Kobzarev 190 ;: SEARCH FOR 150Nd AND 130Te 20-DECAY AT BAKSAN k OBSERVATORY ;. A.A. Pomansky 202 *•• THE STUDY OF DOUBLE BETA DECAY OF 10OMo Yu.G. Zdesenko 209 SOME NEW EXPERIMENTAL RESULTS ON DOUBLE BETA DECAY E. Bellotti 216 82Se TIME PROJECTION CHAMBER FOR DOUBLE BETA DECAY A.A. Hahn 231

BARYON NON CONSERVATION MEASUREMENTS ON PROTON DECAY - EXPERIMENTS WITH ii CERENKOV AND SCINTILLATION COUNTERS | F. Reines Suppl [\ NUCLEON DECAY EXPERIMENTS WITH CALORIMETERS f E. Fiorini 235 | NUCLEON DECAY EXPERIMENT IN KOLAR GOLD FIELD I S. Miyake 256 | NEUTRON OSCILLATION jf M. Baldo-Ceolin Suppl i'i, ASTROPHYSICS i" NEUTRINO MASS IN ASTROPHYSICS AND COSMOLOGY r A.S. Szalay and Ya.B. Zeldovich 257 | PROMPT LEPTON GENERATION ATMOSPHERIC MUON AND • NEUTRINO SPECTRA AT HIGH ENERGIES I, G.T. Zatsepin 267 I THE PROBLEM OF SOLAR NEUTRINOS I' G.T. Zatsepin Suppl I THE PROBLEM OF SOLAR NEUTRINO FLUX PULSATIONS AND GRAVITY OSCILLATIONS OF THE SUN Yu.S. Kopysov 274 I } VIII. M' I ASTROPHYSICAL CONSTRAINTS ON LIGHT PSEUDOSCALAR ; PARTICLES : •" H. Yoshimura 282 ;: MUON STRING RESULTS AND DUMAND STATUS F.A. Harris 288 I'•) ADVANCES IN THE DEEP UNDERWATER HUON AND NEUTRINO ; EXPERIMENT ON THE LAKE BAIKAL : G.V. Domogatsky 296 r STUDY OF THE EARTH STRUCTURE BY MEANS OF NEUTRINOS I'. I.P. Nedyalkov 3OO

f THEORY C GUTS, ASTROPHYSICS AND SUPERUNIFICATION § 3. Ellis 3O4 |f THE STANDARD ELECTROWEAK MODEL - EMPIRICAL STATUS f• AND ALTERNATIVE POSSIBILITIES f J.J. Sakurai 346 } QUARK AND LEPTON MASSES AS ELECTROMAGNETIC SELF %• ENERGIES f H. Fritzsch 365 £." PROTON DECAY IN SU (5) MODELS h: V.S. Berezinsky 375 :| PROTON LIFETIME I D. Tadife 387 I LOCAL CONFINEMENT OF CHARGE IN MASSLESS QED ? V.N. Gribov ,....;. 399 h OUTLOOK f: V.N. Gribov 4O5 IX.

Volume II .)

NEUTRAL CURRENTS PRELIMINARY RESULTS ON v + e" •* v + e~ N.J. Baker 1 PROGRESS REPORT ON AN EXPERIMENT TO STUDY WEAK NEUTRAL CURRENT ELASTIC SCATTERING OF NEUTRINOS R.E. Lanou 9 MEASUREMENT OF THE RATIO a(v e •+ v e)/a(v e •*• V e) C. Santoni 2O ELECTRON NEUTRINO-ELECTRON ELASTIC SCATTERING AT LAMPF T.J. Bowles 30 CHARGE ASYMMETRY IN U±N DEEP INELASTIC SCATTERING £. Zupancié 38 MEASUREMENT OF THE NEUTRAL TO CHARGED CURRENT CROSS SECTION RATIOS FOR V -INTERACTIONS ON PROTON AND * NEUTRON P.H.A. Van Dam 51 NONDIAGONAL Z-DECAY - Z -»• ë + u T. Riemann 58 STRUCTURE OF ELECTROWEAK INTERACTIONS g, F. Niebergall 62 I' PARITY NON-CONSERVATION IN ATOMS ;: L.M. Barkov 89 f A SEARCH FOR THE ELECTRIC DIPOLE MOMENT OF THE h NEUTRON fv V.M. Lobashev 107 y I DEEP INELASTIC SCATTERING - STRUCTURE FUNCTION JÍ RECENT RESULTS FROM THE CHARM COLLABORATION |: A. Capone 121 If, NEW RESULTS ON CHARGED CURRENT REACTIONS FROM THE CDHS - GROUP B. Pszola 133 X.

NEUTRINO CHARGED CURRENT STRUCTURE FUNCTIONS A. Bodek 149 NEW RESULTS FROM THE COLUMBIA GROUP P. Igo-Kemenes Suppl ANTINEUTRINO TOTAL CROSS SECTIONS FROM FERMILAB 15 FT BC EXPERIMENT H. Bingham Suppl QCD THEORY OF POWER CORRECTIONS TO DEEP INELASTIC SCATTERING A.I. Vainshtein 159 HIGHER ORDER TWIST EFFECTS J. Morfin

1 DEEP INELASTIC SCATTERING - FINAL STATE ig STUDY OF CHARM PRODUCTION BY NEUTRINOS fi, C. Baltay Suppl V- ANTINEUTRINO QUASIELASTIC SCATTERING IN NEON AND it, TOTAL CROSS SECTIONS FOR CHARGED CURRENT t- INTERACTIONS IN THE ENERGY RANGE 1O to 5O GeV il' S. P. Krutchini n Suppl :V; SOME NF,W RESULTS ON HADRONIC FINAL STATE | H. Bingham SuppJ P' HADRON FINAL STATE RESULTS FROM BEBC r A.M. Cooper 165 J SKAT-RESULTS ON HADRONIC FINAL STATES t R. Nahnhauer 180 ;";•-- HADRONIC FINAL STATES IN HIGH ENERGY MUON-NUCLEON ; SCATTERING, RECENT RESULTS FROM THE EMC •• F.W. Brasse 186

e+e" AND pp COLLISIONS RECENT RESULTS ON e+e~ STORAGE RINGS H.P. Söding Suppl RECENT RESULTS FROM CESR S. Herb 3O5 ; RESULTS FROM THE SPS ANTIPROTON-PROTON COLLIDER K. Eggert 214

'(•• xi.

DETECTORS NEW TRENDS IN DETECTOR CONSTRUCTION K. Kleinknecht 233 NEUTRINO AND PROTON DECAY DETECTOR WITH STREAMER OR GEIGER PLASTIC TUBES E. larocci 234 . A NEW NEUTRINO DETECTOR FOR THE SERPUKHOV ACCELERATOR S.A. Bunyatov 249 PROPOSED HIGH INTENSITY NATIONAL NEUTRINO FACILITY AT LAMPF T.J. Bowles 260

ACCELERATORS STATUS OF THE CERN LEP PROJECT G. Plass 267 FUTURE US ACCELERATORS H. Bingham Suppl IHEP ACCELERATING-STORAGE COMPLEX (STATUS REPORT) A.M. Zaitsev 289

CONCLUSION CONCLUSION TALK AT THE INTERNATIONAL CONFERENCE "Neutrino - 82" V.M. Lobashev 291

LIST OF PARTICIPANTS 305 OPENING ADDRESS

• G. Osxtrovszki

Vice-president of the national Atomic Energy Comission

Ladies and Gentlemen,

Study of the structure of matter, of particles constituting the universe, has become a major task of Jbasic research in the second half of our century. From the early seventies onwards more than a little attention has been paid to one of the most simple, one of the most frequently occurring particles, yet the most difficult to observet the neutrino. It is not only because any insight into the properties of the neutrino presents a prime example of sophisticated technical challenge which provokes stimulating and concentrated efforts in advanced research and development; it has turned out, in addition, that this ubiquitous very special radiation presents a unique probe for the exploration of the innermost structure of nuclear particles and of the stars. Realization of this fact prompted the organization of a aeries of international neutrino conferences which started here in Balatonfüred 10 years sgo. Since then, annually, the most prominent theoreticians and experimentalists of this special and essentially interdis- ciplinary branch of research have gathered. They gather to get acquainted with one another's results, to put forward their ideas, their conclusions, and they discuss their concepts about future trends of research and development.

I have learned that a neutrino is capable of cutting through the mass of the Earth in a fraction of a second. Dynamical movement is also demonstrated by the change in venue of our conference. Xt has moved from the Bhore of take Balaton to the foot of Mount Elbrus, to the southern corner of Sicily, to the fjords of Norway and to the Islands of Hawaii. We know well that Balaton cannot compete with the fjords or with the Pacific. Our gently sloping vine-lands are eclipsed by the snow-capped peak of Blbrus. That is why we Hungarian scientists are particularly happy that the Inter- national Neutrino Committee has now chosen, for the third time, this little resort on the shore of Lake Balaton to be the site of the loth neutrino Conference, tie shall do our best to provide a friendly atmosphere, the opportunity for a frank exchange of ideas. Humanity has now a pressing need for such exchanges of ideas and the progress of science is inconceiv- able without benevolence and frankness. Thank you for having joined us from nearby countries and from faraway continents. I wish you successful creative work in the coming week. It would be our greatest pleasure if this meeting at the Balaton were to be memorable due to the results to be reported by you here. Ladies and Gentle- men, I declare the Conference open. Just ten years have elapsed since the first Neutrino Conference in Balatonfüred. Since then the commemorative trees planted.by Richard Feynaan and Bruno Pontecorvo on the promenade along the shore have flourished. To commemorate this tenth anniversary. The Roland Eötvös Physical Society commissioned the casting of a medal by the world famous Hungarian sculptor, Miklós Borsos, who lives here in Tihany facing Balatonfüred. The medal Í

shows a process intitiated by the neutrino. It gives me great pleasure to t' present a medal to each of the ten organizers of the preceding Neutrino Conferences. They are all well known to us, and are worthy researchers of this topic.

?,'- • • -- Prof. FRED REINES, who was the first to observe a neutrino, who has ./ I! supported the organization of neutrino conferences and himself organized in 1972 a consultation on : the problems of solar neutrinos.

•• "rof. GYÖRGY MARX, organizer of the 1972 and 1975 Neutrino Conferences/ , secretary of the International Neutrino Committee.

;. Prof. SID BLUDMAN, organizer of the 1974 Neutrino Conference. ' Prof. HELMUT FAISSNBR, organizer of the 1976 Neutrino Conference. } Prof. ALEXANDER POMANSKY, organizer of the 1977 Neutrino Conférence.' I Prof. BARL FOULER, organizer of the 1978 Neutrino Conference. if Prof. CECILIA JARLSKOG, organizer of the 1979 Neutrino Conference. I Prof. ETTORB riORINI, organizer of the 1980 Neutrino Conference. I Prof. VINCENT PETERSON, organizer of the 1981 Neutrino Conference. I Prof. DEZSÖ KISS, organizer of the 1982 Neutrino Conference. I .

NEUTRINO OSCILLATION I SEARCH FOR NEUTRINO OSCULATIONS - A PROGRESS REPORT

f CALTECH - SIN - TUM Collaboration i1. Presented by: R.L. Mössbauer f Physik Department, Technische Universität München

f ABSTRACT

£ A progress report on a continued search for neutrino oscilla- ; tions is presented. The v spectrum has been measured at a f distance of 37.9 m from the core of the GOESGEN power reactor, - using the reaction V +p—l>e*+n. The data analysis uses experi- ; mental information on the different v spectra emitted by the |j reactor core. New limits for neutrino oscillation parameters H are presented.

&!• Bf 1 . INTRODUCTION '&, - Je A search for neutrino oscillations of the type v "*~*X has been i£ performed at a distance of 37.9 m from the core of the GOESGEN § power reactor (experiment II) by the CALTZCH-SIN-TUM collabo- ?.'.' ration . This search succeeds a previous experiment which had f been carried out at a distance of 8.76 m from the core of the |í ILL reactor (experiment 15 by the CALTECH-ISN-TUM collaboration . I- l| Oscillations will occur if neutrinos of definite flavor instead •V of beirg 'mass eigenstates are linear combinations of them. In j£" this case, neutrinos of one flavor, e.g. electron antineutrinos £ emitted by a fission reactor, will exhibit intensity oscilla- '• tions in space. In the most simple two neutrino case, these vi oscillations are characterized by parameters Ai=Jm2-m2| and I'; sin*20, where 0 is the mixing angle. The intensity of the origi- fc nal flavor oscillates with distance L according to P

(E- in MeV, h in m, A2 in eV2)

The search for such oscillations is hampered by the limited resolution in space (core and detector extension) and in energy (detector resolution). By consequence, the oscillation angle •»2.5A*L/E- experiences a smearing which is given by a + (AE3/E-| J*

',/:) A crude estimate of the resolution limit for the mass parameter ; M A1 is obtained if one notes that the limit for separating two ?'j oscillation peaks is given by A$=2ir. Thus, one arrives at a VÀ resolution limit t *• <îiS LL5 + (AE-/E-)2Jî I(AL)1 • (AE-)2(L/E-)21I

ï:j Note» that changing the distance L does not modify the contri- •> bution from the spatial extension of reactor core and detector, ;',) while such a change does influence the impact of the energy F? uncertainty which» in fact, grows in propertion to L/E-. I) Considering typical resolutions in space and in energy of order J1; of 10% and 15%, respectively and typical reactor neutrino ener- ffe gies of order of S MeV, we arrive at resolution limits: I A1 < 8 (eV2) (experiment I; L • 8.76 m) |> . A2 < 2 (eV2) (experiment II; L = 37.9 m) íz Experiment II was performed in an effort to scan a range of • - mass parameters lower as studied previously. Simultaneously, an .t. improved limit for the mixing parameter is obtained in the domain of large mass parameters, where the oscillation term aver- ; ages out and P(E-,L,A2,0) in Eq. (1) reduces to 1 - |sin220.

? 2. NEUTRINO DETECTOR

+ : The neutrino detector uses the reaction v_+p—*e +n which has a !| threshold energy of 1.8 MeV. We therefore have in very good ? approximation E(e+)=E- -1.8 HeV. The detector is used to search i;: for the disappearance of the v state due to neutrino oscilla- i"- tions. The detector assembly consists of four JHe wire chambers | (serving as neutron detectors) intercalated between five planes of six target cells each (serving as proton target, liquid scintillation positron detector and neutron moderator). This central detector unit is a modified version of the one employed in experiment I. The new unit allows for position sensitive detection of positron and neutrons events, thereby enabling a rather effective suppression of accidental coincidence events. - 3 -

In fact, a reduction by a factor of seven in the accidental background rate was achieved, at the modest cost of a 8% loss in detection efficiency. The modifications introduced for this purpose consist in the introduction of time of flight registration techniques for the light pulses in the positron detection cells and in the replacement of the single wire readout system of each *He chamber by a multiwire system. The sHe proportional chambers now have each 16 groups of four resistive wires (Cr-Ni;25 am) arranged in a plane with 1.7 cm spacing . Charge division techniques are employed to determine the position of an event along a wire. The exclusive use of stainless steel and teflon in the chamber walls and wire sup- : porting frames made it possible to keep the natural radioac- j '%, tivity down to previously achieved low levels. f fr Fast neutrons generated by cosmic radiation and giving rise 5 | to proton recoil pulses in the target cells succeeded by |- neutron pulses in thes He chambers are the most serious source j£ of possible false coincidence events. An efficient discrlmina- f tlon is achieved by means of pulse shape discrimination tech- I nique:.. I > {- The central detector unit is completely surrounded by veto ' 1 counters followed successively by 5 mm of B.C, 20 cm of H_O, ; 15 cm of steel and 2 m of concrete with an additional 2 m of : concrete overhead. The entire assembly is positioned outside i the reactor building, which provides an additional 8 m of concrete shielding from the core. The reactor associated background is assumed to be negligible, since this was demonstrated - to be already the case for the less optimal shielding conditions of experiment I. : i(• • 3. NEUTRINO SPECTRA if.! "'•• Neutrino oscillations according to Eq. (1) depend on both energy "if E- and distance I». An interpretation in terms of oscillation ,j parameters of neutrino rates measured ás a function of energy 1 at only one fixed distance L requires a knowledge of the perti- J nent reactor antineutrino spectrum and uncertainties in this 4 i spectrum are propagated into the oscillation parameters. This >| source of error can be largely eliminated if experimental data | - 4 -

are available for two or more different positions under otherwise equivalent conditions. Semi-theoretical evaluations of reactor associated antineutrino spectra due to differing assumptions about unknown beta decay schemes differ substantially in their spectral distributions 4'S. A special program was therefore initiated at ILL to accurately measure and cali- brate the electron spectra of the most important fissile Isotopes and the derive the associated neutrino spectra by inversion procedures. As a result, neutrino spectra are now available for the isotopes *isU and ISSPu6, as shown in Pig. 1.

St»sU)-St S(Eç)/M«V fission S| »5

2 3 4 5 6 7 E7[MtV]

Left part: Electron antineutrino spectra emitted by the fission products off 2ííU and ÎJ*Pu, as deduced by Schreckenbach et al. from their absolute measurement of the beta spectra6.

Right part: Relative difference of the spectra shown on the left.

These «pectra involve emission processes with neutron exposures of the fissile isotopes of at least 1.5 days, which effectively correspond« to secular equilibrium for the neutrino energies <>2.7 MeV) employed in our oscillation experiments. - 5 -

The GOESGEN reactor (2806 MW thermal power) releases energy essentially by the fission of tM0, lJtPu, *••» and 2*1Pu, with fission contributions of 61.1%, 27.8%, 6.7% and 4.3%, respectively, averaged over the duration of the measurements . The fission rate for each fissile isotope was obtained from the values of the energy released per fission . The composite time averaged neutrino spectrum due to the beta decay of the fission products is then obtained by combining these fission rates with the neutrino yields per fission. For the latter we have used the data of ref. 6 (shown in Fig. 1) for the two dominant isotopes 21SU and iJ*Pu, while calculated yields were used for the relatively small contributions from the remaining isotopes.

4. MEASUREMENTS

Data collection and detector calibration followed essentially the procedures employed in experiment I, with the added com- plexity introduced by the position determination of observed events in the target cells as well as in the 3He chambers. A total of 10,930 ± 220 neutrino induced events were recorded in experiment II during a six months reactor-on period (3441 h of data acquisition). Background measurements were taken for 551 h during one reactor-off period. The deadtime, largely due to cosmic ray events in the veto counters, was 15.8%. The measured coincidence rate is shown in Fig. 2a. Fig. 2b gives the experimental positron spectrum.

5. DATA ANALYSIS

The neutrino Induced positron yield in the simple two neutrino model is given by

2 J! Ï(E +.L.* ,0) - /Y(E,L',A ,G)-a(Eo+)-r(Bii+,E)*h(L,L')-dEdL' (2) c 6 6 where

2 i YtE,!.,* ,©) * YnQ ogc(E,L).P(E-,I.,& ,0) Yno osc(B'L) * Y(E,L,O,O) - iyo(E-> »C'S(E-)/(4nL*) * positron yield in case of no oscillations - 6 -

-.iM neutrino oscillation function, Eq. (1) acceptance of pulse shape discriminator. (varies with energy from 94% to 97%) positron response function of detector h(L,L'> weighing factor for extension of reactor core and detector h mean distance between reactor core and detector Ev energy of neutrino

counts T I a) MeVh m (a) Reactor—on and reactor-off spectra. reactor on The dashed curve reactor off indicates the contribution of the accidentals.

b) Reactor-on minus reactor-off spectrum» giving the experimental positron yield

?e . The solid curve represents the predicted positron spectrum assuming no neutrino oscillations E +(MeV) (ïno ose* *

Fig. 2 Experimental résultat Coincidence rate (e*,n) as a

function of observed positron energy E#+. Bin width 0.305 MeV. The errors shown are statistical. - 7 -

E E- -1.8 MeV - kinetic energy of reaction generated positron total energy deposited by positron within detector (observed energy) number of protons in the liquid scintillator ír 0ÍB-I reaction cross section t-' net detection efficiency (windows for neutron energy and for coincidence time and position correlation Imposed for positron and neutron counter events); e - 0.166 t 0.005 S(E-) neutrino spectrum at I» • 0» comp. Fig. 1

The positron response function r(Ee+,E) was obtained by Monte Carlo calculation. The effects of positron annihilation in flight and at rest, positron entering from the lucite walls of the target cells, gamma ray multiple scattering and photon statistics were taken into account. Fig. 3 shows the positron response function for a few selected energies.

.If Fig. 3 Examples for the response

function r(Ee+,E) for monoenergetic positrons with kinetic energy E.

E_+ is the positron energy observed in the detector.

Ec*(MtV)

We shall now consider the ratio R of the positron yield Y to the yield Y predicted for the case of no oscillations. Fig. 4 * no ose F , shows the ratio R.v_ (i«1,2...16» of the experimental data I 4 p Y to ? _ plotted as a function of L/E-. For the integral exp no ose v yields we find (for E- > 2,7 MeV):

Í - 8 -

osc

> 1.05 t 0.02 (S.D., statistical) * 0.05 (S.D., systematic)

1 1 I rtxp 'no ox # 1.2 -

*~ 1.0 -^)

OJ - Af«0.8eVf,$in»29»0.15

1 t I 15 L/E7 (m/ticV)

Fig. 4 Ratio of experimental positron yields Y~M_ to predicted . exp no oscillation yields Ï* ___» for the 16 energy bins employed no osc In the experiment. The errors shown are statistical. Oscillation functions obtained by parameter fits (see text) are shown (or several sets of oscillation parameters. Assuming independent data points with approximately Gauss I>n distributions (yield measurements in 16 energy bins and in addition a measurement of the energy gain g (t.2% S.D.I and of the spectral normalization N (5.3% S.D.), altogether 18 data points),th« log likelihood function reduces to the expression I "9 '

QMA'.e.K.g) - E -^r (R* - N-R2 + i« 1 a. * " p

where

Q1 was minimized for a large number of fixed values of Az and 9, varying N and g. The values of Q2 would follow a X2 dlstri- bution (with the number of degrees of freedom given by the number of data points minus the number of parameters with respect to which the minimization is performed) in case the fit parameters would enter in an uncorrelated fashion. A maximum likelihood test was performed for the parameters A and 0. For this purpose one evaluates the function

A(Aa,0) = §{Q2(A2,0,ft ,g ) - Q2(22,0 .ft ,g )} (4) 2 1001111 where the roofs indicate parameters obtained by minimization of Q2. Here, the quantity U2(S2,0 ,N ,g ) = 11.8 (with Â2 = 0.18 eV2 n » Oil. 11 1 and sinz20 = 0.04) is the minimum of Qz in the Az-0-plane. In the ideal, case of uncorrelated parameters, X as defined above would exhibit a X* distribution. Confidence contours could then be readily obtained, a procedure corresponding essentially to an F test. For our situation, an expected A distribution was evaluated by repeated Monte Carlo simulation of the data points. Confidence contours in the A2 and sinz20 plane were then determined by selecting such pairs of values of A2 and 0, for which the experimental data lead to Q2 values in Eq. (3) and to related A values in Eq. (4) corresponding to the considered confidence level in the A distribution. The 68% and 90% confidence limits obtained in this way are shown in Fig. 5. The regions to the right of the contours are excluded. The same procedure was - 10 -

applied to the ratios of the data of experiment I to the present

date, Rexpd.-8.76m)/Rjxp(L-37.9m). These ratio« are rather insensitive to the uncertainties in the neutrino spectrum following the fission of *»»u and are essentially independent of the uncertainty in the energy scale (g is kept fixed at g»1). ,¥ However, the experimental conditions in experiments I and II cannot be considered equivalent, because reactors with different compositions in fissile isotopes were used and because modifications made on the detector between both experiments result in somewhat different efficiencies. Besides, experiment I has a more moderate statistical accuracy. The result of the maximum likelihood test, which is shown in Fig. 5 with the label I/II, therefore, is not very selective.

SI 2 in A* (tV ) IOJO

•â; Fig. 5

Limits on the neutrino oscillation parameters A2 and sin220 given by the present experiment II. The regions to the right of the curves are excluded at the confidence level indicated. Limits obtained from the ratio of experiment T |L*8.76m) to experiment it

OJ02 0.0 0.5 1.0 sin2 29 - 11 -

6. CONCLUSION ^

We conclude, that on a 90% confidence level there are no neutrino A oscillations with parameters In the area to the right of the t contour plots labelled II In Fig. 5. In the limit of large mass p parameters we find sin*20 < 0.17 (901 CL). In the opposite case of large mixing angles we obtain A2 £ 0.016 eV* (901 CL). These new limits are substantially more restrictive than the bounds established in experiment I. The disagreement with the results of ref. 9 la further enhanced. The experiment is being continued at a larger distance from the core, in order to arrive at a situation, where measurements at different distances can be com- > pared under otherwise equivalent conditions. Furthermore, a special effort will be made to restudy the range around A* = 1 eV*, where the presently available sensitivity to |_; oscillations prevents the realization of more restrictive limits. 'f-

REFERENCES

1) Experiment II: CALTECH-SIN-TUM Collaboration, J.-L. Vuilleumier, F. Boehm, J. Egger, F.v. Fellltzsch, K. Gabathuler, J.L. Gimlett, A.A. Hahn, H. Kwon, R.L. Mössbauer, G. Zacek and , V. Zacek, Phys. Lett.,in print • 2) Experiment Is CAIVTECH-ISN-TUM Collaboration, H. Kwon, ; ;; F. Boehm, A.A. Hahn, H.B. Henrikson, J.-L. Vuilleumier, Y| J.-F. Cavaignac, D.H. Koang, B. Vlgnon, F.v. Feilitzsch * and R.L. Mössbauer, Phys. Rev. D2_4 (1981) 1097 1 3) G. Zacek, et al., to be published ; 4) F.T. Avignone III and Z.D. Greenwood, Phys. Rev. C22 (1980) 594; W.I. Kopeikin, Sov. J. Nucl. Phys. 32 (1980) 780; H.V. Klapdor and J. Metzinger, Phys. Rev. Letters 4JÎ (1982) j 127 and Phys. Letters 112B (1982) 22 |j "~"~~~~ !-v-r 5) P. Vogel, G.K. Schenter, F.M. Mann and R.E. Schenfcer, if Phys. Rev. Ç_24 (!981) 1543 |^ 6) K. Schreckenbaeh, H.R. Faust, F.v. Feilitzsch, A.A. Hahn, J K. Hawerkamp .md J.-h. Vuilleumier, Phys. Lett. 99B (1981) - 251; F.v. Feilitzsch, A.A. Hahn and K. Schreckenbach, "i to be published 'Ä 4 - 12 -

7) G. Meier and N. Sauser, KKW GOESGEN, privat* coraaunleatlon 8) M.F. Jane», J. Mucl. Energy 23 (t969) 517; J.N. Parait«, Technische Mitteilung Nr. TM-45.81-19, Swiss Institute for Reactor Research, WUrenlingen, Switzerland 9) F. Reines, H.H. Sobel and E. Pasierb, Phys. Rev. Letters 45 (1980) 1307

He acknowledge financial support from the BMFT of the Fed. Rep. of Germany and from the U.S. DOE. - 13 -

PAST AND FUTURE OSCILLATION EXPERIMENTS IN CERN NEUTRINO BEANS

H. Machsmuth CERN, r.encvn, Switzerland

In previous neutrino experiments at the CERN PS and SPS in the • 0.01 m/MeV no evidence was found for neutrino oscillations. Throe experiments using the PS at Ï2-18 GsV and the SPS neutrino detectors at ^ 1 km distance arc prepared and scheduled for 1983 and will explore possible v oscillation phenomena in the l/K range of ^ 1 m/MeV. Appendix: ;;;

In preparing an e-capture experiment to measure the mVe mass, an ISOLDE group could reduce the present limit of 4.1 keV to 1 keV. f •'.

,? 1 • IÎ!î!iQ!2UÇÏlQÎÎi_!î2MKNÇUTyRE_AND_AÇ»_UEyABLE_UMITS i Accelerator neutrino beams obtained from * and K decays consist mainly u v of muonic neutrinos ( u) with only a small (.5 to !t) contamination of

V electron neutrino? (v^) from v and Kc3 decays (1|. This feature was used X- to establish the existence of the two neutrino types (2) and to confirm the :: law of lepton number conservation (3]. It can also be used to search for i; small deviations from lepton conservation caused e.g. by oscillations from i? one kind of neutrino (v. ) to another (v.).

It The conditions for such oscillations are (4]:

: (a) Non-zero neutrino masses (present limits: m- < 3S eV, mv < 4.1 fcev, > "v *5Z 0 keV> "v *2S 0 MeVK and â»îj » *\ - m* + o- '

^ {bi The weak charBed current eigenstates v^, v^, etc. are superpositions (• ("mixings") of mass eigenstates v,, v,, etc., such that « neutrino \ which is born« e"8- «s a \ develops in time like (in case of two : states with one mixing angle a):

l ví*í " -u> sina exp(-iCit) • vi cosor exp(-iEit)

.4 - 14 -

Oscillations would then manifest themselves: (a) either as an excess of one type of neutrino measuring the probability e.g. for a v to appear after time t or distance I as a v

• sin'Za . sin' j (Ei - Ej)t

- sina2a . sin'U.27 Am* g )

(mainly in bubble chamber experiments determining v event rates with typical accuracies of 0.11 relative to v rates),

(b) or as the disappearance of the same type of neutrino measuring the

probability, e.g. for a \>e to remain a v^:

- sin'Za sin'(1.27 Am* ») e*e

(mainly in experiments insensitive to v measuring event rates typically with 10 to 20t error).

The factor of sin*(Am2 g) shows that only when Am' is of the order of 1/E will there be oscillatory behaviour in the composition of the v beam. For Am2 << l/E there will be no effect, for Am* >> t/E only average effects are observable. In conventional v beams l/E ranges from t .005 to "*• .04, , in special long base-line beams (as prepared at CERN for 1983) from -*> 0.S to ^ 1 m/MeV.

The achievable limits on a or Am* are then givan by the accuracy with which an excess or lack of a certain type of v can be determined: for the extremes of large mixing angle

for large m' differences

un11* j s in*2aWn 2 R~föT" lfZ in case

Extreme limits for the two types of oscillation experiments are as follows:

Sin for 100 < t> ^ 1 3 .03

20 .2 - 15 -

In lift» kl the so limits depend on the neutrino energy spectrum and require mute elaborate analysis if simultaneously oscillations between »or« tbnn two types of neutrinos are considered JS|.

Location, distances and average neutrino energies Cor past (and future) v» experiments are indicated in fig. 1.

A list of the neutrino experiments at CERN having published oscillation analysis results is given in table. 1.

«0« canfl 1 1 I 4«' lila I« . 1) »I» »« (4a • -I «GM (PS) »1 V I« •" -.0) I .1 1*1 < 1 (u • •) .001 V II .' .01 I .07

«tue IM MO il •' .04 « .11 < II (a • a) .»

•f.»C («I |l| 10 »J «". .17 • .11 < 10 (• • al .•7 < 1.7 U« a) .01 « I (u • 1) .01 (*> III < J.I . ID' « «.'ivy .«•I

«UM (SPSI < .004 « Î (» IIUI « 4 (V

10 u, * I« st < t « *0 (* • .7* "prtiapt"

•# pro«pt CIIMM Illl H«î > SO (a • >) II,ISI

(•I «k • »I4> bind, ni • nirr«« bund, MI • beaa 4uap.

In all hnavf liquid bubble chambers experiments (Gargamelle (GGMJ with propane or freon, BEBC with a Ne/Ha mixture) electron event rates «re

compared with those predicted from the ve admixture In tha beam. Summarizing table 1, no evidence for v oscillation is found. The interpretation of the beam dump result f12] - with lass significance *l»u

observed in the other two beam dump experiments (11.14J - as «e disappearance is not confirmed by the BEBC narrow band and wide band experiments [7,8|. - 16 -

3. £!ÍÍÜHE_w_OSCiUATiON_|XPERIMENTS_AT_

Apart from experiments having taVen datn already (the BRBC-KASO Collaboration might improve the P_.» -measurement from y- 200 v events In Ne/IU ) or are taking data now (the three beam dump experiments will study further the e/n event ratio), several proposals have been made to study w oscillations with largertsensitivity than previously accessible. Two have

been deferred: a special \>c beam from K* decays with the SPS \> beam line (151 and using BEBC as d detector and a tong base-line experiment using two fine grain calorimeter detectors the second of which should be placed behind the Jura mountains (16).

3 • * Three experiments [18-20] using the PS and directing a 12 or 18 GeV proton produced v bean towards the neutrino detectors used presently in 400 GeV v beams have been approved and will run in 1983.

These experiments require the construction of a new neutrino area (17) (indicated on fig. 1): a fast ejected proton beam with transport onto a Be target, target area useable with or without a new magnetic horn (for parent focusing), * 45 m long decay tunnel, 4 M iron shield with muon flux detectors after 2 m (for beam monitoring). This beam area is nearly completed.

3.2. The_coun_t er_exgerjjügnt s

The CDHS [18] and CHARM (19) Collaboration want to compare v event rates in their present detectors (i 900 m distant from this new target) with those in similar but smaller detectors closer to the target (^ 140 m) to look for the disappearance of v^ in the distance between the near and the far detector.

The near detectors consisting of modules identical to those of the far detectors will be mounted inside an ISR intersection hall (fig. 1) at the same angle with respect to the v beam as the far detectors (22»), in order to approach identical detection efficiencies.

The CDHS near detector will consist of six modules: 2 with.2.5 cm, 2 with 5 cm and 2 with IS cm thick Fe plates, equipped with scintillators. The CHARM near detector will be formed of three of the 13 modules of the far detector (marble plates with layers of scintillators, proportional drift tubes and streamer tubes) followed by a u catcher (20 Fe plates 4 x 4 x 0.08 m* Interleaved with proportional tube layers).. Fig. 2 shows the efficiency for detecting events with a muon (Charged Current (CC) events) in the two detectors as calculated by the CHARM group. - 17 -

The beam should be run without horn focusing in order to have a simple spectrum relation at the two distances (about ^(distance)"1).

3.i The_BEBC_exEer±ment

A Padova-Pisa-Athens-Wisconsin group proposes [20] to use BEBC with a 7SI Ne filling to search for electron events in excess over those expected

from the «e admixture in the v beam. The beam would be the same as for the counter experiments but horn focused (to increase the event rate) and directed towards BEBC (Z4S with respect to the high energy beam axis).

At the far distance the beam will produce i 6 events per ton and lü'* protons without and up to i 70 with horn focusing with an uncertainty due to the poorly known particle production. The rates given in table 2 take cuts and detection efficiencies into account.

Sensitivities are limited in the counter (• vy-disappearance) experiments by uncertainties in the far to near event rate ratio due to beam geometry, » production model, difference in detection efficiencies and backgrounds (101 v loss should be measurable at 90t CL (fig. 3)) and in B6BC by the v beam component and event misidentification (altogether O.S» of the v„ events). The three proposed experiments are summarized in table 2 and their expected limits for sln*2a and &m* in fig. 4.

Sumer? of 1913 v oscillation experiment* »t CERN

Collaboration Search Detector Distance Hast No. «'«at« «V ein'zs tor (a) (t) per lo" pr. CIHIS dl># Fe-plate MO 3S0 »000 v » icint. • 2S .12 arra? »70 1200 2000 CIIAHM Marble plate no «0 ÎS00 • iclnt. .1% .IS - .« » prop, tube 13S 200 appearance array 900

PPAK KtC (7St Ne) 11.« . 2S0 .1 .02 • .0} 140

v -appearance 4. CONCLUSIONS The search for neutrino oscillation re*«ins an important field of research. Accelerator v beams will extend in the near future the t/E region and hence sensitivity. However, also this will represent only A small window on the large scale of l/E, and oscillations might happen with much smaller mixing angles than accessible to accelerator experiments.

I APPENDIX

At the CERN Synchrocyclotron an ISOLDE group is preparing an experiment to determine the vg mass from the inner bremsstrahlung spectrum accompanying e-capture in ' "Ho [21]. In preparatory experiments (22) during which the Q value for the '*'Ho-lc>Dy transition was determined to 2.3 * 1 keV and a " 5Ho half-life of (7 * 2).10'y was deduced (see also the contribution by Yasuml to this conference), th« ve mass limit could be 'reduced from 4.1 keV {23] to 1.3 keV. In an experiment testing the method s with " Pt a mv,e limit of about 1 keV was derived (24). - 19 -

Jlj II. h;irhsmiiili. Physics of Neutrino Beams, in: Weak Internet ions, Proc. "Inrico I-IT mi" School I eels M. Baldo Ccolin) (1079) 145-163. k: [21 0. U.mhy ct ;i I . , phys. Kev. Lett. 9 (li»62) 36. f |J| M. Block ot al., I'bys. Lett. 12 (1964) 281; K. lîorcr et ni., Phys. Lett. 29B (1969) 614.

.'/ |4| B. PoTitecorvo, Zh. Eksp. Theor. Fir. 53 (1967) 1717 (JETP 26 (1968) 9«4|; S.M. Itilenky and B. Pontecorvo, Phys. Rep. 41 (1978) 2Z5.

|S| V. Burger, K. Whisnant and R.J.N. Phillip;;, Phys. Rev. 022 (1980) 1936. (6) t. Bellotti et al., Niiovo Cim. Lett. 17 (1976) 5S3; J. Blietschau ec al., Nucl. Phys. B133 (1978) 20S. |7] |{. Dcden et al., Phys. Lett. 98B (1981) 310.

[8] 0. Erriquez et al., Phys. Lett. 102B (1981) 73.

(9j A.M. Cooper et al., Phys. Lett. 112B (1982) 97.

(lOj N. Armenise et al., Phys. Lett. 100B (1981) 18.2.

Ill] P. Fritze et al., Phys. Lett. 96B (1980) 427.

[12] M. Jonker et al., Phys. Lett. 96B (1980) 435..

| 1.31 A. OeKújtila et al., CERN report TH 2788 (1979). (14 I H. Abramowicz et al., Z. Physik (1982). IIS) B. Jongegans et al., CERN/SPSC 80-77 (P150). f16I T.C. Bacon et al., CERN/SPSC 82-20 (P178) {17} D. Dumollard, P. Lazeyras and D. Simon, CERN/PS/MU/EP 81-6. (18) H. Abramowicz et al. (CDHS Collaboration), CERN/PSCC/PSO.

[191 F. Bergsma et al. (CHARM Collaboration), CERN/SPSC/P37.

120j M. Bal do Ceolin et al. (Padova-Pisa-Athens-Wisconsin Collaboration), CERN/SPSC/P77, PSCC/P33.

(21| A. De Rújula, Nucl. Phys. 188B (1981) 414.

(Z2| J.U. Andersen et al., CERN/EP 82-50, submitted to Phys. Lett. B. (23) E. Beck and H. Daniel, Z. Physik 216 (1968) 229. (24) J.U. Andersen et al., CERN/PSCC 82-7, M97. - 20 -

1979 BEAM DUMP I (fí NB : 700 m , (E) -70 GeV vT •o WB :82Om. -30GeV /H ü> SPS I/BEAM SS ?s

Fie. 1

100

»80

CDHS

I.,-

.3 .5 .7 .9 I.I 1.3 1.5 1.7 1.9 -2.1

Fig« 2 - Detection efficiency for CC éventa in the counter experiments Nf

KM, Nc 30-75 cm Fe Detectors at 100m , 900m 1.0

0.8

0.6 I o N9 a:

0.4 b)CDHS

o.; 2 2 2 >m (eV ) Fi 3 - Normalised event rate ratios in far to ,25 ,50 ,75 1,0 Í .25 1.5 near detector, (a) as a function of 1 E (GeV) energy (CHARM) for 2 values of Am , (b) as a function of Am* (CDHS) - 22 -

1 3 1 - \ 1 CHARM )1/ 2 CDHS 3 BE8C I 4 GGM (PS) 2 K \

\ - e CO 1 v 3 \\

v —-=== \ • I— ** _ —1 - 1 | 0.5 1.0 sin2 2o

Fig. 4 - Sensitivity limits obtainable in the proposed experiments compared to the one obtained by the Gargamelle experiment ; - 23 -

DETECTION OF MATTER EFFECTS ON NEUTRINO OSCILLATIONS BY DUMAND

R.J. Oakes

Department of Physics and Astronomy, Northwestern University

; Evanston, Illinois, 602D1, U.S.A.

ABSTRACT

r The feasibility of detecting matter effects on neutrino oscillations with the Deep Underwater Muon And Neutrino Detector (DUMANO) are I discussed. It Is shown that DUMAND 1s sensitive to a wide range of ;' possible neutrino masses and mixing parameters and that detecting the effect of the earth on the propagation of prompt atmospheric neutrinos appears possible.

; In this talk I shall discuss the possibility of observing the , Influence of matter on neutrino oscillations with-the Deep Underwater Muon And Neutrino Detector (DUMAND). The DUMAND array of detectors Is { shown 1n Figure 1 and the deployment site Is schematically depicted In Figure 2. The modules are 13" PMT'S enclosed In 17" benthos glass spheres arranged 1n six rows of six strings, deployed In a flat region of ocean basin at a depth of approximately 4.7 km, with the strings being spaced 50 m apart. Along each vertical string 21 modules are attached at 25 m Intervals. Thus, there are a total of 756 modules (6 : x 6 x 21) throughout a volume of about 3 x 107 m3 (250m x 250m x 500m). Since some neutrino Interactions occuring outside will also traverse pi ' the array, the effective volume 1s actually larger by about an order of magnitude; I.e., ~106 tons, at least for nuon neutrino charged current - 24 -

1 [ 1 ,

1 1 II

i t

i >

Fig. 1. The DUMAND array of detector modules. There are 36 strings, each anchored at the bottom and spaced 50 m x 50 m apart. Along each string there are 21 PMT modules, each spaced 25 m apart vertically. - 25 -

30 KM

KEAHOLE POINT LABORATORY

POWER a SIGNAL CABLES

RETRIEVAL LINES

Fig. 2. Deployment of the DUMAND detector array at a depth of approximately 4.7 km about 30 km off Keahole Point on the western side of the Island of Hawaii. - 26 -

events. The most prominent events will be these charged current nuon neutrino Interactions and the expected counting rate for high energy muons (Ej, > 1 TeV) produced by atmospheric neutrinos 1s about 10,000 events/year.* Some time ago Wolfenstein? pointed out that electron neutrinos propagate differently In ordinary matter than mu and tau neutrinos due to the contribution to their (real) forward scattering amplitude from charged current Interactions with electrons:

^ (1)

The electron neutrinos, therefore, propagate In matter with in index of refraction^

?$ f(o) (2) and consequently aquire a relative phase proportional to the distance L from their production:

e 1k(n-l)L „ e 1 /2 GÍU. (3)

Note that the matter effect on neutrino oscilacions depends only on the amount of matter traversed and is Independent of the neutrino energy E, unlike the vacuum neutrino oscillations which depend on L/E. And since the Interaction 1s weak,the effect becomes Important only for distances L on the terrestiai scale. The general analysis of the Influence of

1. For a nore complete description of DUMAND, see The DUMANO Project Description, V. Stenger, ed., Hawaii, DUMAND Center (1982). 2. l. Wolfenstein, Phys. Rev. 0 ^Z» 2369 (1978). 3. Compare the analogous phenonenon of K° -R° regeneration In matter where the coherent forward scattering, however, Is absorpti.e rather than dispersive. - 27 -

coherent forward scattering In matter upon neutrino oscillations has been given by Barger, Pakvasa, Phillips and Whisnant* and In this talk I will emphasize the possibility of detecting these effects In DUMANO.

/! The main Ideas for observing matter effects on neutrino J oscillations 1n DUMAND are Illustrated 1n Figure 3. All types of I neutrinos result from the prompt decays of heavy, short-Hved hadrons, '\ primarily charm, produced by cosmic rays in the earth's atmosphere. ~i Unlike atmospheric neutrinos, resulting from IT and K decay, the angular y distribution of prompt neutrinos is uniform, absorption before decay -fej being negligible. And with increasing energy prompt neutrinos become a \\ relatively larger fraction of the total neutrino flux. Thus by r I comparing the composition of the flux of very high energy neutrinos ; arriving in the DUMAND array at zenith angles 8 and ir -8 one can, in principle, Investigate matter effects corresponding to distances the . order of the earth's diameter as 0 is varied, as indicated In Figure 4. •J • Next, let us briefly review the general formalism for describing neutrino oscillations?»* which can then be used to discuss the suitability of DUMANO for observing matter effects. The neutrino

states va (a - e.w.t) that enter in the charged current weak Interactions do not necessarily have definite masses but are related to the mass eigenstates vj (i = 1,2,3) by the unitary transformation U : which diagonlizes the neutrino mass matrix: ró i IV 4. V. Barger, S. Pakvasa, R.J.N. Phillips and K. Whisnant, Phys. Rev. D j?2, 2718 (1980). See also the reports of this work given by S. Pakvasa, DUMAND Symposium, Vol. 2, p. 45 (1980) and V. Barger, Telemark Conference, p. 15 (1980). - 28 -

Fig. 3. Prompt neutrinos result from the decay of short-lived hadrons, primarily charm, produced in the atmosphere by incident high energy cosmic rays. Neutrinos arriving in OUMAND at different zenith angles will have traversed vastly different amounts of matter. - 29 -

1 1 1

4 I0 y—"""" "

I03 - I • / LU 100 I 10 -Je

% 1 1 1 1 1 i 0° 30° 60° 90° '120e 150° 180° ZENITH ANGLE 9

Fig. 4. Neutrino path length L through the earth as a function of zenith angle 8. - 30 -

K > - ï "ail»1> (« " e.M.t) (4) 1«i,2s3 Any neutrino state |<>> at a (proper) time t after Us production can be written as superposition of the neutrino mass eigenstates

!•> (t) - I *(t) |v,> (5) 1«ls2,3

Since the neutrinos are produced In charged current weak Interactions

!•>(<>) * |va> (a - e,u, or T) (6) and the amplitudes i>]{t) satisfy the Initial conditions *i(o) - U«i (7)

The amplitude for the transition va + v^ (a,fl * e,u,T) to occur after a time t Is then simply t A(va * v3) = (t) « I l)1e ^(t) (8) 1-1,2,3 and, of course, the probability 1s:

2 P(v« * v0) - |A{va * vß)| (9)

The probability amplitudes

(10)

Here G 1s the Fermi constant and Ne Is the density of electrons In the medium the neutrinos are traversing. Writing Ne * pN^, where N^ Is - 31 -

Avogadro's number, the average value of p for the earth Is about 2 for the mantle and 5 for the core. Rather than Integrate Eqs. (10), we shall discuss their Implications 1n terms of the lengths; I.e., distance from production (L - ct), which charaterize the vacuum oscillations and the matter effects. For vacuum osdlations the characteristic length Is

Ly « 4*E/Am2 « 2.5 E(TeV)/Am2 (eV2) x 103 km (11)

And for the matter effects:

3 LM - 2»//2 G Ne « 6 x 10 km (12)

Note that LM is approximately one earth radius. For matter effects to have a significant Influence on neutrino oscillations there are several criteria that must be met and these will dictate the range of neutrino parameters for which DUMAND is potentially a suitable detector: (1) The distance L from production should exceed a significant fraction, the order of 20%, of thg vacuum oscillation length, which Implies a lower bound on Am L/E.

3 2 2 L > 1/5 Lv ~ 0.5 x 10 km E(TeV)/Am (eV ) (13)

(11) The distance from production L should also be greater than a significant fraction, again, the order of 20%, of the matter oscillation length; but, of course, L cannot exceed the earth's diameter ~ 2 L^. Consequently, L is bounded both above and below. (14) 0.2 LM < L < 2 LM

(Ü1) And for the matter effects to interfere appreciably with the vacuum oscillations we also require 2 °- H, < Lv < 2 LM (15)

which implies both upper and lower bounds on E/Am2. - 32 -

The joint consequences of Eqs. (11) -(15) are conveniently summarized In Figure 5. In DUMAND the direction of muons having energies above 100 GeV can be measured to better than one-half degree, while only above about 1 TeV can dE/dx be used to obtain the muon energy. And above about 100 TeV the neutrino flux has fallen and the counting rate 1s too low to accumulate a statistically significant amount of data in one year's running. Therefore, refering to Figure 5, the zenith angle dependence of the muon signal In DUMAND can be used to explore matter effects on neutrino oscillations In the range 0.02 ev < im < 200 eV . Certainly, this 1s an Interesting regime. And it should be emphasized that the signal Is truly an oscillation phenomenon; I.e., a variation in muon signal with zenith angle. Of course, leaving aside the issue of matter effects, DUMAND 1s sensitive to neutrino vacuum oscillations corresponding to Am as small 3 *• 2 as 10" to 10" eV ; well below any present experimental limits. Even the most recent reactor data, presented at this conference by Mossbauer9, do not limit neutrino mixing for values of Am as small as DUMAND will be sensitive to. And for only moderataly small neutrino mixing; i.e., e < 10°, the reactor data do not restrict Am at all. (The accelerator data reviewed here by Baltay^ are even less restrictive.)

5. R. Mossbauer, these proceedings. !- r 6. C. Baltay, these proceedings. - 33 -

Fig. 5. Neutrino vacuum oscillations occur above the dashed line. Inside the shaded region the influence of coherent forward scattering of electron neutrinos passing through the earth significantly effect the neutrino oscillations. - 34 -

The question of the DUMAND array response to neutrino oscillations and matter effects has not yet been fully explored, but Stenger? has carried out some Monte Carlo simulations of the performance of the actual DUMAND array during one year of running. The angular distribution of muon events was calculated assuming maximal neutrino mixing for a few representative values of Am . In the analysis only a two-neutrino model was assumed and, for simplicity, matter effects were not Included. Nevertheless, using Stenger's results7 only as a guide, It Is not unreasonable that a 20Í effect In the neutrino angular distribution could be observed In one year's running of DUMAND. Clearly, DUMAND shows promise for observing matter effects on neutrino oscillations and further analysis Is certainly warranted. Specifically,"the analysis of what is now known about neutrino oscillations must be carried out for the realistic three-neutrino case. And a great deal of computational effort must go Into realistic Monte Carlo simulations of the response of the actual DUMAND array. Finally, further calculations of the prompt neutrino fluxes must be carried out to obtain more realistic estimates of the expected counting rates. Hopefully, we will have more quantitative answers to these questions to present at the next Neutrino Confer- ence. This work was supported in part by the U.S. National Science Foundation under NSF Grants PHY 78-11067 A01 and YOR 81-020.

7. V. Stenger, DUMAND Symposium (1980), Vol. I p. 190 and NEUTRINO'81, Vol. 11 p. 233. - 35 -

LARGE AMPLITUDE NEUTRINO OSCILLATIONS WITH MAJORANA MASS EIGENSTATES?

S.M.Bilenky, B.Pontecorvo Joint Institute for Nuclear Research, Dubna

1. Qualitative considerations

We wish to give here some physical arguments in favour of the idea that large amplitude and probably large oscillation length neutrino oscillations might be expected naturaly in some schemes with Majorana mass neutrinos» Thus the observation of large amplitude oscillations mught indicate the presence of Majorana mass neutrinos. s Ki Due to the high sensitivity of neutrino oscillation experiments, this is of special significance if neutrino masses are smaller than a few eV, since in such a case the classical way to search for Majorans mass neutrinos - the neutrinoless double ß-decay, is in- practicable (the corresponding decay rates being too small to be , observed). Prom this point of view cosmic and solar neutrino investigations are of the utmost importance. We present at the beginning some qualitative and intuitive remarks. Let us first consider oscillations with Dirac mass neutrinos whereby there are possible only "flavour oscillations" (the total lepton number must be conserved whereas electron, muon, tauon lepton number are not conserved separately) . Por the sake of simplicity and of illustration of

PC-invariance is assumed. There are used the notations v>-t, ^o» i?o» ••• for particles of definite masses and ù . ~ù , >) , ... for the "phenomenological" particles undergoing the usual weak interaction. Among the particles which have no definite masses, those which do not undergo the usual weak interaction will be called sterile (for example the right handed i> and the left handed ~ô s -v © 6 £>eR(ster)» ^ t> - 36 -

our point of view a definite oscillation between two neutrino states is considered below. Guessing the value of the mixing angle 0 from general considerations is impossible. It might be clone to the value 0 - —- , but that would look, at least to us, like an accident in the case of Dirac mass neutrinos. This statement comes about if one recognizes that Ä , U^, "C are different, particles of widely different masses (and so would be presumably the neutrinos of definite masses). In other words the lepton mixing angles reminds us of the Cabibbo mixing angle and is not expected to be large for Dirac mass neutrinos.

On the other hand the situation might be different in the case of Majorana mass neutrinos. If neutrinos have a Majorana mass one should not be very surprised facing special situations, whereby one definite neutrino oscillation has an amplitude close to the maximum

o one. We moved from an analogy with the K <çi' K and n.

a) The mass difference |m^ - m„ | may be comparable with and even larger than the mass of the less heavy neutrino (in K°«=f K° and n^2 n oscillations ^i m « m^m,» the notations being obvious).

Since m1 and m2 must be positive, this leads to the possibility that in certain cases there result two PC-eigenvalues of equal aigns, in other cases of opposite signs. The importance of this point for the neutrinoless double ß -decay has been emphasized by L.Wolfenstein. - 37 -

Incidentally, it should not be forgotten that for Majorana fermions PC-eigenvalues are pure imaginary and only relative PO-eigenvalues have physical meaning.

b) The presence of at least a substantial neutrino helicity leads to effects typical only of neutrinos. This can be seen right away by putting the question: how about the neutrino oscillation amplitude in the case of two Majorana neutrinos with different masses (four states) whereby the mass term is entirely right-left symmetrical? The answer is: the oscillation amplitude is maximum.

2. Some applications

We would like to emplasize here that there are known only a few charged léptons: g, , u, , c • Therefore there is relative small number of conceivable oscillations between neutrino states: i^«=*i> , £*"? L(ster)' is made that for every experimental facility there is only one "relevant" oscillation. So are defined oscillations of substantially large amplitudes and of effective oscillation lengths adequate (that is smaller or about equal to the distance source-detector).

Below 1) >>e^ ^ e oscillations will be considered in schemes with Majorana mass eigenstates. The main application of the oscillation modes 1), 3) is in solar neutrino experiments: as we have stated large oscilla-

? t ' Of course, instead of ù «r* x> oscillations, i> <£ - ^r oscillations might be more relevant. Oscillations £> ^^j- also might be relevant^ Oscillations into sterile states at different flavour (»>«£* ^Lt.L(ster)etc*^ are not considered here, as they are probably of less importance. - 38 -

tion amplitudes are expected, end, as far ao the effective oacilla- tion length is eoncöraod, cither the "Sun-Earth facility" is adequate or the oscillations at issue will nover be observed. ïho modoo

analysis of cosmic ray neutrino experiments, wheroby the "atmospheric" )} intensity is measured underground and compared with the &., intensity expected in the ubsence of oscillations (see eopoclally the Ghudukov group experiment). A similar statement can bo mudo on *\t oxporimonto of the Dumand type and also on M«, experiments which will be the byproduct of the investigations in v/hich proton decay is searched £ox in multilciloton deteotors« In solar neutrino and atmoophoric **-, experiments a cloar sicnature for oscillations may be discovered only if the oscillation amplitude is large* Hence the importance of ilajorana mass schomes, which micht just acoomodatc sue}] a lar^e amplitude* The solar experiments and atmospheric 0.^ experiments, in addition, are quito sensitive from the point of view of the well known paraiaetor VT o j m? - m^ J (that is the experiment is adequate if 1TÄ 10 'eV^ in the solar case and if Wr ^ 10 or in the case of atmospherio ooamic ^t )• How about accelerator and reactor neutrino experiments? The main interest of such experiments is due to the possibility of Getting information on small amplitude oscillations if the oscillation length is adequately small. Therefore the present note, dealing with oscillution lengths much larger than the distance source - neutrino detector in such experiments, is of no relevance for thorn* V/o have been discussing essentially schemes with two tlajorana maaaivo neutrinos* Let us oxami.no in do tail the situation with oscillation amplitude la two concrote examples* - 39 -

3. Example 1. two Ma.1orana mass neutrinos, pure Ma.iorana masa term

Let us consider the case of two Majorana mass neutrinos, the masses of which are not both identically equal to zero. We shall assume a purely Majorana mass term. This implies that the neutrino field components which are present in the mass term are also present in the ordinary weak current. There are no sterile objects. The striking two component weak current structure is fully preserved and the oscillations which arise are of the type, say, .>) *? A-' . If we wish to preserve, the notion of lepton charge (useful even in the case considered, where it is violated), we must recognize that there is only one lepton charge, which has opposite signs for e~ and uT . But this is the scheme proposed by Zeldovich and by Konopinaky and Mahmoud , (renewed in connection with lepton charge non conservation), according to which e~ and /JL* are particles with identical lepton charge. Maximum mixing appears to be very natural in this scheme. As a matter of fact the lepton current is

All the four components or the neutrino field i> (only one!) are present in the current and there is a full symmetry between left and right components.

Within the framework of the scheme considered here, it is natural to assume that d and i) are present symmetrically also in the neutrino mass term. Such a term of the lagranglan has the form

If there were two lepton charges, which are non conserved exactly, we would be faced with eight objects and not with four, as we should. Thus the Zeldovich and Konopinskv-Mahnoud scheme is not far fetched. It is required by our assumptions. Then it is quite natural to expect maximum amplitude oscillations which, as we shall see, are almost implied by the Zeldovich-Konopinsky-liahmoud scheme. - 40 -

where m and O/YL nre real parameters, and *? ~ C x> is the charge conjugate spinor. After dingonalization we have

Here p :>' , ~ and /ri ~-/ri.

It can be neen that there is a full analogy with the case of neutral kaons. As mentioned above, the analogy is limited by the possibility that S/7T-- maybe not small in comparison with m . Por example, if

aa it was m2<0, the neutrino field of mass - m2 is *^ — Y^-^>, » remarked by V.Gribov. In auch a case neutrinos of definite masses have equal PC parities and not opposite PC parities, as in the case of when m.. and nip are positive» The physical reason why the Z-K-M scheme yields naturally a maximum oscillation amplitude can be seen also as follows. In such a scheme there is one flavour shared by the electron and the muon and the oscillations x) ^r*i) ars, in fact, particle ^* antiparticle oscillations, similar to neutral kaon oscillations, because of the muon-electron perfect symmetry. Incidentally, one would expect the oscillations considered here to have a quite large oscillation length (small SmJ)»

4. Example 2. two Major ana mass neutrinos, coexistence of Ma.iorana and Dirac mass terms

This example soems to be at a first glance quite unrealistic, but it serves the purpose of illustrating the situation with oscillations to and from a sterile particle, which are implied by the co- - 41 -

existence of Hajorana and Dirac mass terms. We may think of dealing with only one type of neutrinos, let us say i> , and putting our-

selves the question as to whether oscillations -ù ^^ ei,(ater) may have a maximum amplitude. The oscillation picture is fully des- m cribed by 3 parameters having the dimensions of a mass, act>act * mater;ster • mact;sterf whioh ere Pre8ent ln lepton number violating lagrangian. The notations are self-explanatory. Well, we would not be very surprised if symmetry reasons based on some analogy with the

case of K°^? K° oscillation. s would have the effect that m„„act;ac. „.t mster;ster' In such a case a »a*1»«"11 amplitude of x>^ ^ oscillations would result. We would like to thank S.Bunyatov, I.Kobaarev, H.Shepkin and S.Petcov for useful discussions. - 42 -

TRULY NEUTRAL MICROOBJECTS AND OSCILLATIONS IN PARTICLE PHYSICS

S.M. Bilenky, B. Pontecorvo Joint Institute for Nuclear Research, Dubna, USSR

At present oscillations between different states are widely discussed in particle physics. The oscillating microobjects are not described by stationary states and are "mixtures" of objects with definite mass. One of such phenomena (oscillations K°<==* K°) was first discussed by Gell-Mann and Pais and later investigated in a number of experiments. As it seems, other types of oscillations which were considered so far have not yet been observed (at least these is no certainty about their having been observed). The oscillations at issue are muonium-anti- / 5/ muonium ^ t neutrino oscillations ^ , V°«=? D° ^', n^f n. ' '... If PG-invariance holds, the stationary states describe truly neutral particles . Further we shall assume that PG-invariance does takes place, although this hypothesis looks unlikely in a number of cases. The point in that (small) PC-violations are irrelevant from the point of view of our discussion, which is didactic in nature. Of course the masses of microobjects described by stationary states are different. However, there are also other physical differences. It is just the purpose of the present note to clear up the matter about such differences. In the case of neutral kaons the question at issue is In I entirely clear. It is well known ' , that KL ^ Kg is heavier than

KgO; K^. The decay probabilities in various channels for K1 and Kg and thus their mean lifes are quite different . In the case of neutrino oscillations the particles with definite

Majorana masses '•'' \> 1t O-, ... also differ in their physical beha- /ft/ viour. For example it la proper to say , that "relict" neutrinos are p ^ 0 n% ••• (and not the "weak interaction" neutrinos xL , J »^x i •••)• 3y *űe way» neutrinos A/J, i)«» ••• have different probabilities of radiative decay i), -» D y-Y ' , the lightest c *- 0 neutrino being the only stable one. At the present, after the original investigation of Kuz'min '' and in connecting with Great Unification Theories, there are widely discussed end planned experiments aimed to observe neutron-anti- The case of Dirac neutrinos ' ' is not being considered in the present note« - 43 -

neutron (n .=? n) oscillations '11'. When these are present, in vacuum and in absence of external fields, the particles with definite masses (we shall call them Majorana neutrons) are described by the states

1 ' *- We must not forget that we allow only a small PC-violaticn. If such

violation does take place n1 and n2 will be "quasi-majorana" objects, the average baryon number of which ia not exactly zero (the sign -v/ in Eq. (1) ia just referring to such a case).

Thus how it is possible to distinguish n^ and n2 from each other? One can say again that it is the values of their masses which does distinguish them. However such an answer is obviously right but only partial and thus does not satisfy us. There must be additional physical differences (let us say in decay probabilities of various channels). [

The main decay channels of n1 and n2 are s -decay, which under PC- ; invariance are identical and charge-symmetric» Let us assume that, in addition to the interaction originating n ^* n oscillations, there is also an interaction , responsible } for the nucléon decay ( B = 1, (B-L) •= 0, where B and L are the baryon and lepton numbers).

Then there will be marked differences in some (very unprobable) n1 and nj, decays which are sue to such interaction. In order to illustrate this point let us consider the decays of Najorana neutrons in which ' one neutral pion and one neutrino are emitted. Since n1, no and the yC- meson are particles of definite combined PC parity, the emitted neutrino must be a Majorana neutrino >\y. This decay is permitted for that particle the (relative) PC-parity of which is the same as the PC-parity of >^w ( the absolute PC-parity of a fermion has no physical meaning). In other words either the decay /i -'/c'V ^H or the decay n. •—.> Jc °-t- i>M are permitted but not both. Let us discuss now a similar question, relating to hydrogen-antihydrogen (e~p .£? e+p) oscillations. We shall consider first the "popular" decay of the proton with the emission of one positron and one neutral pion _ s P ~> r?+JL . It is clear that in second order oscillations H«CT H must arise (see Fig. 1). - 44 -

H+7Z Here the neutral microobjects H- — are the PC-even and FC-odd systems7 ; correspondingly« Of course, H. and Hg have different masses. In addition H1 and H„ can be distinguished by the fact that, for example, the decay K -» 7C°+ K?(7(?~-+-/€ ) is permitted but the decay K -*7t "<•-,«: ly is forbidden. A similar situation takes place in the case of oscillations (pt-t~ ) ^(Bi/^ae^ Fig. 1) in the hydrogen cc -atom. If moderately small FC-violations do take place, the differences indicated above in the H.. and Hp decay channels are not so striking. Such violations heve also the effect that the amplitude of hydrogen- antihydrogen oscillations would not be maximum. If the PC-violation is very strong, our argument is no more valid since the microobjects at issue are not even "approximately neutral": they "have no antiparticles". If there is a direct (first order) interaction '"', our argument about different decay channels of "diagonal" microobjects

H( and H2 is valid* . In conclusion we would like to thank M.Baldo Ceolin, L.B.Okun and also S.S.Gerstein, H.A.Markov, B.S.Neganov, H.Ehlopov for discussions.

References 1. M.Oell-Mann, A.Pais. Phys.Rev. 97, 1387 (1955)| see also A.Pais, O.Piccioni. Phys.Rev. 100, 1487 (1955); K.Lande et al., Phys.Rev. 103, 1901 (1956) L.Okun, B.Pontecorvo. JBTP 32, 1587 (1957); P.Muller et al., Phys.Hev.Lett., 4, 418 (I960); J.Christensen et al., Phys.Rev.Lett., 13, 138 (1964); C.Geweniger et al., Phys.Lett., B52, 108 (1974) 2. B.Pontecorvo. JBTP 33, 549, 1957 L.Okun, B.Pontecorvo. JETP 41, 989 (1961); G.Peinberg, S.Weinberg. Phys.Rev.Lett., 6, 381 (1961); P.Bolton et al., Phys.Rev.Lett. 47, 1441, 1981 .

V'l - 45 -

3. B.Pontecorvo. JETP 34, 247 (1958); 53, 1717 (1967); Pis'ma JETP 13, 199 (1971); V.Gribov, B.Pontecorvo. Phya.Lett., B28, 493 (1969) S.Bilenky, B.Pontecorvo. Letters Huovo Cimento 17, 569 (1976) 4. M.Gaillard, B.Lee, J.Rasner. Rev.liod.Phys. 47, 277 (1975) 5. V.Kuz'min. Pis*ma JETP 12, 335 (1970) 6. M.Nakagawa et al., Prog.Theor.Physics 30, 727 (1963) Por a review on oscillations of neutrinos with Dirac (and Majorana) masses and for an extended list of references see S.Bilenky, B.Pontecorvo. Phys.Reports 41C, 227 (1978)} Dan-di Wu. Phys.Rev. D, 23, 2038 (1981); L.Wolfenstein. Proc.of Neutrino-81 Conf.Hawaii (1981); I.Kobzarev et al. Preprint ITEP-153 (1981). 7. I.Kobzarev, L.Okun. JETP 39, 605 (I960) P.Muller et al., C.Geweniger et al., réf. 1. 8. S.Bilenky, B.Pontecorvo. Letters Nuovo Cimento , 28, 601 (1980) 9. S.Petcov. Yad.Piz. 25, 641 (1977) 10. S.Glashow. Harvard Reports, HUTP-79/AO4O; 79/AO59. R.Mohapatra, R.Marshak. Phya.Rev.Lett., 44, 1316 (1980) M.Kazarnovsky ry al., Pis'ma JJSTP 32, 88 (1980) 11. M.Baldo Ceolin. Proc.Conf.on Aotrophyaics and Elementary Particles, Rome, 1980 (Acad.Naz.Lincei, Rome, 1980, p. 251); G.Fidecaro. Preprint CERN-EP/81-136, November, 11981 In this preprint one can find an extended liât of references about n-n oscillations. 12. J.Pati, A.Salam. Phys.Rev. D 8, 1240 (1973) H.Georgi, S.Glashow. Phys.Rev.Lett., 32, 438 (1974) H.Georgl, H.Quinn, S.Weinberg. Phys.Rev.Lett., 33, 451, 1974 See alao for example, M.Converai, preprint CERN-EP/80-217, 1980; L.Sulak, 1981 Rome Workshop on Giant Underground Detectors, to be published in "Gauge Theories in High Energy Physics", North-Holland Press. 13. G.Peinberg, M.Goldhaber, G.Steigman. Phys.Rev. 18D, 1602 (1978) - 46 -

A POSSIBLE TEST OF CP INVARIANCE IN NEUTRINO OSCILLATIONS Bilenky S.U., Niedermayer F.

Joint Institute for Nuclear Research, Dubna USSR

Abstract A method is proposed for testing OF invariance in neutrino oscillations. The method is based on the comparison (at some distance from souroe of fluxes of neutrinos and antineutrinos obtained from K|_ -decays. More- over, it is shown that in the case when properly normalized differences of neutrino and antineutrino fluxes are nonvanishing, their measurement would allow one to test OPT invarianoe and to get information on the number of neutrino types.

1. The hypothesis of neutrino osoillations was made by B.Ponte- corvo more than twenty years ago' '. The verification of this hypothesis would allow us to answer such fundamental questions of neutrino physics as those of nonvanishing of neutrino masses, of neutrino mixing and of OF violation in the leptonio seotor, etc. All these problems become of speoial importance with the progress in grand unified theories. Only recently experiments searching for neutrino osoillations have been oarried out' '. Quite sensitive experiments are being performed (and planned) at present' . Experiments on neutrino beams obtained from KL decays are also in preparation' '. In this note we would like to draw attention to a very favourable way of testing GP-invarianoe in neutrino oscillation« with the help of suoh beams« 2» To start with let us introduce the neoessary relations based on the phenomenologioal theory of neutrino oscillations. The oharged current of the. standard weak interaction theory is given by the expression i If neutrino mixing takes place, we have

(2) - 47 -

Here i>; is the field operator of (Dirao or Majorana) neutrinos with mass Wj, and il is a unitary mixing matrix. Por the amplitudes of ^l-» and 7.-* ^, oscillations we have, respectively,

(3)

(4)

w a where £l='l 'i + p ' , and p ÍB the neutrino momentum (j p | > wi; ) . By comparing expressions (3) and (4) it is easy to see that

is tbe Here f>/JV (s, p) probability of finding \>t' at a distance R from the source of •>£ . Relation (5) is the consequence of CPT invariance'^'. If CP invariance holds, the matrix U is real, and from (3) and (4) it ^ W8'p)-W*'f)- (tvo (for -^'=€ this relation is satisfied due to CPT invarianoe). We mention that relations (6) could hold even for a oomplex matrix U . Indeed, let us assume that *i\- m\ 4t m\-m\ , i - 1,2,..., n-1, ^ s m1 é... < vno) and that /~\ K-^I)g

Consequently, relations (6) are vtilid if inequalities (7) are satisfield. In the case of two neutrino types only one neutrino mass squared difference enters into the amplitudes, and relation (6) is always satisfied. We also mention that if the co sine terms do vanish on averaging over the neutrino spectra, over the distance from the neutrino source to the detector, etc., we have IV |* llL.f-P- - . - 48 -

Large CF violating effeota in neutrino oscillations oould be expected provided the phases of U- are not small. We shall consider Just suoh a case.

3. The neutrino beam obtained from KL decay is a mixture of fy ,

\>e , ÏT and \ . Neglecting small (~ 10""^) CF violating effects in

the KL deoays, the number of v>e (•>?,) is equal to the number of ?« (^) . It is just the CP-symmetry of the initial state of suoh a beam which makes it an ideal tool in searching for CF violation in neutrino oscillations. For this we have to compare the fluxes of -^ s and ~v. 's in the detector. The corresponding asymmetry is

; IF) (10)

Here 1 (i?,p) (íj l«,p)) is the intensity of v 's. (yt 's.) , /, with momentum p , at a distance R from the neutrino source, and

I* Cp),(C«ey/») is the initial intensity of ^'* .

Should it turn out that for any t ( e or j+ or ry... ) the asymmetry A^ la different from zero, this would mean thatt

1) Neutrino oscillations take place (if AefO or A^. + 0 , then v^^r oscillations, if AT>f-O, then s>e5* v»^ and/or ^^^z. oscillations)f 2) CF invariance is violated in the oscillations1 3) The number of types of effectively oscillating neutrinos is 3 or larger and at least two neutrino mass differences enter into the ossl- lation probabilities.

Should the asymmetry êi^{?) be different from zero, the asymmetry AîîP) would have to be different from zero as well* Using CPT invariance (relation (5)), we get

e_ ' _ V ^-L— • (11)

Hence relation (11) is a test of CFT invariance. If there exist three types of neutrinos (.** j^r ; ^x ) * then tne dif~ ference from zero of asymmetries Ae (or A^ ) means that the asymmetry A- is also nonvanishing. In this case we havet - 49 -

This relation is the consequenoe of unitarity of the mixing matrix IX . Indeed, we have f Bre(ß'p)=0 • where

Por the case under consideration it follows from (13) that

(in the general case of oscillations between n types of neutrinos the number of independent quantities D^g is equal to ("-<)("-2.)/a- » and it coincides with the number of phases of the matrix U entering into the oscillation probabilities). Making use of (15) the relation (12) is easily obtained. A test of (12) in principle yields some information on the number of neutrino types effectively oscillating. We emphasize that the relation (12) is based on assumption that

there are only three types of oscillating neutrinos <>e , vy , •>>*. . Howe-

ver, even if, say, oscillations ?& * ^p- were absent, oscillations ve 3? i?x might take place. Should in this case the asymmetry A« be different from zero, this would mean that there exists a fourth type of neutrino and/or

the so-called second class oscillations ^*L~ P*L occur' '. 4. Summing up, we would like to emphasize once more that the measurement of asymmetries in neutrino beams obtained from KL decays would be a direct method of searching for CP violating effects in neutrino oscillations. Por the ratio of the number of I '$ to the number of

4^vV c + Here O"7 ( p ) is the cross Bection of the process \>t (*t) + M ~* ' lw A .

The ratio N{*/Nf could be different from R -

After having completed this work we got the preprint of V.Barger et al. DOE-ER/00881-177 where these relations were obtained using the Kobayaahi-Haskawa parametrization of the mixing matrix. - so -

References 1. Pontecorvo B. JETP (Sov.Fiz.), 1957, 33, p. 549; 1958, 34, p. 247; See review Bllenky S.M., Ponteoorvo B. PhyaicE Reporte, 1978, 410, p. 225. 2. Gargamelle Collaboration, J.Blietschau et al. Nucl.PhyB., 1978, B183, p. 205. LAlfPP, Willis S.S. et al. .Phye.Rev. Lett., 19B0, 44B, p. 522. ABCDLOS Collaboration, Deden H. et al . CERN Preprint CERN/EP, p. BO-164; Reines P., Sobel H.W., Paslerb E. Phye.Rev.Lett., 1980, 45, P. 1307. Boehm P. et al. Proc. of the Conference i> '80 (Brlce, 19B0)} Kondo T. Proc. of Telemark Nuetrino Masa Conference, ed. by Barger V., Cline D. (Univ. of Wisconsin report, 1980). Morrison D.R.O. CERN preprint, OERN/EP 80-190. 3. See Proc. of Telemark Neutrino Mass Conference, 1980. 4. Bugorsky A.P. et al. Serpukhov Preprint, 1980, 80-37. Loveless D. Proc. of Telemark Neutrino Mass Conference, 1980. 5. Cabibbo N. Phys.Lett., 1978, 72B, p. 333. 6. Bilenky 3.M., Pontecorvo B. Lett, al Nuovo Cim., 1976, 17, p. 569s Barger V. et al. Phys.Rev.Lett., 1980, 45, p. 692; Kobzarev I.Yu. et al. ITEP Preprint,ITEP-80. NEUTRINO - 51 -

AN EXPERIMENT TO STUDY THE ß-DECAY OF FREE ATOMIC AND MOLECULAR TRITIUM

R. G. H. Robertson, T. J. Bowles, K. Maley, J. C. Browne, T- Burritt, J. Toevs, M. Stelts, J. Helfrick,8 D. Knapp, A. G. Ledebuhrc

Los Alamos National Laboratory, Los Alamos, NM 87545, U. S. A.

An apparatus is described which will allow the measurement of the g-decay of free tritium atoms and molecules. It consists of an RF dissociator, a long cylindrical decay region open at both ends, a guide field, and a magnetic spectrometer»

There i» some interest in determining whether the electron neutrino has mass. Recently, Lyubimov et al. reported a measurement of the ß-spectrum of H which shows conclusive evidence for an antineutrino mass between 14 and 46 eV at the 99Z confidence level. Despite careful study, no substantial flaw has been detected in their procedure. Nevertheless, many scientists would like to see a confirming experiment. Much of the concern revolves around the use of a solid source (tritiated valine, an amino acid) for which

DECAY REGION RESIDUAL T» 1r r Tt,T DISSOCIATOR ACCOMMODATOR GAS KLEPPNER BOTTLE ANALYZER |T2,T 1 MERCURY Tt Tt 1 PURIFIERS O.R'» ! ß\

EXTRACTION BEAM INJECTION FROM PREPARATION SOLENOID AND ACCELERATION

SPECTROMETER DETECTOR COMPUTER

Fig. 1 Functional diagram of experiment. - 52 -

one may not know the atomic and molecular final states of the He daughter atom, the scattering and energy loss of ß's in the source, and the shape of the background near the end-point as well as one would like. The ideal source would be f^ee tritium nuclei, but this turns out to be impractical owing to space charge limitations. The next best thing, free tritium atoms, may form the basis of a practical source for which detailed «nd accurate calculations of the atomic final states and electron energy losses can be performed. Recent advances in the production of dense gases of spin- polarized hydrogen encourage us to believe that a free-atom tritium source of adequate strength can be constructed. A functional plan of the experiment is shown in Fig. 1. Molecular tritium at 300 mT pressure enters a Pyrex discharge tube cooled to 77 K (LN_). The molecules are dissociated in an RF discharge and emerge through a small orifice into a transition region (also of Pyrex) in which the atoms are cooled (accommodated) to a temperature below 10 K. Because the adsorption energy for atomic H is lower than for H , the molecular component is "frozen out". In the pioneering work of Silvera and rt 1 #» ft Walraven a flux of 2.4 x 10 atoms of H at 8.5 K was obtained, and simple modifications are expected to increase the output considerably. It is not yet known, however, to what extent tritium wil. behave differently from hydrogen. A test apparatus is now in operation at Los Alamos to explore this ^question. Atoms emerging from the accommodator enter a cylindrical decay region ("Kleppner bottle ") whose walls are coated with a thin layer of Pyrex glass, which inhibits recombination. The maximum length of this decay region is set by the recombination rate, which is not known at present, and by the molecular fraction which can be tolerated, about 5%. An equilibrium density of atomic T is built up as established by the influx and the conductance of the tube. The equivalent source thickness integrated along the axis is conservatively ea- 13 -2 timated to be 5 x 10 cm , still a weak source by normal standards, but adequate for an experiment. The Kleppner bottle is placed in a solenoidal magnetic field of about 1 kG with a small axial gradient. Betas (Bp < 463 Gauss-cm) spiral about the field lines. At one end of the solenoid a pinch coil with a peak field of about 4 kG reflects most of the ß's that start with a velocity component - 53 -

directed towards that end; as a result about 90% of the ß's reach the weak- field end of the solenoid. There they are extracted and accelerated through a potential of 20 kV. An important feature of our experiment is that this energy gain is never compensated by deceleration later in the apparatus: the entire decay region floats at -20 kV. There are two advantages in this; first, 18 keV electrons from the decay region are raised to 38 keV and are well above the energy of any g's from tritium that may find its way into the beam transport or spectrometer; and, second, the spatial component of phase space is reduced. Thus, not only is the background in the region of the shifted end point far lower than it would be at 18 keV, but the emit tance of the beam is improved. We might also remark that this idea is equally applicable to solid sources. The price paid is, of course, that higher resolving power is required in the spectrometer. One of the most interesting aspects of the problem is extraction of the ß's from the solenoidal field into a field-free region at the object of the spectrometer. Given that in order to enter the spectrometer, all f$'s must pass through a collimator of radius r at an angle less than tp , we find two general theorems: 1. There is a maximum radius in the solenoid, R, , beyond which no ß can originate and still enter the spectrometer and 2. The maximum fraction of rays originating within R^ transmitted to the spectrometer is 2 V n »

c P where x » sin i[> and p is the (maximum) radius of orbits in the field. P s The electron momenta before and after acceleration are p and p', respectively. The first result follows from conservation of the canonical angular momentum and the second from application of the Poincare invariant. The significance of the first theorem is, of course, that any electrons originating from tritium adsorbed on the walls of the Kleppner bottle can be rejected absolutely, independent of aberrations or imperfections in Che optical system. This is most important, because a monolayer of adsorbed tritium represents 6 orders of magnitude more activity than the gaseous source. A schematic diagram of the entire source is shown in Fig. 2. Hafmlle Huck Call

I RttiricHa« •wuta)"« RttMctl« • • i. /» •

îLrr5*"^^» • •

Mareary alkata» far Matatlh Fit!«

Fig« 2 Source and extraction system showing location of coils.

,..-•-• )"" - 55 - V

Acceleration and extraction ia accomplished by grid* and coils. Electron« p. \- are first accelerated through approximately 40 kV and then decelerated through ' '[-;. 20 kV. This scheme has been adopted for a number of reasons. Spec- trum distortion can result from tritium decaying in the acceleration region, and the volume is minimized by defining it with grids. In the present design, th; fraction of detected decays occurring in the acceleration gap is of order 10 . Plane, parallel grids fora a lens with infinite focal length which does not introduce the relativistic aberration. The deceleration region constitutes a short-focus Einzel lens (which does in principle possess relativistic aberration but operates with particles of fixed energy). Scarfing the spectrum can be performed in several ways, but the preferred method is to vary the potential of the Kleppner bottle and maintain all other potentials and fields fixed. While this causes a (calculable) variation in extraction efficiency, the advantage of presenting the extraction lens, spectrometer and focal plane detector with fixed energy particles is considerable. 4 The spectrometer is modeled on the toroidal design of Tretyakov. Not only does this design possess the highest luminosity of any 8-spectrometer,

Table I Spectrometer Design Parameters

Source - Image. Distance 6.86 m

Orbit apogee 0.90 m

Inner cylinder radius 0.40 m

Entrance angle 24 +_ 1.5

Exit angle 90 + 5° -4 Resolving power (base) 5 x 10 2 Luminosity 0.023 cm

Object radius 0.83 cm

Image length (base) 0.4 cm - 56 -

but it may be constructed entirely of straight conductors. The high performance is thus relatively simple to achieve. We have modified the design in two respects: The size of the spectrometer is approximately twice that of Tretyakov's, and particles enter the field at angles between 22.5 and 25.5° rather than between 85° and 95° to the axis. We find that the input profile of the coils can be straight lines at 125 to the axis (Fig. 3). Some price is paid in luminosity and in cancellation of high-order aberrations, but matching the atomic source to the spectrometer is greatly simplified. With the exception of fringing field effects, detailed calculations on the spectrometer have been carried out and Table I summarizes the important parameters. The ion-optical characteristics of the system can be studied in several ways. A 40-kV electron gun is mounted at the opposite end of the source from the spectrometer and can be used to measure resolution, transmission and aberrations. A very convenient check on the general behavior of the Kleppner bottle, extraction system and spectrometer is to use 1.8-hr Kr, a daughter of 83-day Rb. This isotope is gaseous, short-lived and emits a 17.8-keV conversion line. By appropriate variation of the temperature of the KLeppner bottle the Kr source can be made to roughly mimic the distribution of the tritium. At very low temperatures, the rejection of electrons originating at the wall can be investigated.

Construction and testing of the spectrometer is expected to be a lengthy project, and in the interim we shall make use of a Si(Li) detector at the

/*•

Fig. 3 Cross section of spectrometer showing coil profile and trajectory of ß entering at maximum allowed angle. - 57 -

focus of the extraction system. Its main function will be testing the system,but depending on how well its response can be understood, some consideration will be given to using it for a 0-spectrum measurement.

In estimating the overall performance of the system we are hampered by lack of direct information about dissociation efficiencies and recombination rates for tritium. We have therefore taken data on H from the work of Walraven and Silvera and arrive at focal plane count rates of approximately 1.3x10 /sec in the last 100 eV* Measured background rates in a prototype focal plane detector are of the same order, and Fig. 4 shows the limits that can be placed on m in about 2 weeks running. The counter-intuitive behavior

of these curves (namely the increase in sensitivity with decrease in resolution) reflects the improved statistical accuracy obtainable at poor resolution. However, in practice, count rate will be sacrificed for the sake of reduced likelihood of systematic error, and data will probably be taken at 30 to 40 eV i resolution. Should higher source intensities be available, the spectrometer is capable of substantially better resolution.

20 40 60 80 100 Resolution, eV PWHM

Fig. 4 Limits (2a) on mass obtainable in 10 seconds running for a background rate o.f. _2 -x lO~.. 3/sec. . a. source strength b. source strength 5 x 10** cm~2. - 58 -

a. University of California at San Diego b. Princeton Univeraity c. Michigan State Univeraity

1. V. A. Lyubiraov, E. G. Movikov, V. Z. Nozik, E. F. Tretyakov, and V. S. Kozik, Phys. Lett B94, 266 (1980).

2. I. F. Silvera and J. T. M. Walraven, Fhys. Lett. 2M- 193 (1979).

3. This approach was suggested to us by D. Kleppner.

4. E. F. Tretyakov, Izv. Akad. Nauk. SSR. Ser. Fiz. 39, 583 (197S).

5« J. T. M. Walraven and I. F. Silvera (to be published). - 59 -

MEASUREMENT OF THE MASS OF THE ELECTRON NEUTRINO USING THE ELECTRON CAPTURE DECAY PROCESS OF THE NUCLEUS

S. Yasumi, G. Rajaeekaran*. M. Ando, F. Ochial, H. Ikeda, T. Ohta, and P. Stefan** KEK

M. Maruyama Osaka University

N. Hashimoto Tokyo Institute of Technology

M. Fujioka, K. Ishii, T. Shinozuka, K. Sera, T. Omorl, G. Izawa, M. Yagi, and K. Masumoto. Tohoku University

K. Shima University of Tsukuba

Presented by S. Yasumi

ABSTRACT Very pure 163Ho sources were produced with the 16<*Dy(p,2n) reaction, followed by elaborative chemical separations. From measured intensities of MX-rays and total number of 163Ho in the source, the Q-yalue and half life of 163HO were estimated to be 2.3 KeV ± 0.1S KeV and 900 tWnn y> respectively. This Q-value seems to be compatible with both an electron neutrino mass In the range between 3C0 eV and zero, and with the pairing correction factor for the nuclear matrix element calculation, in the range between 0.2 and 0.5. Feasi- bility of measuring the electron neutrino mass using internal bremsstrahlung spectra at the electron capture in 163Ho is discussed.

\. * On leave of absence from University of Madras j ** On leave of absence from Stanford University SI. Introduction Til.

To get the mass of the electron neutrino, measurements using the B- spectrum of tritium have long been exploited heretofore ' . A. de Rdjula of CERtr' proposed another new way to measure the electron neutrino mass using 4) the radiative electron capture decay process rf th* nucleus. Bennett et al are trying to use the non-radiative electron capture to measure the mass. We are doing an experiment to determine the electron neutrino mass using the electron capture in the nucleus, In particular, in Ho. 163 > The Q-value and half life of Ho nucleus have not yet been known very well . Therefore, first, we tried to measure them from intensity measure- [•' ments of M X-rays from Ho (namely, of the Dy atoms). J Basing on this Q-value, the feasibility of neutrino mass measurement ?'', using the spectrum of internal bremsstrahlungB at the electron capture In Ho is discussed.

1 o §2. Preparation of the Ho sources

Holmium-163 nuclei were produced with the Dy(p,2n) reaction. The excitation function for the reaction was calculated using ALICE code , as 164 shown in Fig. 1. The energy of incident protons and thickness of the Dy- metal target along the beam direction were chosen so as to integrate effectively an area under the (p,2n)-excitation curve, as shown in the figure. To prepare the Dy-metal target, enriched Dy<>0? (from Oak Ridge), i at was first fluorinated into DyF,, which then was reduced into a metal plate by the calcium reduction method in an argon atmosphere, followed by pressing and rolling processes. Proton irradiation was made for 24.1 hours with an average current of 100 ^1A using an AVF cyclotron installed in the Cyclotron and Radioisotope Center, Tohoku University. After irradiation, silver and copper (from the brazing metal with which 164 the Dy-metal plate (target) was bonded to a cooled copper block), were removed by a precipitation method, and then a holmium fraction in a suitable solution was separated from the base by an ion-exchange method using AG 500W- X8 cation-exchange resin with an a-hydroxy-isobutyric-buffer solution as an eluting agent. These processes are indicated in Fig. 2. The observed nuclldes Indicated in the figure were identified using a Nal(Tl) scintillation counter and a Ge(Ll) or LEPS spectrometers.

* We are indebted to Mr. I.-Sugal of Institute for Nuclear Study, University of Tokyo, for preparing Dy-metal plates. - 61 -

An élution curve obtained in the separation process, is shown in Fig. 3. Activities indicated in the figure were also measured with Ge(Li)-SSD and LEPS 163 NH«OH spectrometers. The Ho fraction corre- «tr.Htn. © sponds to the region from #300 to #499 in 18»w the figure, having a volume of 300 ml. Gamma ray spectra of the Ho fraction Ag.Cu |AG5OW-X8(NH4FORM)| are shown in Fig. 4. In the figure, some «fcofSiZn 0.4BM AHIB W5.f (PH3.15) «9cd <6

««»«Tm. 205J06B, %..Cr. , 52.5«Mn.

10 K7.Ka.M9p,. 1431u '

Fig. 1 Excitation curves of Dy(p,Xn) Fig. 2 Chemical separations ^lo-reactlons calculated by ALICE 5) Code

•PH3.1S PH3.34

10: '^V z Ii03 •- 163Ho fraction

KM 200 300 400 500 600 700 ELUTION VOLUME/FRACTION Fig. 3 Elution curve obtained in the separation process - 62 -

Warmat60tfor12h, thenat80°Cfor2h pH2

51 . 4N HCI Cr Evapn. to dryness 121Te | HCI. fuming HNO3 )2lmT« Evapn. to dryntss «3 T*&% } HCl.H2O2(CnVl)-Cr(W)) Evapn. to dryness Fig. 4 Gamma ray spectra of the holmiura 0.1NKOH fraction Br2 (Cr(i)-Cr(VI)) aiNHCI Fe(ID) 0.1NK0H IS : 0.1 N HCI O.INNH4OH Repeat

X HCI 2051206e, Evapn. to dryness I 6NHCI (12NHCI) IDQWEX1-XBI J

Evapn.to dryness

Fig. 6 Gamma ray spectra ot the *'ig. 5 Refining processes for separa- 163 Ho source tion of the I63Ho

51 203 206 ftS radioactivities from Cr, JBi, "°Bi, and Y can still be seen. We proceeded 1 ft"\ with further refining processes for separation of the Ho. This process is indicated in Fig. 5, by which 51Cr, 205Bi and 206Bi were completely removed from the Ho fraction as shown in Fig. 6. 1 ft *\ Ho was electroplated onto a nickel foil by electrolysis using a 0.05 M ammonium lactate solution. 163 S 3. Total numbar of Ho nuclei in the source

We tried to estimate the total number of Ho nuclei in the source using the "PIXE" (Particle Induced X Ray Emission) - method in the following way: Another Ho source whose intensity of HX-rays was already measured, and a reference Ho foil whose dimension are the same as the (Ho) source and whose weight is known, were simultaneously Irradiated with 38 MeV protons. The Ho K X-ray spectra from theje two samples ate shown in Fig. 7. By comparing Ho K X-ray intensities of these two samples, and using the ratio of M X-rays for two Ho sources, the total weight of Ho atoms in the source was - 63 -

200 •

10 1.5 ZÖZ5 400 450 X-RAV ENERGY (keV) I fk"\ Fig. 7 "PIXE"-measurement on total Fig. 8 Photon spectrum from Ho number of Ho nuclei in the source in vacuum (The setup of the measurement in also shown in the figure.)

estimated to be 2.67 + 0. 163, Thus, we concluded that the total number of Ho atoms in the source is 0.986 x 1016.

163 §4. Photon spectrum from the Ho - source measured with a Si(Li)-SSD. A

The photon spectrum of the Ho source was measured with an EG & G Ortec Si(Ll)-SSD having a Be window of 0.3 urn thick. The measurement was performed both in an air atmosphere and in vacuum. In the latter, the source was installed in a vacuum box, surrounding the Si(Li)-SSD, as shown in Fig. 8. Such a spectrum thus obtained in vacuum, is also shown in Fig. 8. After corrections for attenuation of materials in the X-ray path and the solid angle, Intensities of the Ho MX-rays were determined as indicated in Table 1. - 64 -

Table 1. Intensity of characteric X-rays from Ho (of Dy) measured with a Si(Li)-SSD

Measured Net FWHM uBeÄBe X-ray energy Intensity (eV) (eV) of counts

2010 0.90 0.96 0.93 2774 0.75 M 119 0.92 ,3 l°2 ±12 ±0.02 ±0.01 ±0.01 ±198 ±0.14

1703 0.85 0.94 0.99 21534 5.94 M2N4 149 0.90 ±12 ±0.02 ±0.01 ±0.01 ±628 ±0.80 M1N2 ,3

1502 0.78 0.92 4.29 127 0.99 13504 0.87 M3N4 ,5 ±15 ±0.02 ±0.01 ±0.01 ±881 ±0.74

M5°3 1309 0.67 M5N6 ,7 0.88 0.98 76468 27.A 131 M ±12 ±0.02 ±0.01 ±0.01 ±1830 0.95 ±3.3 4°2,3 M4°6

993 0.42 0.82 0.96 4938 3.18 M4N2 118 ±13 ±0.04 ±0.01 ±0.01 ±633 ±0.87

Remarks: 1) A denotes the correction factor for the self-absorption of the source,, 2) Escape correction factors are 0.98 for M,00 , and unity for the others . 3) Values of FWHM were also measured in this experiment.

55. Non-radiative capture probability in Ho

Non-radiative electron capture probability from i-th shell in an atom is given by

A. - y£ |»| 11)1.(0) |' (1) where

Fermi coupling constant, \n\ nuclear matrix element, electronic wave function at the origin, exchange and overlap correction factor , Q value of the decay process, binding energy of the electron in i-th shell, mass of the electron neutrino. - 65 -

The nuclear matrix element relevant to the transition

l63 163 Ho ff; Dy + ve ,

was calculated by us based on Nllsson model wave functions. We get

\m\2 = 1.09 x R (2)

, where R denotes the pairing correction factor. The electronic wave function at the origin, i|>.(o), has been calculated by 7) Mann and Waber using the self-consistent relativistic Hartree-Fock method. We use their results. Exchange and overlap correction factors ace tabulated in a review article by Bambynek et al . Finally the following formula were obtained for the Ml and M2 shells in the holmium nucleus;

11 2 2 ;T, AM1 = 6.2981 x ÎO" ^ -(Q - 2.047)/(Q - 2.O47) - m (3)

for L, - 1.065, r and

12 2 Z XM, = 3.112 x 10" «R '(Q - 1.841)^0. - 1.841) - m (4) HZ P V

for B^ - 1.

56. Q-value of the Ho nucleus

Using the measured intensities of M X-rays (Table 1), the total number of Ho nuclei in the source, capture rates (Equations (3) & (4)), radiative widths, and total widths of atomic shells, we can estimate the Q-value and

mv . In this calculation, radiative partial widths of the dysprosium atom calculated by Bhalla and total widths calculated by McGwire were used. The tentative Q-value we obtained is: . 2.30 ± 0.15 KeV . , In this estimation the Q-value, M and R are very interdependent. And >-•' this Q-value seems to be compatible with both an electron neutrino mas? in the ; range between 300 eV and zero, and with the pairing correction factor, R , for Pl21 : the nuclear matrix element calculation, in the range between 0.2 and 0.5 .

12) * This value is in good agreement with Q-value obtained by CERN's experiment . - 66 -

Corresponding to this Q, we can evaluate the half life of the Ho

nucleus to be 900 _2Qg y.

We are going to measure the internal bremsetrahlung spectra for the electron capture in Ho with a crystal X-ray spectrometer using a multlwlre proportional chamber for a position detector. To do such a measurement, we first estimated

" G " H fk Ädk 'kmax-50eV K

for K-IBEC, following the Glauber-Martin theory ' and A. Je Rújula calculation method . It turned out that the G-value, for the present Ho source, does -4 change drastically from about 1 event per second to about 10 events per second, as the Q-value increases from 2.10 KeV to 2.30 KeV. So we now feel that, in order to reach the final goal, we had better take two approaches: radiative and non-radiative electron captures.

References;

1) K. E. Bergkvist, Nucl. Phys. B39(1972) 317 2) . V. A. Lubimov et al., Phys. Lett. 94B(1980) 266 3) A. de Riíjula, Nucl. Phys. B188(1981) 414 4) C. L. Bennett et al., Phys. Lett. 107B(1981) 19 5) M. Blann, private communication (19dl); also, Ann. Rev. Nucl. Sei. 25(1975) 123 6) S. J. B. Reed and N. G. Wave, J. Phys. E5(1972) 582 7) J. B. Mann and J. T. Waber, Atomic Data 5(1973) 201 8) W. Bambynek et al., Rev. Modern Phys. 49(1977) 77 9) C. P. Bhalla, J.'Phys. B: Atom Molec. Phys. 3(1970) 916 10) E. J. McGuire, Phys. Rev. A5(1972) 1043 11) R. J. Glauber and P. C. Martin, Phys. Rev. 104(1956) 158 12) J. U. Anderson et al., CERN-EP/82-50, April 29, 1982. - 67 -

AN EXPERIMENT TO DETERMINE THE MASS OF THE ELECTRON ANTINEUTRINO

R.N» Boyri, J. Spizuoco, B. Sur and l\ Koncz Department of Physics, The Ohio State University, Columbus, OH 43230

Abstract An experiment, presently being set. up at The Ohio State University, is described which will be used to measure the mass of the electron antineutrino. The experiment will examine the end point region of the electron spectrum resulting from the ß-decay of tritium by means of electrostatic analysis.

1. I n t.rqduct ioii The importance of the masses of the neutrinos to a variety of subjects in nuclear physics, particle physics and astrophysics demands that we determine those masses as well as possible,. Their values are critical to the Grand Unification Theories of particle physics, to closure of the universe and, possibly, to the missing mass question in astrophysics, and to a general understanding of a variety of nuclear phenomena under the rubric of weak interactions. Furthermore, in view of the difficulty of measuring the masses of the u and T neutrinos, the value of the mass of the electron neutrino or antineutrino, together with results of neutrino oscillation experiments, may well hold our best hope for determination of the masses of all of the neutrinos,. Several direct measurements*'^' ) of the mass of the electron antineutrino, hereafter referred to as the "neutrino", have been performed over the past several decades. The recently published result of Lubimov, et al.*) apparently has achieved the highest precision: they determined the value of the neutrino mass to be between 14 and 46 eV/c . However, such experiments are extremely difficult. Furthermore, the result is of such far reaching consequence that it must be confirmed in an independent measurement, preferably with as different an apparatus as possible, to achieve full acceptance by the physics Community,. Accordingly my colleagues and I at The Ohio State University are devel- oping a scheme to measure the mass of the electron antineutrino. We are applying some modern refinements to a rather old technique, that of electrostatic analysis. This technique was first applied to the neutrino mass measurement by Hamilton and Gross^) in 1950. In my talk I will first describe some of the general features of our apparatus. I will then give some of the parameters appropriate to it. Finally I will describe the approach we plan to use in coaxing our data to yield the mass of the neutrino. - 68 -

2. Experimental Apparatus Our experiment, like most direct neutrino mass measurements, will examine the spectrum of the electrons given off from the ß-decay of tritium. As mentioned above, however, we will use electrostatic analysis to determine that spectrum. There are some basic differences in the form which the data take in this experiment from that obtained in the magnetic analysis experiments, a point to which I shall return shortly. But first I will describe the basic features of the equipment to be used in this experiment.

, FOCUS GRIDS t SOURCE ENERGY ANALYSIS GRID

ACCELERATION GRID

DETECTOR

Figure 1. Basic features of the neutrino rcass measurement setup. Figure 1 shows the basic layout of the apparatus. There is cylindrical symmetry about the center axis. Electrons emitted from the tritium source first pass through a field free region to a spherical equipotential grid (Grid 1) 7.5 cm away. From there they are decelerated in a radial electri- cal field maintained between the first grid and a second one 20 cm from the source. This second grid acts as the energy analyzer: nearly all of the electrons having initial kinetic energy sufficient to surmount the potential of the second grid will be transmitted through it. A series of precision potential defining rings establishes the potential everywhere in the decel- leration region to the required accuracy. After the electrons pass the energy analysis grid they are accelerated radially to a third grid. Then a grid system consisting of a large cylindrical grid and a smaller spherical grid accelerates them back up to the energy which they had when they - 69 -

left the source, and focusses them onto a detector located on the symmetry axis 75 cm from the tritium source. Our calculations of the equipotential surfaces for the various grids suggest that these surfaces can be defined to about 3 volts out of the 18.6 kV required to stop the most energetic electrons given off by the tritium. Most of that uncertainty results from the variation of the electrostatic potential in the plane of the energy analyzer grid from the grid wires to the centers of the open portions. The calculations also show that the effects of the finite source size are less than 10 eV with our design parameters. Figure 2 shows the results of several ray tracing calculations.

Figure 2. (upper) Electron trajectories for several emission angles for electrons 300 eV above the threshold energy, which is 500 eV below the end point energy, (lower) Electron trajectories for three (emission angle, energy above threshold) values. - 70 -

In the upper hölf of that Figure are shown electron trajectories (the tritium source is at the left) for four emission angles. For these calculations the energy analyzer grid was at 500 eV below the tritium end point energy. The electron energy was assumed to be 300 eV above the threshold energy established by that grid. As can be seen from the Figure, electrons at an emission angle of 45° cross the symmetry axis rather sooner (4.3 cm) than those emitted at smaller emission angles. However those with emission angles less than 35° all cross the axis at about the same location. . In the lower half of Figure 2 are shown three rays assuming both different emission angles and energies above that established by the energy analysis grid. Also indicated on that Figure at the right is a detector of the size we plan to use» It is seen to intercept easily all of the ravs indicated on that Figure» These calculations, along with numerous others we have performed, suggest that the collection efficiency of our apparatus is independent of the angle of emission of the electrons for electrons with energies within the last 500 eV of the spectrum, as all electrons in that, energy range which are emitted within a cone of half an>ile of 35° with respect to the symmetry axis will be focussed onto the 2.5 cm diameter detector. We are planning to have our source be solid tritium. Since the freezing point of hydrogen is well above that of liquid helium, the source can be created by freezing out a few atomic layers of tritium onto a smooth source button held at liquid helium temperature,. Our discussions with low tempér- ature physicists have convinced us that the distribution of the tritium will be quite uniform over the surface of the button, and that the binding effects of the solid tritium matrix will introduce at the very most a few eV of uncertainty into the final result. The energy loss of the electrons passing through the layers of tritium is negligible. The limitation on the source thickness appears to come from the binding of additional tritium layers to those already there. The entire vacuum box will be pumped by cryopumps operated at liquid helium temperature to avoid, as much as possible, contaminant buildup on the source button. A valve which seats over the source button has been designed to allow fabrication of a new source simply by warming the helium dewar, pumping away the tritium and other gases given off, recooling the dewar, and freezing out a new charge of tritium. A negligible amount of heating of the source button will occur due to electrons produced by ß-decays in the source button. We also anticipate - 71 -

that sputtering of the tritium by those electrons which are turned back by the energy analysis grid will be negligible. For a detector we are planning to use either a low noise solid state detector cooled to liquid nitrogen temperature, or a gas ionization chamber. In either case, the electrons would lose roughly 20% of their energy in getting to the active volume of the detector. The resolution in either case would probably be about 30% FWHM. We are presently doing tests with an ionization chamber, but we feel that either detector could serve adequately. Some of our basic design parameters are as follows: The intensity of the source will be 0.4 mCi, corresponding to 5 monolayers of tritium uni- formly distributed over the 0.93 cm diameter source button. The acceptance solid angle of our apparatus is 1,2 sr, or \0% of a 4TT geometry. These parameters result in a count rate of about 30 counts per minute in the most energetic 100 eV of the spectrum, and about 30 counts per hour in the most energetic 25 eV of the spectrum. As noted above we will have some energy resolution from our detector. Most previous neutrino mass experiments have not had this feature, so no energy discrimination between real and background events could be made. We feel that this discrimination should be very helpful in reducing background effects. This feature will also allow us to determine the number of events caused by electrons hitting grid wires and causing secondary electron production. Those occurences will be observed as single events of anomalous energy. We plan to use a simple cold cathode field emission electron gun to measure the variation in detection efficiency of our apparatus with emission angle and emission point on the source button. The electron gun produces monoenergetic electrons to within 1 eV, so this device should allow an accurate measurement of the resolution function of our apparatus as well. Standard internal conversion sources ( Sn, Tm) will be used to determine the absolute energy calibration. 3. Data Analysis • Since our experiment measures all electrons emitted with an energy | above that determined by the energy analysis grid, it gives essentially an integral of the electron energy spectrum from the threshold energy to i the end point of the spectrum. The yield curve obtained in the magnetic analysis experiments is generally linearized by presenting it as a Kurie - 72 -

plot, I.e., by plotting the function f(E) = (Y1eld/p2)l/2 Instead of the actual yield curve. The advantage c/r this form of presentation Is obviously that effects of the nonzero neutrino mass can then be observed as deviations from linearity of the fit to f(E). For testing we generated synthetic data by applying a Monte-Carlo simulation to a yield curve calculated with an assumed neutrino mass of 30 eV/c and an end point energy of 18.610 keV. With a yield corresponding to the (rather large) source strength and solid angle of our experiment, and one-half day of run- Ing, the fit to the synthetic data produced a best fit value for the neutrino mass of 26.6 eV/c2 and an uncertainty of ± 8 eV/c2 at the 90X confidence limit. The end point energy was found to be 18.608 keV from this best fit to the synthetic data. A similar linearization of the data from our experiment 1s not possible, since the observed yield is, 1n the limit of a zero width resolution

yl/3

18.30 18.40 ,18.50 18.60 E, keV Figure 3. Fit to synthetic data from the electrostatic analysis experiment. - 73 -

function, the integral from the energy of the analysis grid to the end point of the spectrum. However, a cube root of the yield is approximately linear in the end point region, so it is that which is displayed in Figure 3. Shown there are the synthetic data which were generated with the Monte-Carlo simulation, again assuming a neutrino mass of 30 eV/c , an end point energy of 18.610 keV, and a running time of one-half day. The curve shows 2 the best fit to these data. It results in a neutrino mass of 33.8 eV/c , o with an uncertainty of + 10 eV/c at the 90% confidence limit. The end point energy fron1 this best fit was found to be 18.614 keV. That representation of the data from the electrostatic analysis experiment is seen to bear a close resemblance to the conventional Kurie plot in the energy region shown. In both Monte-Carlo simulations of the data, the effects of a 30% probability of an excited residual He ion were included,, Backgrounds were assumed to be zero. Both the generated data and the fits assumed a resolution function of width zero, although the analysis program can include, as an input parameter, the resolution function we will ultimately measure from our experimental apparatus. Fits with resolution functions of nonzero width generally result in essentially the same results as those from calculations with the resolution width zero» The uncertainties resulting from the analyses of the magnetic spectrometer and electrostatic analysis type data suggest that the two experiments should be capable of giving equivalent results in the same amount of running time assuming the count rates from the two experiments are equal. It should be noted that the presentation of the data in the linearized form is not essential to determination of the neutrino mass, as that is determined by a fit to the data in whatever form it is achieved. It is presented in that form only as a convenience to the observer. Thus the inherent rtonlinearity of the results from our apparatus does not represent any fundamental difficulty to the determination of the neutrino mass. The equipment for this experiment is designed and is presently being constructed. If assembly goes well we expect to be able to take data in about a year. We are grateful to S.L. Blatt for several helpful discussions, to D.O. Edwards and J. Gaines for assistance with various aspects of the frozen tritium target, and to M. Spizuoco for assistance vrith the statistical aspects of the analysis. We also acknowledge the U.S. National Science - 74 -

Foundation and The Ohio State University for partial financial support of this project.

1. V.A. Lubimov, E.G. Novikov, V.Z. Nozik, E.G. Tretyakov and V.S. Kosik, Phys. Letters 940 (1980) 266. 2. K.E. Bergqvist, Nucl. Phys. B39 (1972) 317. 3. D.R. Hamilton and L. Gross, Rev. Sei. Instr. 2J. (1950) 912. - 75 -

DETERMINATION OF AN UPPER LIMIT OF THE MASS OF THE MUONIC NEUTRINO FROM THE PION DECAY IN FLIGHT

H.B. Anderhub, J. Boecklin, H. Hofer, F. Kottmann, P. Le Coultre, D. Makouiecki, H.H. Reist, B. Sapp, P.C. Seiler.

ETH - Zürich

Presented by P. Le Coultre

Abstract An experiment has been preformed at SIN to determine an upper limit on m, from pion decay in flight in the forward direction. The kinematical analysis and' the inherent calibrations lead to the result : = (-0.14 t 0.20) ÍMeV/c2)2 (68ÎJ CD, and m,M $ 0.50 MeV/c (902 CD.

There exist two methods of determining the mass of the muonic neutrino : three body decays, where one gets the mass from the spectra via theory, or tuo body decays, uhich give the mass squared from the kinematical analysis. Table I shows recent results. Concerning the second method all authors measure the muon momentum from pion decay at rest. Here ue uould like to shou that analyzing the kinematics of the forward pion decay in flight gives a very reliable result, due to the calibrations and the monitoring of the apparatus with undecaying pions (also muons) during data talcing. Our method consists mainly in measuring for each pion decay the pion and muon momentum simultaneously in the same spectrometer.

The neutrino momentum p^ is given by the measured difference of the pion and the muon momentum. On the other hand the neutrino momentum can be calculated fro» the quantities :p,,fi,^, m^. , m£ , m2,^ . Assuming a vanishing neutrino mass for the calculation the difference betueen the measured p* and the calculated p% is proportional to m2, :

P. - PÎ = 6(m2 = 0

gotten from the expansion of p, in m2^ . This approximation is valid on the 10"* 2

spectrum of pions -or muons- uhich go twice through our spectrometer. They give a measurement of the momentum loss of these par tit; les in our detectors and the shape of the spectrum. Therefore one knows precisely the corrections to be applied on the neutrino momentum shift.

Contrary to this peak shifting method, measuring the muon momentum of the pion decay at rest (Fig. 1c), allows only to observe the muon spectrum, but not the energy losses of the muon. According e.g. to the other SIN experiment the muon momentum is scanned in a magnetic spectrometer by variing the field. As shoun in Tig. 1c you observe the edge of the muon spectrum. The shift is proportional to itij^ . Because there 4s no calibration the shape and the contribution to the shift coming from energy losses have to be extracted via carefully calculated distributions of the ir-stop and of the muon energy losses in the scintillator uhere the pions stop.

Fig. 2 shous the apparatus. Via three col limators the beam is led into our spectrometer magnet, uhich together uith four spark chambers allons to measure their momenta. The pion then reaches the 6.7 m long decay region. Four proportional chambers are used to measure the small decay angle. The muon momentum is obtained again in the same spectrometer, in order to minimize the systematic error on the pi on-muon momentum difference. The trigger for a good event is given by a time-of-flight signal gotten from the tuo scintillators Z1 at the entrance and Z2 at the exit of the figure-eight beam arrangement. Due to the fact that the muons have a slightly larger velocity than the pions CßH = 0.96, Dir = 0.93 at p^. = 350 MeV/c) the time-of-flight method (TOF) can be applied to localize the decay point. At 350 MeV/c a variation of 110 psec corresponds to a variation of the decay point of In. Care has therefore to be taken in order to get very good and stable conditions. The obtained resolution, including variation in time and in beam path length, uas o = 140 psec. This corresponds to a spatial resolution of the decay point of i 1.25 m (o). In our set-up non decaying pions or muons can travel along the uhole beam line system. They give calibration peaks, in our TOF-spectrum. Me therefore can monitor the stability of the TOF measurement and correct for eventual shifts. The time interval of events uith their decay point within the decay region can be defined relative to these calibration peaks. There is a check to see uether the vertices of the decay events are realy inside the defined decay region : the observation of a decay angle uith our proportional chambers.

From calibration events ue obtained the distribution of the spatial angles for straight tracks, giving therefore the angular resolution inherent to our proportional chamber system (0.84 mrad) (Fig. 3a). Fig. 3b shous the measured angular distribution of our good decay events. The points agree uith the calculated distribution (solid line) gotten from the dotted spectrum folded uith the calibration spectrum. In other words : the dotted spectrum represents the distribution of the true decay angles. The mean true decay angle 1s determined to be <&B^ > = (3.35 i 0.15) mrad, this for measured angles betueen 0 and 13.5 mrad. Later in the analysis ue shoued that the neutrino mass is independent of the maximal accepted measuredfi«-«., providing our ability to understand perfectly the experimental decay angle spectrum.

The spectrometer has a field uhich is homogeneous over 195°. Fieldmip measurements and part of the stabilization control are done by NMR-probes, identical to the ones used in the (g-2) experiment. The precision of the knowledge of the absolute field value is ± 50 ppm. The deviations from the nominal 11.7 kC along the track are up to 100 ppm (20 ppm mean) and the reproducibility, thanks to • careful turn on procedure, is 1 ppm. After correcting for the inhomogénéi ties ue got • total uncertainty due to the magnetic field on the measured momentum difference of A (Bp) = 0.55 keV/c.

As mentioned before, 4 precision spark chambers are mounted in the vsccuro box of our magnet. Tuo planes uith 10 um thick uires are used as electrodes. The - 77 -

wires are all spaced by 400 tim, the positioning of each is better than 1.4 |im. The 6 (im thin mylar Hindous are supported by stainless steel grids. The thickness of the homogeneous part of the chamber, including the gas, is X 2 mg cm"2. The energy loss of a pion is therefore kept very low : x 5 kev (the straggling < 1 kev), and the multiple scattering angle of a 350 Mev/c pion is 0.2 mrad. Thanks j to the focussing effect of a 160° turn the error on the measured radius due to the error of the small also measured angle of incidence is reduced (AR / R ** <2/2). The overall momentum resolution of the spectrometer, including the 225 |im chamber resolution (-1/2 Hire distance), amounts to 79 keV/c at pv - 350 NeV/c. ' After the pion momentum has been determined between SC2 and 3, the pions loose energy in SC3 and 4 in DK A and B before they decay (Fig. 2). The muons loose the "same" amount of energy in OK C and D in SCI and 2 before their momenta are determined (the SC's and OK's are all built identical). The measured neutrino- momentum has therefore to be corrected for this effect. Tor this we have again our calibration events : pions (ni -> IT2) and muons (u.i -» U2) uhich go tuice through the spectrometer. We are therefore able to measure precisely their momentum loss and the shape of their momentum difference spectra. Our corrected neutrino momentum is' then given by pj = p^ - pT - 1/2 (p-ir î " Pin • P/u.i " PiM • In order to reduce possible non-linearities in the chambers, the readout system etc... He chose a particular beam layout, nfmely calibration events uith -: momenta and geometrical pathes through the spectrometer uhich coincide :* practically uith the ones of our good decay events. Fig. 3c shows the spectrum of the momentum differences of Tin calibration events (the \i\i case is analogue) : it is asymmetric and it has a structured tail. The same is true for decay events : Fig. 3d. Here the asymmetry is more pronounced due to the decay angle distribution. The determination of the relative position of the tuo shoun peaks is therefore only possible if one is able to reproduce their shape uith a calculation. Ue may therefore try first to explain carefully the calibration spectra ; first a line spectrum uas calculated according to the different mean possible momentum losses in the chamber gas, uindous, wires and grids, and weighted them by the hit probability. Then a momentum loss straggling distribution uas superimposed on this spectrum. We chose the Landan distribution. This choice is arbitrary and doesn't matter, since the chamber resolution -uhich has also to be included- dominates the uidth dramatically. (The other straggling distributions are very similar for our small straggling). Therefore the asymmetry / of the calibration distribution could be explained as caused by hits of the particles uith the uires and the uindou supporting grid. In fact the secondary peak corresponds to a hit of one support grid. Four free parameters uere introduced in the fit of the calibration spectra : the height of the main peak, it's position, the chamber resolution and the height of the secondary peak. All types of calibration spectra could be perfectly fitted uith this method and the positions (Lu, Lu.) of the main peaks are the respective momentum losses (p-ir 1"FSrj.- Piti - p^u.z) of the particles in the chamber gas and uindous needed to correct p« . The shape of the decay-event-distribution is obtained from kinematical calculations using the n-momenta and decay angle distributions, folding the resulting spectrum uith the calibration spectrum. The latter has the same four free parameters.

Thanks to the measured momentum losses Lj (Table 2) ue are nou able to express P= as follows: Pe, = P°i - L, • V2 (LT, • L^), Lj representing the shifts discussed above, where lv contains both the momentum loss and the effect of the neutrino mass. Ue therefore end up uith a corrected neutrino momentum shift of Sp'J = p*-, - p°, = 6.4 keV/c. In Table 3 ue list c : all «rrors (90 '/. CL) uhich have an influence on 6p 4 . Ue notice that the major contribution is due to the "chamber non linearity". To determine this systematic error ue could use : first the observed discrepancy betueen the measured momentum loss difference Lu - Lu and the calculated one, and second, the observed variations of Lu (and Lit) if one samples the calibration events uith respect to their position in the chambers. Statistics is the second point in importance, the - 78 -

third is due to the error on the decay angle.

He get finally • 6p<^ = (6.4 ± 14.5) keV/c (90 X CD, uhich yields a negative mean value of the neutrino mass squared i

Comparing our result uith the most recent ones, ue sec that our method can easily compete. Better detectors, as e.g. thin microstrips and a neu spectrometer magnet uith larger bending radius would improve our results by a good factor.

REFERENCES

a) Phys. Rev. S3, 533 (1974) b) Phys. Rev. JIM. 778 (1956) c) Phys. Lett. 15J, 376 (1967) d) Phys. Lett. 17_B, 115 (1971) e) Phys. Lett. 16B, 39 (1967) f) Phys. Lett. 13B., 539 (1973) g) Phys. Lett. 218, 126 (1978) h) Phys. Rev. Lett. 15, 1066 (1980) i) SIN - Neusletter 14, NL12, Jan. 1982. i) To be published in Phys. Lett. £.

FIGURE CAPTIONS

Fig. J : Method

Fig. 2 : Apparatus

Fig. 3 a i Spectrum and fit of the measured angles for calibration events

3 b : Spectrum and fit (solid line) of the measured angles for decay events ; the dashed line is the unfolded spectrum of the decay angles.

3 c : Spectrum and fit of the momentum difference for uu, calibration events (nit - case analogue).

3 d t Spectrum and fit of the measured neutrino momentum. - 79 -

UBSJtl

Method: Author i Measured quantity i •„ • Itolt « Ml. 'So * ci K\ -* v± |ii V Clark 74 », < 0.65 «eV^c* 0.65 (dtV/e'l (a) I v± •» iii y ^ H"U •• r T V »± * (it^. Barkas 56 3.5 Cb) Hayman 67 •V 2.2 (o) Shrum 71 -1.55 í 1.» 1.15 Cd) 11 Booth 67 1.6 (•) Backenstoas 73 -0.29 ± 0.90 , 1.15

TABLE Z (stat. errors)

« 350 rteV/'c •• Lu = (114.5 i 2.2) keV/c (90X CD

i 351 MeV/c -» L|t = (100.5 i 1.5) IceV/c ( " ) = (349.2 i 0.2) MeV/c •• Lv = (101.1 • 7.0) keV/c I " )

TABLE 3 s Error summary (90 » CD

e errors on p«« Influence on Gp pion mass =1.5 keV/c1 0.16 KeV/C muon mass ^ =0.4 KeV/cl 0.06 Decay angle AOTTU. = 0.15 mred <•> = 3.35 5.32 pion momentum 4 s 26. KeV/c 0.40

errors on pc^

from statistics 7.13 " "chamber non- 11.40 " others 1.35 errors on PCJ — PB« from 4 = 5.10"s 0.55 total error ) = 14.54 KeV/c (90 X CD - 3.8Î KeV/c (68 X CD - 80 -

rfj- Pr 3SO fitV/c 3.SS. 1- MeV/t-

•fí-otn muons loosing e«

23. 8 H*VA- - 81 -

360.

240.

120

2 4 6 8 10 12 K mr«d

2 4 6 6 tO »2 1* mrad

900

600 iil 300 / i ^ \ PurPut -1 f MeV/c

120

5.4 MeV/c - 82 -

RADIATIVE DECAYS OF DIRAC AND MAJORANA NEUTRINOS {RECENT RESULTS)

S. T. reicov

Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1184, Sofia, Bulgaria

Abstract« Some recent results on the radiative decays of Dirac and Majorana neutrinos are reviewed.

I. Introduction. In spite of the existed considerable literature on the possible radiative decays of neutrinos' '

where v^ (i= 1,2,...) denotes neutrino with a definite mass (m.), this process as well an the more general problem of the neutrino electromagnetic properties have been widely discussed again recently . Three circumstances stimulated the new investigations. Pirat, an is well-known, effects of nonzero neutrino masses were /12/ claimed to be observed by two experimental groups and the subsequent critical analises were not able to exclude this possibility. Second, in all previous studies it was assumed that the neutrinos ere Dirac particles, while some of the currently popular theoretical ideas, especially that of grand unification, imply mnssive Majorana neutrinos' ' . And third, it was realized, perhaps one more time, that even extremely weak neutrino-photon effective couplings may lead, if they exist, to important and even directly observable astrophysical effects' '. In particular, it was shown' ' that photon fluxes from the radiative decays of neutrinos in the galactic halos or/and of relic neutrinos with masses greater than several eV may be feasible to experimental detection even if the corresponding neutrino lifetimes exceed considerably the supposed age of the Universe (-10 yrs). The neutrino radiative decays may occure if some of the neutrinos have nonzero masses and if there exist lepton number nonconserving interactions. Both conditions are naturally realized in the gauge theories describing the electroweak forces. - 83 -

In the present talk we shall review the recent results on the radiative decays of Dirac and Majorans neutrinos, obtained in the framework of these theories.

II, General remarks'1 •» The type of the massive neutrinos in a gauge theory is specified by the neutrino mass matrix, and more precisely by the symmetries it has. The amplitude of the process in question with Ou mass-shell photon in the final state has the following general structure in the case of standard Dirac neutrinos :

S(q + p.. - p.) (2) where fJîA are transition moments (i.e., the values of the corresponding formfactors Fj[îA(q2) at q2 = 0), depending on the theory, and the other notations are obvious. The S-roatrix unitarity and the crossing symmetry (which obviously,, are valid in the gauge theories) lead to the relations: 3 * » If further the theory is CP- (or T-) invariant, FYÎA should be reali v . VA» Pïî = ' In the diagonal case, when v ., «• v., ePa^ and i-8F?ji are just the induced magnetic and electric dipole moments of the Dirac neutrino*^?: v . k± * ePii» di " iePii (5) It follows from eq.(3), that P^ should be real while F^ should be pure imaginary. Therefore if CP is conserved, the electric dipole moment of a Dirac neutrino, as like the electric dipole moment of the neutron, should be zero. The massive ISajorana neutrinos, arising in the gauge theories *In the nonrelativistic limit the amplitude (2) corresponds to the interaction Hamiltonian: ^.H + ipA^.fJl where

can be described by four component spinorsO¥(x), satisfying the condition: 1, CP-noninvariant theory (6) 1 or (- 1), CP-invariant theory where C is the charge conjugation matrix.(.When GP is conserved, t i is :'ust the Ci>~ Pari*y of the neutrino \> * and in this case the Majorana neutrinos might possess different CP-parities' The radiative decay amplitude for Majorana neutrinos has the same structure HB that for Dirac neutrinos. However, the condition (6) imply that, if a set of interactions might induce the transition 3 . -• -P !f + V" (in case it was energetically allowed) « x0 -\li«iM ' they would contribute also to the V 4 -<* »> . + Y decay /7 q/ •*• J O amplitude' * , so the formfactors now consist of two termsi

It is immediately seen from eq.(7), that in contrast to the Dirac neutrinos, the massive Majorana neutrinos can have neither magnetic nor electric dipole momenta. In a CP-invariant theory we should get (as follows from eqs.(3) and (4))» i.e., the neutrino radiative lifetimes, as emphasized first by Wolfenstein''17'', depend on the *7 -factors of the initial and final Ma.iorana neutrinos. As a consequence of eq.C8) only one of the formfactors PYÎ should be different from zero, which, in general, does not hold in the case of Dirac neutrinos. It should be stressed, that under the mentioned conditions the relations (3)» (4) and (7), (8) are valid for the form- factore F^[îA(q2) and ^ijA(°.2)» respectively, as well. Given the amplitude (2), it is easy to obtain the correspon ding neutrino radiative lifetime: g Kj ^;^ g55 3 j Having in mind the numerical estimates we shall make further, it is convenient to express it in the farm: 4- 4 - 85 -

It should be mentioned also that the expressions and relations obtained above for the case of Dirac initial and final neutrinos are valid for the decay of a Dirac neutrino to a Uajorana neutrino. However, if a Majorana neutrino CPj) can decay to a given Dirac neutrino (v>?)» it will decay to its antipartiele (ö?) as well, the second transition, being characterized by the formfactors (- F-H 9i)> Noting that the amplitudes of the two processes do not interfere, we get using eq»(3J t >+ r (*ï-7J • y ) III« Existing Constraints. We shall assume further that the initial neutrino is much heavier than the final neutrino and that tha- neutrino masses satisfy the cosmological bound: ?mi *10 ° eV The analyses of the existing astrophysical data, performed under the assumption that the neutrinos decay predominantly radiatively, exclude then lifetimes smaller than (iO1^ f 10 ) yrs. There exist possibilities'1'' to improve in not very distant future the sensitivity of detection of astrophysical fluxes of photons with energies in the far ultraviolet region (i.e., exceed- ing few eV) by several orders of magnitude.

IV. Decays of Dirac Neutrinos. Massive Dirac neutrinos appear in the minimally extended standard SU(2)xU(i) Glashow - Salam - Yfeinberg theory of the. electroweak interactions, which contains the right-handed components of the neutrino fields ^RCX) (1 - er^*,.„.) as SU{2) singlets. At one loop level the neutrino radiative decay amplitude is generated by the diagrams with exchange of virtual W -bosons and charged leptons. The GIM suppression mechanism is operating and in the case of three generations of leptons we have » i

where U is the lepton analog of the Kobayashi-Maskawa mixing matrix i ( 31L - "u^iL» I-«./«-.*» « 1.2.3). It is easy to derive a lower bound for the corresponding radiative lifetimesi rïï*it>»y». (2LÄ>5 (14) Apparently, the radiative decays of neutrinos with masses satisfy- - 86 -

ing the cosmological restriction (12J would be beyond observation if this bound is valid» It was noticed only recantly/6»7/ that much shorter lifetimes are possible if there exists a fourth generation of sequential leptons with a relatively heavy charged lepton

>. exiO^re. {3*

Let UB recall that as a rule the neutrino radiative decay rates can be much larger in the theories with right-handed weak currents' ',

V» Decays of Ma.iorana neutrinos« The results of the general analisis show that the radiative lifetimes of the Majorana and Dirac neutrinos, determined by interactions universal for both types of massive neutrinos ( as is the standard weak interaction) do not differ substantially. However, massive Majorana neutrinos arise in the gauge theories due to specific couplings (most often between leptons and Higgs bosons and/or Higgs bosons themself) /18/ changing the lepton numbers by two unitB' . They might enhance considerably the neutrino radiative decay rates even if the corresponding theory does not contain right-handed weak currents. Examples of schemes in which this possibility is realized were given in ref./7,8/ and we shall discuss them briefly. As was pointed out by many authors' , a Majorana mass term for the left-handed neutrinos >?•,, (l • e,jtc,...) can originate in the SU(2)xU(i) theories, containing the minimal set of lepton om doublets and singlets (i.e., no ^1R). f*" ïukawa type interaction of the doublets and th^ir CP-conjugate doublets with a triplet of Higgs bosons H =(,£• ®§*\ Provided *-h°>o f 0. A combination of the charged scalar field present in the triplet and of that in the standard Higga doublet (4'(p) ) corresponds to a physical charged scalar particle H+. It couples to leptons with a typical for the Higgs bosons strenghts

where tgot « 2#/^°> . If the mass of H* is in the range - 87 -

C20 - 80) GeV, the contribution to A(^¥-»,?^ + v- ) determined + « 0 /7/ by the lepton-H interaction is dominant. In this case' vin i^ . p p Hp p p s Gini^ i.\ni [i j u u m(1, m, „ m m ïi ^ »l»la S £ ii ïi -i - -?> (m-fH - 1+ -£> (17) and if there are four generations of leptons we have»

Much shorter lifetimes are possible in the model of neutrino masses and mixing suggested by Zee' , which is based on the SU(2)xU(i) theories with more than one Higgs doublet and can be accomodated within the- SU(5) grand unified theory. Majorana mass terms for the left—handed neutrinos v -, T arise in this model as finite radiative corrections to the initial mass Lagrangian, generated by lepton number nonconserving interactions of an SU(2) singlet charged scalar field h*+ with the lepton and Higgs doublets and their CP- and C- conjugate doublets, respectively. It is, in essence, the only mechanism of neutrino mass generation in the> SU(5) theory that yields sizeable neutrino masses, mass differences and mixing angles' '. The expressions one gets for the moments v\l are particularly simple in the case of three generations, flavour diagonal lepton-Higgs doublets couplingn and weak flavour dépendance of the h*+-lepton coupling constants« This version of the model of Zee has several remarkable features' ' ' worth mentioning. First, of the three massive

are Majorana neutrinos two, say 0 0 ? almost degenerate in mass %\ to and much heavier than the third v4 , i.e. we have mo - m,'«»m,*' op c 3 \

m.ni|l/ni| . Second, CF is conserved and V. . * -1, while ji - » +1« Third, the neutrinoless double A -decay amplitude is predicted to be to the light neutrino masse m. and even for m, , v 30 eV is strongly suppressed even if m_ 1 - ~ 30 eV. Fourth, v«*- ^z oscillations are not necessarily suppressed and axe characterized by an oscillation lenght proportionation21al to (m^m^ + m^))"11, which can be in the range ((0.1 - i)eV2)"*1 1. Finally, th¥e i?¥-»i?"" *Y transition moments have the following unusual tons/ ' %

C/t(i -^(1^^ j^. i - 2,3 (19) - 88 -

where S* +1 or (-1) but cannot b» fixed yet, and if two Higgs doublets and, consequently, two physical charged acalar particles

H. - with masses mM are present in the theory m2 1'2 m2 2 | -§* - 1) - <2-M)), 1 ~ ftt. (20) Hj_ 1 The corresponding neutrino radiative lifetimes may be as snmll as 101'yrs. for m., ^~ 30 eV and relatively light charged Higga bosons

(i.e., mH - 20 GeV and mH *• 100 GeV)s Ç, •> ÎO17 yrs. C^-SÏ)5, i - 2,3. (21) Por further details see ref»/8/. i

VI. Conclusions. The examples we have considered indicate that the massive Majorana neutrinos may have radiative lifetimes in the 17 ?? range (10 f 10 ) yrs. Both for Dirac and Majorana neutrinos lifetimes in this interval are possible only if new particles 8nd couplings beyond those present in the standard theory exist.

References 1. For an early discussion see, e.g., M.Nakagava et al., Prog. Theor. Phys. 29. (1963)727. 2. S.T.Petcov, Sov. J. Nucl. Phya. 25.(1977)3405 erratas 25.(1977)698. 3. W.J.Marciano and A.I.Sanda, Phys. lett. 67B(1977)303. 4. B.W.Lee and R.K.Shrock, Phya. Rev. Di6(i577)i444; G.T.Zatzepin and A.Yu.Smirnov, Yadernaya Fizika fSTi978)i569 and the references quoted therein. 5. It is not possible to give here a complete list of references, which includes more than fifteen papers. Most of them are quoted in refs./7-H/. 6. A. De Rujula and S.L.Glashow, Phys. Rev, Lett. 45(1980)942. 7» P.B.Pal and L.Wolfenstein, Phys. Rev. P2g(1982)766. 8. S.T.Petcov, "Remarks on the Zee model", rev, version, May 1982. 9. J.Schechter and J.Valle, Phys. Rev. D24(1981)1883; erratas ibid. ( 1982)283. 10. ÏÏVShrock,eh preprint ITP-SB-82-2, January 1982. 11. F.W.Stecker and R.W.Brown, NASA preprint, October 1981. This paper contains also a review of the astrophysical constraints on the neutrino radiative lifetimes and the relevant references. 12. V.A.Lyubimov et al., Phys. Lett. 24JH1980); F.Reines et al., Phys. Rev. Lett. 45(198O)13O7. 13. For a review see, e.g., J.Ellis, CERN preprint, TH-3174, 1981. 14. A.Cisneros, Astrophys. Space Sei. 1O(198O)87. 15. In this section we follow closely TRV analisis of R.Shrock, 16. B.Pontecorvo.Pontecorvo, OETP 34(1958). 17. L.Wlft.Wolfenateini , PhysTiettPhTt . 107B(i982)t ffuel. Phys. B175(1980)93. 18. Seeee, , e.g.g,, T.P.Cheng and L.FTLT.T,, Phys. Rev. 022(198072860. 19. A.ZeeZ , PhysPh . LettLtt . 93B(1980)36993B(1980)369. 20. J.F.Nieves, Nucl. Phys. B189(1981)182. BEAM DUMP - 89 -

PROMPT NEUTRINO PRODUCTION BY 400 GEV PROTON INTERACTIONS

R.C. Ball, C. Castoldl, S. Childress, C.T. Coffin, G. Conforto, M.B. Crlsler, M.E. Duffy, G.K. Fanourakls, H.R. Gustafson, J.S. Hoftun, L.W. Jones, T.Y. Ling, M.J. Longo, R.J. Loveless, D.D. Reeder, T.J. Roberts, B.P. Roe, T.A. Romanowski, D.L. Schumann, E.S. Smith, J.T. Volk, E. Wang.

FIRENZE - MICHIGAN - OHIO STATE - WASHINGTON - WISCONSIN Collaboration

Reported by R.J. Loveless University of Wisconsin

Abstract

A Pb-llquld scintillator detector of 80 metric tons located 56m from a W target measured the prompt neutrino flux In a 400 GeV beam p dump experiment. Assuming o(DB) - (1-x) e l the observed 850 vp CC events with Ey>20GeV imply a charm production rate o(DC) - 18 ±4 lib.

For Ev>25GeV the flux ratio v^/v^- 0.65 ±0.30. The ratio of ve/vv -

1.0 ±0.3 for Ev>30GeV where vfi flux was computed by subtracting the expected NC interactions. Utilizing ve CC events we find no evidence for diffract ive charm production. Using longitudinal shower development to separate vfi CC from NC interactions we find a vfi rate consistent with the previous method.

1. Introduction

Previous beam dump experiments have provided evidence for an excess of prompt neutrinos or muons (presumably due to charm production) and for a vefrv ratio - 0.6 instead of 1. This experiment was designed with a number of goals in mind to refine these early results: (1) increase the solid angle of the detector; (2) decrease upstream background; (3) increase prompt v relative to non-prompt v; (4) separate %(%) from neutral current events. In large part these - 9O -

goals have been accomplished as this preliminary report will demonstrate.

2. Experimental jSetup

The 400 GeV proton beam was bent twice through ~30mr before hitting the full or '/3 density tungsten target. Downstream of the target were a series of solid core magnets for ranging hadrons and deflecting muons (flg. 1). As a result of this magnetic deflection the neutrino detector was only 56 meters downstream of the target, rather than "800 neters as In previous CERN experiments. The residual muon c in flux at the face of the detector was 3.0x10 per 2x10 protons on target, a typical pulse.

The detector Is a calorimeter which consists of 30 modules, each of which has 12 6.4mm Pb plates with 6.4mm gaps of liquid sclntlllator for a total of 14.4 radiation lengths and 0.S absorption lengths (103 gn/cra ) per module. A module Is divided Into S horizontal cells, each 28cm high viewed on opposite sides by a phototube. Thio calorimeter has a linear energy response with a measured resolution °/E-*55//E for hadrons and <27//E for electrons.

Between the modules are 2 planes of horizontal and vertical PWC wires with 2.5cm spacing operated in a proportional mode with pulse 'height readout. The transverse dimension of the sensitive region is 3x1.5m and the fiducial tonnage is 80 metric tons. Beam is centered vertically and 0.75m from one side. This horizontal asymmetry allows us to record neutrino Interactions up to 40mr.

Downstream from the detector is a muon spectrometer consisting of 5 superplanes of drift chambers (each superplane having x, x , y, y , u wires) and 3 magnetized iron toroids of transverse dimensions 2•4x3«6m • Upstrean of the detector is a double wall of veto counters« - 91 -

For the spring '81 run the calorineter was triggered by a energy deposition within a segment of 26 cells. Because of light attenuation within the nodule the trigger threshold varies horizontally. This threshold effect was calibrated with muon brensstrahlung from the copious muon flux. The trigger was everywhere aore than 955! efficient at 10 GeV and at some horizontal locations the 95X threshold was as low as 7 GeV. UBlng this calibration, trigger efficiency corrections were applied to the data.

In the spring '81 data run there were a total of 1.0x10 protons with O.78xlO17 on full density W and O.21xlO17 on x/3 density W. Because the 1 sec. spill length allows considerable cosalc ray background we added another 1 sec. gate when beam was off, which monitors the cosmic ray flux. The typical trigger rate was 30 per pulse, of wich ~12 were cosmic rays, 0.2 were neutrino-induced interactions, and the remainder were caused by incoming auon Interactions. Typical neutrino events are shown In fig. 3a (ly) and 3b (0u).

3. Upstream Background

In a prompt neutrino experiment control of upstream background is essential. Approximately 30 monitors were placed around the upstream beam pipe and calibrated by introducing known material Into the beam. No scraping effect was found upstream of the final bend. From the final bend to the target we estimate -* 3xI0~6 absorption lengths of material (~0.3Z background), half due to beam-gas Interactions and half due to scraping. Lowering the beam pipe vacuum from 50|i to 10u reduced the halo rate by 2/a. Material just upstream of the target (SWICS, SEM, etc.) introduced a larger, but calculable background of 8.3%. We corrected for this upstream material and for hadrone punching through the 3X targets by reducing the effective density ratio of the two targets from 3 to 2.7. - 92 -

As a test we detuned the beam and removed the Incident 400 CeV protons from the target while keeping the bean monitors at the nominal rate. Me found 0 neutrino events where we would have expected 22 events, normalizing to the beam monitors. We also removed the meson center target (upstream of the two bends) and found no effect on the neutrino rate In the detector with a 17. statistical error. We believe the beam 19 exceptionally clean and well-monitored.

However, our experiment has a background advantage over previous beam dump experiments due primarily to the W target and the large solid angle. The W target, because of higher density, interact» more n'a and K'B before they decay. The non-prompt neutrinos tend to be at small angles and form a larger fraction of data for the CERN detectors (which cover < 2 mr) than for our experiment. The extent of this difference can be seen In Table I which shows the ratio of signal (prompt neutrinos) to noise (non-prompt neutrinos) for several experiments.

Table I

Exp. Ofull density target)

CDHS, CHARM (lu) 0.4 Cu CCFRS (u beam dump) 0.1 Ke this experiment (lg) 1.1 W this experiment (0y) 4.6 W

4. Data Analysis

A computer analysis requiring a "good" neutrino event with Evls>2° GeV reduced the trigger rate from 225000/1016 protons to 1000/10 . The remaining candidates were visually double scanned (see fig. 3) for flu events (typical ve or NC interactions), lu events (v CC interactions), and lM(mlss) events ( v Interactions with a muon outside - 93 -

the spectrometer acceptance). The double scan efficiency for 0 candidates was 94%.

The efficiency of this computer selection for Ou events was determined from the l|i data by deleting the nuon from the PWC and calorimeter data to create "pseudo Ou" events which were typical of v-lnduced NC Interactions. These "pseudo On" events were randomly Interlaced among normal triggers with a signal/noise ratio of 1/17 compared with the normal 1/7 In the scan. The "pseudo Op" data was then processed In the normal manner; the computer analysis found 88±2t of the hidden "pseuco Op". The scanners found all "pseudo Op" events found by the computer giving efficiency of 100_sZ.

We found 101 1M(miss) events In this scan. From the number of vy CC events and the geometry of the detector we estimate 94 ±11, a good agreement.

v 5. y CC Results

Neutrino interactions with a secondary muon have an unambiguous signature In the detector. We required that the muon pass through at least 2 drift chamber planes, the event vertex be at least 15cm from the edges of the ?b plates and within modules 3-25, and the reconstructed energy of the event be greater than 20 GeV. The acceptance is calculated both by Monte Carlo techniques and by event weighting. The overall efficiency (scan, muon reconstruction, etc.) for keeping good events is estimated to be 79Z. Table II shows the raw data and the corrected results for v and v , Including the extrapolated results for prompt v production. - 94 -

Tabl« It 1 u Results

^_/densltv_ protons (xlO ) raw events corrected events/10 _protoiw

2.7 2.1 197 208 ±15

vp 1.0 7.9 415 116 ±6 prompt 62 ±14

2.7 2.1 93 80 ±9 1.0 7.9 145 42 ±4 prompt 19 ±7

The conversion of this data Into a cross section for prompt neutrinos Is relatively model Independent since It requires available knowledge: ov, a-, nucléon structure functions, and the characteristics of the apparatus. However, to extract a charm production cross eectlon, we are forced to make a number of assumptions (some of which can be verified by our data):

' assume DB production major source of charm.

* assuma excitation function of O(DB) ~ s1*3.

* assume proton elasticity ~ 0.3.

* assume A* dependence.

* assume a specific form for O(DB): E -d-i - c(l-x)ne~bpX dp3 ' assume Dß production ratios of e e~ and - 95 -

For n«3 and b-2 we obtain a charm production cross section of IS ±3 (statistical) ±3 (systematic) Mb. Other beats dump experiments have li reported results for slightly different models, so we have translated their results to this model as shown in Table III.

('l Table III Comparison of Beam Dump Results with Identical model (see above)

Experiment flavor o(DP)

this experiment (0-37mr) v 18 ±4 yb BEBC (0-2mr) v^ 45 ±15 vb

T ve 26 ±15 ub

\ CHARM (0-2mr) vp 14 ±5 yb ];. CCFRS (0-40mr) y 15 ±5 yb ', (350 GeV protons)

J. Leveille has proposed a model with n-5 and b»3.45 with

!-' «JL"(PJ."*«D) substituted for px for which we obtain 30 ±6 yb. The

energy distribution fits Leveille's model marginally better but the pA distributions agree with either model.

Host charm production models predict equal v and v fluxes. From the prompt v , v rates (see Table II) we find the flux ratio

• \/vv - 0.65 ±0.3 for Ev>25 GeV.

6. Vvy Results

The sample of Oy data contains ve(ve) CC events, vu(ve,ve) NC events and cosmic ray events which have not been identified as such. Throughout the analysis the beam off data has not been distinguished : from the beam on data. Therefore, the number oi events in the beam off ; data is indicative of the number of cosmic ray events in the beam on data and can be subtracted. The number of v NC events can be C } estimated by making an Euaj>20 GeV cut on the v CC events. Table IV F.. naa |i - 96 -

•hows the raw data, bean off data, v^ NO estimates, and the corrected Oy results.

Table IV 0 v Results

protons raw bean off corrected 1/density (xlO16) events events events/1016 events/1016

2.7 1.9 189 12 125 ±9 39 ±3 1.0 7.6 563 26 96 ±4 21 ±1 pronpt 79 ±8 10 £2

NC NC the If we assume no anomalies (I.e. 0V ^v ) - ^ G f CC C NC events can be subtracted fron the Op data. We find the ratio of VV|i to be:

î - JMP?™^.-^™!?^ - 0.78 ±0.19 20 GeV) p lu(prompt) - NC(prompt) vis

Fig. 4 shows the energy dependence of this ratio. The energy of the 0)i events was corrected to account for the differing calorimeter response to electrons and hadrons (see sec. 8). Most of the systeaatic effects (acceptance, energy calibration, scan efficiency, etc.) are largest at the low energy liait. At this stage of the analysis the acceptance for v^ CC events fron 20

) - 97 -

The v data require no muon acceptance correction which la particularly useful for lnvestlgartng the model dependent features of cnarra production. In fig. 5 the normalized NC energy distribution Is subtracted from the prorapt Ou data resulting In the energy dependence

for prompt ve + ve CC events. The curves come from the model calculations, with b-2 and n«3(solid) or n»5(dashed). At this point the preliminary data favor n-5. The angular dependence of the neutrino spectrum is shown In fig. 6 along with the model calculation. The agreement with the charm production model is good.

7. Diffractlve Charm Production

Dlffractlve charm events would tend to be energetic (see fig. 5). To search for evidence of dif(tractive production we can normalize the

Leveliié model (n=5, b»3.45m^), to data with Evl8<120 GeV. The model E predictions for vi9>120 GeV can be subtracted from data and the excess attributed to dlffractlve production. For a dlffractlve model with n-I, b-2 we find that less than 5.3% (90Z confidence level) cf the prompt neutrino events on tungsten come from diffractlve A^B production after correcting for the different acceptance of diffractlve and central events. Assuming diffractlve production -A, central production ~A1#0, and BR(A*+e) - 4.5 ±1.7Z this translates into a limit 0"(A£D) < 13 Mb (90Z confidence level), substantially lower than recent suggestions of 150 ub .

v g e-NC Separation

A primary reason for using Pb in our calorimeter (rather than Fe or marble) was to accentuate the difference between electrons and hadrons in the longitudinal shower development. Sine? each module had 14.4 radiation lengths but ~ 1/2 Interaction length most of a typical electron shower Is contained within one module whereas a typical hadronic shower spreads over 5-6 modules. The basic idea of the ve-NC separation is to estimate the hadronic energy (Including *°) deposited In the first module from the observed energy in modules 2 - n. If the observed energy in the first module - estimated hadronic energy we have - 98 -

an NC Interaction. If the observed energy In module 1 Is larger than

estimated, the event Is probably a vfi.

In practice, of course, the situation Is more complex. The v Interaction can begin anywhere within a module, not only at the beginning. Hence, the electron energy Is usually spread over two modules. We calculate the origin of the event from the ratio of the first module energy (Ej) to the energy of the 1st and 2nd modules

where ZQ IS the upstream position of the first module.

After determining the z origin of the event, the observed module energies are shifted «o the event occur» at the beginning of a "shifted module". The consistency of the data taken at different energies shows that this shifting procedure Is largely Independent of energy. The prompt electromagnetic energy Is now In the first "shifted module".

We define an estimate of the scaling variable ys as:

E _ had _ •*2n - ( 79 \ Etot

ls tne where E2n observed hadronic energy In shifted modules 2-n and E ls the tot total energy In all modules. Using yg and the measured response of the calorimeter (Eeiec " nep/5.56, E^a

nep T.'56"-"T.Ï6~78~

For NC events, yg should be ~ 1.0 with a spread characteristic of

t° production fluctuations. Figure 7a shows the distribution of yNC for "pseudo Oji" events (see section 3) which simulate NC Interactions. This peaks near 1.0 while that for Incoming electrons (dashed curve)

peaks near 0.0 since E2n ~ 0 for a pure electromagnetic shower. A v CC Interaction will, of course, be a linear combination of these two curves (see fig. 7b) but an NC event should approximate the solid curve of fig. 7a.

From the yg distribution for the OJJ data sample In full density W we subtracted bin by bin the cosmic rays (determined from beam off data) and the v NC Interactions, normalized to the v CC data, both prompt and non-prompt. The resulting distribution in fig. 8 contains

only ve, ve, and NC(vft & ve) events. This data was fit to a linear

combination of the expected y distribution for v (ye~), vg (ye+), and NC (y^jg) évente.

o*—

where Ci » overall normalization, c, • flux ratio of v /v_, and NC °V l e e

Preliminary results for this analysis show that for EvlB > 40GeV 2 16 the fit (x -16/19) indicates prompt vß + vfi CC events/10 protons equals 28 compared to 34 ±3 found by subtracting all NC data. For 2 20 < Evl8 < AOGeV the fit (x -20/19) gives 21 compared to 27 ±3. For each of these fits c2 was set to .65 (fron v , v flux ratio) since the fit is insensitive to %L / v_ flux ratio. If the results of the NC - loo -

subtraction method are substituted Into eq. 4, the x2"21/20 for E vl9 * ^OGeV and 30/20 for 20 < Bylg < 40GeV, a reasonable agreement.

We believe the beam Is exceptionally clean and well-monitored; upstream background Is small and relatively less Important than In previous beam dump experiments. The charm production cross section, O(DD), IS "20 ub and comes predominantly from central production. The flux ratio of v, /v « 0.65 ±0.30, consistent with equality. We find no

evidence for dlffracttve charm production. The ratio »e/vM -1.0 ±0.3 for Ey>30GeV, a result obtained by the subtraction of NC Interactions.

Using the longitudinal shower development to separate. ve and NC events

we find a ve rate consistent with that obtained by the subtraction method.

References

1. P. Aliban et al., Phys. Lett. 74B, 134 (1978). 2. P. Frltze et al., Phys. Lett. 96B, 427 (1980). 3. M. Jonker et al., Phys. Lett. 96B, 435 (1980). 4. H. Abrauowics et al., CERN preprint EP 82-17. 5. J.L. Ritchie et al., Phys. Lett. 44, 230 (1980). 6. J. Leveille, Michigan preprint UM HE 82-20. 7. S. Brodsky and C. Peterson, SLAC preprint PUB-2888. £-613 Beam Dump Experimental Arrangement

CALORIMETER VERTICAL 2 IRON 3000 g/cm TOROIDS PITCH DUMP MAGNETS JU SPOILERS Iftl . MAGNET + _ Âmm\ 10ft i [Tv/'f'/, ', STEEL. V BEAM AXIS INCIDENT o PROTON BEAM i TARGET: 3A6e.Cu.orW

VETO SHIELD ORIFT CHAMBERS 183 ft.; 55.8 m

Fig. 1 E6I3 DETECTOR - PLAN VIEW

DETECTOR MODULE DETAIL:

12 Pb PLATES PLANES (2) TOTAL 86.5g/cm2 LIQUID SCINTILLATOR MAGNETIZED IRON TOROIDS, 2.4 x 3.6 m2 INCIDENT SEAM AXIS o S3

k- JO MODULES, EACH-IOOg/cm2, 1.5 XJm2 DRIFT CHAMBERS 3m (10ft)

Fig. 2 -v.

- 103 -

TYPICAL In EVENT

G«V/«

IT: I 7 DRIFT CHAMHM J>

IT"! TYPICAL On EVEWT rwCl In* ••••>

ORI'T CHWKHI

Fig. 3 "V - 104 - Ratio of CC(cî to CC(|j)

•

ü 1.0 Ü I

• i

n t • • • • • 20 40 60 80 100 120 Neutrino Energy (GeV) Flg. 4a

EXTRAPOLATION TO INFINITE DENSITY

F1g. 4b 16 dN/dE (events/10 protons)

I S m en I - 106 - \.

Angular Distribution for 0/J. p-\ W target 92% prompt v to c 2 ioJ Q. ; H1 I t \ Si JO"

a . • 10 20 30 40

F1g. 6 - 107 -

y8 dist. for NC events ft Electrons o"NC" events Electrons

2.0

Simulated v dist. for v\vj CC S 6 6 c

1.5 2.0 Fig. 7b - 108 -

O/i. events -CR-

30 \ Evit> 40 GeV = 16/19

to c 20 S \ NI I?

10 \ i\] to 0 0.5 1.0 1.5 2.0

Fig. 8 - 109 - t f A STUDY OF THE FORWARD PRODUCTION OF CHARM STATES AND jj PROMPT MUONS IN 350 GeV p-Fe and 278 GeV n" -Fe ' INTERACTIONS

A. Bodek, R. Breedon, R.H. Coleman, W. Marsh, S. Olsen, J.L. Ritchia, and Ian Stockdale; University of Rochester, Rochester, N.Y. 14627, USA B.C. Batiah, R.L. Messner, M.H. Shaevitz, and E.J. Siakindi California Institute of Tehcnology, Pasadena, CA 91125, USA F.S. Merritt; University of Chicago, Chicago, Il> 60637, USA H.E. Flak, P.A. RapidLs,and Y.Fukushimai Fermilab, Batavia, IL 60510, USA G. Donaldson and S.G. Wojcickii Stanford University, Stanford, CA 94305, USA

Presented by A. Bodek at the "Neutrino 82" Conference •' Balaton, Hungary June 1982 ;

Abstract

The forward production of charm states in 350 GeV p-F« and 278 GeV ir~-Fe interactions has been studied via the production of prompt single muons with momentum P > 20 GeV/c. The data indicate equal production of single p+ and u" in proton interactions, and a large assymetry in pion interactions. The observed momentum distributions of the prompt single muons can be satisfactorily fit by the hypothesis that D mesons are produced with an invariant cross section proportional to (l-x)n, and do not favor large diftractive cross sections predicted by intrinsic charm models. The total cross sections and the x dependence of the forward production of charm states is extracted for D's and D'B in proton and pion interactions. 1. The Experiment \ - We have investigated the forward production of charm states in hadronic *', collisions in «n experiment that measured the production of proapt single --••"• muona. Data were taken with both 350 GeV protons and 280 GeV n~'s incident on an iron "beam dump" instnmented with scintillation counters. Single muonB and dimuons were detected in a large acceptance iron-scintillator wmn identifier which was followed by a solid steel torold muon spectrometer. The density extrapolation technique was used to separate prompt muons from non-prompt muons originating from the decays of long-lived particles such as IT'S» K's and hyperone. The mean interaction point was kept fixed for the three target densities used. The most compact density of the target calorimeter was about 3/4 that of steel, The density of the first 10 interaction lengths was varied in the ratio 1J2/3:1/2. Data were taken with beam intensities varying from 104 to I05 interactions per second end with two different triggers. The triggers required a single incoming hadron to interact in the first 25 cm of the calorimeter and be in coincidence with a downstream muon. The first trigger required a muon with a momentum P > 8 GeV/c. The second trigger required a muon to penetrate the entire toroid spectrometer system. This corresponded to a requirement of P > 20 GeV/c. We report here on the analysis of the P > 20GaV;6âata for both proton and pion data samples.

2. Analysis The mementum and incoming angle of each incident hadron were determined with a proportional wire chamber tagging spectrometer. Geometrical cuts were placed on the angle of the final state muon with respect to the incident hadron to ensure identical angular acceptance for all target densities. Accidental coicidences between a beam muon and hadron were eliminated by requirements of a single incident track, proper timing to within 1 RF bucket

(18 ns)r and a muon vertex requirement. In addition, halo muons were vetoed in hardware using a large counter with a hole for the beam. These requirements and the requirement that the momentum ofeachincoming hadron be within ± 0.5% of the beam momentum ensured that there was no background from upstream sources. As a test special runs were made with additional material placed upstream. The trigger rate for such runs (which had 10 times upstream material) remained unchanged. Events were classified aa either single muon dp) or dimuon (2p) events using the counters and chambers in the muon identifier (see Figure 1). The rate of ly and 2y events were plotted versus 1/p where p is the density of - Ill - !••'

the target calorimeter. The intecepta at 1/p « 0 of the lines drawn through ' the single U+ and \T event ratri are the prompt |i+ and ji~ signals. Tor !,_ incident piona, there was a contribution fron on-momentum beam muons which interacted in the calorimeter. Theae muon interactiona were removed fro« the data sample prior to the extrapolation uaing the difference between the short electromagnetic showers of the muon interactions and the long hadronio showers of the hadron interactions» »B determined from the shower shape information in the target calorimeter. The largest background in the single muon «ample came from highly assymmetric dimuon events because muons of momenta less that 5 GeV/c were not identified. This background was subtracted with the aid of a Monte Carlo calculation which was normalized to the observed number of dixuon events. The calculation included all sources of dimuon» including those from production by secondary hadron« in the hadronio cascade and by aethe-Heitler conversion of photons frout IT* decays. Backgrounds arising from nonlinearities in the extrapolation procedure (e.g. from finite lifetime hyperon decays) were calculated to •• negligible. Backgrounds from decays downstream of the expanded region of the calorimeter (after 10 interaction lengths) were calculated using a ahowor nonta-Carlo propagated to six showor generations. The contribution of the non-expanded region was less than 3% of the prompt signal. The prompt «ingle muon distributions are shown in Figures 2 and 3 for proton« and pions respectively.

3. Results, 350 GoV Protons The measured single muon rates are (6.83 ± 0.92) x 10"6 and (6.80 ± 0.77) x 10"6 per proton interaction for li+ and y~ respectively. Using the ratio of prompt (2 W)"/<2 U)+ " 0.90 ± 0.01 as a measure of the acceptance differencefor V 's wsrsus V 's ve obtain a corrected ratio of HT/1U+ - 1.10 ± 0.21. These data do not confirm the large difference observed by the CDHS neutrino beam dump experiment^ which Masure» 0.4»*?'.?^ for the prompt vy/vy ratio. One must note that the neutrino experiment 1« only sensitive^ to the very large values of x (Xp * 0.8) in contrant to the larger acceptance of our P > 20 GeV/c data (xp 5 0.03). Note that the P > S GeV/c data has large acceptance for XQ > 0.05. The prompt lu distributions were compared to the predictions of a model in which D mesons production is described by E fL_ a (l-x)n e" ' . Single d a muon «vents resulting from the semileptonio decays of O'a generated according - 112 -

to the model predictions were propagated through the apparatus usirni A Monte Carlo program which included the effects of multiple scattering, dB/dx and resolution. The resulting Monte Carlo data tapes were then analyzed in the same way as the regular data. The model predictions included D meson production by secondary interactions in the target- calorimeter (which amounted to -16% and ~8% of the primary contributions for protons and pions, respectively). The incident energy dependence of charm production was taken from a QCD production model3. A comparison of the model distribution with the 1U+ and lv>~ momentum distributions indicates that the invariant cross section for D and D production has a (1 - x)6 * 0.8 dependence (for x > 0.3). Extrapolation of the fit to x = 0 yields a total charm production cross section of 24.6 ± 2.1 (+ 3.3) yb/nucleon (-1 8 GeV/c data is completed, the extracted cross section would be much less sensitive to the assumed form of the x distribution.

4. Results, 278 GeV Pions The measured prompt single muon rates per pion interaction are (6.84 ± 0.73) x 10"6 and (13.91 ± 1.00) x 10"6 for y+'s and \I~'B respectively. Taking the ratio of prompt (2li)"/(2p) + » 0.91 ± 0.01 as a measure of the difference in acceptance for positive and negative muons we obtain a corrected ratio of dti'/lM*) ° 2.23 ± 0.29. This large difference in pion interactions is in contrast to the near equality of the prompt rates in proton interactions. A comparison of the prompt single iy+ distributions with the D production model indicates the D mesons are produced with a (1 - x)3'4 Î. ^'° distribution (for x > 0.3). A comparison of the model predictions with the 1 y" data indicates that D mesons are produced with a (1 - x)1'3 * °*8 distribution (for x £ 0.3). Extrapolation of the fits to x - 0 yields aD- 9.1 1 1.0 (±2.3)!Jb/nucleon and Or - 10.6 ± 0.7 (±2.8)l»b/nucleon for (x > 0), assuming an 8% branching ratio and a linear A dependence. The pion data implies either a difference in the x distribution for 0 and D - 113 - y > -

mesons or indicates that the forward production of D"'e and D*'s dominates |7 over the production of D+ and D°'s. The difference in the semileptonic *•?• branching ratio of the D~ and D° would account for the p~/u+ assymetry. There are indications from CERN experiment NA16, which us«» the high resolution bubble chamber LEBC, that forward production of D"'s and D*'s ia dominant in the ir~P interactions.

5. Results on Intrinsic Charm A comparison of the data for P„ > 50GeVfc with the momentum distributions predicted using the intrinsic charm model^ indicates that diffractive cross sections of only a few microbarns can be accomodated by the ', pion and proton data. This means that the intrinsic charm component (in the proton and pion wave functions) is < 2 x 10" . • More details on the analysis of both central and diftractive produc- ; tion are presented in reference 6. Low limits on the intrinsic charm 4 components of the pion and proton were also extracted from our data on dimuon events with missing energy1. *\ References : 1. A. Bodok et. al., Phys. Lett. 113B (1982) 77. 2. II. Abramowicz et. al., Z. Phys. C13, (1982) 179. 3. C. E. Carlson and R. Sauya, Phys. Lett. 81B, (1979) 329. à. Talk by C. Fisher at the 21st High Energy Physics Conference, Paris, '•'• July 1982. ; 5. S. J. Brodsky et. al., Phys. Lett. 93B, (I960), 4SI) Phys. Rev. D23, (1981), 2745. 6. J. L. Ritchie et. al., UR828 and UR829 (1982). ;

Figure Captions ; 1. Plan view of the detector 2. Momentum distributions for the prompt (a) 1)J+ and (b) \\T events, for incident protons. The solid curve is the prediction if D meson production is ct(l-|x|)\ 3. Momentum distributions of the prompt (a) lu and (b) ly~ events for incident pionB. The solid curve is the prediction if D meson production is (1 - x)s (for u+>s) and ÏÏ meson production is (1 - x)' (for V~'B). - 114 -

MUON IDENTIFIER -RANGE OETECTOI

»M

I IRON TOROID TAROET SPECTROMETER CALORIMETER

Fig. 1

O O

3 g CENTRAL OC CENTRAL 00 I /"(I- 12

Iu INTRINSIC INTRINSIC I I CHARM -il; CHARM "»o 40 80 120 0 40 80 120 P/t*(CeV/c) P/f (GeV/c) Fig. 2

o .(I-X)1 (I-X)3 T INTRINSIC INTRINSIC /-•V"-' CHARM HARM -A O i 0 40 80 120 0 40 80 120 P/i*(G*V/cl Pii" (GeV/cl

Fig. 3

- 115 -

NEW PARTICLES AND THEIR WEAK CHARGED-CURRENT COUPLINGS

K. Kleinknecht

Institut fttr Physik der Universität Dortmund Dortwind, Federal Republic of Germany

Abstract New results on the T neutrino and on the production of charmed and bottom quarks in neutrino and e+e~ reactions are summarised. Constraints on the angles 62 and 63 in the Kobayashi- Maskawa 6-quark mixing scheme are derived.

In this talk, I concentrate on those new particles whose existence is reasonably well established. The following topics arc included! 1. Lepton sector 1.1 T lifetime 1.2 Indirect evidence for the existence of the sequential T neutrino 2. Quark sector 2.1 Production of single charmed quarks in neutrino reactions 2.2 Like sign dileptons and associated charm production 2.3 b quark couplings 2.4 Constraints on weak quark mixing angles in the R-M-scheme. - 116 -

1. LEPTON SECTOR

1.I Measurement of x lifetime

First measurements of this lifetime have been reported by the Mark II collaboration . Using 284 events containing 306 three- prong T decays from the reaction e e •* T T , they determine the vertex of those three-prong T events. The distance between the interaction point and this vertex is the decay length, as shown in fig.I. The distribution shows a small shift towards positive decay lengths, and the result on the lifetime is T • (4.6 t 1.9)10 2)3) T sec. Other groups have also given values of T as summarized in table I.

Table I Measurements of T lifetime

Group Ref Year Result (10"l3sec)

Mark II 1 81 4.6 ± 1.9 TASSO 2 81 - 0.25 ± 3.5 MAC . 3 82 4.9 ± 2.0

Average 82 4.07 ±1.28 predicted from p coupling 2.8 ± 0.2 90 X C.L. upper limit 5.7 • io"'3sec Tt * - 117 -

I » I ( i I i i I I i 7 ! I I I I'l I I I " i 'n cr <8nnnn tr <4mm 15

E I 10

• . i nl • i • •! i • n n i . i • -24 -12 0 12 24-12 0 12 24 DECAY LENGTH (mm)

Fig.I s Distributions in flight distance for 3-prong T events with vertex uncertainties less than (a) 8 m and (b) 4 im (ref.l)

d.s

charmed hadron i-

Fig.2: Diagram illustrating fragmentation of charmed quark and fragmentation va-iable z - LIB -

The expected lifetime in the sequential lepton scheme is

if we denote the (v e) W coupling with *GZ and the (v r)-W coupling with ^G~, and B(T •* evv) » (0.176 ± 0.016) is the electronic decay branching ratio of the T. If the neutrino v has the T lepton x — I "l number, then G - G_ and we expect T • (2.82 t 0.2)10 " sec, in agreement with the experiment.

1.2 Indirect evidence for the existence of the sequential T neutrino

We know from the precise measurement of the electron spectrum from T-decay by the DELCO group, that the o value is p • 0.72 t 0.15, in agreement with p — 0.75 expected from V-A coupling with a nwss- less neutrino. We can conclude that there must be an unspen li^ht spin 1/2 particle in this decay, T •* ev v . If v is not a sequential neutrino with T lepton number, then it must be a mixture of the known \> and \> . This means that T couples to a v + a y , where a2 + a2 « G /C_. e U T F Limits on the T coupling to these two neutrinos can be obtained from neutrino experiments searching for T production. For thn u case this has been done by the Columbia-BNL group . In J bubble chamber exposure, the reaction u M •* T + X was looked for. An upper limit of a2 < 0.025 at 90 % C.L. is obtained. Electron neutrino beams can be obtained in beam-dump experiments, where the prompt neutrino flux from charmed particle decays is expected to consist of equal numbers of vg and v . The BEBC collaboration , using such a v source, quotes an upper limit for T production, a < 0.35 at 90 Z C.L. Combining the cwo experiments, one obtains a2 + a2 < 0.375 at 90 Z C.L. Using now the upper limit on the T lifetime from table I, we obtain a lower limit for the T coupling strength, o2 • a2 » G /G„ > (2.82/5.7) • 0.495 at 90 % C.L. The two limits on a2 + a2 disagree at more than 2 stand, deviations, giving indirect evidence that the - 119 -

unseen particle v i» t • w v^ decay vuac be • r-liLke sequential neutrino.

2. QUARK SECTOR

2. i Production of single charmed quarks in neutri.no and antitteutrino reactions

o\ o\ In the 4 quark (GIM) ' or 6 quark model», charmed quarks can be produced in neutrino reactions in the following reaction* v + d •*• ii~ + c with coupling U . v • s -»• u + c with coupling U v + d •+• u + c with coupling U , v + s •*• u + c with coupling U In the quark-parton picture, this leads to the differential cross- sections for charm production on isoscalar targets:

||L. - S3SA [u2d (u(x) • do» * |uc8|* 2.(»] 0)

where u(x), d(x), and s(x) are the quark density distributions in the proton. Experimentally, the observation of char«'production has been done mainly by three methods: 1. Direct observation of Che short-lived decay of charmed hadrons in emulsions, 2. observation of semilepConic charm decay c • s • u • v in counter experiments, 3. observation of seai lep tonic charm decay c -*• s • >s + v in bubble chambers.

2,'i'i. £ra.8meBtJLtí.on. íuILcÍ.*i£nJoí. £«£"2«^ quarks

In experiments, the observed particle is alwayu a charmed hadron, not the chnraed quark produced in the hard scattering. The fragmentation of the quark into the hadron, as sketched in fig.2, - 120 -

is described in terms ot the fragmentation variable z » P (charmed hadron)/p(charmed quark), where P and p are momenta. A measurement of the distribution function D(z), the fragmentation function, is needed for any study of charm production because many experimental quantities, as e.g. acceptances, dopend on it. The first measurement of D(z) has been done by the CDHS collaboration . Based on 10381 neutrino induced dimuon events, the momentum p » of the y from semileptonic charm decay vas used as a measure of the charm momentum. Indeed, the variable used was the fragmentation variable z, - p ,/(p - + E , ), where p , + E . corresponds to the total visible hadronic energy in the reaction. Kig.3 shows the distribution of events in ?.. , together with curves based on different fragmentation functions D(z). A function falling as (l-z)2 is clearly incompatible with the data, and even a flat D(z) is not favoured. The best tit for D(z) in 5 bins of z is shown in fig.4, and the first moment of D(z), » 0.68 + 0.08 at a >» 20 (GeV/c)2, is compared with theoretical expectations based on QCD in fig.5. Another measurement of D(z) has been contributed to this conference By the Fermilab emulsion experiment E53I . In this case, all momenta of charm decay products seen in the emulsion are added up to give the momentum of the charmed hadron, and the charmed quark momentum is p - p . The first moment of D(z) is here • 0.61 i 0.04 (stat) ± 0.12 (syst) at ^ 5 (GeV/c)2. The two experiments agree reasonably well, and we can conclude that the fragmentation of charmed quarks is "hard", as it is expected from the theoretical idea that, due to its mass, a heavy quark would transfer most of its-momentum to the hadron into which it fragments.

A summary of recent experiments is given in table II. The advantage of emulsion experiments is the fact that the semileptonic branching ratio does not enter, bubble chamber experiments can observe electrons down to a momentum of 0.3 GeV/c, while counter - 121 -

im Fig.3: r Olilm KW Od) «ta Distribution of neutrino i s Oft) »M ri' dirauon events in the variable no l 1 z. compared with Mont« Carlo MO 1 résulta (ref.JI). 1 i X» 1 1 ,-\ KO !/ m t 400 i » A no 1 \\ i \\ no i \>\ 0.9 a

5.0

•f CDHS •$• E531

&: 0.2 Q.U 0.6 0.8

Fig.4: Charm fragmentation function D(z); data from CDHS (ref.ll) and E531 (ref.15);.theoretical curve from M. Suruki (ref.14). - 122 -

1.0 FRAGMENTATION COHS charm quark oES31

0.5

gtuon

5 10 20 50 100 200 500(GeV/c)'

Q2 - FÍR.5: First moment of fragmentation function vs. , theoreticnl curve from ref.12.

• V.

1 -

< T ( t f 1 T M 1 ! ' s -H V il i Y1 ' i • COHS WBB 1982 < D LBL collab. a BW. collol)

•+J-• *• i __1 .i — . _i. ... 1 100 200 G, (G»V)

Fig.6s oW(2u)/oV(l.u) from CDHS (ref.ll), LBL Coll. (ref.17) and BNL Coll. (ref.18) Table II Recent experiments on single charm production by neutrinos

:oliab. Year 1Target Beam echn. Events Events plept Corrections ai:lied Fragm.func- miss, slow [Ref] v ind. v ind. cut ;eom. kin. tion used acc. ace. ene;£. resc. - + + — V » V U CFR[22] 77 Fe NBB var. Ctr. 67 28 range X - >l.8m CDHS[23] 77 Fe NBB 2OOCeV Ctr. 257 58 3.5GeV/c - - flat FHOPRW[2l]78 Fe/Sci QT, SSBT Ctr. 199 49 5 GeV/c X - e-3z CHARM [ 24 ]8l C WBB Ctr. 495±32 285+29 4 GeV/c - ? IjJ - + + - U e V e Col-BNL 77/011 Ne WBB 400GeV BC — 0.3GeV/c X X X X [18] 77(813 81(249) BFHSW[|7]81 Ne/H2 QT 400 GeV I5ÏNAL 49 14 0.3CeV/c X X - charmed hadron Î 53I[16]82 Em. WBB 35OCeV Em. 41 « — X X - -0.61+0.12 - + • - V V \ CDHS[ll] 82 Fe WBB 350/400 Ctr. 10381 3513 4.7GeV/c X X X X <«>-O.68iO.Oi - 124 - f

experiments , in particular the recently finished experiment % of the CDHS collaboration - have by far the largest event sample. V In order to extract the charm production cross-section, several corrections have to be applied to the observed ratio of charm events to the total number of neutrino events. For the emulsion experiment, these are corrections for geometrical and kinematical acceptance and a correction for the kinematical suppression of charm production due to the charmed quark mass, the "slow rescaling" correction 25 ). For the dilepton experiments, in addition there is the neutrino from charm semileptonic decay which escapes detection, and therefore the total energy visible in a dilepton event is incomplete. This missing energy has to be corrected for before rates of dilepton and single muon events are compared in bins of energy. The percentage of missing 7 energy in dimuon events has been measured in the CDHS experiment Y to be (12 ± I) X, in good agreement with the expectation, (12.3 ± 2)X j from a simulation assuming only D mesons to be produced and decaying to Kviv, Kyv and iryv with branching ratios of O.37/O.56/O.O6 '. In table II is indicated which of these corrections have been , : applied in the experiments. The resulting ratio of neutrino induced charm production and single muon cross-section from dilepton experiments is shown in fig.6, not corrected for slow rescaling. p-e universality requires ; equal branching ratios for c ••*• ev and c * uv, such that the u~e and u p cross-sections should agree, which is reasonably well ful- 27) filled . A comparison of dilepton and emulsion cross-sections ; requires a knowledge of the semileptonic branching ratio B of that mixture of charmed particles which is produced in the neutrino reactions. This number can be obtained from the branching ratio B'of the mixture produced in eV reactions26)28)29), 44Z D+ : 56X D°, the information on the composition of charmed particles produced above 30 GeV neutrino energy in a 350 GeV wide band beam as given by the emulsion experiment , and the (coarse) measurement of semileptonic branching ratios of D° and D separately. The result i« B - (7.Í t 1.3) X. Using this number, we can obtain total charm production cross- - 125 -

aectiona from the CDHS experiment and compare them to the emilsion results. Fig.7 shows that above 100 CeV neutrino .energy, this cross- section converges to about 10 X of the total cross-section, and that counter and emulsion experiment agree. In order to obtain the coupling parameter U ., the contribution of charm produced from the strange sea s and s quarks has to be eliminated. According to the cross-sections given in sect.2.I, this can be done by using30 the weighted difference of neutrino and antineutrino cross-sections:

BUÍ (3) 1 - R where R is the ratio of antineutrino to neutrino total cross-sections, R - av+/ff^_ - 0.48 ± 0.02 . The dimuon to single-muon cross-section ratio obtained by the CDHS collaboration, corrected for acceptance and slow rescaling, are shown in figs. 8 and 9. The results for U|dB are given in table III. The average in the energy region 80 < B < 160 CeV is U2.B - (0.41 ± 0.07)io"2. With the value for v ca

8 quoted above, we obtain |Ucd| -0.24 ± 0.03. In the GIM nodal U . is just the sine of the Cabibbo angle, and this experimental

Table III Diauon to single-suon cross-tection ratios (corcccetd for slow reicaling) and the quantity V*AB (in units of IO~*)

Ev °;-».» vr «cd« (GeV) S- 30-40 0.3610 .05 0.7310.08 0.0110 .12 40-60 0.6710 .04 1.0210.07 0.2310 .10 60-80 0.7810 .04 1.1310.06 0 .3010 .10 80-100 0.8210 .06 1.1210.09 0 .3610 .13 100-120 0.8110 04 1.0610.10 0 .3910 .11 120-140 0.8810 03 1.0510.12 0 .4810 .14 140-160 0.8310 07 1.0210.13 0 .4310 .17 80-160 0 .8310. 025 1.0710 05 0 4110 .07 - 126 -

o (v-»charm)

10 y.

COHS v-»nV o £531 y -* u"* charm not corractcd for slow reseating

100 200 GtV

Fig.7: Cross-section for single charm production from E 531 (ref.16) and CDHS (ref.11) using seaileptonic branching ratio of 7.1 ± 1.3 Z.

Correct«! 'or «low mealing

- t } f \ 1

too 200 EV

result is in good agreement with -ehe accepted valu« sin 0 » 0.230 32\ °

± 0.003 '. In the KM model, U , - sin 6j cot 82, where sin 8t -

0.228±O.Oir"".This therefore implies cos 82 » 1.05 ± 0.14. This is probably the first measurement of 82, and is consistent with 6j

small. Upper limits are sin 92 < 0.50 and 92<33°, at the 90 Z confidence level. 2.1.3 Strange sea structure function and the coupling parameter U cs

The amount of the sea can be determined from the shape of the neutrino anoi antineutrino induced dimuon distribution. According to eqs. (I) and (2), and given the fact that the x dependence of s(x) is experimentally consistent with the x dependence of u(x) + d(x), it should 6e possible according to eq. (I) to fit the x distributior of neutrino induced dimuons with a -mixture of xs(x) as given by

the antineutrino x distribution and x [u(x) + d(x)} * l/2[F2(x) + xF3(x) - 2xs(x)]. This has been done by the CDHS collaboration and good fits are obtained (see fig. 10), which give the results of table IV, whera rsea an<'r q are '^ s^ow rescaling factors for sea and quark distributions, and the capitals denote the integrals of the quark structure functions: U - /xu(x)dx, D - /xd(x)dx, S -,/xs(x)dx.

Table IV The fraction of strange sea

l«csl 2S 2S 2S E r . • 0.056 v .e. rq Ucd U + D Û + D Ü + D (GeV) z 'K 35-60 2.11 1.33 1.10±0.16 8.6 ± 1 .8 0 .4810. 10 60-110 1.53 1.19 1.34±0.10 10.5 ± 1 .8 0.5910, 10 110-160 1.36 1.13 1.23 ±0.17 9.6± 2.0 0.5410. 11 > 160 1.24 1.10 1.36 ±0.20 10.6 ± 2 .2 0 .5910. 12

> 35 1.53 1.19 1.1910.09 9.3± 1.6 0 .5210.09 - 128 -

Correct«! lor slow rcicaling • Í

_1 , 100 ZOO E, (GeV)

Fig.9: Cross-section ratio o(2\i)/oUv) corrected for slow reBcaling for antineutrinos (réf.11).

including trnw mettmg (m, .15 G»V)

Ot 10

Fig. 10: xv£a distribution for ditnuon events. The histograms represent the data, a) Antineutrino; the solid curve is the sea distribution obtained from single-muon data (ref.3l), the dashed-dotted curve demonstrates the effect of slow rescaling. b) Neutrino; the curves show the decomposition into 48Z strange-sea contribution taken from the data of fig.10a (dotted curve) and 52 X quark contribution Cdashed-dotted curve). The dashed curve i« the sum of both. - 129 -

The experimental result for 2S/(U+D) is converted into the more interesting result for the ratio of strange to non-strange aeaa 2S/(Ü+D) on the basis of the results obtained in the charged-current

neutrino experiments , U + D + 2S - 0.070 ± 0.005 and }?2 (x)dx - 0.438 ± 0.022, as well as the result of this experiment, 2S/0J+D) - 0.052 ± 0.00b without the correction for slow resettling. With these values (Ü+5)/(U+D) - 0.13 t 0.02. The final result, averaged over neutrino energy, is

If, consistent with the preceding result on 82, we assume e2 small and also assume 63 small in line with the results of the comparisons 33 2 of 6, muon, and K decays *, so that Ü^C/|U|8I - tan 6c - 0.056 ± 0.005, then the result for the amount of strange sea relative to the up-down sea becomes: 2S/(Û+D) - 0.52 ± 0.09. (5) Therefore, if 82 » 83 - 0, the strange quarks carry about half as much of ehe nucléon momentum as the up or down antiquarks, i.e. the nucléon sea is not SU(3) symnetric. The energy dependence of the ratio of strange and non-strange sea momentum fractions 2S/(Ü+D) is shown in fig.)I. Alternatively, we can use this result to obtain a limit on the coupling strength lü | of charmed and strange' quarks. cs The maximum value for the strange-sea momentum fraction is reached for the symmetric case, 2S » Û + 6. From eq.(4) it follows that u (9 3 1>6) U and tfiece£ore u 59 at the 90 l c3l - " * cd' l cal > °- * confidence level. 2.2 Like-sign dileptons and associated charm production 2.2.1 Neutrino^induced^like-£Í£n dimuons

Reactions of the type v N + p« (e~) X and vN + uu(e)X have been observed at a rate one order of magnitude below the 34-39) opposite-sign dilepton rate . Th« question whether part of these events is due to a prompt source is a longstanding problem 39). The - 130 -

1 2S [ for 0.057 0.« o«i -

O.t - -

0.2 -

i i 50 100 ISO GtV 100

Fig.lit Ratio of momentum fractions of strange nea (28) and non" strange sea (Ü+D)vs. neutrino energy (ref.ll).

Fig.12: Distribution in visible energy Eyig of single-nuon (CC), opposite-sign diimion (u~g+) and like-sign diimion (u'lO event« from 300 GeV NBB (CDUS collab.). - 131 -

main nonprompt background to this reaction ia due to charged current events vN + u X with one IT or K from the hadronic shower X decaying into u v. There are two approaches possible to this problem: A) calculate this ir/K background with a Monte Carlo simulation based on the momentum distributions and multiplicities of n and K mesons observed in bubble chamber neutrino experiments, B) use neutrino detectors of different density and extrapolate to infinite density in order to obtain the prompt like-sign signal. All experiments have used siethod A, though method B has been used as a check of the Monte Carlo result by the FHOPRW collaboration . A further difficulty in these experiments has been the normalization of the like-sign dilepton rate. The most direct comparison can be made between like-sign and opposite-sign dimuons because they have similar geometrical and kinematical acceptances. This ratio has smaller systematic errors than the one of like-sign dimuons to single-muon events. The CDHS collaboration has obtained new data from a 300 GeV narrow-band neutrino beam exposure. For this run, the total sample of single-muon events (45 • 10 ), opposite-sign dimuons (235) and like-sign dimuons (35) has been reconstructed. The distribution of these events in the visible energy E . is shown in fig.12. After subtraction of the ir/K background from the opposite-sign rate (13 X), the ratio of rates r - R(M~U~ raw)/R(p~y prompt) is obtained. For a niuon range cut o£ •»» 3.4 mFe corresponding to a momentum cut of 4.7 GeV/c, r - (17.3 ± 3.0)«2, for a 9 GeV/c momentum cut r - (9.7 ± 2.5) Z. These raw ratios and the corresponding numbers from other experiments are plotted in fig.13 and fig. 14 versus the effective hadronic absorption length A in the different detectors. The highest density detector ' has X»26 cm. For the muon momentum cuts of 4 to 5 GeV/c, the data agree, and the calculated slopes for the TT/K background are able to account for the observed increase in raw u p rate with decreasing density. For the muon momentum cut of 9 to 10 GeV/c, agreement is leas good. Also the calculated n/K background of the FHOPRW group is - 132 -

/ / Fig.13: RliíirmO / «l»Vttl / Ratio r « R(y v raw)/R(ii y prompt) / from experiments with different / *• target density vs. effective /COMS-NBBMC hadronic absorption length X ... Data from CHARM (ref.38), FHOPRW (ref.37) and CDHS (300 / ''i GeV NBB prelim.) Muon momentum / ' cut 4-5 GeV/c. 1 «.i • i' A i • tniu IMTMV M» p >UO.VÍ( • (HAHH MII p >4jMi«Vk D FHOPRW p > SGaV/C

i i ELL o FHOPRW S GtVfc R(|l-M* OCHARK « CwV/c xCOHS30»GtVNSB*7GtV/c C»B-MC/ 03 .-5( i«V/c

0.1 •

0 NCFHR OlKirl.B tï>9 « J • MCFRR DxhrB pu>9 - ' v CDHS NB6 P >9 i i «0 200 GtV 300

SO \«ff »0 cm 150 Fig. 15: Ratio r » R(M IJ prompt)/ R(p~uR(pu + prompt) vs. Eyjyjg g Fig.U: Ratio r as in fig. 13. for momentum cut at 4-5 GeV/c. NCFRR (ref.36). Momentum Data: refs. 37,38. cut 9-10 GeV/c. - 133 -

less than the one from the CDHS collaboration. The ir/K background slope of CDHS fits the low density points of FHOPRW better than the FHOPRW Monte Carlo. The higher raw rate and the smaller background subtraction leads, for the 10 GeV/c momentum cut applied to the FHOPRW data, to a slightly larger prompt M U rate than the one obtained by CDHS. This effect is however statistically not significant, as is shown in figs. 15 and 16, '/here the ratio r - R(y M prompt)/R(vi u prompt) is shown in bins of visible energy. Again, for muon momenta above 4-5 GeV/c, the agreement is good, while for the 9-10 GeV muon momentum cut the Fermilab experiments.have, in the energy bin above 200 GeV, a higher rate than CDHS. Considering the error thin is only a 2a effect, where a large fraction of the effect come» from the different background subtraction. The data, therefore, seem to be compatible, and an increase in r above 200 GeV cannot be considered significant. P However, the existence of a prompt u v signal seems to be established. If the prompt y v rate relative to the prompt \x v rate is plotted versus the muon momentum cut applied p (fig.17) the CDHS data indicate a decrease of this ratio r with p _ This _ _ _ P cut. means that the second \i in u M events has a softer momentum spectrum than the M in u y events, which is expected if the |i comes from a c •* s y vdecay in an associated cc production, as compared to a y from a single charm production. The Fermilab data at the highest p are at variance with such a decrease of r but there is no significant discrepancy in the data considering that a large part of the difference stems from a different background subtraction. The quoted visible cross-sections of u p events corresponding —4 to the ratios r are, at energies above 200 GeV, between 10 and 10 of the single-muon cross-sections, sitill uncomfortably high for theoretical models calculating the cc production in neutrino reaction« ' or b production by gluon fusion ). - 134 -

OFHOPRW a CH«OH « (OH5 NBB »06*1 ANCFRR ÖT o fHOWW x CDHS NBB MOGtV * «FUN 01 * (ws wee 03 * COHSnOGtVMB

«.1 M S » G«V o-tut

Fig.16: Ratio r as in fig.15 for Fig.17 : Ratio r es in fig 15 for momentum cut at 9-10 different momentum cuts. GeV/c. Datât refa.36,37. Data: refs.34-38._Curve» Monte Carlo for cc production.

Fig.18Î Visible cross-sections for a) neutral and b) charged K mesons in e+e" reactions vs. cms energy H around the ) <

10.4 106 108 11.2 W(GeV) - 135 -

axitineuttÍDp_s:eactioaB^ sj limitsjcm u-b-coupling

~ïf The published prompt V UV rate in v reactions can be used to set a limit on b production from u quarks by antineut.rinos: v + u •* u* + b, because this reaction could be detected through + 44) the decay chain b * c and c •+• v v The cross-section for u U production from on isoscalax target would then be

2 2 il2. (v -»• wV) - £i£ U b (U+D) Tb B(b-c) B(c-^viv) • (1-y) (6) where U . is the u-b-coupling, U and D are the integrated quark momentum fractions of up and down quarks, T. the threshold factor caused by the b quark mass, B(lr+c) the fraction of b + c decays, and B(c->-suv) the semileptonic charm branching ratio. • :J This can be compared to opposite-sign dimuon production fron d '"•'h quarks only:

I o(v •*• y v ) ,,v " • 1} , (U+D) T B(c •* |j\i),

:'' In the ratio of these two cross-sections, the semileptonic branching • ratio and other factors cancel, such that we have, for an interval Osysa U T ' * pV) ub B/v , b f d cd c : :: In order to deduce an upper limit on U . from thin, one can use the 35) - ; prompt experimental like-sign rate in v reactions in the interval 0 S. y S. 0.4 as an upper limit. Using for normalization ref.ll and taking the value for B(b •* c) from section 2.3, one obtains '• U2 < 0.62 • IO~ T /T. with 90 X confidence. Thia limit can be UD C a improved by assuming that the origin of the neutrino-induced like- -sign dimuona (where, in the 6 quark scheme with left-handed currents, the contribution of v~ •* bji is negliaibly small) is also contributing to the v induced signal in proportion to the total cross-section. If this contribution is subtracted, the limit becomes 2 U2& < o.aa • !0~ Tc/Tb. For the masses roc - 1.5 GeV and i^ - 5 CeV, T /T, ^ 8 for 350 GeV wide band beams. Due to the severe kinematical C D suppression of b production at present energies, the limit becomes U , < 0.18. This is a direct determination of this coupling, in line UD ' with the limit within the Kobayashi-Maskawa (KM) model where V^ - s.s. < S| • 0.23. - 136 -

A more sensitive method to obtain a limit on U . within the KM 33)50) u" " scheme is obtained by using the known coupling U , from a comparison of neutron and nuclear B decay to muon decay and U from us strange particle decaya, and the unitarity relation [V |z » 1 ' 'Uud'2 " '"ua'2 " (0-4 * °-*>10"2. «*ich give« |vj|| <0.l and sin 63 < 0.42 at 90 Z C.L. 2.3 b quark couplings

ü/iL'-L Limit £n b_*_u coup_iing_ .ffomJ^jJecays^ in£P_K°. or K_

At the CESR storage ring, the reaction e e~ •• Y(4S) * BB can be used as a B meson factory. In the CLEO detector.45 ), amongst 21000 -•' hadronic events on the Ï(4S), K mesons were identified by time- of-fligbt and K° mesons by their n n decay. The visible cross- sections for hadronic final states with a K or with a K are shown in fig.18 as a function of cms energy W. Clear enhancements around the Y(4S) can be seen. The kaon momentum spectra for continuum and Y(4S) events are shown in fig. 20. This signal amounts to a total of 3.38 ± 0.34 (stat) ± 0.68 (syst) K mesons per Y(4S) decay assuming the Y(4S) to decay into BB. In order to obtain a X limit on b •*• u decays, the double ratio R » (Kaona/Y(4S) event)/ v (Kaons/continuinn event ) is considered. CLEO obtains R " 1.88 t exp 0.28, whilfl .8e0 th±0.e theoretica1 l expectation is , 10 for b •*• c Rtheo "JO.9L —0 ±- -,,O.Io for b • u. Denoting the fraction of b •* c decay by f, one -obtains f - r(lr+c)/r(D+all) - 1.09 ± 0.33 (stat) ± 0.13 (syst) and a 90 X C.L. upper limit r(b-Hi)/r(b-+c) < 0.5. Taking into account the phase space factors, the total b decay rate i.s 46') rb - rb ( 2.75 lu I2 + 7.7 lu .I2 } (9) total o cb ub where 1/r o • 0.93 * lo" sec. The limit above is therefore transformed into a limit on the coupling parameters

0.18 90 X C.L. (>0) cb - 137 -

Or '"üb1 ' |Ucb' < °-63-

2.3_.2 Lepton momentum spectrum from B decays

The electron momentum spectrum from semileptonic B decays has - >»5) 47) ; been measured by both the CLEO and the CUSB collaborations, as shown in fig. 19. In principle, the two possible decays, B •*• evX and D •+• evDX can be distinguished by measuring the end point of the ß spectrum. In practice, the analysis is model-dependent because of the theoretical uncertainty which X state with which mass is populated in the decay. In addition, there are experimental difficulties with acceptance and resolution around the endpoint. Making model IÇ assumptions, the CUSB group obtains g T(B + evX ) I r(B ~ evD) 1 °'32 " Xu - l GeV <. 1.5 if X -1.8 GeV.

From the JADE group48', an upper limit has been obtained: -12 T. < 1.4 • 10 sec at 95 Z C.L. Using the relation for the total ; decay rate eq.(9 ), this implies the following limit:-.

2 2 3 |Uc(j| + 2.8 |Uub| > 2.4 • IO" (95 I C.L.) (J|)

which means that U co, and U ub. cannot vanish at the same time,

2.4 Constraints on weak quark mixing angles in the Kobayashi- Maskawa scheme

In this generalization of the Cabibbo mixing, the 3x3 matrix of quark mixing can be expressed by 3 angles 6., 9., 8. and one - phase 5 in the way shown in fig .21. CP violation could be related to the phase 5 by |e| - |sin 0_ sin 8- sin 6\ ^ 2 • 10 . Thus, if &2 and 63 ar* not vecy smallt ic i» suggested that sin 6 be 0(1/10) or smaller. For simplification, her« only tht case - 138 -

Û3 8-evOX — MoX= 2.2 GeV B-»evX I — M,«2jOGeV is o 0.2 —-M,»25Q#V olo. •ol-o CLEO

0.1

1.5 20 Z5 (GeV/c)

B -»evDX M,»1.86eV/c

CUSB 0.2

'±-1^. 1.0 2.0 3.0 Ee(GeV)

Fig.19: Momentum distribution of electrons from B decay; topi CLEO results (ref.51), bottom« CUSB results (re/.47). - 139 -

Fig.20:

• K* Kaon momentum distribution« for a) continuum events and 4 ol Conlmüum b) Y(AS) events with continuum subtracted (ref.45). 3 r 2 ! 1 / > d. / • •• * «P 0 'ill If*- •V/ë) M TI4S) 3

2 1 /IÄ . •í! 0 10 TZ0 3.0

Kobayashi -Maskawa mixing matrix

s,c3 s,s3

-s,c2

li6 s,s2 -c1s2c3-c2s3e

Fig.21 s Kobayashi-Maskava quark mixing matrix (r«f.9) with tht phase convention of Harari (ref.52). - 140 -

«in S I»» O is considered, i.e. 6 • 0 oi í • ». The angle 6. is determined very precisely from weak decays of nonstrange and strange particles, with the result ». • sin 8. • 0.228 ± 0.011. We can then, for a fixed phase S, use the constraints on the elements of the K-M-matrix obtained in the preceding sections in order to obtain coupled constraints on the angles 0_ and 49V5O) v 6. . Choosing for graphical representation the plane sin 92 *> sin 6_, we indicate the forbidden regions. There are two constraints where only one of the angles (and no phase 6) enters: i) the limit from dimuons on the cd coupling (s«cc. 2.1.2)

0.24 ± 0.03 - Ucd - sin 6, • cos «2 gives directly s~ " sin 9, * 0*5 at 90 X C.L. ii) the limit on U , » sin 8. sin 6. from the unitarity argument yields (sect.2.2.2)

s3 - sin 63 < 0.42 at 90 X C.L. For the other constraints, the two angles and the phase 6 are coupled, iii) the liait on c-s coupling from dimuons «xcludes, via the relation (sect. 2.1.2) Ucs " CI C2 C3 * 92 93 •** for ô - 0 : a large band in the »„a. plan« for ~~2.4- io"~~

excludes a small corner around the origin of the (s2,»3) plane. Superimposing the excluded regions from iii) to v), one obtains the remaining white regions for s. and a-, for the tvo casas 6-0 and ir (figs.- 22 and 23), and similarly figs. 24 and 25 for all constraints. Obviously there is a lot of work to do before we can really pin down the value* of the angles 82 *nd 9a responsible for the mixing between different generations of quark« in our present picture. Fig.22: Excluded regions in the (sin 62, sin e3) plane by limits on U from dimuons, |Uub/Ucb| from kaon yields, and B lifetime for 6 - IT.

~~6 = 0~~

~~.2 -~~

~~Fig.23: Same as in fig.22 for 0=0. Fig.24: Same as in fig.22, but limits on Ucd from dimuons and on U . from unitarity added.~~

~~Fig.25: Same as fig.24 for 6=0. - 143 -~~

Acknowledgements It is a pleasure to thank B. Renk for his valuable help in preparing this talk, to Profs- D. Cassel, E. A. Paschos, S. Pakvaaa, M.Perl and E. Reya for fruitful discussions and communications, B. Buchholz for help with computations and Mrs. E. Lorenz for preparing the manuscript.

fi. J. Feldman et al., Phys. Rev. Lett. 4£, 66 (1982) 2. J. G. Branson, in Proceedings of the 1981 Int. Synp. on Lepton and Photon Interactions, Bonn 1981, p. 279 3. W. T. Ford et al., SLAC-PUB-2913, May 1982 4. I have heard this argument first in a seminar by M.Perl at CERN, march 1981 5. W. Bacino et al., Phys. Rev, Lett. 42, 749 (1979) 6. A. M. Cnops et al., Phys. Rev. Lett. 40, 144 (1978) 7. P. Fritze et al., Phys. Lett. 96 B, 427 (1980) 8. S. L. Glashow, J. Iliopoulos, L. Maiani, Phys. Rev. D 2, 1285 (1970) 9. M. Kobayashi, K. Maskava, Progr. Theor. Phys. 49, 652 (1973) 10. CDHS Collaboration, J. Knobloch et al., Proc. of 1981 Int. Conf. on Neutrino Physics and Astrophysics, Maui, Hawaii 1981, Vol.1, p.42i 11. Experimental Study of Opposite-Sign Dimuons Produced in Neutrino and Antineutrino Interactions, H. Abramowicz et al.j preprint CERN-EP/82-77 June 1982, submitted to this conference and to Zeitschr. f. Physik 12. H. Georgi and D. Politzer, Nucl. Phys. B 136, 445 (1978) 13. J. D. Bjorken, Phys. Rev. D 17, 171 (1978) 14. M Suzuki, Phys. Lett. 71 B, 139 (1977) 15. Characteristics of Charmed Hadrons Produced by Neutrino Inter- actions, N. Ushida et al., E 531-Collaboration, contribution to this conference (N. R. Stanton) 16. Cross-sections for Charm Production by Neutrinos, N. Ushida et al., E 531-Collaboration, contribution to this conference (N. R. Stanton) 17. H. C. Ballagh et al., Phys. Rev. D 24, 7 (1981) 18. C. Baltay, Recent Results from Neutrino Experiment in Heavy Neon Bubble Chambers, in Proc. 1979 JINR-CERN School of Physics, September 1979, p. 72, Budapest, Hungarian Academy of Sciancer, »980; C. Baltay «t al., Phy«. Rev. Lett. 39, 62 (1977) - 144 -

19. J. Blietschau et al., Phys. Lett. 58 B, 361 (1975) J. Blietschau et al., Phys. Lett. 60 B, 207 (1976) B. C. Bosetti et al-, Phys. Lett. 73 B, 380 (1978) 20. J. von Krogh et al., Phys. Rev. Lett. 36, 710 (1976) B. C. Bosetti et al., Phys. Rev. Lett. 38, 1248 (1977) 21. A. Benvsnuti et al. Phys. Rev. Lett. 34, 419 (1975) A. Benvenuti et al. Phys. Rev. Lett. 35, 1199 (1975) A. Benvenuti et al. Phys. Rev. Lett, 41, 1204 (1978) 22. B. C. Barish et al. Phys. Rev. Lett. 36, 939 (1976) fi. C. Barish et al. Phys. Rev. Lett. 39, 981 (1977) 23. M. Holder et al., Phys. Lett. 69 B, 377 (1977) 24. M. Jonker et al., Phys. Lett. 107 B, 241 (1981) 25. R. Brock, Phys. Rev. Lett. 44, 1027 (1980) 26. W. Bacino et al., Phys. Rev. Lett. 43, 1073 (1979) 27. This agreement ig at variance with a recent theoretical suggestion than an e/u asymnetry in the semi leptonic branching ratios of charmed particles (caused by a Higgs boson exchange) could explain a possible ve/vp asymmetry in the CERN beam dump experiments, V. Barger, F. Halzen, S. Pakvasa and R. J. N. Philips, Preprint UH-5H-465-82 (April 1982) 28. J. M. Feller et al., Phys. Rev. Lett. 40, 274 (1978) 29. R. H. Schindler, Ph. D. Thesis, SLAC report 2J9 (1979) 30. A related formula is used by E. A. Paschos and U. Türke, preprint DO-TH 82/07 (1982) 31. J. G. H. de Groot et al., Z. Phys. CI, 143 (1979) 32. M. Roos, as quoted by K. Kleinknecht, in: Proc. 17th Int. Conf. on High Energy Physics, London, England, 1974, p.Ill, -23. Chilton, Didcot, Berks.: Rutherford High Energy Laboratory, J975, ami by M. Nagel et al., Nucl. Phys. B 109, 1 (1976). See also M. Roos. Nucl. Phys. B 77, 420 (1974) 33. R. E. Shrock, L. L. Wang, Phys. Rev. Lett. 41, 1692 (1978) and 42, 1589 (1979) 34. M. Holder at al., Phys. Lett. 70 B, 396 (1977) 35. J. G. H. de Groot et al., Phys. Lett. 86 B, 103 (1979) 36. K. Nishikawa et al., Phys. Rev. Lett. 46, 155S (1981) 37. T. Trinko et al., Phy-i. Rev. D 23, 1889 (1981) 38. M. Jonker et al., Phys. Lett. 107 B, 241 (1981) 39. For earlier references see M. J. Murtagh, Proc. tne. Symp. on Lepton and thoton Interactions, Chicago 1979, p.277. E. Fisk, Rapporteur's talk, in Proc. Int. Symp. on Lepton and Photon Interactions at High Energy, Bonn 1981, p.703, Bonn, Universität Bonn, 1981 - 145 -

40. H. Goldberg, Phys. Rev. Lett. 39, 1593 (1977) 41. B. L. Young et al., Phys. Lett. 74 B, 111 (1978) 42. G. L. Kane et al., Phys. Rev. 0 19, 1978 (1979) 43. V. Barger et al., Pbys. Rev. D 24, 244 (1981) 44. I would like to thank S. Pakvasa for suggesting this point. 45. A. Brody et al., Phys. Rev. Lett. 48, 1070 (1982) 46. M. K. Gaillard and L. Maiani, Cargèse 1979, Plenum Press, p. (1980) 47. L. J. Spencer et al., Phys. Rev. Lett. 47, 771 (1981) 48. W. Bartel et al., DESY 82-014 (March 1982) 49. S. Pakvasa et al., Phys. Rev. D 23, 2799 (1981) 50. J. J. Sakurai, Proc. Int. Conf. on Neutrino Physics and Astro- physics, Maui, Hawaii 1981, Vol.11, p.457 51. A. Silverman, in: Proc. of the 1981 Int. Symp. on Lepton and Photon Interactions at High Energy, Bonn 1981, p.138 52. H. Harari, Phya. Rep. C 42, 235 (1978) - 146 -

~~NEW BEAM DUMP AND REACTOR DATA ON PENETRATING LIGHT PARTICLES~~

~~Helmut Faissner III. Physikalisches Institut Aachen Institute of Technology D 51 Aachen, Germany~~

~~0. Introduction~~

~~Penetrating light particles emerge from many theories: from the grand unification of all forces , from supersymmetry , and from attempts to protect QCD against imminent violations of CP and T 3'~~

Experimental information has been scantier: At the Neutrino- Conference 1980 at Erice I could report only about a few electromagnetic showers, observed at the CERN PS, and travelling closer to the beam axis than expected from known processes . One year later, at MauiB, there was clear evidence of 2y-states of small (< 1 MeV) invariant mass, pointing back to the well shielded 600 MeV proton beam-dump at SIN, and coming apparently from a decay . Besides, we heard first reports about 2Y-coincidences registered near a nuclear reactor at Jlilich* '

It seemed becoming to associate these observations with a theoretically desirable pseudoscalar particle, the axion ' . But this interpretation ran into difficulties: a specific nuclear axion transition was not seen in the predicted strength ; neither 13 ] If K-mesons nor J/i/i-particles did decay under axion emission as expected , and high energy axions presumed to emerge from high energy proton beam dumps16 did not seem to interact with the required strength . Indeed, the apparent discrepancy at low energy could be removed by giving the axion slightly more general interaction properties than originally assumed9'11. But a recent experiment at a power reactor 9 seemed to contradict the earlier HO 1 1 observations , leave alone their interpretation ... All that lent support to the idea20, the axion might well exist - but - 147 -

~~with such a small coupling and mass, "that even Faissner will not be able to find it."21~~

We shall see that! - But it is certainly indicated to separate cleanly observation from interpretation, and fact from fiction. In this spirit I shall describe the mounting evidence for the 2y-decay of a new, 1'ght, penetrating object at high, intermediate, and low energies (Sect. 1-3). It will become clear that the apparent contradictions amongst the reactor measurements result from unfounded assumptions, rather than from conflicting measurements. At very high energies, instead, there is a real crisis for the axion - unless one invents a process damping axion production asymptotically to small values (Sect. 4).

1. Possible radiative decays observed at the CERN PS f f The sought-for particles are supposed to interact half- weakly, both, in production and decay (or re-interaction). This leads to a weak event rate, akin to neutrino interaction rates, (as i'i- neutrinos are in effect produced strongly.) It is not surprising, therefore, that the first indications for the existence of such objects came from casual observations of side-effects in dedicated neutrino experiments. '\

Historically the first of these was tie observation of a '• small, but significant excess of electro-magnetic showers, induced in the Aachen-Padova Ai, spark chamber at small angles to the ' (anti-)neutrino beam from the CERN PS6"8. Of course, this statement rests on a certain expectation: we have spent years to find out, how many showers we should see from neutrino- electron scattering recoils 3, and how many from neutral current produced TT°'S 7»2". it was only on the basis of this painstaking work that we dared to decide there are too many single showers at small angles. It helped that this surplus occured mainly at Jç>w energies (see Figs. 1a and ? of Ref. 23): as a matter of fact this "anti-kinematical" behaviour gave1 the first hint, these low pT showers might be due to a decaiy, rather than to an interaction. - 148 -

But there had been rumors even earlier that the single gamma rays, registered in the early heavy freon exposure of GARGAMELLE to the CERN PS neutrino beam, did show a peak in forward direction. Actually, as early as in 2 5 1974, Cundy warned me to attempt a ve-scattering spark chamber experiment, as "this well-known y-peak" would be mistaken as due to recoil electrons. We detected ve-scattering anyway - but with great care for confusing gammas, and avoiding the dangerous region of small angles and low energies by suitable cuts (see Table I of Ref. 23). Much later only we started wondering where the GARGAMELLE peak had been left. And we found it: in a list of single y's prepared by Morfin in a background study for the v e-search , and (with larger statistics) in the corresponding survey for the final v e-paper . Fig. 1 of this publication is a scatter plot in angle e and energy E of all jsingle gammas, electrons, and positrons found by then. As everybody can convince himself, the single gammas in this plot, when projected on the e -axis, and subject to the standard

energy cut of .2 < Es < 2 GeV, do already show a quite respectable peak - about which nobody seemed to care, (the present author included). The final data, corresponding to an exposure of 18 2 9 5 x 10 protons, was collected by Hasért and Wachsmuth , and is shown in Fig.1. No doubt - there is a peak; if one fits a flat background through the points at angles >10" it is a 8 standard deviation effect. But this peak can have many causes: a) One (or even two) gammas from coherent (or diffractive) NC induced TT° production off the whole nucleus ' 3 0 b) Single gammas directly NC produced off the nucleus. c) Axion-like particles transforming coherently into single gammas off nuclei , and d) Coherent processes engendering gammas by the interplay of other unusual particles ' ' .

The Aachen Theoretical Group are presently busy to check if the GARGAMELLE peaks can be explained by a super-position of these it0 and y production processes by themselves. Their preliminary - 149 - |i l estimates have been inserted In Fig. 1. These are over- ; estimates in the case of originally produced IT0's, since 10% of Î them had been assumed to produce a single shower. But we know this " to happen in less than 10% of the cases ; normally the two decay gammas are recognized separately and registered as a v°. Thus it seems improbable that the forward peaks seen in the GARGAMELLE exposures, will be explained by v or v interactions. Besides, these peaks (like those of Aachen-Padova ) are intermediate energy effects. They do not appear, if one restricts 82 2 5 the analysis to energies > 2 GeV , or to those < 0.2 GeV . But all coherent and diffraction-like processes get more important at _ higher energies. This is clear theoretically; and in the case of coherent weak tro-product1on 1t has been observed by Aachen-Padova * . Thus, chances are that a certain fraction of the GARGAMELLE ? events represent the radiative decay of a new, penetrating, fairly • light particle x°» either X° - Y • ? (1) or even x° •** 2 Y « (2 ) The latter is, of course, the only possible axion decay, after its decay Into an electron pair has not been found One should not be surprised to find s^ome 2y-states amongst the 1y-cand1dates of GARGAMELLE. They had been collected to assess the Y-induced background to v e and v e scattering ' ". And since emission and conversion of hard bremsstrahlungs quanta 1s quite common in heavy freon, care was taken to retain each possible single gamma, even though it looked like two. A cursory inspection of part of the sample revealed in fact, besides clear single gammas and a few identified ir°'s, some events, like that reproduced in Fig. 2, which are hard to explain as anything but the 2y-decay of a light object. The example shown 1s particularly clear, since both gammas converted closely enough for making it difficult for either of them to simulate a brems photon from the other one. Rather, both showers point back, in any of the stereo views, to an empty point in space, about one radiation length in front of their conversion points. Hence their invariant mass becomes some ten MeV (or smaller). - 150 -

~~2. Two-photon decays at SIN~~

To be sure: it has to be checked that 2Y-events like that in Fig.2 do not appear in a true ly-sample (say from identified it°'s) taken under identical conditions. But when this is established, these GARGAMELLE photos are the most direct confirmation of the observations of an Aachen Group at SIN ' * ' .

Their apparatus is sketched in Fig.3: It was an optical spark chamber, containing altogether 40 thin (0,1mm) copper foils. This was thick enough ( s= 0,3 X ) to convert photons of about 100 MeV with fair efficiency (* 15%) into electron pairs. But it was too thin for all other particles to give disturbing interactions. The SIN 590 MeV proton beam dump was to the left of Fig.3, well shielded behind 8m of iron (and j iron-concrete). There was a 2m long decay region between j. shield and a lead converter (2,5mm thick) in front of the chamber. The idea was to convert one gamma there, and the second one inside the spark chamber. This would make pattern recognition easy, and permit a check on the measured electron pair directions by connecting the two conversion points.

Accordingly the counter trigger was chosen to be AB C.D. (see Fig.3). Only relativistic particles going from A to CD. ''[ were admitted, which eased the cosmic ray problem somewhat. A more important remedy was to have the particles from the !" beam dump going ti£ (by- 20°) in order to reach the detector. \

The experiment yielded (15 i 5) 2y-events of small (i.e.MeV) invariant mass, travelling (within angular resolution) along the beam dump direction. The background was rather flat and could be understood by a superposition of cosmic ray and accelerator induced electron pairs. The suspicion, the second photon might be a brems from the first electron pair, was disproven by measuring their respective average energies: they turned out to be equal. An important role played the iron wall, indicated in Fig.3: When it was shifted from the beginning to the end of the decay region, it removed the effect completely. This - 151 -

~~"null-test" was taken as evidence for the photons to originate in the decay region - rather than e.g. in the last part of the iron wall, by an interaction.~~

Nothing has to be taken back from these statements. But, 9 3 5 natural enough, the first publications * left still some questions open. An obvious one is, whether single gammas have been observed converting in the lead foil and making their way through the spark chamber to trigger the counters behind it? - The answer is YES: Fig.4 shows their angular distribution (plotted in angle squared)11' . There is a clear forward peak over a flat background, quite akin to the one published for the electron pairs converted inside the chamber ' * ' . This is non-trivial, since multiple scattering in the lead converter is much more violent than in the thin chamber foils. But this is compensated in part by the higher energy of the electrons penetrating the whole chamber. In addition to these (10 Í 4) haTd single gammas, we collected also (7 ± 3) soft ones with counter A in anticoincidence Another widely discussed shortcoming was that the iron wall, when placed at the beginning of the decay region, did reduce the 2Y-peak somewhat1'11 . Even our most exasperating critics eventually agreed this could be a fluctuation , but considered it improbable. They forgot, however, that our angular accuracy is limited by multiple scattering - also a stochastic process. Therefore, Doris Samm imposed better measurabi1ity on the ?n electron pair of the 2Y-sample, by demanding an opening angle 0 < 5° between the two electron tracks . The result is shown in Fig.5 , in a way suggested to us by Fetscher38, namely plotting the angular distribution: a) without iron wall, b) with iron wall in front, c) at the end of the decay region, d) with beam off - and all distributions normalized to the running time! Thus the rates are directly comparable: we have lost a few good events, but the background has gone down even more. The statistical significance is thus enhanced, and comparing "Fe in front" (b) and "Fe in back" (d ) by themselves does now yield a significant effect. - 152 -

But Doris went further still: She restricted the analysis to those "gold-plated" events, where at least one electron from the first gamma did reach the spark chamber, and reconstructed the first conversion point. Remarkably enough, this sharpening of signature reduced the background to cosmic ray level. Then she projected also the second conversion point onto the converter plane, using the measured Yj-direction. The distance of the two points in this plane, 6, is a measure of the average invariant 2y-mass. Had we measured <5, one of the gamma directions, and the two gamma energies infinitely well - we could reconstruct the decay exactly. This is not the case, mainly because the distance between converter and chamber was too large. Thus we decided to reconstruct an average mass by fixing the distance between Pb and X° •* 2y decay point to half the available decay length d, and z get: 26 YY ~ <ï 12' The distribution of this quantity is given in Fig.6 for a) effect, b) cosmic ray, c) null-test runs (as before). Since we have two independent yo-directionr measured, we can ask for consistency of both of them (to within _+ 5°). Besides, we know that the retracted iron wall in the null-test (c) scatters background down from above. Therefore, we used only the lower 75% of the chamber as fiducial volume. The events left after these two cuts are marked by cross-hatching: the background has essentially vanished, and the remaining "very good" events show a broad mass bump near 5 MeV - our resolution.

This means the 8 remaining 2y-events in Fig, 6a with invariant masses < 10 MeV are almost all effect. The background (expected from b, c and large-mass a combined) is 0.6 t 0.3 events. This clear-cut effect, together with the numbers from the angular distributions, collected in Tab. I, leaves no doubt that low-mass 2y-events from the SIN beam dump have been detected, and that they originate from a decay. The measured frequency - 153 -

ratio of ty to 2y events suggests.a 2y-, rather than a ; 3y-decay. Besides, the agreement between computed and measured y-energy spectra makes it improbable that a third, invisible particle (say a neutrino) emerges from that decay. Thus, all the evidence hints at a bos_(>n, probably of spin zero. What remains to be done, is to measmre its mass, and - if possible - its parity.

~~L^£- Pi t.-. coincidence s _a t_ a_ _JU lj_c h_rea_c tor (and possibly_ elsewhere)~~

To get a handle at the surmised particle's mass, was the main motivation for going further down in energy - to a nuclear reactor. Clearly, if the high and medium energy results mean the production of a new particle \n, this "achion" has to show up at nuclear energies too: the finite production cross section (around 10 cm ) implies a finite (half-weak) coupling of the new object to nucléons. Thus an excited nuclear level can radiate achions, in place of" the usual gamma rays, provided its excitation energy is larger than the achion mass. This argument is quite general and absolutely compelling.

The detailed properties of the particle (i.e. its quantum numbers) are unimportant - they just determine the selection rules. As it is easily seen, they coincide with those of magnetic multipole radiation for pseudoscalar particles, and with those of electric multipoles for scalar objects. In either + - + + case monopole transitions, from J~ * J+ and .)" •+ J", respectively, are possible too. This wide possibility of transitions, combined with the enormous number of excited nuclear states from fission, and neutron capture, leads one to expect effectively a continuum of achion energies, akin to ths continuous gamma spectrum one actually observes from fission fragments . Realistic estimates ' of the branching ratio R of axions to gammas - fi - *î from a nuclear reactor range from 10 to some 10 . - 154 -

4 4 3 Early limits ' , based on casual observations in the course of Reines reactor-neutrino experiments'*'' seemed to indicate much lower rates than that. But the first dedicated achion search, at the 10 MWatt research reactor MERLIN of the Nuclear Research Center Jülich, resulted in a Zy-coincidence rate well within the expected range ' ' . A brief search of the Cal tech-Munich Neutrino Group at ILL, Grenoble, is not in conflict with this rate . Actually, a devoted experiment there gave a significant 2y reactor effect" , comparable to that seen at JUlich. And this is even true for the purportedly negative result of Zehnder et al.l9: Since these authors had no reactor OFF time, they measured, instead, with their two Na I counters covered by lead. There was a significant reduction in both, single counting'rate, and 2y coincidence rate, as compared to their measurement without lead. The difference in the coincident energy sum spectrum agrees in shape (and in order of magnitude) with the ON-OFF difference, as obtained at Jü1 ich (Fig. 7). The published claim of much more stringent limits is based on the unproven assertions that a) the rate difference actually seen is due to cosmic rays, and b) that the axion/achion reactor spectrum shows isolated lines.

As Fig. 7 shows, this is certainly not what is seen at Jülich. The energy sum spectrum registered by the two Nal counters, placed side by side (as in Zehnder's experiment19) is a soft continuum, and it follows quite closely the shape of the well-known gamma spectrum from nuclear fission . Of course, the Nal cristals have been protected by plastic VETO counters against charged particles entering. A 50 cm thick shinld of normal concrete, lined on the inside by 1 cm thick boron-loaded plastic, followed by 5 cm of lead, surrounded counters and decay region. A 2 * 2 m large anticoincidence counter on top of the concrete house provided some additional rejection of cosmic rays. - 155 -

Even so, cosmic rays are a problem: they constitute typically about 90» of the trigger rate, and under advantageous conditions the reactor ON-OFF difference in the "effect region" (< 1 MeV) reached about 30% of the cosmic level.

A crucial test in this experiment will be to check, if the 2y coincidence ON-OFF rate (of order 10" sec" ) stays the same, when the local shield is strengthened. Load limits did not permit this to be done so far. Thus it was checked, instead, if the effect did depend on geometry as expected for the 2-body decay of an object with small mass. To this end, the energies deposited in either Nal counter (and also the relative time-of-f1ight ) were written on magnetic tape, whenever a fast trigger occured. The final analyses was done off-line.

Definite energy correlations were observed: the spectrum observed in one of the Nal counters did depend on the energy, seen by the other one. In particular, if an energy > 4 MeV was required in.either of them, the other counter registered close to no reactor effect at all. This correlation did depend on geometry: In a "co-axial arrangement" the 5" diameter counter A was BO cm in front of the 12" diameter large counter B, the central part of which was shielded by a 20 cm diameter lead disk of 10 cm thickness. As Monte Carlo calculations show , this geometry favours asymmetric decays; and in fact a harder effect spectrum was observed in counter 6. Placing the two counters symmetrically side by side, as indicated in Fig. 7, made this difference disappear. This is clear, if one assumes a 2y decay. Background radiation, on the other hand, has no reason to change its properties under this simple re-arrangement.

Yet one might be registering coincident y-rays following neufon capture, somewhere in our set-up. Actually, in our first meas'irements the Co lines8'10'11 were seen - but washing the lead bricks on the inside of the concrete house made them vanish. £: Isolated y-lines from n-capture in Pb (or Fe) have not been found. And a large number of runs, summarized by Ermer et al. , do in i fact suggest that the 2y coincidences do not come from the walls, but from the decay region in front of the counters. - 156 -

This conclusion was recently confirmed with the side-by-side arrangement of Fig. 7, and with the electronic threshold of each counter as low as 150 keV. As a first move, the lead wall closing the decay volume was brought from 141 cm to 40 cm distance from the counters: there was no great change! Then a 2 cm Pb separation wall was installed between the two counters, protruding into the decay region with variable length I. Clearly, this wall eliminates all 2y-decays at a distance z < $., but leaves decays farther away unaffected. Leaving an opening between Ä. and f._ would select a definite range of decay distances.

This was done by soft-ware: Fig. 8a shows the difference in energy spectrum of the small counter A (in various windows of B), between no separation wall at all ("0 cm"), and its full length of 40 cm. From the previous run one expects the full decay effect between 0 < z < 40 cm, and that is, in fact observed (Fig. 8a). If one selects an effective decay region 20 cm < z < 40 cm (Fig. 8b), only about 20% of the effect is left, and this is in accord with the soft spectrum. It is not so clear, if the spectral shape changed according to expectations; we will have to refine the Monte Carlos by taking the energy response of the counters into account.

Yet the comparison between Figs. 8a and 8b is striking. It is particularly so, since the change in geometry, considering the tons of lead around, is minute. It is hard to see, how neutron capture in all this lead could possibly react so dramatically to the insertion of but a few kilogramms. Chances are that some of the effect left in Fig. 8b really stems from a 2-body decay. The decay distance of (30f 10)cm fixes each decay angle roughly to 0 0, s 0 2 * 30

~~Since < > < s i n ö 1 * 2 1, we get from Fig. 8b~~

~~•>•• ~ 300~~

~~This is the range of masses, inferred already from the previous, co-axialco-axial ,, arrangementsarr; 8'10*11. More elaborate fits are under way (see Fig. 9). - 157 -~~

A. C on c 1_u s i o n_s Let me first summarize, what is known^ about the new phenomenon: I. There are 2y (1"y) states of low mass (p ). They have been observed at various places, and at energies ranging from f GeV's to < 1 MeV. The worry with statistics is over •'• (see Table I ). II. From kinematics and from dedicated experiments, manipulating the decay region, these 2Y(1Y) states stem most probably from a decay. •' y° - 2Y • (2)

~~III. The primary particle .••:"' (the "achion") is seen to be i neutral (at CERN).~~

~~IV. It is penetrating, as evidenced by its passing through~~

~~more than 1000 X , or ?Q0 An.~~

~~V. It is at least as long-lived, as to reach a distant detector. - This places an empirical limit on the life-time~~

~~of: 1(1 > 3 -•• 10 sec (from CERN and SIN), and > 4 >• 10 nee (from JUT ich) .~~

~~VI. There is no hint for a decay product beyond the two photons. Thus the achion is a boson.~~

~~VII. Since it decays into two identical bosons, its spi_n is even (probably zero),~~

~~VIII. The high and medium energy events yield a limit on the mass of some MeV. The geometrical decay definition at Jülich, combined with the measured y-ray energies, suggest~~

mQ = (300 ' 100) keV, and the error will shrink soon. The pari ty is not yet known, but it will be measured from the polarization correlation of the two decay gammas, either at SIN, or at Jii 1 ich. - 158 -

This summary of what we experimentally know is quite impressive. Thus I can be brief with the more subtle question, whether or not this has anything to de with the axion ... As far as our own 2Y-measurements are concerned, we may identify the achion with the standard axion '", provided we give it a mixed isovector and isoscalar coupling , and, for N = 3 generations of fermions, a Higgs parameter X = 0.40 ± 0.05 . (6)

~~If According to theory (!) this corresponds to a mass of~~

~~™s = (200 ± 20) keV (7)~~

~~and to a life-time of~~

~~T5 = (13 ± 8) msec (8) , not at variance with what we know from direct observations.~~

This value of X is also not in conf1ict with the narrow rapge of X, allowed by J/<(i -»• a0 decays . And T •* a0 decays are now getting very incisive! Dr. Herb has already presented one such candiate to this Conference . This may signalize the turning point, whence limits turn to effects as it happened to weak neutral currents!

As mentioned before, this value of X gives nuclear branching ratios of order 10~ with respect to gammas. This is in agreement with both, theoretical expections, and the direct observations mentioned. Heinrigs has performed a more general analysis of the SIN data, admitting also N = 4 (N > 4 is not compatible with the data). He gets two solutions for each N. But since the isoscalar solutions (near X = 3) are excluded by Zehnder's Ba experiment * , the final answers for m and T. come pretty close a a to the values given above. Also the nuclear transition amplitudes are almost the same. All these results have been obtained, assuming axion production to happen through mixing with TT°'S and n°'s ' ' .At very high energies this may lead to inconsistencies. In particular, there are much less axion produced lepton pairs observed, than one would expect from an incoherent mixture of n° and n° contributions ' . One may conjecture that the respective amplitudes - 159 -

tend to interfere away. But a more fundamental approach was made by Kim, Rodenberg and Stamm22: they replaced the axion-meson- mixing by a bremsstrahlungs type of axion emission via direct interaction with quarks and giuons. This provides the necessary damping at high frequencies, but one has to see, how well this model describes all the other phenomena.

If it fails to do so, the achion is not identical with the standard axion. It might well be a scalar! Then the difficulty with meson mixing eliminates itself - since there are no low mass scalar mesons. The nuclear situation would be somewhat different - more transitions would be expected. And some very daring theories may be happy with this scalar , . ?. , 5, SO achion ... ' '

The author acknowledges stimulating discussions with his co-workers and friends. He is particularly thankful for the help received, in preparing and writing-up this talk, by Wolfgang Heinrigs, Andreas Preussger, Dieter Rein, Doris Samm, Engin Isiksal, and Lalit Sehgal. The neat typing by Irene Gojdie, and the skillful drawing of the figures by Hubert Schulz, are gratefully appreciated. Finally he wants to thank his Hungarian friends, notably Desö Kiss and George Marx, for the kind invitation and a happy time at the Balaton.

Note: In a letter to the Organizing Committee, Prof. J.-L. Vuilleumier claims that there are "several inaccurate statements concerning the axion search performed at the Goesgen reactor" in the rapporteur talk of Professor Faissner. For details on the investigation at the Goesgen reactor, the interested reader is invited to consult the paper of Zehnder et al., PL. 110 B (82) 419. - H.O -

~~Possible Achion/Axion Effects at High, Intermediate, and low Enerqips. (N - No of candidates. B = Background, E - Effrct)~~

~~Primary Source Sig- E t N B Rpm-irks Group (Lab) beam Strength nal E --N-B , _ Eo~~

~~18 GGM (CERN) 26 GeV p v ).5x10 p 'Y 26 •• 6 •:?0 --7 0.? ' E ' ? GPV 1 f 50 '>• published 18 GGH (CERN ) " VI 4.5x10 p or 35 -10 <25 -8 in Nucl.Ph. 114B,~~

~~F'irsl. evidpnrr 18 13 3.5 AC-PD (CERN) " v+v 8x10 p ZY 26 n NEIJÍRIND 'ÍÍQ~~

-. Nn assoc. hadron AC-PD (CERN) 26 GeV p v> 18 21 6 15 6 2x10 p MM ( R '-4A ,ro-planar AC 2x1018p ue 18 6 12 5 J Z.'phys. 10C {1 981 ) 95 !3 CDHS (CERN) 330 GeV p v 12 î 4 < 8 ú 4 E 8x10 p ÏÏM had * ' ^ •f dump mmi ' ' '"

~~Coulomb:~~

~~AC (SIN) • 600 MeV p dump 47 1Y 11 4 7 3.3 see Conférence Reporfí .-81 129 1Y 16 6 10 4 and Bonn '81~~

~~•• • " ZY 13 I 11 7 Re-ana lys Is of 1Ï<(1>) 10 4 6 3 PL 103B (198!) 234~~

~~AC(SIN) TOTAL •• 176 1Y+2Y - - 34 9 Ciparest effect~~

~~LAMPF 780 MeV p \) 1270 »Y 620 PR D24 (1981 ) 2001~~

~~5 AC-JUlich Fission Reactor 10 MWatt 2Y •v.10 80-90"«; >10 Soft continuum~~

~~3 « 2 ILL (Gren.) 57 " 2Y •M0 ^10 3 No discrete lines~~

~~4 3 SIN (Gösgen) •v. 1 MeV 1300 " 2Y .10 MO > 37 PL 110B (1982) 419 - 161 -~~

~~References~~

~~1 J. Ellis, Lectures at the Les Houches Summer School (1981), LAPP-TH-48, Ref. TH-3174-CERN (1981).~~

2 J. Wess and B. Zumino, Nucl . Phys. B_70, 39 (1974), and Phys. Letters B6JJ, 361 (1977), P. Fayet and S. Ferrara, Supersymmetry, Physics Reports 32^, No 5, 249 (1977), P. Fayet, Phys. Letters 6JJB, 489 (1977), 84B, 421 (1979), 86B, 272 (1979); Nucl. Phys. 187D, 184 (1981), G.R. Farrar and P. Fayet, Phys. Letters 76B, 575 (1978), 79B, 442 (1978), and 89B, 191 (1980).

~~3 R.D. Peccei and H.R. Quinn, Phys. Rev. Letters _38, 1440 (1977), and Phys. Rev. ÇJ_6, 1791 (1977).~~

- S. Weinberg, Phys. Rev. Letters 40, 223 (1978), v- F. Wilczek, Phys. Rev. Letters £0, 279 (1978), W.A. Bardeen and S.H.H. Tye, Phys. Letters 74B_> 229 (1978), W.A. Bardeen et al. , Phys. Letters _7M' 580 (1978), T.W. Donnelly et al. , Phys. Rev. 0J_8, 1607 (1978). s L.B. 0 kun, Proc. Internat. Symposium on Lepton Photon Interactions at High Energies, ed. W. Pfeil, (Univ. Bonn 1981 ) p. 1018.

~~6 H. Faissner, Report to Neutrino '80, Erice, not included in the Proceedings, but available as Aachen Report PITHA 81/03 (1981), see also CERN Courier (May 1981), p. 161/~~

~~7 H. de Witt, Doctoral Thesis, Aachen Tech (1981), to be pubiished.~~

~~8 H. Faissner, Proc. Int. Neutrino Conf. Maui 1981, ed. R.J. Cence (Hawaii), p. 159, available as Aachen Report PITHA-81/32 (1981). - 162 -~~

~~9 H. Faissner, E. Frenzel, W. Heinrigs, A. Preussger, D. Samm, and U. Samm, Phys. Letters V03B_, 234 (1981).~~

10 W.R. Ermer, H. Faissner, E. Frenzel, E. Hermens, H.R. Koch, 0. Schult, H. Seyfarth, and R. Yogeshwar, Proc. Sympos. on (n,y) Reactions and Related Topics, Grenoble (1981), ed. T. von Egidy, p. 687, H. Bechteler, H. Faissner, E. Frenzel, H.R. Koch, 0. Schult, H. Seyfarth, and R. Yogeshwar, KFA JUlich, IKP, Annual-Rep. 81, Jul. Spez. _H6, 69 (1982).

~~11 H. Faissner, Proc. Internat. Symposium on Lepton Photon Interactions at High Energies, ed. W. Pfeil, (Univ. Bonn 1981) p. 797, available as Aachen Report PITHA 81/33 (1981).~~

~~12 A. Zehnder, Phys. Letters 104B, 494 (1981).~~

~~13^ Y. Asano et al. , Phys. Letters 1£7B, 159 (1981).~~

~~lh C. Edwards et al. , Phys. Rev. Letters 48, 903 (1982). ls I. Antoniadis and T.N. Truong, Phys. Lett. JjOjtë, 67 (1982).~~

16 P. Fritze et al., Phys. Letters _96B, 427 (1980), M. Jonker et al . , Phys. Letters JÎ6£, 435 (1980), and Refs. quoted there. 1 7 CDHS Collaboration: B. Renk, Contribution to the Spring Meeting of the German Phys. Soc. Karlsruhe (1982), and private communication, see also K. Kleinknecht, Neutrino '82.

~~1 S A. Barroso and N.C. Mukhopadhyay, Phys. Letters 106B, 91 (1981).~~

~~19 A. Zehnder, K. Gabathuler and J.L. Vui1leumier, Phys. Letters 110B, 419 (1982).~~

~~20 M. Dine, W. Fischler, and M. Srednicki, Phys. Letters 104B, 199 (1981 ), M.B. Wise, H. Georgi, and S.L. Glashow, Phys. Rev. Letters 4_7, 402 (1981 ). - 163 -~~

~~?1 B. Zumino, Proc. of the European Soc. Int. Conf. on High Energy Phys., Lisbon (1981). in press.~~

~~2i B.R. Kim and C. Stamm, Phys. Letters 105B, 55 (1981), B.R. Kim, R. Rodenberg, and C. Stamm, Karlsruhe (1982), and to be published.~~

~~73 H. Faissner et^aj^, Phys. Rev. Letters 4±, 213 (1978).~~

~~21* H. Faissner, Proc. XVI Rencontre du Moriond at Les Arcs, ed. Tran Thanh Van (Orsay 1981) p. 335.~~

~~H. Faissner e_t_al_!L, Phys. Letters, to be published.~~

~~25 D. Cundy, private communication.~~

~~26 J. Morfin, private communication to the GARGAMELLE Collaboration (1976). - The author thanks Fred Bullock (Univ. College, London) for providing him with this list.~~

~~27'J. Blietschau et__a_l__._, Phys. Letters _73B, 232 (1978).~~

~~28 J. Blietschau et• ±\_j_, Nucl. Phys. 114B , 189 (1976). The scatter plot of 1y events (Fig. 1) contains already a significant forward peak.~~

29 H. Wachsmuth and F.J. Hasért collected the final \y statistics, 18 — corresponding to 5 * 10 protons on the v-target, which is about twice as much as published in Ref. 28. 30 D. Rein and L.M. Sehgal , Phys. Letters 1_04Ji, 394(1981), Ann. Phys. (N.Y.) j_33, 79 (1981), and priv. communication. 31 S. Barshay, H. Faissner, R. Rodenberg, and H. de Witt, Phys. Rev. Letters 46, 1361 (1981).

~~32 E. Belotti et al., Phys. Letters 2âi» 223 (1978).~~

~~33 H. Faissner et al., Phys. Letters 96£, 201 (1980), and refs. quoted therein. - 164 -~~

~~31* The author is indebted to Franz Josef Hasért, Paul Musset, Horst Wachsmuth, Maria Willutzki, and Engin Yshiksal for their help with this search.~~

~~3S H. Faissner, Proc. XVI Rencontre du Moriond at Les Arcs (1981), ed. Tran Thanh Van, p. 315. Available as Aachen Report PITHA 81/20 (1981 ).~~

~~ss W. Heinrigs, Doctoral Thesis, Aachen Tech (1981), to be published.~~

~~37 H. Faissner, E. Frenzel , W. Heinrigs, A. Preussger, and D. Samm, submitted to Phys. Rev. D (1982).~~

~~38 W. Fetscher, private communication.~~

~~39 D. Samm, Master Thesis, Aachen Tech (1981), to be published.~~

~~"0 See R. Vandenbosch and J.R. Huizenga, Nuclear Fission v (New York and London 1973) p. 360.~~

"* R. Wilson and J. Selinger, Harvard pre-print (1981), and private communication. The Aacben-Jülich group appreciate interesting discussions with Dick Wilson, and valuable information about his power reactor experiment on axions, under way in collaboration with B. Vignon et al.

~~112 A. Barroso and N.C. Mukhopadhyay, Phys. Rev. 24C, 2382 (1981).~~

~~1(3 G. Micelmacher and B. Pontecorvo, Nuovo Cimento Letters 21, 441 (1978).~~

~~-- H.S. Gurr et al. , Phys. Rev. Lett. 3JÎ. 179 (1974), F. Reines et al., Phys. Rev. Lett. 3±, 315 (1976). The author has commented (in Ref. 6) on the limits derived thence in Refs. 4 and 43.~~

~~"5 J.L. Vuilleumier et al., Phys. Letters 101B, 341 (1981). - 165 -~~

~~"6 H. Borner and S.A. Kerr, private communication.~~

~~"' A. Zehnder, private communication. We thank Alex Zehnder for a most interesting exchange of experimental data. lf8 J. Bechteier, private communication.~~

~~1(9 S. Herb, contribution to Neutrino '82.~~

~~50 H. Frenzel, private communication. - It is most intriguing that Frenzel's theory contains a neutral scalar particle of about 400 keV mass, which is mainly produced at low energies. - 166 -~~

~~£j 3 V-ZI?__£• íLP t ions~~

~~Fig. 1 : Angular distribution of "clear single y-rays", AS~~

~~observed during the early CF3Br runs of GARGAMELLE in the CERN PS v beam (black points and histogram). The curves are theoretical predictions by Rein and 1 0 Sehgal.~~

~~Fig. ?.: Forward shower from an early GARGAMELLE PS \>-run, exhibiting two cicely separated electron pairs, pointing to a common origin near the lower edge of the photo: candidate for x° •* 2Y-~~

~~F_i_f[_. _J: Apparatus used by the Aachen Group in the beam dump experiment at SIN .~~

Fig. 1 : Angular distribution of single gammas converting into electron pairs in the Pb in front of the spark chamber and triggering. Only a) shows an effect, compatible with the angular resolution (dotted), and far below the angular acceptance (dashed).

Fig. 5: Angular distribution of electron pairs converted inside the chamber, when only opening angles <- 5° are admitted: a) No Fe-wall, b) Fe-wall in front, c) at the end of the decay region, <•) Beam OFF.

2 Fig. 6 : Distribution of m „ reconstructed for 3e- and 4e-events, assuming a decay point at the center of tfie decay region: a) No Fe and Fe in front, b) Beam OFF, c) Fe retracted. Only the cross-hatched events survive the cuts. Fig. 7: Energy sum spectrum of 2y-coincidences , registered 5 m from a JUlich reactor (difference between reactor ON and OFF). Dashed the Monte Carlo expectation for a decaying mass of 400 keV. - 167 -

8: Energy spectra registered (with reactor ON) in counter A, in coincidence with the energy ranges indicated for counter B. a) No separation wall minus 40 cm separation wall (* full effect). b) 20 cm separation wall minus 40 cm wall (i.e. decays between 20 and 40 cm distance admitted).

_9: Distribution of geometrical mean energies, as observed in 2y coincidences using the side-by-side geometry indicated. - When multiplied with the appropriate opening angle O , this quantity gives the invariant mass. 20 4 GGM Freon PS v/iy

~~8Y = angle of first y to beam~~

~~-coherent \y • = No of events per 50 deg2 ~L = averaged over 100 deg2~~

~~0\ diffractive TCC 03~~

~~o loo 200 300 400 500 600 700 800 wo 1000 [deg2] el - 169 - Paraffin Spark chamber modules Counter Lead 12 3 4 CD, 2f iron Y/À Concrete~~

~~PÍS- 3 - 171 -~~

~~a) Beam on~~

~~16 lèvent, 5 cm Pb v levent.ScmPb+ZOcmFe 12 \~~

~~Averages 5.4+0.7 8~~

~~n b) Cosmic Rays~~

~~TD CD lèvent CD 6 LO Average = 2.5+0.5. -^ 4 t/7 ~~~

~~c) Null Test lèvent,Fe-wall retracted 6- reflected from above~~

~~Averages 2.0+0.4 = 3.8+ 0.8 K> 2- JZh~~

~~100 200 300 400 500 600 deg: ~.2~~

~~{TV (12'1Z (16*)' (19*); (2D7 (2O2 (26*)'~~

~~Pi«. 4 30 a), no Fe 8" —1 b) Fe in front 3 6 •20~~

~~2 4- •10 CD S 1 2- CD~~

~~s to d) no beam 3 c) Fe at end 2 •10 1~~

~~100 300 500 700 100 300 500 deg: square of angle with beam dump direction~~

~~\ Fig.S - 173 -~~

~~Effect-Runs a)~~

~~Cosmics b) > eu 2:~~

~~c eu -TU Null -Test c) 4 3- 2- 1- n 0 20 40 60 80 120 160 200 240 280 MeV~~

~~Fig. 6 - 174 -~~

~~600~~

~~Sum-energy spectrum Reactor ON - OFF~~

~~500~~

~~B 400 • * 141cm *" .c o \ a» \ 8 300 M.C.fm=4O0keV~~

~~I/) o c~~

~~Í200 o o~~

~~\ 100~~

~~-..G n~~

~~MeV) Fig. 7 - 175 -~~

~~2*00 (Difference in the Energy Spectra 2000 - in Counter A (Reactor ON) o 1600 - 0cm-«0cm Separation Walt~~

~~1200 a) 0.1$ EB< 0.6 MeV o 800 -~~

~~«00 - O o o 0 i~ xz o 1200 jr b) 0.6« EB< 1.5 MeV~~

~~i 800 A~~

~~«00 «J A A A !2 0 « * A â C Co i~~

~~1200 c)1.S< [:„« 3.0 MeV~~

~~800~~

~~Q O 0 n n p n n Channrt No 20 60 80 100 120 i i i I I • A— i i 1 • 1.0 2.0 3.0 M«V Energy in Counter A Fig. 8a - 176 -~~

~~Difference in the Energy Spectra in Counter A (Reactor ON) • í\ n n 1000 20cm-40cm Separation Wat!~~

~~800 o) O.NE~~

~~b) 0.6~~

~~400 ces / i~~

~~200 A~~

~~Coincide n 0 i i A A ^ A A «A A~~

~~600 c) 1.5~~

~~400~~

~~200 » a i a a 0 - Ç Channel No o» 20 40 60 80 100 120 1.0 20 3.0 MeV Energy in Counter A Fig. 8b - 177 -~~

~~1200 -~~

~~Reactor ON - OFF (d-U1cm)~~

* 141cm •"

~~'MC(mxiOOkeV)~~

~~is Fig. 9 - 178 -~~

~~NEW BOUNDS ON HEAVY NEUTRINO MASSES ANO MIXING~~

~~FROM KlZ AND n^ DECAYS~~

~~Tosltimitfiu Yamazaki~~

~~Department of Physics and Meson Science Laboratory Faculty of Science, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan~~

Abstract Recent experiments aimed at heavy-neutrino search in Kjj2 and TTJJ^ decays, as proposed by Shrock, have yielded new bounds on neutrino masses and mixing In the 5 - 300 MeV region. In particular, a new dedicated experiment on K^j decay at KEK is described.

~~1. INTRODUCTION~~

~~The problem of neutrino masses and mixing is one of the central problems of elementary particle physics and cosmology, but we have very little knowledge. If neutrinos are massive, each neutrino of~~

~~a given flavor \\>0> is not necessarily the mass eigenstate, but in Jo general expressed in terms of a linear combination of mass eigenstates |v.>:~~

~~v v > for |vji> = T u\ i ' £ = e, u, T, ••• i = 1, 2, 3, ...~~

~~The neutrino-mass measurement in the usual sense is to determine the mass of a neutrino that is dominantly coupled to one~~

flavor eigenstate: \v.>* |v > , |v2>- jv > and |\>,>=jv > . The presently known values [1-5] are listed in Table 1. Except for the experiment of Lubimov et al. [2] all the experiments give only upper limits on the masses. The trouble with v is its smallness compared to the beta decay energy and the instrumental resolution. The experiments for V use two-body decay IT •+ )j v . For a small finite neutrino mass the momentum of I is shifted only a little 2 (approximately by m /1K). Furthermore, the ambiguity in the parent

~~?;.•• - 179 -~~

~~Table 1 Masses of neutrinos~~

~~Flavor Charged-lepton Neutrino Method Ref. ma88 mass (90X C.L.)~~

~~0.5110034 MeV 60 eV End point of T beta decay 14 - 46 eV~~

~~H vp 105.65946 MeV < 0.57 MeV 11+* P 3~~

~~1784 MeV < 250 MeV T~ •* e" VT 4 "VT 5~~

ma ss will eventually contribute to the accuracy in m . A similar situation exists for v . It is still an open question whether or not these direct methods will yield conclusive answer to the problem of finite neutrino masses. An alternative method was proposed by Shrock [6]. This is to look for a heavy-mass neutrino v. in the decay of a pseudoscalar meson M •* ív , where M = n or K. The principle Is illustrated in Fig. 1. The nomenturn spectrum of í shows a normal peak corresponding to the dominant ly-coupled light-mass neutrino at

Such a shift is, however, masked by a finite Instrumental resolution as well as by an ambiguity in the parent mass. If a subdominantly-coupled neutrino has a substantially heavy mass, then another line, well separated from the dominant one, should be observed at

~~" T" • 1 + x2 + y2 - 2(x + y + xy) where~~

~~The relative branching ratio is given by - 18O -~~

~~NEUTRINO MASS SPECTROSCOPY IN M+— £*V~~

~~Zero-mass Light-mass~~

~~Heavy-moss 2M • Instrumental resolution~~

Momentum of A*

~~Fig. 1. Principle of neutrino mass spectroscopy in M -*i. v decay.~~

~~Fig. 2 Momentum and kinematical factor versus neutrino mass for K* and ir+ decays.~~

~~'0 100 200 300 400 500 ÍMeV/c2) - 181 -~~

~~where pj is the kinematics! factor Including phase apace and heliclty balance:~~

~~» ix + y ~ 2^ / 1 + x2 + yz - 2(x + y + xy)~~

~~x(l - x)2~~

The .nomentum and p In the cases of K •+ I V , and if •+ I v, where Jt " ?r+ or e+, are presented in Fig. 2. This method can be called "neutrino mass spectroBCopy", as each mass elgenstate |v.> shows up In the spectrum with the spectroscoplc factor l^n-il*" Already some experiments have been performed. The decay «ode 7r+ •* u+v has been studied by Calaprice et al. [7] and by Abela et al. [8]. The latter gave the best limit for |U | 2 as low as 10~5. The decay mode 7T+ •* e+v was studied at TRIUMF by Berghofer et al. [9] using a Nal(TH) spectrometer and a limit for II) J2 as low as 10~ô was obtained. . . ' ei1 The decay mode K •* y v was studied by us at KEK [10] using a range telescope which covered the mass region 160 -220 MeV. Another constraint was obtained indirectly from the non-existence of K+-* u+vvv event in the experiment of Pang et al. [11]. The lower tail region of the K •+ e v peak measured by Heintze et al. [12] at CERN can be used to deduce another constraint on |U I2. We will summarize these results later. While the unknown range of neutrino masses and mixing is extended almost infinitely, the present spectroscopy covers only a" small portion. Then, the possibility to catch a heavy neutrino may seem to be miraculous. However, if we assume the electron neutrino mass to be finite, say, around 20 eV, as Indicated by Lubimov's experiment, what do we expect for the v and v masses? The neutrino oscillation experiments [13] are looking for tiny differences , but it is more natural to expect a certain relation between m and m.. One candidate is a quadratic relation

~~as derived from grand unified theory [14]. Then we expect a relation In the diagram of n^ versus m^, as shown in Fig. 3. The broken - 182 -~~

~~IMtV 10 MO IGtV K) tOO WOO~~

~~Fig. 3. Empirical relation between neutrino masa and lepton masse.~~

line touches the presently known upper limits for V and v . Of particular importance to us is, as emphasized liy us [15], that the V may have a mriRB nround 200 MeV, which is just within the region of detection In the K •*• \i v decay. Therefore, we were encourged to do a dedicated experiment. A new dedicated experiment using K -*• u v was announced at Neutrino 81 at,Maul [15]. Actually, this experiment has been carried out at KEK. We will describe the experiment in § 2 and its reRult together with others in |3.

~~12. NEW EXPERIMENT ON K+-»/v DECAY AT KEK~~

The known decay branches of K ( Me* » 493.669 MeV ) are given in Table 2. We have to look for a discrete line above the continuum background coming from the three-body decays. Because we don't know with what masses and mixing ratio such a peak may appear, we decided to make a new magnetic spectrograph to achieve broad momentum range and - 183 -

~~Table 2. Decay modes of K~~

~~Mode Branching ratio Momentum~~

~~P+v 63.5% 235.5 MeV/c e+v 1.54 x 10"5 246.9 „V 21.5 X 205 y+vn° 3.2 X <215 e+VTro 4.8 Z <228 0.58 X -Í235.5 AV 5.6 Z <125~~

high sensitivity to a small peak. The design aims are as follows: 1) High resolution as good as 1 X FWHM or better. 2) Large solid angle as much as 100 msr. 3) Broad momentum range: 100 -250 MeV/c. 4) Effective veto system using Nal(TH) counters against the three-body decays involving n * and y . 5) Good particle Identification ír /p/e/ using T.O.F. counters and range counters. The experiment was started In October 1981 and the first phase of run was finished in March 1982. The first report of the experiment Is being prepared and will be published elsewhere [16]. Here, we describe the experiment and Its result as of today. Fig. 4 shows a schematic diagram of the spectrograph. The experiment was performed at the K3 beam channel at KEK 12 GeV proton synchrotron. A DC-separated 550 MeV/c K beam was degraded In a 7 cm copper dégrader, and was stopped In 10 layers of plastic scintlllators (seven 8 x 20 x 0.6 cm , two 8 x 20 x 0.2 cm and one 8 x 20 x 0.1 cm ) tilted 30 degrees to the beam. The K/ir ratio was typically 25Z, and the number of stopped K vas about 5000 per beam spill. Minimum-ionizing muons lose about 1.7 MeV In each 6mm stopping counter. Misidentification of the K stopping layer would thus lead to poor momentum resolution and spurious shoulder. Therefore, the K - 184 - stopping layer in the stopping counters was carefully dotcrmincd by using both pulse-height and timing information, and ambiguous events were rejected. Charged particles from K decays were momentum-analyzed by the magnetic apectrograph, consisting of 2 entrance multlwire chambers (PCI, 2), a 10 kG C-type rectangular-pole magnet with the dimensions 80 cm x 150 cm, and ?. exit chambers (PC3, A). The time difference between K arrival and the TO counter at the spectrograph entrance was measured to

~~KEK E89 K* BEAM SSO M~~

~~.--MAGNET POLE »»HO GAP 21°" ^^^ »~~

~~-ANTI SCATTER!« COUNTERS AT POU FACE~~

~~RANGE COUNTERS~~

~~Fig. 4. Schematic layout of the neutrino mass ßpectfograph used fit KEK. - 185 -~~

ro.jKrt prompt events, mostly due to K decay in flight. Time-of- fllght menBiirements between the TO counter and the TOF stop counters, and range Information from 46 range counters were combined to identify muonn. Among the major decay branches the K -* \i vir" and K -• \i vy decays produce a continuous background to the tnuon momentum spectrum, below the 236 HeV/c main peak. To achieve high sensitivity to small discrete peaks, these decay modes must be vetoed. We employed 112 modular NaI(T£,) counters (6.5cm x 6.5cm x 30cm) with discriminator threshold set around 1 MeV, and surrounded the K stopping region to veto IT" and y from these decay modes. The veto efficiency of the \) vit" mode was quite high because of two-gamma emission, better than 99%, while the y vy mode was difficult to eliminate. Even with 92% solid-angle coverage by the Nal counters, more than 30% of the JJ \ry photons escaped undetected; low-energy photons are preferentially emitted along the muon momentum direction [17]. Much effort has been paid to achieve best momentum resolution: large bending angle, first-order horizontal focussing, high-resolution 2-dimensional readout of the MWPC's, and a helium gas bag between the magnet poles to minimize multiple scattering. Momentum reconstruction was performed by using a parametrized track model, and a x2 test was applied to eliminate spurious tracks. The reconstructed momentum was then corrected for energy loss in the K stopping counters by using the pulse-height information.

Final spectra are shown in Fig. 5. Open squares represent the over-all charged particle spectrum without photon veto; major K decay modes such as \i v, IT IT , y V tr'and n tr it can be readily identified by distinct peaks and shoulders as indicated in the figure. Closed squares represent the final muon momentum spectrum with photon veto and particle identificalion; total of 1.9 x 10 decays were observed. The momentum resolution at 236 MeV/c is 1% FWIIM with a perfect]y-gaussian line shape. Note that the ordlnate is in a logarithmic scale, and the upper tail of the 236 MeV/c \i v peak falls quadratically almost 5 orders of magnitude. Also note the wide momentum acceptance of the spectrograph, which ensures almost flat acceptance of about 100 mstr between 100 MeV/c and - 186 -

250 MeV/c. The continuum in the union spectrum and the slight lower tail of the 11 v peak is due to the p VY decay, which evaded photon veto. This assignment was checked by Monte Carlo calculations, and was found consistent. To investigate the peak region, a better spectrum from only the down-stream thinnest stopping layer showing FWHM = 0.5% was used.

~~0 10« 7T+7T~~

~~10"'~~

~~S. Without Nal veto . a> "S I0'3 o o a> •o io- g~~

~~a.a~~

~~10,-t~~

~~too 140 ISO 220 260 Momentum (MeV/c)~~

Fig. S. Momentum spectrum of charged particles from K+ decay. Open equaree shew overall spectrum without Hal veto. Clo8ed squares represent the final mton spectrum with photon veto and particle identification. - 187 -

~~3. DISCUSSIONS~~

Flg. b shows no distinct peak In the muon momentum spectrum except for the normal, one at 236 MeV/c, which sets the upper limit on the mass and mixing of heavy neutrinos. In Fig. 6a, we show the region excluded by the present experiment on a mass vs mixing plane. In terms of the mixing ratio |U J|2, where i is presumably 3 in the ordinary Vs V.. and v ~ v_ assignment, the 90% C.L. limit is about 10~ for m - 110

~~Mum Momtntum p, (McV/cl Eltclron Monxntum t, (MtVft) 2B ao ao m zoo BO WO HO IZO WO WO HO M 800 WO IW i lor Ktt ! 1 ; j HM» 40 » 0 i i for W„ i J . 1 i~~

~~!• i \ I i 10' 1~~

~~Ktt j 10" I CERN 1 Wtt T RIUMF 10' (00 200 300 100 MO NMtrkw Moil »„ (IMVA I N«utrino MOM mh (MtV/cM~~

~~Fig. 6a Fig. 6b~~

~~Upper bounds of |fu^ versus Upper bounds of \U .\* versus neutrino masa. neutrino mase. - 188 -~~

MeV/c2 and 10~ for m = 250 MeV/c2. The limit becomes exceedingly —A 2 loose for lighter masses as shown, 10 for m "=70 MeV/c , for instance, due to the y vy background and the finite momentum resolution of the spectrograph. In the same figure, bounds given by other experiments are also shown. Marked "KEK" is the result of our previous K range measurement + [10], "LBL" is from the rare decay experiment K •* p+vwf 11] . The bound on fU |2 in a different mass range can be obtained by using n decay. The result of Abela et al. [8] is indicated in the figure. A wavy line is the bound from the result of v - v oscillation experiment [18], which is relevant to the V . mixing in our terminology. The figure shows how sensitive the present method is in comparison with neutrino oscillation experiments. Only the mass range that is not accessed by either K+ or ir+ is < 5 MeV and 30 - 70 MeV. A similar plot on the bound of II) , I2 can be made by using the K „ r ' ei1 e2 data by Heintze et al.[12] and the recent result of He2 measurement with a Nal(Td) spectrometer at TRIUMF by Berghofer et al. [9J. These experiments set upper bounds in the mass range 50 - 160 MeV/c , as'shown in Fig. 6b. The upper bound of |U .j2 already exceeds 10 ,, but It is generally believed that |U |2 is much stipuler than |U . |2t because the former is related to the generation gap of two. So far, there is no positive evidence for the existence of heavy neutrinos in the mass range 5 - 300 MeV/c , but such a possibility still cannot be excluded. In particular, the lower tail region around 220 MeV/c still suffers (to the fraction of 10~ .'! ) from contamination sputtered from the main peak. Further experiments with improved momentum resolution and background suppression aimed at increased sensitivity to smaller mixing are under way. In connection with this study, another experiment is being carried out at KKK to measure the longitudinal polarization of the dominant \\ + + 2 in the K •* u v decay [19]. If a heavy neutrino of mass, say, 50 MeV/c is hidden in the dominant peak with appreciable mixing, the overall polarization of \l should be reduced accordingly, as calculated by Shrock [6]. A careful and precise measurement will give some new information on this point. - 189 -

The author would like to thank Dr. R.S. llayano for flie enthijgla.it lr col Inbornt Ion and dnlly conversations on this work, and other members of tin.' K(i group, T. Tfinfßuchi, T. Yamannka, T. Tanlmori, R. F.nomoto, A. ishlhnshi , T. Ishlkaua, S. Sato, Drs. K. Nakairmra, S. Kuroknwa, S.R. Srhnft7.fr, Y. Takada and Prof. T. Fujii. He is grateful to Prof. R.E. Shrork for tlie stimulating discussions and to Prof. T. Nlshikawa, S. (ist.'ikf, A. KuKunifßi and H. Stig.wara of KEK for their encouragement and support.

RKKKKKNCICS |l| K.T.. Perkqvist, Nuc.T. Phys. ]H9 (1972) 317. \?) V.A. l.ublmov et al., Phys. I.ctt. 94B (1980) 266. MIM- l>.T"tn er ,11., PJiy«. Rev. WO (1971) 269?.. |-'i| W. iiiiclno (>i nl., Phys. Kov. Lett. 42 (1979) 749. \5\ ('.A. Blmkfi, rliys. l.«tr. 109B (19K2) 109. |6| R.V.. Slirock, Pliys. Lett. 96B (14B0) ]">9, Phys. Rev. P24 (1981)

~~\JVZ, 12 7 :>. [71 F. Cal «price »>.t~~

[fi| R. Abel a et al., Phys. l.i;tl. ]£5B (1981) 263. [')| 1). Rorptinfpr et al., Pror. 1981 Int. Conf. on Neutrino Physics and Astrophysics, Maul, ll,iv;j i i , Vol. 11 , p.67. flOl Y. AîMino et .(1., Phys. Lett. lO/iB (1981) 84.

~~[Ill C.Y. Panp ft fil., Phys. Rev. 1)8 (1973) 1989.~~

[121 .1. (Icintf.i! ct al., Nucl. Phys. BJ49 (197'») Kiri. I 13| F. Reines et al., Phys. Kev. Lett. V\ (I«1RO) 111]/; K. lloohm Gt al., Phys. l.ert. 9?J (1980) .')IO. [141 For instance, L. Wolfensteln, t'roc. I9RI inf.. Cenf. on Neutrino Physics and Astrophysics, Maul, ll.-iw.i I I . V'nl.H, p.32''; R. N. Mohtiparra ?nd (;. .SrnJ.inovlc, Pliyü. l!i-v. Lflt. '*'< (1980) 912. I1 f> 1 T. Yamazakl and R.S. Hayano, Prec:. l'»81 Irtl.. Conf. on Neutrino Physics and Ar.trophys 1rs, Hani, Hawaii, Vol.11, p.49. [16] R.S. Iliyano et ni., to be published. I 17] B.R. Neville, Phys. Rev. ^24 (J96I) ?017. [181 N..1. Baker et al., Phys. Rev. Lett. 4_7_ (1981) 1576. [191 R.S. Hayano et al., KF,K proposal R99 (1982). j i- \

~~LEPTOIM CONSERVATION - 190 -~~

~~LEPTON NUMBER CONSERVED?~~

~~I.Kobzarev Institute of Theoretical and Experimental Physics~~

~~Abstract The phenomenological . framework for the description of £ -violating processes is described, existing possibilities to observe /_ -violation are compared.~~

In this paper a short review is given of some problems connected with phenomenology of possible lepton number violations. There are known two conservation laws, which were introduced around 1950 on phenomenological ground» and are now in doubt: the law of barion number iß) conafcr- jration introduced by E.Wigner and Ya.Zeldovich in 1949-1 y'_>ü L ~ -I and the law of lepton number conservation introduced in papers of•G.Marx, Ya.Zeldovich and E.Konopinsky and M.Machmo«d L4" &J. The present mass assault on

law shall correspond a massless gauge field. As there are no massless fields besides electromagnetic and gravitational fields«) there' should be no exact conservation lav/a besideu conservation of electromagnetic charge and energy-momentum. Obviously this reasoning assumes that there are no raassleae fields with couplings too small to be seen at present. Both /S and / are violated simultaneously in minimal GUT SU(5)-versionL'j leading to proton decay + p e + 77° and others, and this is possibly already seen in experiment (S.MyaJie, thi3 conference), but in SU(5) J3 ~Z is conserved. What we will discuss below Id mainly.the phenomenology of independent violation of L, - number. This possibility is also naturally incorporated iri - 191 -

~~such GUI-models as S0(10) and there are two subjects connected with it which are now intensively investigated experimen-~~

~~tally Î neutrinoless 2B -decay or (0#) 2& )-decay~~

and neutrino oscillations« Both subjects are known for a long time. The connection of (0,' 2ß ) decay with /. -violation was discussed in papers*-*""^ and it was just the neutrino oscillations of type V —* Y. which were discussed in pioneering papers of B.Pontecorvo of 1957-1958••«*,• The present state of art will be described below' we would like to mention already here that although both kinds of processes ( (0, Xß )-decay, oscillations) can be easily Incorporated in present theoretical framework« if they would be discovered, their absence in the region of parameters now accessible to experiment would cause no big problems,

2. Some definitions. The phenomenology which is described here is the most restricted one. It is assumed that all /_ -nonconaervation can be absorbed in general neutrino mass-matrix« and no right-hand currents are present in low-energy phenomenology« This corresponds to the assumption that L. -breaking is due to processes with the energy scale much above 100 GeV (it may be the usual GUT-scale), Only J*J approximation to GWS- electroweak theory is needed

~~where~~

~~and - 192 -~~

( V\j- in standard Bjorken-Drell notations!.9_/ ±g equal to (**). It is assumed that Z =1 for C^ /**, £** and Ye, VJu, ^?~ and ^~ B "1 •for corresponding antiparticles. The variants when Z. = 1 for e~ and -1 for Jlt,~ are not discussed. As is shown in*- •* they can be generalized for any even number of lepton generation; from The point of view used here they would correspond to a specific choice of general neutrino mass-matrix. The expression (4) is to be considered as implicit definition of V^, V^ V£- states. ( V£ is the state created by e~ absorbtion at ~£ = 0 etc.) It is not necessary for them to be eigenstates of complete Harailtonian and their time-development corresponds to neutrino oscillations« The expression for J — (3*~J defines the V states. We assume also the definition of CP operation corresponding to the definition

~~where V^ f V/j are states entering into (3) - (5).~~

3. T?n fínoraenology As was stated earlier we assume that all effects connected with L. -number violation are due to the neutrino mass Lagrangian. The most general form of it is * Si Kt* •*• »>t K-Tc KtI *

~~T Here C is charge conjugation matrix C =< -C . - 193 - y~~

, tii ttl ,^ •' ^ " M g- o .../ .>-l ...3' 0/. î In standard notationsl Indices & A* correspond to neutrino flavours. It is simpler to discuss general case i, /< =" •/, ... jV instead of 3 generation case ( J\f = 3). Here is assumed that besides V£. neutrino appearing in GWS-lagrangian V^ states also are admissible in c>Cy . The probability that V# states in some aen3e "exist" seems to us rather large. Especially if they are completely excluded, we would have to write gravitational interaction of neutrino in the form explicitly violating P-invariance. To escape this we have to introduce V# in gravitational interaction01-12J. if y^ enter in the gravlton vertex for neutrino they could be generated in strong gravitational fields« CP-invariance is not assumed« The Dirac mass-matrix in óC/^f is then a general complex matrix, "Majjorana" matrices />? Í*. and symmetrical complex matrices. This general form of cZfif is known for many years (see review £"-/). The Dirac term in c«/y conserves Z. -number, terms /??<<•• and m£t violate it. (ál =12 ). One can exclude V£p from low energy phenomenology assuming its mass to lie in GUT-region. Then the Dirac masses do not appear in low-energy phenomenology end so the most natural version of effective aC^f for low-energy region is

* A C (7)

Such Lngrangiaa (for 2-generation case) was considered and solved in Gribov and Pontecorvo paper in 1969*- ^*. (They used identification L(e~)-£(*€?-+/, ^ 0*7-1(^x4). The Dirac oscillations were described in^ ^~ -*. Although oc/y (7) does not conserve L. th« phenomenology of oscillations is very similar Jy/'/^pure Dirac case. It is connected with the fact that for - 194 - I

~~Majorana case chlraMy number takes the role of lepton ?>~~

number and all L -violating processes like )/e -t- f> —» ].' —j^ €.*"+ /Z- which appear due to Majorana transition of !--. kind Vo —9 ")/e have small amplitudes of order li/ifrv »' so practically the case of pure Dirac ( AWr" sr fft/^ — Û ) and pure Majorana (only f*?tu ïfi & ) are indistinguishable More interesting would be the case of general oC/y • In this case for given spin-projection there would be JcJ\f~ )' V -states and correspondingly the diagonalization of o\/y would lead to j?Jf eigenstates. The oscillation

in this case could lead to sterile states ( \/e'£ —* ^ £, )$ so in principle in this case the total flux of active neutrino would oscillate, and this would be a direct expression of jL? -nonconservation. Practically it would be difficult to discern this from the Dirac oscillations into the new flavour 3tates connected with charged heavy loptons with masses above the reaction threshold. The possibility mentioned above meets also with objections of astrophysicists. In big bang theory the production of H

He a /H ZZL 0.22. For every n additional Weil neutrino 0.02 unit3 ore added. There exists the opinion that ratio He /y^ - 0.28 corresponding to 3 additional i^» neutrino (3 generation case) is already untenable.

~~4. Diagonal otates of Tho explicit construction of diagonal states for general c£/y was given in papers'- J appear£<« in 1980. The diagonal states for {&/ have the form - 195 -~~

~~(8)~~

~~Here are the Majorana-like operators of the form~~

~~(9)~~

~~These operators satisfy the condition~~

~~(10)~~

As distinct from old Majorana theory* are neither C nor CP invariant if ocjy iIs notnotjan, and C and CP operations are determined as in (5)* This fact does not lead to substantial changes in properties of y£p , as they are determined essentially by the condition of absence of particle-antiparticle mass-degeneration* The <^_ , 9^^ operators in (8) are determined in usual way and do not correspond to mass-eigenstates. The matrices LJ, \/ form together the matrix K

~~ín)~~

~~The authorsL °J took the trouble to prove that K io unitary matrix KK+ » 1. To do that one have to solve the - 196 -~~

~~relations (8) and use the condition ^a'*~ &(&» equal to~~

should be simultaneously equal to <*-. v^ & • If in low-energy domain no right-hand currents are involved and (2-4) are valid then the matrix £//jt' and the masses of ,/V" (or 2ff) diagonal states contain all information entering into the description of Z -violating processes if they exist. The counting of number of parameters involved and detailed discussion is contained in paper^ °J» To end this subject we should mention two points. Waiting for future experiment let us consider the Gedanken-experiment. Consider the two-stage process

where initial and final processes occur on infinitely heavy nuclei with spin 0 and in intermidiate state V7-oscillations go on. In'- ' the amplitude of such process was calculated for any values of tV)# masses (for M*/£ not small). Then it comes out that if for the case of pure Z -Majorana oscillation the ratio of total flux of V to total flux of V as measured by lepton (and antJLepton) production is equal to

~~K ?£/£ U„ (/+ (13)~~

~~and does not oscillate. This means that there A fein pur« Majorana mass-matrix case no oscillations between y '~~

The second remark ÍB that the diagonaltzation (8) is not a diagonalization in one-particle states space. The operators V£ V^. entering the formulae (8) have complicated Heissnbero. structure, and in Schrodinger picture the formation of diagonal V^y -states is connected with rearrangement of vacuum state. The simple

~~example was considered by B.MartemjanovL--'J# —~~

~~the mass of diagonal neutrino is equal to~~

for IU -rV /M, If /ut -term in <^/V is considered as the perturbation, then the expression (14) appears as the difference of contributions to the energies of one particle state and vacuum state corresponding to transition with pair creation caused by ,tt -tern in

~~(15)~~

~~.5. Neutrinoless -decay. In terms of picture (0,' 2 fo ) decay is described by diagram~~

~~- P y~~

~~P €> - 198 -~~

~~and so its amplitude is proportional to We* term in Majjorana mass matrix. The probability is equal to~~

~~Here Z\ is the mass difference of initial and final nuclei, ^fx) ~ kineraatical factor, accounting for the electron mass~~

~~r~ - Coulomb factory~~

~~•*»•* • # and <^ 2/ ^-a tne ">atrix element for nuclear transition~~

The expressions (16-18) were obtained by E. Greuling and R.C.Wíífctení. ZJ and then by many authors independently. The indeterminocies in estimates for (18) which are present in literature are rather large. The simplest estimate is obviously

~~calculated values vary approximately in interval -«— 0.1 to -v- 10. The simplest model which may be not so bad - f-ermi gas approximation^^ gives C 'v> 0.1, The largest A for - 199 - r~~

(0, 2ß ) decay is realized for Ca48 ( A ~ 10;*«,). t The present limit T^^ >2,f:/0J/yr. for its (0, 2/3 ) t decay'- -* gives /Tf^, <" 50 eV. Earlier indications for (0, 2/% ) decay from Te , T (leochemistry are now in doubt (E.Belloty report at this conference). To bring this limit at least two orders of magnitude lower i3 an important task.

It should be noted that the f*>£& element of fWCJe - mass-matrix could be 0 but the masses of diagonal states obviously need not be zero in this case. (Por 2- -generation consider ft) — , J%™) J « So the absence of (0, 2ß ) decay does not mean necessary the absence of mass in H measurement'- '-' and others of this type; thus these two kinds of experiments are logically independent. The models for situation mentioned ( /&&. — & ) were discussed by L.Wolfenstein'- J and S.Petkovl-2°J.

^. Theoretical remarks» The most natural framework to incorporate neutrino masses is GUT is S0(10) symmetry. There 15-plet of SU(5) is completed to 16-dimensional representation of spinors of 0(2 \/ ) group. The additional particle for SO(10) is just the V^ neutrino. Its absence from low-energy phenomenology can be explainedL3QJ by giving to it Ma;jorana mass of order <-»— 10 ^ GeV by 126-Higgses vacuum expectation. Then ^/. neutrino acquire masses by going to the Y„ by Dirac mass-matrix.

~~•*-•~~

~~This gives naturally small scale for neutrino masses. we et 10 2 eV Assuming />j^ ^ />?„, E *Y)V ~ ^^^j **- ~ » - 200 -~~

The system of Higgs expectation for any GUÏ is flexible enough to accomodate larger or smaller masses if they would be jdefinitlu discovered. Recent discussion Eay be found inL31-7. At present it seems that the most reliable knowledge comes from astrophysics, where symple argument due to Gerste in and Zeldovich^ ^ gives

for stable neutrinos. An exotic possibility connected with . -violation should be mentioned. As discussed in papers /. may be broken spontaneously by Higgs-expectations giving rise to Majorana mass matrices, without corresponding degree of freedom being gauged ~ as opposed to SO(10) case» In this case there appears a masaless Golistone connected with /_ -violation baptized, Majoro/1 by the inventors» Two realizations were discussed in framework of SU(2)X U(1) weak group, the Schemel'*' -"leading besides /pajoron to the large family of Higgses including new comparably light massiv® Higgs and charged and double charged ones with masses

~~The characteristic feature of modelt-^4 in low-energy domain is the appearance of the decay~~

where "^ is Majoron o\ light Higgs, competing with usual (0, iß )-decay. As noted in^*47 the existence of masalees Majoron would lead to appearance of new long-range forces. I have to thank M.G.Schepkin for the discussion of the subject of this paper« - 201 - KEPÉKEN o. V. 3 1. E.Wigner. Proc.Am.Phil.Soc. .9J3, 521 (1949). 2. B.Wiener. Proc.lTat.Ac.Sci. 30. 449 (1952). 3. Si.B.39JihA0Btw. JíAH 86, 505 (1952). 4. G.I.Iarx, Acte Phya.Ac.Sci. Hung till fasc. 1, p. 55 (1953). 5. fí.E.SeJiBAOBHM. ME 91, 1317 (1953). 6. E.J.Konopinski, M.MachmoMi, Phya.Rev. JJ2, 1045 (1953). 7. HeGeorgi, S.L.Glashow. Phya.Rev.Lett. J32., 438 (1974). 8. E.M.noHTeKoppo. K3TS 33, 549 (1957), I3T$ 34, 247 (1958). 9. J.Bjorken, S.Drell. lîel.Quant.Kech. Me. Grow Hill. 10. S.M.Bilenky, B.M.Pontecorvo. Phys.Lett. 102B. 32 (1981). 11. M.Goll-Mann. "La theory Quantique de ChömoS." Concr. de Phys. Ed. R.Stoops Bruxelles 1962, p. 135. 12. H.K).Kítf3apeB, JÎ.E.OKyHB. S3T$ 43, 1904 (1962). 13. C.M.BiMeHbKHÜ, E„M.noHT6KOpBO. y

19. H.KJ.KotísapeB, B.B.MapT6MbHH0Bf JT.B.UKyHSx^.$n3. 32,1590 (I960). 20. V.Barger, P.Langacker, J.Leveliié, S.Pakvasa. Phys.Rev.Lott. 4£, 692 (1980). 21. E.Majorana. lîuovo Cim. 21» 171 (1937). 22. I.Yu.Kobzarev et al. Preprint ITEP-153 (1981), 23. B.V.Martemyanov. Preprint ITEP-154 (1980), 24. E.Greuling, R.C.wArbten. Ann.Phya. V^, 510 (1960). 25. M.r.UíenKHH. Sti^pm» 17, 820 (1973). 26. R.K.Bardin et al. Nucl.Phya. A158. 337 (1976). 27. B.A.JmöHKOB H «p. M3T* 81, 1158 (1981). 28. L.V/olfenstein. Nuol.Phys. B186 (1931) 147. 29. S.T.Petcov. Phya.Lett, ,11 OB. 245 (1982). 30. M.Gell-LIann, P.Rámond, R.Slansky. Rev.Mod.Phys. jjO, 721 (1978). 31. E.VYitten. Phys.Lett. 9TB, 81 (1900). J.A.Harvey, D.B.Roisa, P.Ramond. Nucl.Phys. B199. 223 (1980). 32. C.G.repinTcilH, H.B.3OJII.AOBÍIM. IîHCBMa B XÎ3TÎ, £, 174 (1966). 33. V.Chikashice, R.N.Mochapatra, R.D.Peccei, Phys.Lett. 98B, 265 (1981). 34. G.B.Gelniini, M.Roncadelly. Phys.Lett. 9_9jB,- 411 (1981). 35. H.M.Georßi, S.Glashow, G.IÍunsinov. Nucl.Phys. B19.3. 297 (1981)» - 202 -

~~SEARCH FOR 150Nd AND 130Te P0-DECAY AT BAKSAN OBSERVATORY~~

~~U.P.Baskov, A.A.Kiimenko, E.L.Koval chuk, A.A.Poraansky, A.A.Smol'nikov, A.H.Temmoev Institute for Nuclear Research of the USSR Academy of Sciences~~

Abstract Previous works /1-4/ concerning neutrinoless 2p -decay do not exclude the possibility that euch a process can proceed through a right handed current, A -resonance, X -majoron or scalar particle. The probability of the 2ji(0v)-decay by these modes,in some cases, can be comparable with the process for mvfto,^=0. In the present paper, the installations for the multidimensional analysis of 2p- decay are described and the preliminary results obtained are presented.

Method The main objective of the present work is to set up a modified experimental installation which will enhance the possibilities of using the simple spectrometer not only to observe the total kinetic energy of 2ß(0V)-electrons /5,6/ but also to investigate the energy spectra of single electrons, with due consideration of their angular distribution. The following possible modes of the 2^-decay are considered: 1)mv^0, >=0; 2)mv=0, X£0; 3)X°-ma;joron; 4)A -resonance at 0+-0+ transitions for 2p(0v)-decay; 5)0+-0+ for 2y as well as Ov; 6)0+-2+ for 2v as well as Ov« The plan is to detect separate gamma quanta accompaning 0 -2 on the one hand and gamma quanta along with 2/j-decay electrons, on the other. Simultaneous observation of different characteristics of the 2ß-decay must decrease the background of the Installation without reduction of its efficiency, At the same time it is intended to set up an installation less complicated than those used by others/?,8/. Besides, the installation must work with as well as without the sample. The insertion of a sample must not have any influence on the response function of the detector. In comparison with the existing methods of investigations, the proposed method will invariably provide with more clear information both about the real 2p-process and also about the lower limit of T,, ,2(2jj). - 203 -

In the work /5/, background without sample could not be measured in principle. In the work /6/ the energy resolution of the detector was worsened significantly after insertion of the sample. It is also necessary to make measurements with samples of a few hundred grams having sample thickness (50-100fi) which smears the energy spectrum of the emitting electrons negligibly. Apparatus The installation consists of the main plastic scintillator detector, Nal(Tl) y-spectrometer, electronic equipments, two multichannel pulse height analysers NTA-1024, with on-line mini- computer EMG-666B, passive shield of the main and Nal(Tl) detectors. The installation is placed in the underground laboratory at the depth of 660 mw.e. The shielded detectors are placed in a special low-background room free from the electronic equipments. I The construction of the main detector is shown in Fig.1^ It •- consists of 4 scintillator layers (50cm x 25cm x 5cm) and each viewed by 4 photomultipliers through 5cm plexiglass lightpipes. The light collection nonuniformity is less than 2%. The energy resolution (FWHM) is equal to 25% for 1 MeV energy release. Each scintillator is covered by aluminiumized mylar (thickness 10/n), both as a reflector of light and as a shield against acts light penetration from one scintillator to the other. Thin foil or powder sample of the supposed 2/i-active enriched isotope is placed between two inner scintillator layers (Fig.1). The passive shield of the main detector consists of 20cm electro- , litic copper, 10cm plexiglass and 5cm tungsten. Emphasis can be given to the fact that inside low-background room by using special concrete, the environmental y -activity was reduced by a factor of 200 in comparison with the surrounding underground rock /10/. High sensitivity low-background y -spectrometer consists of Nal(Tl) crystal with 200mm diameter and 200mm thickness. The detector has a well of 100mm diameter and 100mo depth. The energy resolution of the detector for *'Cs full energy peak (0.662 MeV) is equal to 10.7%(FWHM). The peak efficiency of the registration of 0.662 MeV }f -quanta of 157Cs, which placed inside the well, was found to be 46%. The detector was surrounded by 3cm tungsten and 20cm iron shield. - 204 -

Data Collection and Event Selection The block diagram of the electronics is shown in Fig.1. Pulses from phoioinultifliers are integrated and after prearoplifi- cation, fed to the logix and time selectors. Only ouch events are selected which have envisaged value of the sum of the two inner scintillator layer pulses. The position and width of the discriminator window are chosen in accordance with the sum energy of two electrons in 2jj(0V)-decay. Pulses which were chosen in such a way, are transfered to the buffer memory which is adjusted to the time shifter. It adjusts 4 scintillator layer pulses with corresponding parts of the multichannel analyser memory (4x1024) and vetoes input devices to accept pulses during transfer of data from analyser to the computer memory. The differential discriminator is switched off for the 2(i(2v)-decay study and the total energy spectrum is observed. After the end of the pulse analysis the computer clears analyser memory and allows an acceptance of pulses by input device. A cycle of operation from veto to allowance is not more than 1 s. With the help of a special programme, the pulse height-time information is registrated in the computer memory as a multidimensional correlative matrix which includes full data of all 4 scintillators. The mini-computer works on-line with analyser. The main information is stored in a two-dimensional correlative matrix (64x64) corresponding to two-dimensional spectra of the scintillator layers 2 and 3 (Fig.2), between which ths sample is placed. If an event in such a matrix is accompanied by pulses in scintillator layers 1 and/or 4, analysis will depend on the considered 20-decay mode. In the case of 0+-0+ transition such events are rejected. In the case of 0+-2+ transition one need to take into consideration only such events which fit gamma energy release in 1 or 4 layer. Three-dimensional plots of different spectra are shown in Fig.2. X and Y axes correspond to the analyser channels, and Z axis correspond to the intensity. Multidimensional spectra of the different modes of the 2ß-decay are calculated by Monte Carlo method. In the above calculations, the detector energy resolution, thickness, Z and A of samples, and transfer energy between 15°Nd-15OSm and 13OTe-13°Xe were taken into account. Approximate results of the calculation for ^Nd is shown in Fig.2. It is seen that due to multidimensional analysis, it became - 205 -

possible to study the existence of the 2^(0v)-decay process through sum of two electron energy and also through single electron energy spectra analysis. Different possibilities of 2/i-decay process can be chosen by analysing the multidimensional spectrum shape as well as by using the relation between the counts along the axes and the counts in the matrix field for different angular distributions. Preliminary results The 240 grams enriched Te(9!?%) sample was put into the well of Nal(Tl) detector. 0+-2+ transition for the 13°Te-15°Xe was studied. In this case y-quantum with E =0.5.56 MeV is emitted. Up to present time, measurements have been made for a total of 530 h. Total number of counts, under supposed 0.556 MeV peak (FWHM), for the measured time, is equal to 595101. During the same time, the background without the sample was also measured. Total number of counts in the same energy interval, in this case is equal to 394-356. As the difference between numbers of counts of the first and second runs is less than the error of this difference, the + + lower limit of the T/|/o(0 -2 ) of * Te can be determined from this ' + + 10, error. We obtained T^ »2 (0-2 )£ 4.1x10 ,y at 90% confidence level. From the same measurements we also obtained data for the transitions 0+-2+*(E =1.122 MeV) and 0+-0+*(E =1.79 MeV), and the corres- 1 1 ponding results are T^ ,2£ 2.7x10 ^y and T^ ,^ 2.5x10 ^y respectively. The approximate Nd with background multidimensional spectrum of main detector is shown in Fig.2. The sample consists 15 150 of Nd2O3 enriched <32%) by °lTd. Total mass of the Nd is equal to 72 grams. The background counting rate of an inner scintillator layer in the 3.0-3.5 MeV energy range is equal to ~1.5 per hour.

B2„ of ^ Nd is equal to 3«39 MeV; the experimental energy range shift from 3»39 MeV results due to the energy loss by electrons inside the sample before reaching the scintillator. As the time of the present preliminary measurement (400 h) is not enough for good statistics, which is needed throughout the multidimensional matrix field, the estimated limit of the mode independent T^^^Nd 2/î-decay), was calculated from the spectrum of the sum-energy electrons, without background subtraction. 150 + + 2O We obtained T1/2( Nd 2/J-decay, 0v;0 -0 ) £ 1.9x10 y at 90% c.l. - 206 -

However, it is interesting to estimate the ^^/2 limits for probabilities of mvjí0, A=O and mv=OfjAjÉO modes, taking into account all counts which was accumulated in corresponding regions of the correlative matrix. In this case of the neutrinoless 2(j- decay of ^Tid, we get without background subtraction: 15? 2/»-decay, OvjO+-O+» m^O, >=0)> 3.4x1019y at 90% c.l. + 19 2ji-decay, 0v;0 -0*; mvíí0, A=0)^ 1.1x10 y at 90% c.l. Preliminary results allow us to hope for raising the existing

limits of T^y2(2j»,0v) for different isotopes. Acknowledgements Authors are very thankful to Dr.M.G.Schepkin for useful discussions and help in calculations of energy spectra and angular distributions of electrons and to Dr.S.O.Hoy for great assistance. References 1. M.Doi et al.»Progress of Theor.Phys.66,1759 and 1765(1981) 2. S.P.Rosen»Proceedings of the '61 Conference, Maui,Hawaii,£,76 3. A.Yu.Smirnov, Pisma JBTP (in press) 4. V.Barger et al., MAD/PH/15-preprint, September of 1981 5. E.Piorini, Proceedings of the '77 Conference, Elbrus, £,315 6. Yu.G.Zdesenko, Pisma JETP 22,62(1980) 7. B.Cleveland et al., Phys.fiev.Letters 55,737(1975) 8. M.Moe, D.Lowental, Phys.Eev. 022.2186(1980) 9. E.L.Koval'chuk e$ al., Proceedings of the 1980 Low Activity • Conference, High Tatras (in press) lO.G.T.Zatsepin et al., Eratkie soobschenija po physike NS6,20(1975) as o ce s: a ANALYSER DD Id t-1 MTA- 1C2-

~~COMPUTER EMG - 666 O~~

~~COMPUTER SM -1301~~

~~Pig.1 Block-diagram of the main detector - 208 -~~

~~0» ;0+ -0+;m /0; A = 0; 2n; N ! ;inv^0;Ä/ 0; ?n~~

~~+ + 2V;0 -0 ; 2n ;0 -0+; 2n~~

~~2y;0 -2 ,2n; 0 -$ ,N background~~

~~Fig.2 Multidimensional spectra of different modes - 209 -~~

~~THE STUDY OF DOUBLE OETA DECAY OF 100Mo~~

~~Yu.G. Zdesenko, V.N. Kuts, I.A. Mitsik, A.S. Nikolaiko~~

~~Institute for Nuclear Research Ukrainian Academy of Sciences, Kiev, USSR (Presented by A.A. Pomansky)~~

The experiment was carried out on the research of 100 neutrinoless double beta decay of Mo with energy release of 3032,6 keV. The sample of molybdenum is used, enriched by the isotope 100Mo to 99,5%. The total mass of 100Mo is equal to 390 g. A half-life of lower limit of > 2,1*10 y for the neutrinoless 2n -decay at the 68% confidence level was established.

In 1930-82 a great interest has arisen concerning to the investigations of double beta decay, since this prooess is considered to be the unique information source about the mass of neutrino and about the possible existence of right handed currents and lepton nonconservation [1-5] • Constraints on the masses of Majorana neutrino ( /71ft? < 10-50 eV £1-5J ), obtained on the basis of experimental data on double beta decay of ^Ca, Ge, Se and Te, stimulate the increase of experiment sensitivity and expansion of a number of investigated nuclei. The aim of this experiment is to research the neutrinoless double beta decay of Mo- Ru, the expected energy of which is 3032,6*8,6 KeV [6] . The investigations were carried out with set-up [ 7J , used before in the study of double beta decay of 130Te [üj and 96Zr f9 J . In.fig.1 the general view of a new detecting system is presented situated in a working cavity of low-background installation. The main detector consists of 145 plastic stintillators, between the side faces of which the investigated samples are situated. Each detector is made of polystyrene, in the form of rectangular parallelepiped 10*10'05 mm . All detectors are thouroughly polished and wrapped up with aluminiuraized mailar film (5 mem thickniss). The height of block of detectors is 65 mm and in cross-section it is inscribed into tho circle - 2.1O -

of 148 mm diameter. The scintillators were connected by lucite light pipe of 120 mm height and HO mm diameter to photomultiplier tube (PM-49B). Separate scintillators-parallelepipeds were taken by light output (the spread is - 13/5) energy resolution (for 1 MeV 19Í25Í) nnd non-uniformity of light collection (± 8?S) during the irradiation of scintillator by collimated source of conversion electrons. The calibration and measurement of energy résolution of detecting system no assembly mm carried out by ^-sources of 137Cs, 22Na, 20ÜTl. Por extraction in the compton opectrum the electrons with maximum energy the method of registration of backscattered photons was uoed [1O3 . A number of factors 3uch as nonuniformity of quantum efficiency of the photocathode, the losses in light pipe and spread of light output of separate scintillators resulted in deterioration of energy resolution of a set of detectors as a whole. So the resolution for energies of 1062 keV ( Ha) and 2382 keV (20öTl) is 30JS end 20# respectively. To carry out the expérimenta in the state Fund it was received 330 g of 100Mo up to 99,5& and 00 g with enrichment coefficient up to 92,2#. The samples were examined on possible radioactive contamination by registration of its i, the othicknesf detectins igs aystem158 rog/cm. So )th whice totah coverl mas,s alolf theM ooute is rabou surfact 39e0 g. lOfl The experiment on the search of neutrinoleos double-beta decay of Mo includes the measurement of detector background with the samples of 100Mo during 1521 hours. The information was derived once in a day. The energy scale io regulurly calibrated with sources of cNa and Tl. The measured spectrum is shown in fig.3 where the region of neutrinoless - 211 -

double beta decay of Mo is shown by hatching. The absence of any peako in thia region only allows to establish limit 1OO rate of neutrinoleoa double beta decay of Mo. In order to determine the detector efficiency the programme v/as developped by which in accord with Monte-Carlo method the events of neutrinoless double beta decay were modelled taking into account the sample thickness, real detector characteristics and theoretical suppositions about spectrum forms and angular distribution using the model of double beta decay on two-nucleon mechanism with non zero mass of Majorana neutrino. As a result it is seen that maximum of energy distribution from the events of neutrinoless double beta decay corresponds to the energy of 2775 keV, the half-width is equal to 520 keV and the total efficiency of registration in region 2,5-3,3 MeV is 44?5. To evaluate the boundary probability of Mo neutrinoless double beta decay the assumption was used about the equality of limit rate of the decay of statistical accuracy (to one standard deviation) of intensity background determination in selected enorgy range 21 lim T1/2(1O y) >, 47,65 g«m«t/A. \/N" where g*0,44 registration efficiency; rt) «349 g - active isotope mass of 100Ho; A - atomic weight of 100Mo; t-1,521 thousands of hours - measurement time; N«2777 - a number of background counts registrated within the range of 2,5-3,3 MeV. As a result at the 6ii% confidence level the half-life lower limit of > 2,1«1021 y for the neutrinoless 2j3 -decay of Mo was established. A rigorous estimate of neutrino mass is impossible on the basis of this result so as the precise values of nuclear matrix elements (ME) of Mo double beta decay is unknown. So we make an assumption that ME for the transition studied is almost of the same order of magnitude as for decays of 76Öe-76Se and 82Se-Ö2Kr. In that case using the résulte of paper [2 ] we may obtain the following dependence between the half-life and neutrino mass

~~(y) 12 13 T1/2 " <5-1O - 5-1O ) - 212 -~~

whex*e tW? and ffle - neutrino mass and electron mass respectively and the spread in values of numerical coefficient 12 13 (5*10 - 5*10 ) is related to uncertainly in nuclear matrix elements. Substituting, in the last formula the experimental limit 1 no Twoi Mo) we can see that within the range of accepted assumptions the upper limit of Majorana neutrino mass may be in the following interval: lim r>V4 (25-30) eV

~~In the future the limitations on neutrino mass may be made more precise by using the results of precise calculations of matrix elements, earring out in present time.~~

~~References~~

1 .Doi M., ivotani T., Nishiura H., Okuda K., Takasugi £., University of Osaka preprints: OS-GE 80-27 O980); OS-GE 81-28, OS-GE 81-29, OS-GS 81-33, OS-GS 81-34 (1931). 2. Haxton Vf.C, Stephenson G.J.Jr. and Strottman D., Phys. Rev. Lett, v.47, No.3, 153(1981). 3. Ya.B.Zeldovich, M.Yu.Chlopov, YETP Lett, v.34, No.3,148(1981). 4. Vergados J.D. CERN Preprint TH.3154, (1981). S.Fayans S.A., Khodel V.A., J.Phys.G.Nucl.Phys. v.3,No.3, 359(1977). 6.zdesenko Yu.G., Sov.J.Phys.Part. and Nucl. v.11,No.6,1370(1980). 7.Zdesenko Yu.G., Kuts V.N., Mitsik I.A., Nikolaiko A.S., Sov.J.Prib.Tekh.Ekap. No.5, 47(1979). 8. Zdesenko Yu.G., JETP Lett, v.32, No.1, 62 (1980). 9. Zdesenko Yu.G., Kuts V.N., Mitsik I.A., Nikolaiko A.S., Sov.J.Isv. Acad. of Sei. v.45, No.10, 1856 (1981). 10. Dietze G., IEEE Trans, on Nucl.Sei. V.1.NS-26, No.1,398(1979). - 213 -

~~A/o~~

~~MS plisiic Set nilIts tors~~

~~lueiie Light fife~~

~~Fig. Í- TAe e/eiector as s em Sly /0OMo. - 214 -~~

~~°o.- S~~

~~i^c • o~~

~~I» •"•~~

~~«vi~~

~~• •* - 215 -~~

~~3. 7%e of o/ '°%fo.~~

~~10-- .~~

V..., V • • •*

~~—i— —i— j 10 s.o Ô.Û 4.0 216 -~~

~~SOME NEW EXPERIMENTAL RESULTS ON DOUBLE BETA DECAY~~

~~Enrico BELLOTTI latituto di Fiiica dell'Université e Sezion« INFM - MILAN.~~

~~Abstract.~~

Th« raaulta of two new expérimente on doubla beta decay are reported. In the first one, by T.Kirsten (Heideberg), the half-lifes of Tellurium 128 and 130 have been measured; results are in agreement with theoretical predictions for 2>>s emission and don't require any contribution from neutrinoless decay, in strong disagreement with previous results. In the second experiment, by the Milan group, new limitB on the half-life for transitions on ground and excited levels of Germanium and other nuclides have been obtained.

~~1 - Introduction.~~

In the past year new intereuting results on double ft decay have been obtained by various groups and many new projects are in progess. Part of them have been reported by A.A.Pomansky ; this paper vill be devoted to two new experiments carried out by the Heidelberg group on Tellurium and by the Milan group on Germanium. (2) Some theoretical background has been given by I.Yu.Kobzarev and by PomanBky; here only a few points will be recalled. Double ß decay of a nucleus (A,Z) can occur through, two channels: (A,Z)—» (A.Z+2) + 2e" + 2v| ( 2 J>'a decay) and (A,Z)—» (A.Z+2) + 2e~ ( 0\>'a decay) wher*e (A,Z) and (A.Z+2) are usually 0 even-even nuclei, The 0 p's process is by far the most interesting, because its existence would imply lepton number violation and would give informations on neutrino mass ana on right- handed weak currents. The final nucleus can be left in an excited state, generally a 2 state: (A,Z)~—•> (A,Z+2)*+ 2e~(+ 2V) I > (A.Z+2) + Y It has been recognized ' ' that 0+—» 2+ nuclear transitions can be engendered only by an admixture of opposite chirality currents; then it is in principle possible to distinguish experimentally between mass and .right-handed current mechanisms, once the 0 y 's (3A decay would be discovered. - 217 -

Other processes which give essentially the same informations are; (A,Z)—* (A.Z-2) + 2e++ (2"^) (A,Z) + e~-» (A.Z-2) + e++ (2-^) (A,Z) + 2e"—> (A.Z-2) + (2^) i.e. double positron decay, electronic capture and positron decay, double electronic capture whether accompanied or not by two neutrinos. Theoretical estimates of decay rates are laborioua and affected by large uncertainties; in fact decay rate9 computed by different authors disagree by more than an order of magnitude. Explicit calculations can be found in literature^ j here the results of Doi et al. ' will be shortly reported to serve as a guide in the interpretation of experimental results. The 2i)'s, 0 •—>0 transition is dominated by the two nucléon mechanism and, in general, the 2 V, 0—?2 transition is negligible with respect to 0—>0 . The decay rate can be written as:

~~where most of the symbols are self-explanatory and~~

~~t M'/w^ « K, />l^~ l^at/^, j)»^ ^^ being the mass of the intermediate nuclear state and M„, M „ the masses of the initial and final nucleus ; ÜT,~~

~~To= transition energy (measured in m ) + The 0*—?"0 , 0 V" s decay is allowed either if my ?* 0 or if r.h. coupling is /0 and the decay rate is given by (see eq. 3.7 of ref. (1*) )~~

~~ws^ and A IS the relative coupling of the r.h.c. (for the exact meaning of w and X. aee ref. U) j A£ ift&X A'^depend on the transition energy and on the average distance between the~~

~~two nucleous (quarks) which exchange the virtual y j £>A refera to the A resonance contribution. The decay rate for 0 v's, 0^—» 2* ia given by (see eq. - 218 -~~

~~3.7 of réf. (U) )~~

~~Table I reporte, some values of A1s and B as they can be daduced from raf. k, for76 Ge, 128Te and130 Te.~~

~~Table T~~

~~(y.ears)~~

*6XJe g.I IP5 7.53 101* 3.15 105 U.1» 107 2.98 1O5 U.135 1O6 1.3 1022 128Te 2.8 1O3 1.17 1O2 U.6 1O2 9.5 1O5 1.5 1O3 3.35 10** 1.2 1025 130Te 9.78 10U 2.86 IOU 1.68 105 1.16 108 6.35 105 1.5 107 2.8 1021

Various methods have been used to search for aft decay, but they can be divided in two main categories: - geochemical methods: the content of a radiogenic nucleus in an ore sample containing the parent nucleus is measured. Samples are generally small( few grams), but their age is old By this method it is not possible to distinguish between 0 j?1 s and 2 y's decays and between 0-—yO and 0• >Z* transitions, direct methods: in these methods the two decay electrons are detected and their energy measured at the instant they are emitted. Samples are larger (from few tens of grams up to kg1») than in the previous case, but the observation time is. much shorter (^ 1 year)

~~2 - A new geochemical measurement on Te and Te half-lifes and their ratio.~~

~~Tellurium has two isotopes which hare double Ô active: X26Te (is. ab. 32*) and 130Te (is. ab. 35*). Their transition 12 130 energies to Xe and Xe are quite different, being 1.7 mg~~

~~and 5 m0 respectively. The relative magnitudes of 2 >»'s and Op'a~~

•-.\ - 219 - ia very different. The half-lifes of the two isotopes can be measured at the same time and then possible systematic errors vould cancel out in their ratio. Moreover theoretical estimates of the half-life ratio are believed to be less uncertain than the absolute half- life computations because equality or nearly aquality of the tvc nualear matrix elements ia generally assumed . iv, According to Doi et al. Ik)one expects:

—j.9r«io^. s CfÇiOO for the two l>'s decay (this value ia computed T\ [ Te.) _ I M T taking into account the slight difference in.the value of w/ aa estimated by Vergados ) and •_&, Ajo /£ 1$ for the Oy's decay and in the hypotheses /t=0 andtm^O. Experimentally the following ratio is measured;

-1

~~The ratio R is expected ^^300 if only 2 's channel is present} a value of R~~

or n [ U)'>U.y-iO ty it if level. a Fig. 1 shows the half-life values as obtained in different experiments jthey are quite spread out, but taking into account that the absolute values is affected by the uncertainty û on the age of the ore and on its "story" during *10 years, the discrepancies are probably not serious. The ratio of the half-lifes gives:

This value is not compatible with the previous Honnocko'u ruoult and this Btrong dioagreemont must be understood in the future. The Kirsten's results are in good agreement with the pre- (1») dictions for the 2 v? P|S decay and they don't require any contribution from neutrinoless decay. It is also possible to set stringent limits on m and X ; they are m<20 eV ifA»O A<10"5 .if m-0 at 3 std dev. level. If one assumes etrict equality, of \—rr^ the previous limit on m is m<10 eV at 1 std. dev. level.

~~3 - A new direct measurement on Germanium and other nuclides«~~

In I960 a new experiment was designed by the Milano group, based on the use of a Germanium detector. Two were the aims of the experiment: - to search for doubled decay on excited levels of various nuclei using external samples and detecting the deexcitation V ray; - to improve the limit obtained by Fiorini et al. X 'on Pfi decay 76 of Ge isotope which is present (l.% is.ab.) in natural Ger- manium, taking advantage of actual detectors technologies. The present detector, supplied by POT Europe, is a true: - 221 - coaxial Ge (Li) crystal of VL3O era active volume and á2 KeV (at M. MeV) energy resolution. The electronic chain, supplied by Silena (Italy) is a standard one, but the spectrum stabilizer vhich allows measurements lasting more than one thousand hours without noticeable loss in energy resolution. In auoh a kind od experiments, background is the "Enemy"• There ara three sources of 'background: a) natural radioactivity of air, concrete, etc. This background was reduced to a negligible level by shielding the detector with HCOF (high conducti- vity oxidon l'ruu) conpor, low und iiovuiul loud, und filling with plexiglass any cavity around the detector to avoid the presence of air clooü to the dulue lor (l''ití.2) b) cosmic ray. This, source of background was pratically eliminated by setting-up the detectors deep underground, in the Mont Blanc laboratory where the Italian proton decay experiment is also settled (1U . Fig. 3 shows the energy spectra collected in Milan and in Mont Blanc: the effective reduction factor in the counting rate is ^15 between .5 and 2. MeV and >100 for energy larger than 2 MeV, where the contribution of cosmic rays is prevailing. In these conditions, data were taken in a run lauting M200 hours, with a sample of Neodymium; data on other nuclei were collected in shorter runs in Milan and results will be reported later. (Run I) c) The measurements just discussed allowed us to reepgnize the remaining sources of background among the materials very close to the detector . Therefore some components have been replaced; more specifically the crystal.holder is now in HCOF copper and the end -cap in titanium. A further reduction of Vf was achieved; (Fig. 3)» now we are taking data in these improved conditions. (Run II). Fig. k ehowa part of the energy spectrum obtained in M.300 hours, from which is possible to deduce the good energy resolution and the low counting rate of the detector.

~~k - Results.~~

~~Table II report some of the results obtained in meas. I - 222 -~~

~~Table II Decay Final state Ti/( yearn ) { JP , E ) (902 i-.i ..'~~

~~1oo . -i(J~~

, Kel/ 21 S*

These limits refer to the total jäßdecay (0 y's + 2 y's) because only the deexcitation \f rays are observed. A rough comparison with theoretical estimates of half-life allows to set a limit on lepton number violating -2 -3 76 parameter X^IO "vj.0 . In the same measurement a limit on Ge to that of Fiorini et al. * was obtained. 2° meas. I will report the data obtained in a measurement of 1397 «ours. Fig. k shows the energy spectrum in the region of 2OU5 keV, corresponding to_ Ge —>' Se. The counting rate is ^2.2 10 counts/(keV x hours). From the figure and detector.; raass^the sensitivity of the measurement results

3.28'1019 T (hours) hi where T is the measurement time (in hours) and N is the numbers of counts in a bin of It keV (peak width). Then, in a measurement of 500Öhours it would be possible to reach a limit only *i3,S1oyears, with an improvement of a factor ^5 with respect to the previpus limit. Present limits. Transition energy is known with an accurancy (+2 keV) almost equal to the energy resolution of the detector. Then Ifc values were computed at different energies around the central value of the transition energy. Fig. 5 Bhows the results obtained with a simple maximum likelihood method. Corresponding to the central value of the transition energies data show a small excess (corresponding toXvJO years) which is not compatible, at level withii'o»; but all the data are compatible with"J^,«oûat a level of - 223 -

two atd. dev. In any case ly'Z.I+'lO years ("/ Similarly, no peak appears in the region of ^ikbi keV, corresponding to the transition Ge—* Se (2 , 559• keV), where a line is expected if the decay occours and the deexcitation y ray-., escapes from the detector (escaping prob.~95Í). The limit, computed as in the previous case, is ~\i/ (0+—>2+, 559 keV)j£. 8-1021 (4

~~5 - Hew projects.~~

Many projects exiat on pß decay and a list of them,which refers to U.S.A. and western Europe, has been compiled by M.S.Witherell at the S.ta Barbara Conference in Jan. '62. Five of them refers to Germanium: these experiments are similar to that I described; they differ in detector dimensions and in shielding nature (active shielding like Nal, or passive one). Two new projects regard Selenium (see Hahn ) and other two Xenon.

~~Germanium~~

~~Battelle Pacific/North Vest/South Carolina Ge + Nal Caltech Ge + Veto Guelph/Aptec/Toronto Ge + active shielding Milan Ge deep underground U.C. S.ta Barbara/L.B.L. 1000 cm3 Ge + Nal~~

~~Selenium~~

~~Brockhaven/Cuny/Oak Ridge 10 Kg Se 02 tinting of Bingle atom counting of KB U.C.Irvine Time Projection chamber - 224 -~~

~~Xenon U.C.Irvine Liquid Xenon T.P.C. Milan Pressure T.P.C.~~

~~Conclusion.~~

The KirBtan'a result on Tellurium is of graat importance ; in fact it can be interpreted in term of 2\)'B decay.only and it allows to set very stringent limits on possible contributions from neutrino mass or right-handed currents mechanisms. Of course, the disagreement with the Hennecke'a result must be clarified. Regarding Germanium, the limit on Ge —>Se (2 ,559 keV) transition, improves by a factor ^3 previous results. Because of a slight excess of counts in the region of 20k$ keV, the limit on the half-life for the 0 —PO* transition is comparable with the old Fiorini result, but the sensitivity 22 of the experiment will allow to set a limit of few times 10 years. Many direct experiments are planned or in progress and new limits - or 23 positive results - at level of 10 years will be reached for the next neutrino conference.

~~* * *~~

~~I would like to thank prof. T.Kirsten for kindly sending his data on Tellurium and prof. Fiorini for many enlightening discussions.~~

~~References.~~

(1) A.A.Pomansky - Report to this Conference (2) I.Yu.Kobzarez - Report to this Conference (3) S.P.Rosen - Double beta decay and Majorana Neutrinos: Right-handed currents or non-zero masses? Invited paper to Orbis Scientiae 1981 - Jan. 19-81 (I») M.Doi et al. - Phys. Lett. 10313 (1981), 219* Progr. Theor. Phys. 66 (1981), 1739 and 1765 (5) see f.i. S.P.Rosen - Proc. of the 1981 International Confernce on Neutrino Physics and Astrophysics, Mavi July 1-8 19Ö1 vol II pag.76, and references therein - 225 -

(6) This assumption is critically discussed by Haxton in "Lepton number conservation and the double beta decay Te and Te" , Preprint LA - NR 21 - (7) J.P.Vergadoa - Phys. Rev. Ç13. (1976), 865 (8) H.Takaoka and K.Ogata, Zeit, fur Naturforschung 21 (1966), Qk (9) E.W.Hennecke, O.K.Manuel and D.D.Sabu - Phys. Rev, Ç11 (197$), 1378 (10) B.Po&tecorvo - Phys. Lett. 26 B (1966), 630 (11) V.A.Lubimov, Z.NozBik, E.G.Novokov, E.F.Tretyakov and V.S.Koaik - Phys. Lett. B2ÍL (I98O), 266 (12) T.Kirsten - Report to "Low Energy Testa of High Energy Particles Physics" S.ta Barbara, Jan. '82 and private communication (13) (1) M.Inghram and J.Reynolds - Phya. Rev. Jj. (1950), 822; (2) ref. 8; (3) Kirsten et al. Phys. Rev. 20 (1968), 1300; (1*) E.Alexander et al. - Earth and Plan. Sei. Lett. £ (19Ő9), Vf8; (5) B.Srinivasan et al. - Jour. Inorg. Ifucl. Chem. 3jj. (1972), 23Ö1; (6) B.Srinivasan et al. - Econ. Geol. 6j_ (1972), 592; (7) see ref. 9i (8) see ref. 12 ilk) E.Fiorini, A.Pullia, G.Bertolini, F.Cappellani and G.Restelli - Nuovo Cimento A13 (197»»), 7U7 (15) C.Liguori, A.Sarracino, P.P.Sverzellati, L.Zanotti - "A low Activity Gamma Ray Spectrometer" to be published on Nucl. Instr. and Method (16) E.Bellotti; E.Fiorini, C.Liguori, A.Pullia, A.Sarracino and L.Zanetti - Lettére al N.C. 32 (1982), 27 (17) A.Hahn - Report to this Conference - 226 -

~~130 128 Te Te~~

~~Va 21 25 10 (6) 10~~

~~en + 00 10 -0.5 (8) (3) 2>~~

~~(4) (1)~~

~~í (2) R =1.6 1.05 103 (7)~~

Fig. 1 - Experimental values of Te and Te - Authors, origin of the ore and year of the measurement are: i)lnghram, Sweden '50; 2) Takaoka, Japan '66, 3)Kiraten.Colorado '68; ^Alexander, Ontario '69; 5) Srinivasan, Sweden '72; 6)Srinavasan, Australia '12; 7) Hennecke, Australia '72; 8) Kirsten, Colorado '82 (see ref. 13) - 227 -

~~0 '10 20 cm~~

~~Wood~~

~~Fig. 2 - Sketch of the detector and shielding - 228 -~~

~~10.~~

~~o s~~

~~10 • MONT BtANC (TI *nd-cap)~~

~~'"I ' íOű 1500 2Sűű 3S00 ENERGY (ntv>~~

~~Pig. 3 Energy spectra obtained in different conditions. Counts have grouped in large energy bins to exhibit the general trend of the background. - 229 -~~

~~-8 >r~~

~~O LU I~~

~~Hi CO~~

~~Csi~~

bû

~~13KIKlbH0 / SimOO 'KJ - 23O -~~

~~OP (y) j; • •~~

~~'a •~~

5 10 .y • •*

• '•*

~~Iff allowed region~~

~~I I 2043.6 E= 2.0457 2048~~

~~21 10: 76 76 Ge —> Se + 2e~- 0 V~~

~~Fig. 5 Half-life limits for 7íGe + 7íSe (see text) g.s. - 231 -~~

~~82Se TIME PROJECTION CHAMBER FOR DOUBLE BETA DECAY~~

~~M.K. Moe, H.B. Brown, A.A. Hahn~~

~~Department of Physics Univeristy of California Irvine, California 92717~~

~~ABSTRACT~~

~~A progress report on the UCI Time Projection Chamber (TPC) is given.~~

I would like to describe an experiment being constructed at UCI which will be coming online within the year. This experiment is a continuation of an earlier Wilson Cloud Chamber 82 ( 1^ search for double beta decay in Se by Moe and Lowenthal. Table 1 gives the results of that experiment as well as other experimental limits. i2»3^ The new experiment was designed to overcome the low (2%) efficiency of the cloud chamber and also allow a more automated analysis of the data. Figure 1 is a schematic frontal view of the experiment. The noteworthy points are the Helmholtz coils, the lead shielding house, the 4TT multiwire proportional chamber cosmic-ray veto» and finally the TPC itself. Opa can see the crossed anode and cathode wire planes which giro the X and Y positional information. Figure 2 is a side cut of the TPC showing the wiring configuration u£ rne cathode, anode, field 82 and grid wires. The 38g (97% enriched) Se sample is contained between the two aluminized mylar sheets. Both sides of the source are active. A typical double beta event is also shown in Figure 2. Two electrons, emerging from the same point on the mylar sheet, spiral around the B field (688 Gauss), and finally are stopped in a 1.3 - 232 -

cm thick Lexan sheet (for clarity the electrons are shown emitted into opposite hemispheres). The secondary ionization electrons produced in the He-Methane gas mixture, drift in the Ê field toward the grid plane. Passing through the grid, the secondaries avalanche around the anode wires, while at the same time inducing a signal upon the cathode plane. The depth (Z) information is obtained from the drift time of the secondary electrons, which is divided into 20 "Time Buckets", each representing 1 Us of drift time or 0.5 cm of spatial resolution (the same as the X and 7 resolution). Since the energy of the primary electrons is determined from the spiral itself of the electrons and not dE/dX, only logic signals for each time bucket are necessary. These signals are provided by chamber mounted amplifier-discrimin' r cards. The ] logic signals are latched into eighty 8 chai 1 wide 80 bit deep ; shift registers (located within a CAMAC crate) whenevar at least one wire has fired its discriminator. A trigger signal is made whenever the pattern of the time buckets signifies that a complete path from the source foil to the Lexan has occurred. The trigger causes the readout of the hit shift registers into a microcomputer (LSI-11) and consequent storage onto either hard disk or magtape. The event reconstruction will be made off-line. Typical event triggers are expected to occur at the rate of 5s~ and to be primarily straight through single electrons (cosmic rays are hard-wired vetoed). : The principal background event is the beta decay of a natural ' radioactive nuclide into an excited daughter nucleus, which then deexcites by as internal conversion electron. This gives two electrons emerging from the same source point on the foil, exactly like a double beta event. These events were successfully discriminated against in the previous experiment and we expect that the same success can be achieved in this experiment. Assuming the rate for the 2v mode seen in reference 1, we expect to see about 200 events in one monta's running time. As regard to the Ov mode, one year of running with the present setup 22 should be able to set a limit of less than 10 years for the half- life. - 233 -

~~References~~

~~1.) M.K. Moe and D.D. Lowenthal, Phys. Rev. C 22, 2186 (1980)~~

~~2.) B. Srinivasan et al, Econ. Geol. 68, 252 (1973). 3.) B.T. Cleveland et al, Phys. Rev. Lett. 3E>, 757 (1975).~~

~~TABLE 1~~

~~Mode T-l/2—Í22S) Ref.~~

~~Ov + 2v >2.8 x 1020 2.) -1.0 (0.4) x 1019 1.)~~

~~Ov >3.1 x 1021 3.)~~

~~Pb House _ ( 10 cm ) •"""" ^ \_ HelmhoKz Pig. l Coils Schematic frontal view cf the experiment. - 234 -~~

~~82 Se Source -IOOO Volts Cathode Field Wires 0 Volts \ (200 Volts)~~

~~Grid 0 Volts Anode' 2000 Volts~~

~~20 cm e~ Drift Velocity SO.5cm^ Fig. 2 A side view of TPC BARYON NON CONSERVATION - 235 -~~

~~NUCLEON DECAY EXPERIMENTS WITH CALORIMETERS~~

~~ECtore Fiorini Dipartimento di Fisica dell'Universitâ di Milano Istituto Nazionale di Fisica Nucleare - Sezione di Milano~~

The theory of nucléon decay ia going to be reviewed by D. Tadic [1) and experiments based on scintilla tors and Cerenkov detectors have already been described here by F. Reines [2]. I will therefore be concerned only with nucléon decay experiments carried out or going to be carried out with fine grain calorimeters* Three of these experiments are already running:

a] Soudan I at a depth of 1800 m.w.e. with a 30 ton detector [3] bj K.G.F. at a depth of 7600 m.w.e. with a 140 ton detector [4] e) Nusex at a depth of 5200 m.w.e. with a 150 ton detector [5] Three other detectors have been proposed or are in the design state: dj Fréjus at 4200 m.w.e. with 1500 tons (approved) 16) e] Soudan II at 2000 m.w.e. with l"000 tons (proposed) |3] f) Gran Sasso at 4000 m.w.e. with 2000-10,000 tons(in design stage) [7] I will report and discuss in some length the results obtained with the running detectors, and only briefly review the planned ones.

1. SOUDAN I This small detector has been installed, mainly as a test set-up, by a Minnesota-Argonne National Laboratory Collaboration in the Soudan Mine in Minnesota at a depth of about 1800 metres of water equivalent. The total ma s s Í6 of 30.4 tons, while the fiducial one is about 10 tons for the most popular channels of nucléon decay. The detector is made of 48 horizontal planes of proportional tubes (3456 in all) inside heavy concrete (taconite) (Fig. 1). The overall dimensions are of 2.9 x 2.9 x 2 m'. with an average density of 1.85. A system of scintillation counters covering the top and lateral walls of the detector is operated in anticoincidence to reduce the background of charged cosmic ray particles [3). A typical muon event and the delayed pulse time distribution for stopping particles (muons) are shown in Figs. 2 and 3. One June 1st, 1982 the detector had been operating for 112 useful days. On a partial analysis, corresponding to a total of 63 days, 190,000 muon events, 1100 muon bundles, 395 stopping muons and 70 muon decays were detected. Up to June 1st no proton decay candidates had been found, with a limit on lifetime of about 8 x 10" years. - 236 -

~~2. KOLAR GOLD FIELD~~

A collaboration of the Tata Institute for Fundamental Research ! (Bombay), the Osaka University, and the Institute for Cosmic Ray Research of Tokyo has installed s nucléon decay detector in the Kolar Gold Field Mine in India at a depth of 7000 hg/cm* which, due to the favourable properties of this rock (high average Z), is equivalent to 7600 metres of water (Fig. 4). The total and fiducial masses are of 140 and 100 tons, respectively. The detector [4] is made of 34 horizontal iron plates of 1.2 cm, interleaved with planes of proportional counters with an internal cross section of 10 x 10 cm1. Since these counters are also made of iron and the wall thickness is of 2.3 mm, the real thickness of each layer is 1.7 cm of Iron. Total dimensions are 6 x 4 x 3.7 ms, with an average density of 1.6. "t

•\ I will not enter into the details of the results obtained so far, j since they were reported at this conference by Prof. Miyake. I will only remind you that in 436 days of effective running time these authors have collected about 700 muon events (t 1.8 per day), 3 muon stops, 12 muon 'j bundles, 24 .horizontal muons mainly due to neutrino interactions in the '. .; surrounding rocks, and about 7 neutrino events. In addition, they have ; found six nucléon decay candidates of which three are totally confined. ' If these events were genuine nucléon decays the half lifetime would range £.,• between 6 and 7 x 10*' years. Later on, I will comment this result. : i ; 3. NUSEX ;'

This Nucléon Stability Experiment has been mounted in the Monte Blanc Tunnel between France and Italy at a depth of about 5000 metres of water \, equivalent by a collaboration of the Laboratori Nazionali di Frascati r dell'lNFN, the University of Milano, the Istituto di Cosmogeofisico del CNR of Torino, and CERN. It has been financed by Italian funds mainly (INFN and CNR). The detector is made of 134 cm thick Iron plates (Fig. 5) interleaved with planes of limited streamer tube, which will be described in this conference by Enzo Iarocci. The pulses in these plastic tubes are read bidimentionally by X and Y strips placed along the tubes and - 237 -

orthogonally to them, respectively. I would like to stress that with this system the thickness per view, is the same as the thickness of the Iron plate, while in experiments like Soudan I and K.G.F. it is twice. Nu sex is a cube with 3.5 metres side and an average density of 3.5, about twice the density of the other two running calorimetric experiments. Total and fiducial masses are of 150 and 115 tons, respectively.

The Nusex apparatus began running in May 1982 with 98 of the 134 planes in operation (the upper ones) and with 112 planes as from beginning of June 82, corresponding to 125 tona. The electronics of the remaining planes will be "debugged" for the end of June. Tlie set-up is triggered by a two-hit coincidence in adjacent planes, plus two other two-hit- coincidencej in any pair adjacent planes or one coincidence of threa or more adjacent planes. In ten days of running time with 112 planes we have collected 238 muon events, two muon bundles and two muon stops. No contained event of any type or energy was detected, which gives a lower limit on half lifetime of about 10'' years for any type of nucléon decay where the charged secondaries have a visible energy of 100 MeV or more. A few events are shown in Fig. 6.

A test model of Nusex with the same granularity has been exposed to CERN beams of electrons and pions with momenta from 150 to 2000 GeV/c and to an unfocused neutrino beam from interactions of 10 GeV protons on Berillium, which strongly ressemble the atmospheric neutrino in its energy spectrum. Pion, electron and neutrino events are shown in Figs. 7 and 8.

~~A comparison between the characteristics of the KGF and NUSEX detector is presented in Table 1.~~

I believe I have to add, on a personal basis, a few comments on the results on nucléon decay of the Kolar Gold Field Collaboration. I would not like however my comments to be interpreted as criticism to this beautiful experiment carried out in time under very difficult conditions. The results and suggestions of our Indian-Japanese colleagues were and are of considerable help to us during the installation and running of our experiment [9]. - 238 -

The three non-confined events can hardly be considered as proof of nucléon decay. During our neutrino run at CERN we found many events (Fig. 10) where a charged particle enters the detector and scatters in it. Since the ratio of the densities of the rock and detector in Kolar Gold Field experiment is similar to the ratio of the densities of the neutrino shield and of the test module at CERN, it seems not impossible that the KGF non-contained nucléon decay candidates be of the same, or similar, origin. A comment on the three contained events is more difficult, also because the details of these events are not sufficient, at least in my opinion, for an unambiguous interpretation of them. I have reported however in Table 2 the expected number of atmospheric neutrino and antineutrino events in three energy intervals of which the central one corresponds to proton decay within the KGF resolution. Since the kinematical features of these events, especially the electronic and neutral current ones, are hard to be discriminated from those of nucléon decay, the interpretation of the KGF candidates can still be ambiguous. It is clear however that these candidates have to be found in the near future in an experiment with a better resolution, like NUSEX, and that the possibility that they are indeed genuine nucléon decay will be tested soon.

~~4. FUTURE EXPERIMENTS~~

The proposal for a nucléon decay experiment to be carried out in a laboratory in the Frejus tunnel between France and Italy was presented by a 0rsay-Palai3eau-Saelay-Wuppertal Collaboration and recently approved and funded by the French and German authorities. This calorimeter (Fig. 11) will consist of vertical 0.3 cm thick Iron plates interleaved with 1480 planes of flash chambers triggered by extruded aluminium Geiger counters. Total and fiducial masses will be 1500 and 1000 tons respectively. It is hoped that the first 500 tons will be installed in the laboratory, at a depth of about 4200 m.w.e., in the next year.

The proposal for a detector to be installed in the Soudan mine (Soudan II) at a depth slightly higher than for Soudan I, has been presented by the Argonne National laboratory, Minnesota and Oxford Collaboration. This deti'ctor of 1000 and 650 tons of total and fiducial masses, respectively, will be made of 50 cm long drift chambers (Fig. 12) interleaved with 0.5 thick vertical Iron plates. - 239 - K

Italian authorities have recently approved, following A. Zichichi's suggestion f7], the construction of a very large underground facility for $ elementary particle and cosmic ray physics to be escavated in the Gran 1: Sasso tunnel, in central Italy, at a depth of 4000 m.w.e. Two options are being considered: a single cavity of 25 x 20 x 100 m' or three parallel galleries, each about 200 m. long, with a cross section of one hundred square metres or more. A large calorimetric is being studied with the use of two different techniques: the Resistive Plate Chambers [8J and the Limited Geiger Tubes which will be described by Enzo Iarocci in this Conference.

~~5. CONCLUSIONS~~

The relative advantages and disadvantages of Cerertkov detectors and fine grain calorimeters have been discussed at length. If somebody were to ask me which detector I prefer, my answer would be: "both!".

Cerenkov detectors are in principle cheaper for large masses, they give a good sense of the direction of high velocity charged particles; they have a good efficiency for electrons and low average atomic number. Calorimeters are easy to test in reduced modules, they offer a better visualization of the events, they are good for detection of hadrons and excellent for muons. Moreover, their detection of nucléon decays would be less model-dependent.

~~The discovery of nucléon decay would be such an important event, and not only in elementary particle physics, that it deserves being proved by two totally independent techniques. - 24O -~~

~~Table 1: Kolar Gold field versus NÜSEX~~

Kolar Gold Field Nusex Running time (days) 436 10 Mass (total and fid.) 140 (100) 150 (115) Density 1.6 3.5 Number of planes 34 134 Number of channels 1600 90,000 Granularity (per view) 3.4 cm of Iron I cm of Iron Spatial resolution 10 cm 1 cm Depth (m.w.e.) 7600 5000 Muons/day 1.8 20 Other Properties Proportionality shower development.

~~Tabte 2: Expected Neutrino and Antincutrino events in the KGK Experiment. (436 days of running time)~~

~~Muonic Events Electronic ev. Neutr. curr. ev. TOTAL Energy (GeV) .3 - .6 3.5 1.8 .6 5.9 .6 - 1 .2 4.0 1.9 .7 6.6 1.2- 6 6.0 2.9 1.4 10.3 Total 13.5 6.6 2.7 22.8 - 241 -~~

~~REFERENCES~~

~~[1] D. Tadic, Proton lifetime - this conference.~~

~~[2] F. Reines, Measurements on proton decay - Experiments with Cerenkov and scintillation counters - this conference~~

[3] D.S. Ayres, The Soudan Nucléon Decay Program, Talk presented at the Workshop on "Physics and Astrophysics with a Multikiloton Under- ground Track-detector", Roms, 29-31st October, 1981 and Status Reports of the ANL-Minnesota Collaboration to the Second and third Workshops on Grand Unification (Ann Arbor, April 23-26, 1981; and Chapel Hill, April 15-17, 1982, respectively); and to the International Colloquium on Baryon Non conservation, Bombay Bombay, January 12-15, 1982.

[4] M.R. Krishnaswami et al., Phys. Lett. 106B, 339 (1981) and Reports presented by the Bombay-Osaka-Tokyo Collaboration to the Second and Third Workshops on Grand Unification and to the Int. Coll. on Baryon Number Non-conservation.

[5] G. Battistoni et al., Proposal for an experiment on nucléon stability with a fine grain calorimeter - Dec. 1979 (preprint) and Status reports by the Frascati-Milano-Torino-CERN Collaboration to the Second and Third Workshops on Grand Unification and to the Int. Colloquium on Baryon Number Non-conservation)

[6] R. Barloutaud, Nucléon decay experiments with a modular flash chamber detector (Orsay-Palaiseau-Saclay-Wuppertal Collaboration) - Talk given to the International Colloquium on Baryon Non-Conservation and reports to the Second and Third Workshops on Grand Unifica- tion.

~~[7] A. Zichichi, The Gran Sasso Laboratory - Invited paper to the Workshop on "Physics and Astrophysics with a Multikiloton Underground Track-detector", Roma, 29-31 Oct. 1981.~~

~~18] M. Conversi, The GUD project - Report to the Workshop on Physics and Astrophysics with a Multikiloton Underground Track-detector, Roma, 29-31 Oct. 1981.~~

~~[9] One could perhaps recall Aristotelis' words: Amicus Plato, aed magis arnica veritas (Plato is a good friend, but truth is a better one). - 242 - (j-;~~

~~FIGURE CAPTIONS~~

~~Fig. 1: Sketch of the Soudan I detector.~~

~~Fig. 2: A iT/'Jon crossing the Soudan I detector~~

~~Fig. 3: Time-delay distribution for decaying particles in the Soudan I detector.~~

~~Fig. A: The Kolar Gold Field detector.~~

~~Fig. 5: Bi-dimensional readout in the NUSEX detector.~~

~~Fig. 6: a. A very high energy muon bundle in NUSEX experiment; b. B inuon bundle in NUSEX (when this event was recorded only 98 planes were in operation).~~

~~Fig. 7: A 500 MeV/c pion in the NUSEX test module.~~

~~Fig. 8: A 500 MeV/c electron in the NUSEX test model.~~

~~Fig. 9: A two-prong neutrino event in the NUSEX test module.~~

~~Fig. 10: An incoming particle scattering in the NUSEX test module.~~

~~Fig. 11: A sketch of the Frejus detector.~~

~~Fig. 12: View of the Soudan II detector. - 243 -~~

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~~>o<>o0o0o|0o'>o0o0ol0o0o<'oOo[0o<'o0o<>o~~

~~Fig. 1 - 244 -~~

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~~Fig. 2 - 245 -~~

~~0 2 4 6\ DELAY TIME l/iSEC)~~

~~Fig. 3 H~~

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NUCLEON DECAY EXPERIMENT IN KOLAR GOLD FIELD*

M.R.Krishnaswamy.M.G.K.Menon.N.K.Mondai,V.S.Narasimham and B.V.Sreekantan Tata Institute of Fundamental Research,Bombay.India Y.Hayashl.N.Ito and S.Kawakaml Osaka City University.Osaka,Japan S.Miyake Institute for Cosmic Ray Research,University of Tokyo,Japan

Abstract A detailed description of the detector and the results of first stage of observation have been published earlier. The experiment 1s in operation during 450 days and we got about 800 events in total. Most of them art- single atmospheric muons and neutrino-induced muons which are in good agreement with expected values. The rest of them are 10 parallel mi ions, 4 inultiprong neutrino interactions,? single tracks having one end inside the detector,2 Kolar events and 6 nucléon decay events. Out of these 6 nucléon decays,Event 87 and Event 251 were reported already. There are 3 special class of event with tracks fully confined to the detector volume and their characteristics are in conformity with the decay of bound nucléons. Event 587 ;P •> e +K.° decay having back to back alignment with total energy of 980 + 20Z wherein the entire mass energy is radiated away. Event 867 ; P -JVV+ft decay. The pion of estimated total energy as 435 MeV,suffered a nuclear elastic scatter and then slowed down and stopped. Event 877 ; P •» u. + K° (TV ,TC ) decay with total energy of 990 MeV + 15%. This event is also consistent with N - e + X. since e shower may flactuate to fit to the observed configuration. Tf it is so, the total energy will be 850 MeV ± I1) Z. We also observed partialy confined event ; Event 722 which can be understood as P -» e+ +Ui° (TV.+ ,n".K.°) decay.

The integrated neutrino background to minic nucléon decay during the observation period is estimated as less than 0,5 event. In particular, it is very small for confined events because of little ambiguities In total energy and momentum balance of secondaries, and it is quite striking that the estimated energies are so close to that of nucléon. The lifetime of bound nucléons is estimated from above 6 events in 100 ton of fiducial volume of the detector, during 450 days of observation, | ' as 6 x 10 years. Reference ; M.R.Krishnaswatny et al, Phys. Lett. 106 B, 4 (1981) 339.

*To be published in a scientific journal.

~~- 257 -~~

~~NEUTRINO MASS IN ASTROPHYSICS AND COSMOLOGY~~

Alexander S. Szalay Astronomy and Physics Dept., Univ. of California, Berkeley Dept. of Atomic Physics, Eotvos Univ. Budapest, Hungary Yakov B. Zeldovich Institute of Cosmic Research, Moscow Institute of Applied Mathematics, Moscow

Abstract The cosmological effects of a nonzero neutrino rest mass Sire reviewed. A neutrino mass of about 30 eV results in superclListers of 50-100 Mpc characteristic scale forming first, with ltfrge hales in between. The superclusters will be strongly nonspherical, flat pancake-like or elongated filaments, in good agreement with recent observations. The presence of density fluctuations and the absence of the fluctuations in the microwave background is easily explained in the neutrino dominated Universe. The dissipationless behaviour of the neutrinos forming the dark component of the Universe provides a natural' answer for the increase of mass-to—1ight with increasing scales.

I. Introduction Our knowledge about the Universe can be divided into three parts, which are also in chronological order. In the first part, from the Planck-time to about 10'%-4 seconds both th«? physics and structure in the Universe are more or less unknown. In the second epoch, up to 10^5 years both the physics and the structure is rather well known, and relatively simple. In the last part of the Universe's history, lasting up to the present, the physics is also well known, but the structure became nonlinear, therefore complicated. In the first, very early epoch of the Universe we ar«? just gaining some insight of the processes, that may have accured there, sg. the creation of baryon excess, Higgs-field phase-transitions followed by exponential expansion of the Universe?. The second stage is cUararterized by being in total thermodynamic equilibrium. The total number of baryons is conserved at this epoch, only trans-formations between neutrons and protons take place. Due to the expansion of the Universe even these processes will fresse out at around 10A10 degrees, - 258 -

and the light éléments are built up from thorn by nurlco- •synthfcfsis. Most of this action takes pi act? in tltn I i r-«-, I-. tiirrv minutes, as discussed in the beautiful book of H. Weinlier i|. The» alow ridiabatic coaling is proceeding, but the Uni vvr'•<•» i •* «till radiation dominated and highly uniform. This will only th^ngr? when the i an izoj hydrogen recombines, at the twnpprature of 3000 degrees. The m.stter possesses small perturbation», whirh beconu* gravi tational 1 y unstable, as the radiation drag, <\<:tii>'} uni y on the free electrons ceases to be effective. In the thirii i;poch thi« will lead to the growth of density contrasts in thi* Uni verse, driven by gravity. Today more ;.tnd more 11 known about the 1 volumes almost free of galaxies, the "voids' recently di-r-cr i bed by Kirshner et.al. (19B1). The layer« comprising g«li<>:ii»r; <..r f? not nvcnly populated. One <:rvn d i '".I: Inqui ct.l:. of gravity would be that it concentrate;; matter in roughly spherical lumps of different. BÍ;:CJS, distr L buted randomly. Dn wt.' n*;ed new forces or very artificial initi.il conditions to explain the observations ? The aim of this article is to provide? a natural explanation for both the character ist íc t.ctiU' and structure of the galaxy distribution. No special initially imprinted seal os, • patterns or new forces are needed for thir> explanation, all is a straightforward consequence of a nonzero neutrino mass. It w.ts suggested already by Rershtein and Zeldovich (1966>, that even a very small neutrino mass may have important cosmological consequences, by contributing to a large fraction of the overall density of the Universe. Marx and Szalay (.1^7?.), Cawgik and McClelland <1972) and Schramm and Steigman (1901) have refined their arguments, showing that our present limite on the Hubble constant and the deceleration parameter of th

~~m < 1OO eV~~

As it turned out since from calculations of the primordial Hi? and D abundance (the most, recent by Olive et.al. 1901), thr amount of ordinary matter in the Uni ver'.-e ran account (or only a email fraction of the critical density, what is needed in - 259 -

order to have a flat Universe. The likely value of the baryon density-parameter lies in the range of O.OK fL% <0.05, independent af the existence of low luminosity stars, etc. This would suggest, that the Universe is open by a wide margin, i-f bsryons arc? the dominating component o-f the density. In such a Univprsp the growth of fluctuations is nearly negligible, as we'shall see later, therefore the presence of structure and the present tight upper bounds on the small scale fluctuations of the microwave background effectively rule out such a case. A 1 arge motivation -for taking massive neutrinos seriously as thf? main component of the Universe came from the experiment of Lubimov et.al. 1980, announcing that from the beta-decay of tritium the mass o-f the electron-neutrino appears to be in the range 16 eV< m^<46 eV. As suggested by Szalay and Marx (1776), a neutrino mass of this magnitude does alter our expectations not only of the global density of the Universe, but it also changes the way fluctuations behave. Neutrinos are col 1isionless particles, therefore they are not affected by the radiation drag due to the photons, as ordinary matter is. This enables much larger fluctuation growth, without a strong influence on the microwave background. On the other hand, neutrinos are subject to thermal pressure, and their Jeans instability gives a characteristic mas^ scale? corresponding to superclusters, as it was realized by many authors recently (Doroshkevich et.al. 1980abc, Bond et.al- 1980, Klinkhamer and Norman 1981, Sato and Takahara 1900). The pressure—free collapse of such systems was shown to 1 t>ad to highly anisotropic structures, 'pancakes' (Zeldovich 177«")), These are not isolated, of course, but -form a cellular structure in the Universe, enclosing huge 'voids* in between them. The neutrino mass »«plains the emergence of this structure in a simple and elegant way. The details of this picture will be given in the next sections.

~~II. Linear Perturbations in a Neutrino Dominated Universe~~

Small, but finite fluctuations must necessarily have been present near the beginning of the big bang itself. Small fluctuations, however, do suffice, if present at a sufficiently early epoch. Mow the grand unification theories guarantee that, if the usual big bang theory were applicable, there could not be any spatial variations in the ratio of matter to radiation densities. The only allowable types of density fluctuations are those, which preserve this ratio, called adiabatic or curvature fluctuations. These fluctuations involve the energy density, including radiation, and accordingly affect the curvature of space-time. Any individual fluctuation behaves in effect like a slightly perturbed big bang model at these early epochs, and so t.lie cur vriturp structure of th

larger masses come within the horizon, defined to bß the light travel distance since the big bang. Once a -fluctuation i'.- within the horizon, it is well described by Newtonian gravity. Already Newton qualitatively, and then Jt?an? quantitatively realised, that perturbations in a self gravitating gas have? » do-finite behaviour - they are unstable, giving rise? to growing density contrasts. There are two competing effectsi gravity attracts th^> particles towards the highest densities, whilp the pry.surH due to thermal motion tries to prevent this. On large destins always gravity wins, matter is collapsing in some partis of the volume, and is rarefied in others. This phenomenon occurs for all kinds of matter, since they are all subject to gravity. This tendnncy remains for the behaviour of perturbations supe?r impound on the expanding Universe. On small scales pressure becomes important. The perturbations behave like acoustic waves; extess density is accompanied by excess pressure. This induces a «notion, where the excess density is travelling with the speed of sound and the locai density oscillates. The plasma still remembers its past outside the horizon when gravity was dominating, and it wan compressed in some regions. Until th<* tiMnpr'rfltijr«1 hits clr i >j»i»< fti to •< -few t hour>rtii(l<; at flc'f|r(M"3, the radiation ia '.itill >.,uf f ici entl y imiinii'Uc to konp the

low matter density the birth o-f galaitiee is impossible ! Thu*a the very presence o-f large density perturbations «itîf.'nîi to indicate, that there in some "hidden" mans in the UniveTî.iî. It is called hidden, because it does not form luminous stars, it is not well-known matter. There être several cori'jlrijints on what the hidden mass cannot be. A new component of the Universe was badly needed: perhaps the neutrino, or soms other weakly interacting particle has a tiny rest IHASS, The neutrino mass of the order of 10 or 20 electronvolts would do •so! Thf? neutrino abundance is of the order of 150 neutrinos of one typ« in 1 cc, which gives the density p=3. 10-s-~0 g/cc. Small as it is, it outnumbers the normal matter density by 20 to 1OO times. Neutrinos, unlike protons or electrons, collide vt?ry rarely. As a fluctuation just enters the horizon, when the» neutrinos become nonrelativistic, the neutrinos are not subjected to radiation pressure, they are gravitationally unstable?. However, the epoch, at which neutrinos turn ncinrelati vi stic can occur well before the decoupling. Thus neutrino fluctuations greater than the Jeans mass can grow for a much more extended period of time, than can matter curvature fluctuations. For in this lnttrr cams, the coupling with thr» r •nil iil'.lun Inhihi bti (|rowth prior to tin* Hi'coupl inrj t'|i(.it:li. At dr.'couplinrj, the amplitude? of thr? neutrino donsity fluctuations gruatly exceeds that of matter and radiation inhomogénéi ties. Yet it is the radiation fluctuations that can be seen directly in the cosmic background radiation and their predicted amplitude is now diminished by an order of magnitude or more. Tho fluctuations of neutrinos will than accelerate the growth of the much smaller baryon perturbations. The above paradox is thus resolved in an elegant way. The growth o-f the different perturbations is shown on Fig.l. for a 30 eV neutrino mass, with a narrow possible range of initial amplitude, limited from above by the variations of the microwave background and from below by the presence of structure. Smaller scale perturbations behave in a different manner. The col 1isionless behaviour of neutrinos has other consequences as well. Initially, being extremely relativistic they move close to the speed of light. Turning nonrelativistic, they move slower and slower, and today a 30 eV neutrino would only have a speed of about 6 km/s. The comoving displacement of neutrinos is thus finite, giving a characteristic length and mass scale. B.?low this scale neutrinos streaming in different directions would mix freely, effectively erasing any inhomogénéi ties initially present. Above this scale neutrinos cannot move from one lump to another, so the effect of their thermal motion ie negligible. The damping scale is well described by

~~3 15 Mv - 1.8 (np i.v-2 - 3.2 10 Mo~~

~~(Bi snovaty-Kcgan and Novikov 19B0,, Bond et.al. 1980, Doroehkevich et.al. 1980c). An asymptotic analytical solution for the change of the spectral shape was given by Doroshkevich - 2hl -~~

et.nl ), and a detailed numerical in tegr stion ui thr cnuplod Einstein- Boltzmann equations has been present«d tiy Bom:! and Sz.alay U9B1, 1982). The rnsul ti ng trati5l"r ftinr.tinn t«l en at different times is illustrated on Fit).2. norm.-»l i zr>d to a fluctuation with mass much above the critical. The ^(.ale factor is a=l. when the neutrinos becume nonrelativistic. It enn b. Jj and 5, when the neutrinos Are semi-relativ»stic, and both the directional dispersion and velocity dispersion are acting.

~~III. Nonlinear Structure in the Universe~~

The absence of pressure has a dominant effect in determining the structure and shapes of the objects format). Thermal pressure is always i sotropic, so if pr es-sur «-.' i i comparable to gravity, this prefers the formation of objects* close to spherical symmetry. Only when pressure is cumpleU'ly negligible, up to the last moments of collapse, can and will anisotropies develop. Furthermore, nearly all of thy matter will collapse into the compressed high density reqions, since there is no pressure to counteract the infall. The probability that matter will be compresr.cd or rar efif-'d along nny one; *« i n is 0.5, respectively. Therefore, the fraction of CMS which will not be compressed along any of the axes will amount only to about 0.125. The exact number will br? -somewhat li."»<5, only \\'/.. since the three a:!e»s are not completely independent. Chi'i hf»s immediate consequences far the expected topology, the np/»t i .itl structure of the final state. Earlier, when the density wa:; nearly constant, one can already draw the boundaries of tho regions to be compressed later. In the pressure-frot? casp this contains 80-907. of all matter, therefore the topology at this point is self-evident i these regions surround the smaller 'bubbles', which never collapse, but will become the huge voids instead. As the particles move along their trajectories, «ud the compression begins 90/Í of the matter will occupy only 1<>7. of the volume, and the small bubbles, containing only 107. of the mass will be rarified, occupying 907. of the volume. Since the initial stage was continously deformed by the motion of the particles, the fact, that the boundaries enclose the «small regions remains unchanged. The compressed regions, though filling only a small fraction of the volume will surround the voids, forming thin walls aii'd strings in a cell-like structure and not the other way around, as one would naively e:ip«.?ct ! We» emphasize once more, that this is the direct consequence ni the pressure-free, cold collapse. The perturbations in the Universe are initially small. At decoupling they are 'smooth', due to the effects of damping, a? seen beforei they are absent on scales smaller than the damping length. When we follow the trajectories of particles perturbed this way, when P--0, at some points these trajectories will intersect, forming 'caustics'. These caustics are similar to the caustics formed in geometrical optics. In a cosmological situation, the possibility of caustic formation by the trajectories of duet particles was already pointed out in an - 26 3 -

early paper of Lifshitr, k.hal atni l-ov arid (-). 1 schul , hut it w.ï<3 no* r*?lfltcd to gala.vy formation at that time. If we (vunslilpr a ç.mal 1 cubical volume o-f the Univrr'.f, it will deform in a similar manner, independently collapsing or expanding along its sup's. It i5 easy to see, that .^ centrally "symmetric i cil 1 au=tf» ig «•j very special caê, indeed. Both the signs and nutqni tutter* of thr> thrpe deformations have to match in cider t n pnidni p this pffpi-t. In general the three? dr-f ormatinns will he random, the cuhe will have a strong collapse slant) one» of it* WPS, and a mild collapTP or expansion alonq the others, it will tie1 highly iniûtropic. The mass inside i <3 pre'-.rrvi'i), «MS whw hath the1 thiefMPSS and the volume o-f the cuhe is approaching ipro, it«; density becomes very high, a flat, "parirak«-»' i « for IHPII, as i t w/>~. suggested originally by Zeldcvich (1970). At first they ar P at isolated soots, where the initial velocity per l.urliat i uns had the 1 arcj(?:»t gradient , but very soon {.hf"i«í regions, grow, they turn into huge thin surfaces which icit t-r sr?ct, tilt and altogether form the walls o-f a huge cellular structure in the Universe, fhe Universe is probably at thi •:» stage toil-a y as dt-'t.îlf?d numerical calculations indicate (Darnaht.evich et.al. 19tl0d, Clypin and Shandarin 19(32,Trenl- et. .al . 1 9(32) . Loiter large clumps of matter form, the above structure will disappear: it. is an intermediate stage. The present observational evidence thur» s.how-3, that the Universe is neither too young, nor too old as far as structure is concerned. So far the general approach in cosmology has been to follow the linear evolution of perturbations in term's of individual Fourier components, assuninq a mixture with random phases, fls soon as nonlinearities develop, this approach is incorrect. Though many short wavp-3 are created, as the nonlinear structure develops, thny have definite phase r'A ftiori'í ' The? only possible approach in this cass is to calculatp the real spatial structure. Methods of catastrophe theory were applied to the analyze? the structure, that develops in potential motion, and it was found, that, piincakes are only th«? lowest order singularities orcuring, but other, more complicated higher order singularities can also be identified (Arnold, Zeldovich and Shandarin 1981). Cio far the effects of pressure were considered to bP negligible, but at this highly compressed stagfî this is no more r.o ' When the intersection of trajectories takes place in the F~0 approximation, pressure builds up, the velocity of thf? ceil líipîng gas exceeds the speed of sound, c\ shock w.we i'a formed. Rather violent processes occur (5unyat.»v and Zeldovich 1972, Doroshkevich et.al. 1978) : the gas heats up to more than a million degrees, it gets ionised, then the collisions of particles result in emission of radiation over a broad spectrum. This energy loss will cool the g*s, especially in the central layer, where the density is higher, thus collisions are mure frequent. This cooling is badly needed: only cold gas is able to form smaller lumps, the seeds of galaxies. However, only part of the matter will be able to cool, the rest remains hot, above a few million degrees. This hot gas will end up in cliisturs of galaxies, emitting X-rays. The gas within the cluster is not completely of this primordial origin, of course, - 264 -

it is known to contain soma iron, created in supernova e::plosi ons. A part of the outgoing radiation will photoiani;e the cold, neutral ga"3 in the outor regions, that has not entered thc=: shock yet, therE?by effectively preventing the possibility, that they -form galaxies. In this way the actual contrast of th«» number of galaxies in the? pancakes and strings over the void1; will be much more pronounced, than simply the contrast of densities, which is only of the order o-f O. 1-O.3 (Zeldovich and Shdndarin 19B2) ! Cosmic neutrino pancakes may lectd to an attractive? explanation of the dark halos of galaxies. Studies of the rotation of our own galaxy and of other spirals have revealed the surprise that Kepler's laws are not obeyed. The rotational velocity does not decrease with increasing galactocentric distance. The accepted resolution is the presence of an I?Ü tended halo of dark matter. If enough otherwise invisible nid'.', iii pr <:>r.i;nt, the rotation velocity rt'm.Unrj ci-ini,l.«nt, .^«i olj'it'i' ved. Dark halo& are known to contain thu bulk of nia:;t! of spiral galaitius as originally suggested by Peeblirvr., Yahi 1 and Ostriker (1974) and simultaneously by Einasto (1974) Jnd F'aal (1973). fin indirect argument suggests, that similar dark material is present in even greater amounts in galaxy groups and clusters (Faber and Gallagher 1979). Such systems would fly apart in an unacceptably short time were it not for the gravitational attraction of the invisible matter. Ninety percent of our universe appears to be in this dark component. Massive neutrinos provide an intriguing possibility for the dark matter. The pancake collapse will distribute the bulk of the neutrinos widely, as the neutrinos acquire large collapse velocities. Some, however, move only slowly at first, «since these neutrinos were initiallly closer to the midplane of the pancake. Around this midplane, a thin gas layer condenses eind fragments, much as it would in the absence of massive neutrinos (Doroshkevich 1980). The slower-moving neutrinos will be rapidly accreted by the baryonic cores, and dark halos will form (Bond, Szalay and White 1982). In denser regions, the neutrinos will also tend to be shared communally, as in gala::y clusters effectively resulting in an increasing mass-to-light ratio. The theory of galaxy formation based on massive neutrinos is still investigated. The results on pancakes, cell and/or string-like structures and large dark voids are confirmed by the recent extensive theoretical and numerical cal culations.

~~IV. Conclusion~~

The neutrino dominated Universe has several advantages over other possibilities, in providing a natural explanation of the presence of structure in the Universe, while also giving a small enough amplitude for the small scale fluctuations in the microwave background. Furthermore, the neutrino mass imposes a characteristic scale on the originally scale-free perturbations in the early Universe. Large voids, thin pancakes and prolate - 265 -

elongated objects mrm predicted! Both the scale and the shapes of the objects are in excellent agreement with observations'of th» galaxy distribution. The neutrinos may also provide the 'hidden' mass in the Universe, needed to «»plain the flat rotational curves of galaxies and the virial equilibrium of clusters of galaxies. kT« 1

Fig. 1 The growth of neutrino and baryon fluctuations versus redshift z. The dashed line denotes the neutrinos» the solid lines correspond to the baryon fluctuations in three different cases. (Doroshkevich et al. 1980a)

~~Fig. 2 The evolution of the transfer function of neutrino perturbations with different wave- numbers versus the scale factor a, illustrating the collisionless damping (Bond and Szalay 1982).~~

~~0001~~

~~k/k.vm - 2Cf> -~~

Arnold,V.I., S.F.Shand^rin, Ya. B. Zel dovi ch. 1982. Grjophyr,. Astrophys. Fluid Dynamics 20,111. Bond, J.R.. G.Ef'stathiau, J.Silk. 19BO. Phys.Rev.Lett. 45,19H0. Bond,.l.R., A.B.Ssalay. 1981. Proc NeutrincTBl. 1,59. Bond,.7.R. , A. S. 5r.al ay. 1982. submitted t.T Ap.J. Bonri.J.R., A.S.Szalay, S.D.M.White. 1982. Biibmittad to Naturo Clypin,A.A.,S.F.Shandarin. 198:.!. submitted to Sov.Astron. Cawsik,R., J.McClelland. 1972. Phys. Rev.Lett. 29,669 Davi5,M.,J.Huchra,D.W.Latham,J.Tonry. 19B1. Harvard preprint. Doroshkc?vich,A.B. . S.F.Shandarin, E.Saar. 197B. M.N.R.A.6. 184,643. Dorashl.evich, A. S. 19BO. Sav.Astron. 37,259. DorashfîFiVj ch, A. G. , M. Yu.Khlapov, R.A.Sunyaev, A.S.Szala/, Ya. B. Zeldovich. 1980. Proc. Xth Tra>:as Symposium on Relativistic Astrophysics, New York Acad. Sei. p.32. Doroehkevich,A.R., M.Yu.Khlopov, R.A.Sunyaev, Ya.B.Zeldovich. • 19(70. Pisma Astr.Zh. 6,457. Dciroshl:evich, A.6. , M. Yu.Khlopov, R.A.Sunyaev, Ya.B. Zaldovich. 1980. Pisma Astr.Zh. 6,465. Doroshhevich,A.G., E.V.Kotok, I.D.Novikov, A.N.Polyudov, S.F.Shandarin, U.S.Sigov. 1980c. M.N.R.A.S. 192,321. Einasta,il., E.Joeveer, E.Saar. I960. Nature 283,47. Fabor,S.M., J.E.Gallagher. 1979. Ann.Rev.Astr.Astrophy«. 17,135. Ber£iht6?in,S.B. , Ya. B. Zeldovich. 1966. JETP Lett. 4,174. Gregory,S.A., L.A.Thompson. 1978. Ap.J. 222,784. Kirshner,R.P., A.B.Oemler, P.L.Shechter. 1979. A»tron.J. 84,951. Kirshner,R.P., A.G.Dernier, P.L.Shechter, S.A.Schectman, 1981. Ap.J.Lett 1 248,257. Klinkhamer.F.R., C.A.Norman. 1981. Ap.O.Lett. 243,1. Li-fshitZjE.M. 1946. JETP Lett. 16,5B7. Lubimov,V.A., E.G.Novikov, V.Z.Nosik, E.F.Tretyakov, V.B.Kozik. 19SÓ. Phys.Lett. 948,266. Marx,13., A.B.Szalay. 1972. Proc. Néutrinu'72. 1,123. Olive,K.A., D.N.Schramm, G.Steigman, M.S.Turner, J.Ydng. 1981. Ap.J. 246,557. Paal.ti. 1973. Proc. IAU Symp. No.63. p 251. Peebles,P.J.E. 1980. The Large Scale Structure of the Universe Princeton University Press Ro5gacheva,F.K.,R.A.Sunyaev. 1981. Pisma Astr.Zh. 8,323» Sato,H., F.Takahara. 1900. Preprint RIFP-400. Kyoto University Schramm,D.N., G.Steigman. 1981. Ap.J. 243,1. SiU;,J. I960. Ap.J. 1S1,4S9. SunyaeVjR.A., Zeldovich,Y*.B. 1972. Astron.Astrophy«. 20,189. Bzalay.A.S., S.Mar«. 1976. Astron.Astrophy». 49,437. Zeldovich,Ya.B. 1970. Astron.Astrophys. 9,84. Zeldovich,Ya.t.,S.F.Shandarin. 1982. Pisma Astr.Zh. B.2S9. - 267 -

~~PROMPT LEPTON GENERATION ATMOSPHERIC MUON AND NEUTRINO SPECTRA AT HIGH ENERGIES~~

~~L.V.Volkova, G.T.Zatsepin Institute for Nuclear Research, Academy of Soiences of the USSR, Moscow~~

Abstract The problem of prompt lepton generation at energies of interacting protons ^ 1 TeV is discussed. Experi- mental data on. prompt muons from cosmic rays /1/ don't contradict within experimental and theoretical uncertainties to Hie results of calculations made with cross- sections and generation spectra of charmed particles received on CCD and normalized to accelerator data In /2/i On the basis of this analysis prompt atmospheric neutrinos fluxes are calculated. Some simple relations between muons and neutrinos intensities are received for different generation sources»

Introduction. The problem of prompt muon search in cosmic reye was put theoretically /3/ and experimentally /4/ many years ago. And many works were made since that time in cosmic rays. Howdays possibilities of deep underwater installations to study the nature of nuclear and weak interactions at ultra high energies with cosmic ray neutrinos are discussed widely /5»6/ (it was considered already in /?/)• As at high energies atmospheric neutrino fluxes are very sensitive to a prompt generation the analysis of this on today is important for discussing possible deep underwater installations and possible experiments. 1 » On charmed particles generation from cosmic ray data and from calculations made on CCD and normalized to accelerator data. Prompt muon generation function in nuclear interactions of primaiy radiation in the atmosphere can be written - 268 -

) «here Qri (£$ " the aunto« of prompt muons generated in &+Xtclx depth with ff rffa£ energies in nuclear interactions; Ptf(c,x) - differential energy nucléon spectrum; AWfc(E,EO/d£l - the probability that in a nuclear interaction of a proton with an energy E a charmed particle with an energy E' is created (a total generation cross-section of a considered charmed particle and a spectrum of a created charmed partical are included into this probability); dWtfl(£JE)/éE the probability that in a decay of a charmed particle with an energy E^ a muon with an energy E is created. This probability contains the spectrum of a generated muon and the semileptonic probability of this charmed particle decay with a muon production. The probability of the particle decay is equal to 1. To take into account its finite life time it is necessary only at E > 5.10 SeV. It is easy to see from Table 1 where so called critical energies for charmed particles are given (energies at which the probability to decay at a nuclear length is equal to the probability of a nuclear interacrion) for different angles of coming to sea level.

~~Table 1. Critical energies for /ic -hyperons, ~D ,T> mesons( >*A » 2.10"*" sec, t ^ » 6.10 ^)~~

~~EGeVS^iC' ° 0,05 0.1 0.2 0.3 0.4 0.6 1 Ei .10™ 26 23 19 13 8,6 6.6 4.4 2.7~~

~~Ép* .10*"7 51 46 38 25 '•7 13 8.7 5.2 SnO »W 69 60 51 33 22 17 12 6.9 - 269 -~~

~~In /2/ calculations of Ac - hyperons generation cross-sections on OCB with their normalization to ac-~~

1 celerator data /8/ and AG -spectrum were made. The difference between two assumptions on the value of interacting proton energy portion taken away by generated Ac and 0.4 D particles (for example 100% or 70%) gives an uncertainty -v 2 m.g.1 Spectrum of nucléons into calculated prompt muon spectrum. responsible for *\ with We use the value 70% in our calcula- a given energy i tions. In Fig.1 the spectra of primary protons responsible for a charmed particle generation and a pion or kaon generation with a given energy B are shown ( Üt and JT generation spectra were taken from /9/). It is seen that effective energy portions »jt taken away by Ac are 2 •» 2.5 times larger than that taken by^«^Tthe effeotive energy - the energy that dévides a partiole spectrum in such a way that a haljf of particles have an energy less than this effective energy and the other one- an energy more than this effective energy). In this figure experimental data /10/ on Ac -spectrum were used ( Ac -spectrum ~flf-V} ' )• Por the semileptonio decay probability the valueB 20% for B-mesons and —10% for hyperons were taken /11/. In 6t /TJpi.j^.2 primary nucléons spectra res- 7ig.2Spectrum of nucléons ponsible for a muon with a given responsible for muons with energy at sea level for different a given energy at sea le- muon generation sources are given. It is seen .that for muons fron X)K -decay» with a given - 270 -

energy primary nucléons with energies 5-6 times larger and with energies~3 times larger from /Ig -decays are responsible. The ratio of differential prompt muon spectrum calculated in this work as it was described earlier to differential muon spectrum from JL/J^ - decays at sea level /4/ ifi given in Fig.3« Dotted line -uncertainties in Aç. -generation cross-section normalization /2/. Really uncertainties are larger because of uncertainties in a portion of a nucléon energy away by 10" 105 E-Gev Ac}"Dj probabilities of semi- Pig. 3 The ratio of prompt leptonic AcjD decays. The hori- muon flux to muon flux from zontal line is an information that can Jt, »& -mesons decays at sea level(vertical direction) be drawn from the experiment on spectrum and angular distributions of cosmic ray muons /1/. Because of large theoretical and experimental uncertainties we can make only a next conclusion: experimental and theoretical data don't contradict each other and the flux of prompt muons becomes equal to one from li,l\. -decays somewhere in the region 20-» 50 TeV. 2. Vertical atmospheric muon fluxes. In Fig.4 for different P< generation channels muon vertical spectra at sea level are given. These spectra are given taken into Fig.4 Differential vertical account that for muon energy atmospheric muon spectrum at ) 1 TeV the value $ sea level for different generation sources in the integral generation spectrum - 271 -

of pions becomes 1.9 instead of 1.65 /1/f /12/ • /14/. In Table 2 the values o( that show what a portion in the generation prompt muons are from pions of the same energy and R that give the ratio of a prompt muon flux to decay muons (from JT/JC -mesons) at sea level for the vertical direction are given. Table 2. The values &• and R. (explanations see in the text).

~~GeV 103 10* 105~~

~~2 6. 5. io- 0. 16 0.23~~

~~R. B.4 .10-3 0 .21 3.2~~

These values have all uncertainies discussed above. Taking into account At, we have not a big increase in prompt muons as ~ t/l 3. Atmospheric neutrino fluxes. Differential electron and muon neutrino spectra at sea level for vertical and horizontal directions are given in Pig. 5a and 5b (fluxes form JC/JC -decays were taken from /16/ taking into account that as it was described earlier JC -1.9 for E« > 1 TeV). It is seen from the figures at which energies prompt fluxes become larger than these from Tc/JÍ-decays. So for the vertical direction prcapt muou neutrino fluxes are larger than those from «/t/A-decays at ~ 10 TeV, for electron neutrinos it becomes» at — 1 TeV. This takes place because electron neutrinos from Jl/JC -decays are only some percents of muon neutrinos (it is easy to understand as at considered energies for muon neutrinos from %UX -decays and 3**NZ decays are responsible, and for electron neutrinos jfCeS decays) and prompt electron and muon neutrinos are generated in the same way. At high energies neutrino fluxes in generally consist of prompt neutrinos and are isotropical. If a primary nucléon spectrum is powerful and scaling takes place then differential spectra of muon or neutrino from different generation channels can be written! - 272 -

~~C We~~

Wi - the probability of a decay in a considered channel; ft - some effective energy portion taken away by a created particle form a decaying or generating particle. Then differential a muon or neutrino spectrum

The values "i are given in Table 3* These values at E } 10%eV depend on energy increase very weakly. Table 3. The values Kl ~—~~ neutrino generation i ~"~ muon channel %^M-^ j£*{MV pTVMpi genera- ' tion channel 0. 15 - - - -

~~2 - 0 .74 - 6.5 .10-* 6.lu" proHpt - 1 - -~~

As our knowledge of muon spectrum and generation channels become bet ter we can recalculate easily new neutrino spectra by using the value KL . Conclusion. The analysis made in this work shows that modern considerations on charmed particle generation at high energies based on CCO don't contradict with the experimental data from cosmic rays. Atmospheric neutrino fluxes at energies ~ tens of TeV are more than an order larger those calculated at an assumption that prompt generation does not change since energies at which experiments on accelerators were made. - 273 -

The authors are greatful to K.G.Boreskov and A.B.Kaydalov for helpful discussions of questions connected with generation cross- sections and spectra of charmed particles generated in iiuclear interactions. References 1. M.A.Ivanova et al.Proc.ZVII ICRC 2,23, 1981. 2. K.G.Boreskov, A.B.Kaydalov, Preprint ITEPh, 1982. 3. O.S.Alekseev, G.T.Zatsopin Proc.Int.Conf.on CR ±,326,1960 4. H.E.Berßeson, S.W.Keuffel et al Phys. Rev.Lett_2J[, 1089,1968 Proc.Workshops on DUMAHD 6. G.T.Zatsepin, V.S.Berezinsky Uspekhi Piz.Nauk (Rua)122.3.1977 7. M.A.Markov Proc.Ann.Conf.on High Energy Phys., Rochester, 1960 8. N.Basile et al. Preprints CERN EP80-214, EP81-22.EP81-23 EyGev 9. L.V.Volkova, G.T.Zatsepin, L.A.KuzL íig.5 Differential neutrino »Bioliev Nuel.Phys. (Rus)_29.. 1252,1979 fluxes 10* M»Basile et al. Lett.Nuov.Cim. 30, 487, 1981 11. L.Foa Proc.Int.Simp.on lepton and photon int at h.a., Bonn, 1981, p.775 12.V.Kawashinta et al.Proc.XVII ICRC J, 16, 1981 13« Y.Mino-- iawa, P.Kitamura, K.Kobayakawa Huov.Cim.^£,471, 1981 14* R.I.Enikeev et al.Proc.of Ac of Sei USSR, ser,phys.(iii press) 1?. M.Basile et al Nuov.Cim. 65A, 391. 408, 1981 16. L.V.Volkova. Nucl.Pnys.(Rus)_3J., 1510, 1980 - 274 -

~~THE PROBLEM OF SOLAR NEUTRINO FLUX PULSATIONS AND GRAVITY OSCILLATIONS OF THE SUN Yu.S. Kopysov~~

~~Institute for Nuclear Research, Academy of Sciences of the USSR, Moscow, USSR~~

Abstract Arguments in favour of solar neutrino flux variations are discussed. It is shown that there is reason to believe in variations in the 37AT production rate in the Brookhaven neutrino detector with periods of 20 - 1, 25*5 - 1.5 months and about 11 yr. A summary is given of the new aeismonuc- lear mechanism of solar neutrino flux and solar activity mo- dulations, which is based on gravity mode pulsations of the solar core. These pulsations underlying behind solar seismic activity are shown to provide a possible explanation of the specific features of correlation between 37jir production rate changes and variations of solar activity indices. 1. Introduction«The problems of solar neutrino flux pulsations and their detection were first discussed by G.Zatsepin and V.Kuzmin four years prior to the Brookhaven solar neutrino experiment /I,2/. This discussion concerned with 11-yr variations connected to solar activity cycles. Then, after the first runs of the experiment had revealed the •''Ar production rate in the chlorine detector to be much too below the predicted one, W.Sheldon /3/ speculated that these runs would be pictured as finding themselves a I: l;he minimum of solar neutrino activity. As the data set of measurements got more plentiful grounds appeared to suspect the large variations interenl in the 37Ar production rates due solely to the statistical as well as systematic errors /4»5»6/. Moreover, R.Davis, Jr. and J.Evans Jr /5/, R.Ehrlich /6/, K.Sakurai /7/, and A.Subramanian /&/ have argued that it is conceivable there are time variations in the data set. Intriguing results have been obtained by K.Sakurai /7/> His crude frequency analysis has allowed him to reveal the quasi-biennial •"Ar counting rate variation in the neutrino detector. He has also reported the presence of the correlation between this variation and that of the sunspot numbers in the 1970-76 yr set of solar activity indexes. Above all , A.Subramanian /8/ has discerned a correlation between the 11 yr variations in similar data sets. Obviously, if such correlations were the case, they should be regarded as the strongest - 275 -

37 argument in favour of the neutrino-induced change in the J Ar production rate. The works in which the authors insisted upon the existance of solar neutrino flux pulsation have been criticized by L.Lanzerotti and R. Raghavan /9/. The main objections reported up to this point against such pulsations can be formulated as follows: 1) The statistics involved is still too poor for the meaningful state- 37 ment about the time variations of counting a few J Ar atoms in the neutrino detector to be made. 2) The periodicities in Ar production rate and solar activity time series as well as the correlation between them, if presents, are non- stable; therefore their existence must be questioned. 3) There is no reasonable theory which could produce solar neutrino flux pulsations with periods of several years. A few recent developments proposed in /10,11,12/ are now available, which should help, to reject these objections. The rest of this report will consist of an abbreviated summary of these developments together with their application to the problem in question. 2. On statistical significance of statements about ^ Ar production rate in time variations in the Brookhaven neutrino detector. The problem called in the heading has been quite recently discussed by V.Gavrin, Yu.JCopysov and lí.Makeev /10/. Here I shall repeat outlines of this paper. In spite of the large errors inherent in individual Brookhaven runs, the available set of •''Ar counting rates is already fairly plentiful for one to be able to make statistically meaningful statements. Let us see how to do them. (1) 11-years variations. Prom the Brookhaven measurements covering the period 1970-1980 /13/ one can readily pick out the data set spanning the interval from August, 1974 to February 1979 (runs No.36+58) in which there was being the obvious overall increase in ^'Ar production rates r^» The mean -^Ar pro-

~~duction rate averaged over these k =23 runs is fma% = O.563. The pro-~~

~~duction rate averaged over the rest runs is rmLn a 0.289. Hence, the depth of modulation with a period of 11 yr is~~

~~= 0.322 (1) vmax - 276 -~~

~~Estimating the statistical significance of the conclusion concerning the 11 yr modulation by means of the Student criterion •i. _ rmax~rmin (2) where~~

i) f k F and n - the whole number of measurement runs , one finds t • 3« 25» Therefore one can conclude that the J kr production rate at a confidence level approximately not less than 99.7 per cent changes within the period 1970-80 with m « 0.322. (2) Quasi-biennial periodicity. The presence of the —2 yr variations originally reported by K.Saku- rai /7/ was looked for using a superposed epoch analyses. The typical superposed epoch plot with a faiding period of fl =1.65 yr is shown in Fig.1. Regions of minimal and maximal •''Ar counting rate were selected for every superposing and the parameter t was calculated by formula (2). The behaviour of t as a function of fl , shown in Pig.2, reveals two high peaks with maxima at 1.65 and 2.12 years and with tJI^ ^3« The as well as the widths of these maximum values of t-criterion, t , peaks at the (t - 1) level imply that at a confidence level approximately not less than 99»5 per cent the ^'Ar production rate in the chlorine detector pulsates with the periods ("1.,= (20 - 1) months and f^ = - (25.5 ± 1.5) months and with depth of modulation m ^ 0>3« These two lines could be considered as a result of modulation of a periodic process with 11^=22 months by another periodic process with the period T a 2nin2/Cn2~ n^) • Taking into account uncertainties inherent to determining fit and flji one finds T to be lying within the range 10 years ^ T ^ 30 years, i.e. the period ~11 yr characteristic of solar activity gets just into this range. However« we failed to select the carrier frequency cJo = 2ir/no» On the other hand, there is no reason for the present to consider one of two frequences = CA)i = 27r/rii and a)2 2ir/n2 as a carrier frequency because it is difficult to regard the peaks emerging around 1.25, 1*5 and 2.7 yr (see Fig.2) to be statistically meaningful. So, 11-years modulation of 37 J Ar production rate may well be envisaged as B. result of beating two periodic processes with the periods fl1 and ÍI2 • (3) On statistical significance The significance levels estimated above are found by means of the Student distribution. The application of this distribution in our case - 277 -

required for the measured r^'s to obey the normal distribution at the "¥7 constant genuine Ar production rate. Such an assumption seems to be called in question. However, the departure from the normal law can be depressed by combining the r^1 s into groups and going to the distribution of the weighted mean rates rj . The departure will be the smaller the greater the number of runs gets in each group. It is natural lor the superposed epoch analyst s to form the groups so as the every one to contain the runs with close values of phase. The example of grouping for 11=1.65 yr with the number of groups n =9 is shown in Fig.1. Taking into consideration the group weights, one can obtain t — 5.1 that corresponds to a confidence level of not less than 99.8 per cent. Another grouping with n = 11 yields t=4.5 that results in the same confidence level. So our fairly high values of confidence levels seem fairly safe and with high confidence we can reject objections against astrophysical nature of the counting rate changes in the neutrino detector. 3« Seismonuolear mechanism of solar neutrino flux and 3olar activity modulation Quite recently G.Bazilevskaya, Yu.Stozhkov and T.Charakhchyan /11/ have obtained a comparatively high correlation coefficient between the 37 changes of JIAr production rate and that of the sunspot numbers. It has proved to be equal to '—0.7, i.e. there is the anticorrelation between these changes. Besides a lag time of 0.5-1»0 yr has been discovered. The presence of any type of correlation between solar activity and the neutrino flux in conjunction with the existance of quaai- biennial periodicity in the solar neutrino counting rate as well as in diverse manifestations of solar activity /7,H,15/ makes credible the hypothesis of the leading role of the solar core in modulating all the phenomena in question. The possible mechanism of such a modulation has been recently proposed by the author of this report /12/, which is based on the allowance for large displacements of material at the solar centre. An essential feature of this proposal is that the active solar cores being kept in the very slightly underadiabatic equilibrium, is oscillating in at least one of its own g-modes. (the concept of such a core has been developed in connection with the 160-min oscillation of the solar surface in /16-18/). - 278 -

~~Modulating the neutrino flux occurs owing to periodic changes in the rate of the reaction chain~~

which, in turn, are due to periodic changea in the He abundance, X,,at the central region of the Sun where dX^/dr> 0. So far as the radial component of a displacement I behaves like r'' U) at the centre, one can expect that such a sufficiently high depth of modulation of the ií neutrino flux as m ?& o.3 can be achieved only for 1 s 1, i.e. for a dipole mode* As follows from our analysis, the solar neutrino light curve supposedly consists of two components, therefore one can suppose the core to oscillate in two neighbouring dipole g-modes. Another important feature of our model is that, in case of small oscillations, the modulating process occurs only as a second-order effect. So, if we define | A t +AzsLno)2t, (5) then the neutrino flux, as well as the energy generation, may be brought into the form, correct to second order in small quantities,

2 2 1 Qre where oi^,c/2 •> and interference amplitudes. There are three quasi-biennial periodicities in the upper form, which have to be separated by our superposed epoch analysis. However, if we compare our period of 25.5 montas with the diagonal frequency 2c»), and that of 20 months with the interference frequency eJf + 0d2 » then the second diagonal term with the frequency 2 a)2 can be easily suppressed by the condition lcí2l/lo(f| ^ o.5, the interference term being also diminished to some extent. One possible solution for periods - 279 -

~~for période satisfying our empirical results ia as follows: y~~

fi,"Zii/fu)^)~ 25 months(2.08 yr), n2 = 2íí/2«)1= 20.6 months (1.72 yr), j : PÍ3 = 27f,/?uX,= 18.2 months (1,52 yr), and l~l5 = 2 í(/(M{-a)2)= 133«8 months (11,15 yr). There is the fourth quasi-biennial period + ri/4 ^A7f/(3d>1 íú2)" 19.5 months (1.63 yr) in the lower form of (6) that can be regarded as the "carrier" one for the modulating period f~L = =11.5 yr. The beat period can not be separated by a superposed epoch analysis. In summary we see that the periodicity picture is far too involved for one to expect its observational manifestations to be stationary. Because the 11yr periodicity is a necessary integral part of this picture, one may infer that the objection against the presence of quasi-bienniel modulation in manifestations of solar activity including the neutrino flux change should be regarded as non-essential. The large modulation depth obtained above suggests that oscilla- -j tions in question fail to be small and are nonlinear. One important I nonlinear effect involves the appearence of radial and qudrupole thermal pulsations of the solar core in doubled friequencies. These pulsations seem to cause parametric resonance which drive the mantle g- mode oscillations due to proper modulating the gravity in the mantle. Following /12/ we can suggest the g-mode with 11=2(15 — 22 yr is also exited by this mechanism. As a result, the Sun will be forced to pulsate in the first thermal overtone, i.e. to contract when the 11 yr surface activity is growing in accordance with the inverse cor- > relation of Rg and mean sunspot number /19/« In thia way all the features of a correlation between the neutrino flux and surface rsanifes- tationa of solar activity could be accounted for. Indeed, because the neutrino flux maximum ia to be reached at the maximal | while the ;, maximi-im of hydromagnetic disturbances seems to be reached at the maximal 5 , neutrino flux changes aeem to be shifted by ff/2 in comparison with that of solar activity indexes. So, the inverse correlation of the neutrino flux and the sunspot number may be expected in accordance with /11/. A lag time of 0.5 • 1.0 discovered in /11/ could be accounted in the same manner because it corresponds to the quasi- biennial 5T/2 phase shift.

In conclusion our model of solar neutrino activity is to indicate the direction in which the theory of solar phenomena has to be developed. In light of that one needs pay a great attention to all observa- tionul aspects of solar neutrino flux changes. - 280 -

It is a pleasure to thank G.T.Zatsepin , A.A.Pomansky and O.G. Ryazhskaya for fruitfuil di.«»c»RBiona . Thanks also are due to R.Davis Or. and B.Cleveland for making available their unpublished data. References 1. G.T.Zatsepin, Int.Conf.on Cosmic Rays, Jaipur, 1963, £,150. 2. G.T.Zatsepin and V.A.Kuzmin, Vestnik AN SSSR N2,5O,(1964) 3. W.R.Sheldon, Nature 221,65o(1969) 4. A.M.Aurela, XV Int.Conf.on Coséic Rays, Plovdiv, 1977, 6_, 215 5. R.Davis Jr and J.C.Evans, Jr., BNL Report N BHL 22920 6. R.Ehrlich, AIP Conf.Proc.N52,129(1979) 7. K.Sakurai, Nature 278,146(1979); Publ.Astrin.Soc.Japan J2.547 ( 1980); Solar Phys.^,35(i981) 8. A.Subramanian, Curr.Sci.48,7o5(1979) 9. L.J.Lanzerott and R.S.Raghavan, Nature 222,122(1981) "J 10. V.N.Gavrin, Yu.S.Kopysov and N.T.Makeev, Zh.Eksp. Teor.Fiz., ] Pis'ma (JETP Lett.)35,491(1982) • 11. G.A.Bazilevskaya, Yu.I.Stozhkov, and T.N.Charakhchyan, Zh.Eksp. Teor.Piz., Pis'ma (JBTP Lett.)_2S,273( 1982)

12. Yu.S.Kopysov, Zh.Eksp.Teor.Fiz.» Pis'ma (JETP Lett.)<3_4.,289 ?-- (1981); Report at the Session of Nuclear Ibysics Department of the : Ac.oi Sei.of USSR, Moscow Physical Engineering Institute, Pebfuary |. 1-4, Moscow ,1962. 13« R.Davis, Jr., 1981, private communication f\ 14. Yu.R.Rivin and T.I.Zvereva, Thesises of Reports at II All-Union f Congress "The Constant Geomagnetic Field Magnetism of Rocks, and ['. Palaeomagnetism" pt.1,19,Tbilisi, 1981. \ •: 15« B.A.Sleptsov-Shevlevich, Proc.Int.of the Arctic and Antarctic 340, 150 (1977) 16. Yu.S.Kopysov, Institute for Nuclear Res.Preprint, P-0041, Uoa- COW(1976) 17. G.T.Zatsepin, E.A.Gavryseva and Yu.S.Kopysov Doklady AN SSSR 221,1342(1980) ; Krqtkie Soobsheni,ya po Pizike, N 10,46 (1981); Solar Phys.to be published 18. E.A.Gavryuaeva and Yu.S.Kopysov, Astronomicheskiy Zhurn.^8, 610(1981) 19.R.L.Gilliland, Ap.J.248.1144(1981). - 281 -

Fig.1 (upper) Superposed epoch plot of the -^Ar production rate in the Brookhaven chlorine detector with a folding period of 1.65 yr. The numerals near each point mark the number of a corresponding measurement run. The vertical lines fence round those over which ^Ar counting rates are averaged, the averaged counting rates shown by the circled points.

Fig.2.(lower) Student criterion t against the Folding period fl which is used to subdivide the whole time interval of the Brook haven data and to superpose the results. Each point corresponds to individual subdivision and 1.65yr subsequent superposition. Pase (yr) of 1.65 yr period

~~t.s 2.0 3.0 Period, fliyr) - 282 -~~

~~ASTROPHYSICAL CONSTRAINTS ON LIGHT PSEUDOSCALAR PARTICLES~~

~~M. Voshimura~~

~~National Laboratory for HJ jh Energy Physics (KEK) Tsukuba, Japan~~

~~Abstract A brief review is given concerning recent works on astrophysical constraints of light pseudoscalar particles postulated in various gauge theories.~~

Weakly interacting particles are very difficult to observe. Familiar examples are neutrino and graviton. It took about twenty years to detect the neutrino after Pauli's hypothesis, and we still do not know existence of the gravitational quantum. Here I wish to discuss what happens if a new, yet unobserved particle has a coupling to matter with an intermediate weakness. At present it is hopeless to detect this kind of particles in laboratory experiments. The best place to search for its trace of existence is in stars. Since neutrino plays essential roles in advanced stages of stellar evolution, one can expect that at least some limit is obtained for coupling strength of a new weakly interacting particle. Indeed, a stringent limit is found by considering energy loss rates due to this particle even in stars such as the sun and red giants. In modern gauge theories various kinds of new particles have been postulated. Some of them have common features relevant to the following discussion: they are pseudoscalar particles coupling to matter rather weakly (strength < /ST. mass of matter field), and very light (mass < lOOeV). I shall mention two examples of this class of particles: DFS 2) 3) axion and Majoron . Astrophysical constraint in the following is sensitive to two coupling constants of this - 283 -

~~pseudoscalar particle U;~~

~~igufTV.U . <„~~

g..f is a y- coupling to a fermion field f and Cj. an induced (dimensionless) coupling of UYY. We shall assume that U is stable in time scale of stellar evolution, which is indeed true in cases of our interest. Light pseudoscalar particles of this kind are difficult to observe, but they may affect stellar evolution drastically. The point is that once they are emitted in the stellar heat bath, they readily escape the star and deplete stellar energy. Typically, their mean free path 9. is much larger than a size of star. For instance, JtMon )~1'^1014Km* (104gcm~3/P) • (eV/m.) 2- (108K/T) 2, e A for the DFS axion of mass nu. If this energy loss exceeds the nuclear energy generation, time scale of the stellar evolution would be accelerated and we may find conflict with observation. Basic, microscopic processes of U emission in stars are Compton-like process, Primakoff process from electrons, annihilation (e~+e+ •* U+Y) , and plasma decay, Y J^U+Y. These processes have different temperature dependences, hence they may contribute «significantly in different stages of stars. Very roughly, if stars are not in a degenerate state, temperature dependences of the energy loss rates per unit mass are as followsr-^T for the Compton-like, VT ï.n T for the Primakoff, and %T exp(-2m /T) for the annihilation process. Assuming that the two couplings, g„ and Cy , are of comparable size, we get the following, qualitative picture: for main sequence stars (T-vlO K) the Primakoff process is most important, while the Compton-like process is significant for red giants (T^IO K). The annihilation process becomes important only at T>10 K, and the plasma decay is always negligible. We note that plasma effects are important in two respects. One effect is a cut off in the momentum transfer in the Primakoff process, namely the factor S.n(T/u)n), because even in the sun the plasmon mass uo>>mass of Ü. The other appears in energy loss of cooling - 284 -

white dwarfs since u/j/kBT=5-20 in this case. We have considered energy losses in three kinds of stars: the sun (a main sequence star), red giants burning helium and cooling white dwarfs. These give more or less similar bounds except a model-dependent, more restrictive bound in red giants. Types of energy sources in these three cases are quite different: pp chain in the sun, 3a reaction in red giants and gravitational contraction in cooling white dwarfs. We shall first discuss bounds in each case separately. The bounds are expressed in terms of inequalities of coupling = 11 11 constants; 911 9Ve^0 and c^ (I) The sun. It emits radiation at the rate of L@=;3.9xlO erg sec" . If the energy loss due to U emission exceeds this luminosity, evolution of the sun would grossly deviate from our present understanding. By demanding that

~~f11® dm ey(T, p) < L© , we find that~~

~~0.028 g^x + 13 c^ < 2.0 . (1)~~

cri(T, p) is the total energy loss rate by U, and we used 4) numerical data of temperature and density as functions of the solar mass variable m(r). A similar bound is obtained by comparing the energy loss at the center of the sun (T^1.5xlO K) with a nuclear energy generation of % Although MQ/TÜ^O. 2, the plasma effect reduces the integral of the Frimakoff process by a factor ^2.5. Since in derivation of the above constraint we used the temperature and density, not observable directly, you might attempt to reconstruct a model of the sun by increasing the temperature to compensate the energy loss. But, this is impossible because the temperature dependence of the enrgy loss

p howevor increases the neutrino flux from U by d factor } compared with the standard estimate, which worsens the solar neutrino problem. (II) Rod giants. A better bound is derived from red giants that burn helium at the core. According to evolutionary calculations a typical set of parameters for a light red giant are as a 4—3 follows: T=l*10 K, [>=J 0 gem and the nuclear energy r = 2 —1 — 1 generation -N 10 erg g sec . By demanding that c^'t' , we find that

2 2 0.96 q iy + 11 c^ - 10~ This bound depends critically on models of stellar evolution which give the temperature and density of a helium burning core. In fact, the energy generation rate of the 3d reaction 40 is very sensitive to temperature, " T in the vicinity of o T=10 K. This makes it possible to compensate the energy loss with a slight increase of temperature. A useful constraint is derived from an evolutionary argument of the globular clusters such as M3. In the Hertzsprung-Russell diagiram of the globular clusters the blue horizontal branch is ascribed to stable helium burning stars after the helium flash . In such stars energy liberation is quite slow and stars are considered to be very old. If the bound, 0.96 g^ + 11 c^ < 2.1 , (2) is violated, the nuclear energy generation should be more than a hundred times larger and the time scale of evolution would become shorter by this factor. This would significantly modify the distribution of stars in the horizontal branch in conflict with obervation.

(Ill) White dwarfs. At an advanced stage of evolution the neutrino energy loss affects the time scale of gravitational contraction in cooling white dwarfs, and the additional source of the energy loss would accelerate the evolution. Some time ago - 286 -

Stothers concluded, from an analysis of the luminosity functions for blue subluminous white dwarfs of the Hyades, that the agreement with observation would be destroyed if the neutrino cooling is a hundred times stronger that that predicted by the charged current weak interaction. We may use this result to give a bound for the energy loss due to U. The relevant neutrino energy loss is due to the plasma decay into a vv pair and its rate is 5x10 erg g sec for a star with luminosity of 10~ * Lp. By taking the allowance factor of 100, we obtain a bound, 1.5 g^ + 4.0 c^ < 5.5 . (3)

~~Here plasma effects are important.~~

~~This summarizes our main consideration of astrophysics 1 constraints. The three inequalities (l)-(3) give bounds on respective coupling strength,~~

11 11 g_^U.e < lxlO" , cUYM Y < 0.4X10" . These bounds lie between the weak (/GT m %2»10~ ) and the -23 e gravitational coupling (/6~ m %4«10 ). In special cases such as the DFS axion and the Majoron there is a relation between these two couplings. For the DFS axion the bound reads m.4xlO GeV.

For the GR Majoron the triplet vacuum expectation value vT of lepton number nonconserva tion is bounded by v^ôOOkeV. We thus see that the stellar evolution is sensitive to a possible existence of pseudoscalar particles.

~~References . 1. M. Fukugita, S. Watamura and M. Yoshimura, KEK preprints, TH40, 41 (1982), and references therein. 2. M. Dine, W. Fischler and M. Srednicki, Phys. Lett. 104B (1981) 199.~~

~~t-U.; - 287 -~~

3. Y. Chikashige, R.N. Mohapatra and R.D. Peccei, Phys. Lett. 98B (1981) 265. G.B. Gelmini and M. Roncadelli, Phys. Lett. 99BU981) 411. 4. 0. Clayton, Principles of Stellar Evolution and Nucleosynthesis, Mcgraw Hill, New York, 1968. 5. B. Paczynski, Acta Astron. 20 (1970) 47. 6. P. Démarque and J.G. Mengel, Astrophys. J. 164 (1971) 469. 7. R.B. Stothers, Phys. Rev. Lett. 24 (1970) 538. - 288 -

~~MUON STRING RESULTS AND DUMAND STATUS~~

~~F. A. Harris, P. Corham, Y. Kawnshlma, J. G. Learned, D. J. O'Connor, V. Z. Peterson, V. J. Stenger, and A. Roberts~~

~~Hawaii DUMAND Center and Institute for Cosmic Ray Research, Tokyo~~

~~Presented by F. A. Harris~~

Abstract The M-.ion String, composed of five 13" phototubes spaced 5 m apart, was designed to measure the muon Intensity and angular distribution versus depth 1 i the ocean, where the overburden can be well determined» Af tjr successful Initial tests In pressure tanks and In the ocean, the Muon String was lost at sea at the DUMAND site before any significant muon data was obtained. The three year DU- MAND feasibility study is nearly complete, and an International collaboration has formed, which proposes to place an array of 756 phototubes, occupying a volume of 1/2x1/4x1/4 km3, in the ocean off of Hawaii at a depth of 4.7 Ian. While the primary objective will be neutrino astronomy, the array will also make significant contributions to cosmic ray physics, high energy neutrino physics, and ocean science.

~~I. Introduction~~

The DUMAND (Deep Underwater Muon and Neutrino Detector) Feasibility Study la In the middle of the third year. Activities have included site measurements, as well as studies of detector, array, and fiber optic cable design; signal processing techniques; deployment concepts; and scientific capabilities. I wish to describe here the present status of DUMAND, Including the results of the Muon String Test.

~~II. Muon String Test~~

The Muon String Test was originally proposed as a way for the DUMAND physicists to gain ocean experience,' while doing useful muon physics.' This experiment, which was really separate from DUMAND, was designed to measure the muon Intensity and angular distribution versus depth in the ocean, where It Is possible to determine the overburden precisely, yielding Improved muon depth- Intensity curves. Physicists Involved in this test were from the Universities of Hawaii, Wisconsin, and California at Irvine; the Marine Physical Laborato- ry of Scrlpps In San Diego; and the Institute for Cosmic Ray Research, Tokyo.2 The Muon String consisted of five 13" EMI phototubes, enclosed in pressure tolerant 17" Benthos spheres, spaced 5 meters apart, as shown in Fig. 1. Muons are detected by means of Cerenkov light. As determined from DUMAND feasibility measurements, the deep ocean off of the Hawaiian Islands Is extremely clear ( A «• 30 m in the blue-green wavelength region)3"1*, and a Monte Carlo program estimates the effective cross section of the Muon String to bo approximately 700 m*. While OUMAND expects to use fiber optic cables for signal transmission, cables of the necessary type are not yet available commercially, forcing the use of standard océanographie cable for signal and power transmission for the Muon String. In order to use conventional High Energy Physl.cs electronics, It vas ni'c<"«.iry to place the electronic!! package In tlir» ocean near the phototube r.. Th«? electronics pressure lion s IHR was hullt by mounting three 11" radius alu-ilniim hemispherical nheltn on p.ic.h side of a V thick aluminum plate, wlilrti v.f. r-.irhfned flt the University of Wisconsin. Conventional CAMAC crates wpr<> n'iiiiit'vi In two nf the spheres, and the power supply occupied the thtrd one. A smart CAMAC ernte controller, an Interface Standards IS11, containing an t.SI 11/02 microprocessor, wan used. The electronics Is shown In Fig. 2. Most CAflAC nodules (tflscrlmln.itors, coincidenc e units, etc.) were proRramm- able, allowing them to be Bet remotely, along with the phototube hlRh voltage. Data wars communicated to a microprocessor on the surface using a Computrol Me — paltnk ( 1 Hegithiiuct) DMA modem. The "downstairs" program was downloaded from thr computer at the surface, and It was posstble to make program changes even while at sea. The smart crate controller continuously monitored sealer rates .in' sensor values. Quantities checked with sensors were phototube high voltages, CAMAC supply voltages, temperature, pressure, and orientation. LED's and radioactive sources In each of the Benthos spheres allowed calibration of th" phototubes. The first tests were conducted In pressure tanks at the Pearl Harbor Naval Shipyard. On Nov 2, 1981, the empty Benthos spheres and the electronics park age were tested to 3000 pal. On Nov 10, the entire system was tested to !D00 pnt, and signal transmission and computei communications were successfully carried out. The first ocean deployment of the empty modules was achieved on Nov 30 to a depth of 1 km. On Dec 18-19, the Huon String with three 13" and two 8" tubes was deployed 10 miles off the leeward side of Oahu to a depth of 0.8 km, using the University of Hawaii research vessel, the Kana Keoki. One of the Benthos spheres containing an 8" tube leaked a small amount of water and failed to work properly. Rates, both singles and fourfold coincidence rates, were obtained, and a muon signal of 3 hz was seen above background d-.irlnj» some runs. Timing and pulse height Information for the Indivi- dual tubes was not obtained during this test. Thn final deployment took place from the USN De Stelguer at the actual proposed DUMAND site off of the leeward side of the Big Island of Hawaii during the period of March 1-10, 1982. The string was lowered to a depth of 1.5 km, and we were In tîie process of plateaulnf» phototube high voltages. High singles rates were obtained, around 3 x 10s hz with the tube sensitive to 1 photoelectron, so It was decided to lower the array to 2.5 km, hopefully below tho level of bioluminescence. Unfortunately, during the lowering, the package .it Hie end of the cable was lost, before obtaining the desired extensive muon slat («-.tics. A double 1/2" steel cable, which connected the electronics pack- ago to the océanographie cable and was designed to carry 20 times the static weight of the Muon String, broke, presumably because of excessive dynamic fort-PS. The cause for the breakage Is still under Investigation. Although the Instrumentation package worked well, a simple mechanical connection failed. This provided a valuable, although expensive, lesson to the experlmen- tors Involved. Analysis Is currently In progress to track muons on the runs tb.it were obtained. The singles rates at 0.8 and 1.5 km are greater than expected from K1'" alone and are possibly due to bioluminescence. The submersi- ble ATJVTN also found large btolumlnescence rates above 1.5 km. In summary, although the muon data vas lost, the electronics package ( "the most sophisticated package ever deployed", according to some oceanographers), worked well, ari'l much valuable experience was gained. - 290 - t y III. DUMAND STATUS

Currently, the International DUMAND Collaboration Is preparing a proposal for the construction of DUMAND. Member groups of the collaboration are the University of Hawaii; University of Kiel; California Institute of Technology; Vanderbllt University; University of Bern; Purdue University; University of Wisconsin; Institute for Cosmic Ray Research, Tokyo; University of California, Irvine; Scrtpps Institution of Oceanography; and University of Aachen. Member groups assume major responsibilities for components of the DUMAND array. In addition, there are Associate Groups, which In- clude the University of Chicago (Astrophysics), Naval Ocean Systems Center, Naval Ocean Research and Development Activity, Naval Research Lab (Cosmic Ray Lab), Harvard Smlthsontan Center for Astrophysics (Mt. Hopkins), and Nor- thwestern University. The proposal Is presently In draft form and will be submitted to funding agencies at the end of August. A total cost of about $10M over ftve years Is estimated for the basic development, construction, and deployment of the array. Next year, activity «t the DUMAND center ( -= pre-englneerlng design) will continue at the same level while the proposal Is being considered.

~~A.) Design ?.~~

The DUMAND array will be located on the ocean bottom at a depth of 4.7 km ; approximately 25 km from Keahole point on the Island of Hawaii. Laboratory 1- space suitable for the shore end of this project Is presently available at Keahole point. The detector modules (21) would be spaced 25 m apart on vertical strings. The strings are arranged Into a 6 x 6 square array with 50 m spacing between strings,'gtvtng a total of 756 detectors. The volume of water y enclosed Is S.lxlO7 m . The effective volume for 2 TeV neutrinos Interacting \, either Inside the array or In the surrounding water and producing a muon that reaches the array Is 2.5 x 108 m3, equivalent to a detector mass of 250 mega- tons. A Monte Carlo program,6 which was written to Investigate the resolution of this array, predicts a muon energy resolution using dE/dx of 50% for muons above 1 TeV and a muon angle resolution between 15 and 45 mr, depending on the '-, track dlrectton and length. For events occurring Inside the array, the energy . resolution of hadron cascades above 0.5 TeV Is also about 502. However, little directional Information Is available until very high hadron energies are reached. The detector modules would consist of 13" EMI or 16" Hamamatsu phototubes enclosed in 17" Benthos spheres. Simple electronics In the sphere would gen- f erate a pulse whose length would correspond to time over threshold. This pulse would be transmitted to the string bottom module over an optical flbei (one per sphere). Power would be distributed from the string bottom module along a single power cable to all the spheres along the strtng. A microprocessor In each detector module would communicate with the outside world along the pow&r cable and would carry out simple control functions, such as control- ling the phototube high voltage and discriminator threshold. A Signal Processing Workshop was held In March 1982. The use of fiber optic cables (one per string) was assumed for data transmission to shore. Pulses from each detector nodule would be digitized (time and pulse height) and multiplexed onto the fiber opttc cable by the strtng bottom module each 13 Msec period, filling the available bandwidth of 44 Mbaud per fiber - a commer- cial standard for which standard components are available. Digitizing Is done In the strtng processor to avoid sending fast clock pulses to each photodetec- tor module. If more than one signal was detected during this period, then el- - 291 -

ther the bif>>:est signal or the signal (If any) that was time coincident with the htrtns; modulo above or below It would be sent. The latter scheme was proposed by Charles Roos (and promptly dubbed Charley's ruse) and allows one to ptc'K out one photoelectron pulses associated with muons In the midst of a lArgu K.''° background. The bandwidth available will accommodate all noise court« up to a 77 Khz rate, which Is approximately the expected rate due to Ku0 decays In the ocean and Implies that essentially «11 pulses that may contain useful Information can be transmitted to shors where the neutrino events can be extracted from the background. A new Idea concerning deployment advanced at the Signal Processing Work- shop7 Is to use a phased deployment scheme, where first a single string Is deployed and tested, then a plane of strings ts deployed and tested, and then additional planes are deployed until all 3lx planes are In place. Each plane Is Independent and has a separate cabl« to shore. This allows modification to be trade to planes deployed later based upon the experience gained from earlier ones, allows the use of a smaller and less expensive ship for the deployment of the various phases, and allows for the possible recovery of Individual plane« from ehe ocean floor, If necessary. However, entanglement of strings becomes a potential problem, unless the strings aren't released until deployment Is finished, which removes one of the main attractions. It will be necessary to have this scheme examined carefully by the ocean engineers. On shore, a set of parallel processors would use simple algorithms, such as testing to see If the phototube times are consistent with causality, to extract possible neutrino and muon events from the data stream (1.6 gigabits per second). Possible events would then be handed over to a standard computer, with the capabilities of à VAX, for further analysis and possibly be written to tape. Simple causality algorithms have been shown to reduce the number of events for further consideration by a factor of 10*.ö The processors could be built from 6tate of the art electronics, and the consensus of those üt the Signal Processing Workshop was that the data rate could be adequately handled.

~~B.) Scientific Objectives.~~

The scientific objectives of DUMAND are (1) high energy neutrino astronomy, (2) cosmic ray physics, (3) high energy neutrino physics, and (4) ocean science and geophysics. Neutrinos; may be produced either atmospherically by cosmic rays or extraterrestrlally. The expected rates versus energy for the former using an energy dependent volume for the DUMAND detector are shown In Fig. 3. Thousands of events per year are expected above a neutrino energy of 1 TeV, which Is orders of magnitude greater than the rates expected for the Case Wlttwatersrand Irvine (CWI)9 underground detector and the Irvine Michigan lirookhaven (1MB)10 proton decay detector. The DUMAND detector will be the only significant source of TeV neutrino events In the forseeable future. The expected event rate for extraterrestrial neutrinos Is much less certain because of the uncertainties In astrophyslcal calculations. We have calculated for DUMAND the Minimum Detectable Flux (MDF), which Is basically the flux which would give 10 sevente per year when the background Is negligible In the angular region of the sky being considered, which Is usually the case for point sources. When the background Is more than one event per year, as It Is when one Is looking at more diffuse sources, then a 5 o effect Is required. The UDF for neutrinos above 1 TeV ts 2xl0~1'' cm~2s~1. This Is again orders of magnitude more sensitive than what can be accomplished In mines. With this sensitivity, DUMAND should be able to detect supernovae in our local cluster of galaxies out to M31, active galaxies like Centaurus A (if powered by black holes)11, and other sources like SS433.12 - 292 -

Some experimental Indication of the flux of hlfth energy neutrinos expected Is obtained from observation« of high energy gamma rays using the atmospheric Chorcnkov technique,1* assuming that neutrinos will be producer! with similar fluxes at these energies» Several sources of TeV gamma rays have been seen, but the brightest TeV source seems to be Cygnus X-3. The flux of gamma rays Is measured In the range of 10~10 cn"2s"' above 1 TeV, within the range of sensitivity of D1IMAND. DUMAND as a neutrino telescope would be romp.-ir.ihlf> to Y detectors In sensitivity. DUMAND will also have a significant capability to do cosmic ray physlr-.s. It will extend the measurements of the non energy spectrum up to 100 TeV, allow the study of direct nuon production up to 2000 TeV, and study thr spectrum and composition of primary cosmic rays up 3000 TeV. There will be about 600 v charged current Interactions above 1 TeV per year occurring Inside the DUHAND array. Although this Is a relatively small number of events, this will be the only source of TeV neutrino events for somr time to come. DUMAND would also be sensitive to neutrino oscillations, by using the variation In atmospheric neutrino path length through the earth.'u

~~IV. )Summary~~

The three year feasibility study has shown DUMAND to be quite feasible - technically, scientifically, and economically; and a proposal by an Interna- tional collaboration to place an array of 756 detectors In the ocean Is nearly complete. The array will make significant contributions to neutrino astronomy, cosmic ray physics, high energy neutrino physics, and ocean science.

References 1. G. Blackinton et al., Proceedlns of the 1981 International Conferenc.p on Neutrino Physics and Astrophysics, Vol. II, p. 246 (1981). 2. People partlctpatln In the Muon strln test were G. Blacklnton, H. Bradner, P. Gorham, F. A. Harris, Y. Kawashlma, J. G. Learned, R. March, R. Mlti- guy, D. J. O'Connor, V. Z. Peterson, F. Reines, J. Richardson, R. Svohoda, V. J. Stenger, H. Yee, and P. Yuen. 3. J. R. V. Zaneveld, Proceedings of the 1980 International DUMAND Symposium, Hawaii DUMAND Center, Vol. 1, p. 1 (198J). 4. H. Pradner and G. Blacklnton, lhld, p. 9. 5. J. R. Lossee, Proceedings of the 1982 DUMAND Signal Processing Workshop, Hawaii DUMAND Center, Vol. I,p.l9 (1982). 6. V. J. Stenger, Proceedings of the 1980 International DUMAND Symposium, Hawaii DUMAND Center, Vol. 1, p. 126 (1980). 7. J. G. Learned, Proceedings of the 1982 Signal Processing Workshop, Hawaii DUMAND Center, p. 185 (1982). 8. A. Roberts, tbld, p. 77 (1982). 9. F. Reines et al., Phys. Rev. D4_,3 (1971). 10. W. Gajewskt et al., Proceedings of the 1981 International Conference on Neutrino Physics and Astrophysics, J^,2O5 (1981). 11. R. Sllbarberg and M. Shapiro, Proceedings of the 11178 DUMAND Summer Work- shop, Hawaii DUMAND Center, Vol. 2, p. 237 O978); Proceedings of the 1979 DUMAND Summer Workshop, p. 262 (1979), V.S. Berezlnsky, V.L. Glnzburg, tton. Not. R. Astro. Soc., 194,3(1981). 12. D. Elchler, Proceedings of the 1980 International DUMAND Symposium, Vol. 2, p. 266 (1980). 13. K.E. Turver, T.C. Weekes, Phil. Trans. R. Soc. Lond. A301_, 493 (1981). Re- view. See references therein. 14. R. J. Oakes, presented at this conference. - 293 -

~~POWER & SIGNAL CABLE «TO SHIP)~~

~~ELECTRONICS PACKAGE~~

~~5 OETECTOR MODULES~~

~~LIGHT PULSER~~

~~ANCHOR~~

~~Fig. 1 Muon String - 294 -~~

~~MUON STRING~~

~~POWER a DATA ON COAX 1-9 km OPERATING DEPTH~~

~~1 "CAMAC" BASED PROGRAMMABLE~~

~~LIGHT SENSOR (I3"pmtt)~~

~~FLIGHT PULSER~~

~~Fig. 2 Electronics and Computer System for tho Muon String. - 295 -~~

~~ATM. V.~~

~~I 10 I (TeV)~~

~~Pig. 3 Predicted v charged current event rates for the DUMAND array and other experiments. - 296 -~~

ADVANCES IN THE DEEP UNDERWATER MUON AND NEUTRINO EXPERIMENT ON THE LAKE BAIKAL Moscow-Irkutsk-Tomsk Collaboration L.B.Bezrukov, G.V.Domogateky, A. M. Klabukov, L.N.Stepanov Institute for Nuolear Research, Academy of Sciences of the USSR, Moscow N.H.Budnev, N.P.Butin, V.I.Dobrynin, G.A.Kushnarenko, M.I.Nemchenko, S.A.Nikiforov, Yu.V.Parfenov, V.A.Polischuk, A.A.Schestakov, B.A.Taraschansky, V.L.Zurbanov Irkutsk State University, Irkutsk A.A.Badardinov, E.B.Karabanov, V.A.Fialkov, P.P.Scherstjankin Liinnological Institute, Siberian Department of the USSR Academy of Sciences, Irkutsk Ii. A. Kuzini chev Moscow State University, Moscow G.N.Dudkin Tomsk Polytechnical Institute, Tomsk

~~Presented by G.V.Doraogatsky~~

~~Present status of work on deep underwater detection of muons and neutrinos on the lake Baikal is reported. Preliminary results of site studies and apparatus tests are discussed..~~

The work to build the deep underwater muon and neutrino detector on the Lake Baikal was begun by Moscow-Irkutsk-Tomsk collaboration in October 1930. We intend as the first step to build not so large arrays (the volume ~10V) with <~10^ optical sensors /1/. These arrays can be considered as prototypes of future large ocean detectors. Besides that, some problems of cosmic ray physics can be investigated by using $hese arrays. The constraction of such arrays «ill give us necessary experience of deployment and operation of deep underwater detectors. Lake Baikal is the unique place for carrying out such program. Here we have a large depth near the shore (a depth of ~ 1300m at the distance of ~ 3km from the shore),, high transparency of water, strong ice during two months, lack of intensive underwater currents, lack of bioluminescence and very low level - 297 -

of background from radioaotive 40K-deoays. The strong ioe cover of the Lake Baikal in a winter time give us a great adrantages as compared with ocean for deployment of arrays. At present the deep underwater optical module /2,3,4/ on the base of photomultiplier $37-436 are designed and tested. The measured sensitivity of this module to Cerenkov light from muon Is: 10 photoelectrons at the distanoe from muon trajectory

~~R = 1m (Pig.1), 1 photoeleotron at R » 5m /5t6/.~~

~~swivei~~

~~pßexigiass~~

Flg.1. Optical module fofgr Pig.2. Apparatus for investiga- .deep underwater Cerenkov tion of temporal variation light detection. of water transparency and longterm influence of Lake Baikal environment on transparency of module window, 1,2,3 - Light diodes. The measurements of natural light intensity as a funotion of depth were performed by using this module/7/. This funotion can - 298 -

be approximated for a depth of 3OO-4OOm by «xp(-h/h0) with h =22m. The light absorption length 1(A) at the wavelength at which 1(X) has a maximura is conneoted with h0 for the Lake Baikal as follows: ljn£Ä % ho/0.8 = 27.7m. Module doesn't detect the solar light below the depth of ~ 800m. We searched the biolumineaoence in the Lake Baikal by using our optical module /S/. The bioluminesoenoe with the duratin of flash more than 100yusec wasn't observed.

~~£ winches shore station ice cover ("im)~~

~~,-7»~~

~~Pig.3. Deployment of apparatus for longterm investigation of the Lake Baikal optical features: - - stage 1, stage 2, stage 3.~~

The apparatus for investigatin of temporal variations of water transparency and longterm influence of Lake Baikal environment on transparency of module window was designed (Pig.2) and placed at the depth of 1280m at the distance of 2200m from the shore during this winter (Pig.3) /9/. The information on pulse heghts from diode, flashes was transwlfted to the shore station by underwater cable. Any variations of pulse heights weren't observed (with accuracy -~ 3%) during two months. Our site studies shows that the most appropriate place for deep underwater Lake Baikal experiment is situated at about 30km - 299 -

~~to south from listvjanka village. The shore station la arranging now. At present the muon string containing 8-16 modules is under preparation.~~

References 1. L.B.Bezrukov, G.V.Domogatsky, A.E.Chudakov. Proo. of Seoond Congress of Soviet Ooeanológists, Xalta, 1982. 2. J.Learned. Froo. 1975 Summer Workshop on DU1IAND. 3. E. J.Stenglaes. Froo. 1975 Stimmer Workshop on DUMAJTD. 4. L.B.Bezrukov. Froo. 1978 Summer Workshop on DUMAND, vol.1,133. 5. L.B.Bezrukov, N.M.Budnev et al. Froo. of Seoond Congress oi Soviet Oceanologiota, Yalta, 1982. 6. L.B.Bezrukov, A.M.Klabukov, N.M.Budnev et al., ibid. 7. L.B.Bezrukov, N.M.Budnev, N.P.Butin et al., ibid.

~~3. L.B.Bezrukov, N.M.Budnev, V.I.Dobrynin et al.( ibid. 9. L.B.Bezrukov, A.M.Klabukov, L.N.Stepanov, N.M.Budnev et al.,ibid. - 300 -~~

~~STUDY OF THE EARTH STRUCTURE BY MEANS OF NEUTRINOS~~

~~I.P. Nedyalkov~~

~~Institute of Metal Science and Technology Sofia, Tchapaev Str. 53, Bulgaria~~

Abstract. The possibility of determining the density distribution of the Barth by means of the measurement of the attenuation of neutrino beams passing through It 1B discussed in the paper. The experimental arrangement consists of a few TeV accelerator as generator of the neutrino beam and of the detector DUMAND as its detector. Formulas from the computerized tomography are used for the model independent reconstruction of the Earth's density distribution.

There exists a variety of models for the distribution of the Earth's density obtained indirectly by means of interpretation of gravitational and seismological measurements, as well as of measurements of the proper frequencies of the Earth's vibrations . There are also suggestions that this problem be studied through the methods of neutrino physics I*»-*' ^-"l , Lf 2 3] The method proposed in ' is model-dependent and cannot be realized with the experimental arrangements described there. But if suitable^ technical means would be available this method would permit to eliminate wrong geophysical models for the Earth structure. Another approach is described in this paper (see alsót-4"'-' ). It consists in the measurement of the attenuations of neutrino beams passing through the Earth in different directions, and the subsequent processing of the information thus obtained by the formulas of the computerized tomography^ ' . In this way the distribution of the density D for each point in the interior of the Earth is determined without model hypotheses. This method may be essential for the Earth science. The reason is that, despite the existence of new ideas, the study of the structure of our planet is basically reduced to the solution of two equations for three unknowns, the unknowns being the principal and secondary velocities Vp> resp. 7 of seismic waves, and the density D. The lacking third equation was to be replaced by different hypotheses. Wow, the neutrino physics giving directly the value of D, not only the values of V and V but also other parameters characterizing the Earth's structure can be found with much greater reliability. We shall now proceed to determine the density distribution D, bearing in mind the central symmetry. Let us consider function D(r), - 301 -

r being the distance to the garth's oentre. The dlmensionless line integral over the density t-5' ' will be denoted by I(t), t being the distance between a neutrino beam and Earth's centre. In order to determine D(r) by means of the computerized tomography formulae» ire should know I(t) for several values of t: ti, t„, ... tn

events per second, where Û gives the direction of the neutrino quantum measured with respect to the beam's axls,v *-^/<~/t , where Rde, t. is the detector radius whose base we assume to be circular. A(©„ ) is the intensity of the attenuated beam having passed a distance £ through the Earth, and B(G) gives the part of the neutrino beam which has been recorded by the detector. In writing A(G), we use the formulas about the dependence on 6 of the energy and Intensity of a neutrino beam generated by the decay of Tï-mesons, as well as the formula about the exponential decrease of the intensity of the volume eourcee of radiation. Further on we shall use a rough mathematical model, where A(©) and B(0) are replaced by their average values A and B respectively for the interval Oííí^, where the angle f- ^v E^ ' is the mass of 7^-meson) defines the cone through which the - 3O2 -

~~half of the neutrinos of the beam passes. On these assumptions» instead of (1) we oan write (2) Nj =4 Soc~~

~~t--cts~c.~~

In the above expressions EQ = 1 TeV, D^ is the density of the detector's sensitive substance and H. ^ - its height,ot = v y' ; /-•/ if y>i , and oC = 0.5,/ = 1B2 if f'< V . The coefficient 0.48X1O"11 is obtained on the assumption that CT^ O.8Oxlo'5B SQ"1 The exponent in A being a small number, we represent N^" by the first two terms of its power series expansion in respect to I. (3) K'a0~^

~~In order to obtain I(t), and consequently also D(r) with a~~

~~relative error CÇ , it is necessary to measure WJ and Rv with a -1 relative error~~

~~(4) . ., ;., J .. T ,, T-il-. scT* o; (,, // [?**>£ >~~

Formula (4) is deduced on the assumption that H, + = 1 km, R, = 0.5 km, D. . »1 g.an ^ï , < p= R and that the lengtCIO Vh of the de +t dex decay tunnel is L = 1.5 km. The neutrinoB are supposed to be gene- f rated by VT _mesons with energy EL,. Ï-0.5E and intensity lLt =

At E = 1 TeV, <^= 3% and if the neutrino beam goes through the Earth1a centre in which case I = 1.6, from (4) one finds T = 4,3 years. Tf the error of the measurement of the attenuation is increased to <5: - i%, then T = 2,4 yeara. This would be a possible realization of the idea of^*' for eliminating wrong models of the Earth's structure.

~~At Bp = 3 TeV and <3T= 1* for the average value 1*1, (4) gives T = \92 years. If a central symmetry of D Is supposed, then - 303 -~~

the function D(r) could be reconstructed with a relative accuracy of 2,4# provided that measurements of the attenuation of the beam in 7 directions be made . So for the model-independent determination of D by means of the methods of computerized tomography, cantral symmetry supposed, a total exposure time of 8,4 years Is needed. At E = 20 TeV, 1 = 1, £Ç= 1# the exposure time is much smaller - T s 0.13 years. Suitable mathematical treatment permits the determination of D for a reasonable total time of measurements in a model independent way even without the hypotheeis for central symmetry. î"or all three cases the neutrino flux must be measured with very high precision. A proposition for a system assuring such high precision measurements is given in^ •• and . The experiment could be so arranged that, as a byproduct to the study of the Sarth's structure, information on the following problems could be obtained: 1. Oscillations of neutrino; 2. Determination of the neutrino-nucleon cross-section at higher energies; 3. Determination of the masses of W- and Z-bosons; 4. Determination of the lifetime of the K- and TiT-mesons. It is also possible the investigation of the above four problems tc be carried out independently from the geophysical experiment. In this case the experimental arrangement will be best protected from the background if the neutrino detector would be placed in a mountain.

References 1. Bullen K.B. The Earth's Density. Chapman and Hall, London, 1975 2. Placci A,, Zavattini E. A CSRN note, Geneva, 9 Oct. 1973 3. Volkova L.V., Zatsepin G.T. Izv.Akad.Nauk SSSR, ser. Fiz., 1974, J8 (5), p.1060. 4. Nedyalkov I.P. Compt.rend.Acad.bulg.Sei., 1980, U, No 12 5. Id. ibid., 1981, 14, No 2. 6. Id. ibid., 1981, 14, wo 3. 7. Id. Ibid., 1981, 14, Wo 4- 8. Nedyalkov I.P. Preprint JINR, P 18-81-189. Dubna, 1981 9. Id. ibid., P 18-81-645 10. Cormack A.M. J.Appl.Phys., 1963, M. 0) 11. Kak A.C. Proc. IKEE, 1979, 68 (9) 12. Eerezinsky V.S., G.T.Zatsepin, UïW 122, 1977, No 1. 13. Nedyalkov I.P., L.0.Nikolova, r.C.Krastev, in print. 14. Wadyalkov I.P. Comptes read.Acad.bulg.des Sei., 14, Wo 11, 1981 15. Id. ibid., 15., No 6, 1982

~~- 304 -~~

~~GUTS, ASTROPHYSICS AND SUPERUNIFICATION~~

~~John Ellis CERN, Geneva, Switzerland~~

1. - INTRODUCTION The organizers of this meeting have asked me to talk about, two subjects - on GUTs and Astrophysics, and on Superunific.ation. To further the spirit of unification I have telescoped these into one talk and will attempt to include some remarks about the implications of superunification for the applications of GUTc to cosmology. Among the "GUTs and Astrophysics" topics discussed are Bifr Bang bar-yosynthesis ' (and a possible connection to the neutron electric dipole moment via thp OCD 6 vacuum parameter) grand unified monopoles (and the possibility that they may catalyze baryon "decay" at observable rates) the new in- 7) 8) flationary universe (which may solve the horizon, flatness and monopole density problems if it can be made to work) and neutrinos (including constraints on their numbers from the late stages of stellar evolution9) as well as Big Bang nucleosynthesis ). The part on "Superunification" starts with some motivations for invoking supersyiranetry (in particular to alleviate the technical aspect of the hierarchy problem in GUTs), some remarks about the low-energy spectroscopy of theories with spontaneously broken supersymmetry ' (including the possible existence of new light neutrino-like weakly interacting neutral fermions called nuinos ) and baryon decay in supersymmetric GUTs . Finally, a section on "Supercosmology" will discuss how the standard scenario for Big Bang Baryosynthesis gets modified " in supersymmetric GUTs 22) (any connection with the neutron's electric dipole moment may be lost ), the chances for realizinß an inflationary Universe (made more difficult unless the supersymmetry breaking scale is very large), and astrophysical constraints on supersynraetric theories (especially nuinos). The final section makes a (not very) facetious suggestion for the title of the next conference in this series. - 305 -

2„ - GUTs AND ASTROPHYSICS 2,1 Update on conventional GUTs There is no need to describe again here the motivation and structure of conventional GUTs such as the SU(5) model of Georgi and 24) Glashow . However, before plunging off into the early Universe it may be helpful to start with a review of the experimental status of GUT predictions for low-energy laboratory physics. First the good news. A successful minimal GUT prediction is for the neutral weak mixing parameter

~~\\) (2.1)~~

where the computation is for the effective value of sin26„ deduced from deep inelastic neutrino-nucleon scattering at an average momentum transfer of 20 GeV2. The quoted error in (2.1) principally reflects our ignorance of the correct value of the OCD scale parameter iW, which has 281 been taken in the range of 0.1 to 0.2 GeV, in accord with suggestions from lattice QCD calculations of the hadron spectrum, and from the most recent generation of experimental measurements (deep inelastic scattering , T decay rate30 )). For comparison, the best experimental value of sin20y is, after radiative corrections have been included in the analysis of the data:

~~vv/ (2.2)~~

If there are just six quark flavours (corresponding to three neutrino flavours) one can also compute • '»33) \ ~ $ W (2.3) in accord with experiment.. Mow for the less good news. With the same assumptions that led to the successful prediction (2.3) one can also predict26)

~~~ X ^KV (2.4) - 306 -~~

Many people think this is too high a value for the short distance current >)' algebra mass of the strange quark, preferring on questionable phenomeno- 'p logical grounds a value m • 150 MeV. My feeling is that we will not £; know the strange quark mass to better than a factor of 2 or 3 until the lattice OCD calculations are sufficiently far advanced to extract a definite number for m from a fit to the mass spectrum of strange par- 26) tides. And now for the bad news. Minimal GUTs al~5O predict

(2.5) which is surely incorrect, as the right-hand side is known to be 1/200 while the left-hand side is inferred from current algebra and PCAC to be 0(1/20). This failure may reflect a need to tinker with the fermion mass speótrum at the level of a few MeV, which could be done without des- troying the previous successful GUT predictions (2.1) and (2.2). We therefore move on to the most exciting low-energy GUT predict on, that of baryon decay. The familiar diagram of Fig. 1 involving the exchange of a superheavy X or Y vector boson yields a decay amplitude « 1/m*, hence a rate a ^""v an(* a baryon lifetime <* m*. In simple X A 35) models such as minimal SU(5) and variants of S0{10), one computes

~~MS 5? and hence with A™ = 0.1 to 0.2 GeV one finds O^ (2-7) 2~~

~~Various estimates of the constant of proportionality to rojt then suggest a nucléon lifetime~~

~~One expects the nucléon to decay predominantly into first generation particles such as e + pions or v + pions. - J07 -~~

The prediction {2.8) is to be compared with the experimental limits of about 2 x 1030 years, and the exciting candidate events reported from the Kolar Gold Field (KGF). These are now six in number, three of which arc completely contained within the detector. Their appearance is consistent with the decay modes expected in conventional GUTs, but the KGF detector is not very sophisticated, and we eagerly await confirmation of their events by the more sophisticated detectors now coming into operation, 2.2 Big Bang Baryosinthesis When poets hear that baryons are now expected to die, they want to know how they were born. A prophetic paper by Sakharov 4) lays down the criteria for conception. 1) There must be interactions which violate baryon number conservation. Such interactions are clearly present in GUTs. ?) The baryon number violating interactions must distinguish between matter and antimatter. This means in particular that they must violate charge conjugation C: as C(q) = q one would have the number of quarks N = N- the number of antiquarks if C were an exact symmetry. The baryon number violating interactions must also violate CP. The parity transformation P does not change or interrelate the number of quarks and antiquarks, but the combination with C enforces K = N- as before. To tha extent that GUTs contain the weak interactions which are known to violate C and CP, we also expect GUT reactions to violate these discrete symmetries and hence fulfil Sakharov's second condition. 3) There must be a departure from thermal equilibrium. One way of.seeing this is to recall that the combination CPT of discrete symmetries is sacred in quantum field theory (here T signifies time reversal). In thermal equilibrium one loses sense of the arrow of time, so T is a good symmetry and hence by CPT so is CP. Then by the previous argument N = N- and there is no net baryon asymmetry. The breakdown of thermal equilibrium is furnished by the expansion of the Universe during which the temperature falls, GUT reactions slow down and are unable to keep up with the expansion rate.

We see that GUTs meet the Sakharov criteria for giving birth to 2) baryons. A specific mechanism generally favoured is the out-of-equilibrium decay of some species of superheavy particle, such as superheavy - 308 -

~~gauge bosons X or Higgs bosons H •* qq or qï. The sacred principle of CPT guarantees equal lifetimes for particles and their antiparticles:~~

~~but their partial decay rates can differ if C and CP are both violated:~~

If we assume that the Universe starts off with equal numbers of X and 5c particles - automatically true if they are initially in thermal equilibrium, but this :aay not be true in which case more complicated scenarios are possible - then the decays of the X and X will yield a net quark asymmetry

~~(2.11)~~

a e where NY and N f" the number densities of asymmetrically decaying bosonsi and of all available degrees of freedom. After q-q annihilation (either via mesons or via baryon-antibaryon annihilation), the ratio

~~(2.11) eventually yields the present baryon-to-photon ratio nß/n . In realistic models~~

~~(2.12) where we denote the C- and CP-violating asymmetry B-5 = e. A sample lowest order diagram contributing to e in Higgs decay is shown in Fig. 2. It yields H ~ (2.13) - 3O9 -~~

~~Indeed In many models c,. can be 0(~~

finding a non-vanishing contribution to eu which is at most of order 0(10"'5) and hence too small. One therefore needs a bigger non- minimal GUT which introduces uncertainties and ambiguities (more Higgses 7 a bigger group ? more fermions?) and hence unknown parameters. The next complication is that 2 *-*• 2 scattering interactions must be taken into account as well as decays, and these tend "J" to wash out any incipient baryon excess unless either ITL. is large enough (>, OdO1") GeV) or the X coupling constant is small enough (< 0(10"')). These two conditions are barely satisfied in the minimal GUTs which have (2.7) m- S 0(2) x x 10l* GeV and OL. • 1/42, parameters for which 2 *+ 2 washout is potantially significant. There are also potential complications due to wrinkles in the evolutionary history of the Universe. Perhaps as mentioned before the Universe was not ' in thermal equilibrium before the X and X particles started decaying? Perhaps one or more phase transitions have given the Universe a complicated thermal history? For example, as discussed later there are inflationary scenarios ' ' in which.the Universe supercools to 0(1010) GeV before the GUT symmetry is broken, and then reheats. It is then a delicate question whether the Universe reheats to a sufficiently high temperature for enough X (or H) particles to be produced for the previous baryosynthesis scenario to be valid. In fact, some authors have argued that during reheating a more-than-thermal overabundance of H (or X) particles may be produced, giving a larger baryon asymmetry than in the conventional picture. It is also possible that there may have been supercooling followed by reheating and excess entropy generation during the SU(2) x U(l) breaking phase transition which could dilute (n„/nY) below the .expectation (2.12). For these and other reasons it seems fair to say that although we now have a qualitative mechanism for baryosynthesis, we are not yet in a position to make it quantitative. - 310 -

There is, however , one CP violating particle physics observable which may give us some information about Big Bang baryosynthesis, namely the neutron electric dipole moment d . There are contributions to d n n from conventional weak perturbation theorthe y which amount to 0(10~S0±1)e-cm in the usual Kobayashi-Maskawa model 47), The CP violating 6 vacuum parameter of OCD can also contribute48)' ID

GUTs may in turn contribute to 6, for example via fermion mass renormalization due to the diagram of Fig. 5 which is closely related to that of Fig. 4 contributing to (n„/n ) and is also proportional to Im TrfabcV). In the absence of cancellations which could be enforced by'some unfriendly symmetry, we have the qualitative order-of-magnitude "lower bound"

~~which combines with Eq. (2.14) to yield~~

~~•18/<*-&., \ (2.16)~~

~~Putting in an astrophysical lower bound on (n„/n ) of about 1.5. x 10*10 we infer that 8 cL > O(3xicT* )*- (2.17)~~

~~47) which is much larger than the Kobayashi-Maskawa value and encouragingly close to the present experimental upper limit of~~

An) >50) reported * at this meeting. Two experimental groups are now trying to improve this limit. If they find a dipole moment in the near future it will signal that there is more to CP violation than just the Kobayashi- Maskawa model: will it be related to the baryon number of the Universe ? - 311 -

Among the symmetries which could suppress d are a U{1) axial asym- 51) ' 52) metry of the Peccei-Ouinn type - which may have cosroological problems - and supersymmetry - to which we return in Section 3.

~~Whenever the U(l) group of electromagnetism is included into a simple gauge group such as~~

it was pointed out by Polyakov and 't Hooft that one expects to find topologically stable magnetic monopoles. They correspond to a "hedgehog" configuration of Higgs vacuum expectation values (see Fig. 6) pointing to different orientations in group space at different directions in physical space. They are associated with different SU(2) subgroups of the GUT, for example that generated by l/2dlag(0,0,T,0) in minimal SU(5). The expected mass of the lightest monopole is

(2.20) in minimal GUTs. Grand Unified Monopoles (GUMs) are somewhat of a cosmological 53) embarrassment . They should have been formed in the early Universe as it cooled past a critical temperature T = O(tiL.) at which the temperature dependent terms in the Higgs potential finally relent and allow the Higgs fields to develop a non-zero vacuum expectation value <0|H|0> é 0 as shown in Fig. 7. The manner in which GUM production is usually envisaged ' is illustrated in Fig. 8. There are domains no larger than a Higgs correlation length where the Higgs vacuum expectation value <0|H|0> points in correlated directions. The Higgs correlation length can be no larger than the horizon size at the condensation temperature T (strictly speaking, the Higgs v.e.v. and the monopole charge only get fixed when the temperature falls slightly lower to the Ginzburg temperature T_). In general, the directions of the <0|H|0> in adjacent causally separated domains will not match up perfectly as in Fig. 8, and - 312 -

the mismatches correspond to monopole formation (cf. Fig. 6). One 53) 54) expects ' a density of monopoles nM > 0(1/10) per horizon volume. This is much larger than that permitted5 by the success of conventional Big Bang nucleosynthesis calculations:

~~or by the present mass density of the Universe if m„ > 0(10IS GeV):~~

(2.22, and calculations ' suggest that M-fi annihilation subsequent to their formation could not have reduced the monopole density to the accep- table levels (2.21) and (2.22). How can one avoid this catastrophic overproduction of monopoles? First of all it should be pointed out that the above argument is not gauge invariant, since the direction of the Higgs v.e.v. <0|H|0> can always be rotated by a gauge transformation. One would prefer a gauge invariant formulation of the domain argument. Independently of the domain argument, one might expect5' • monopoles to be generated by thermal fluctuations with a density subject to a Boltzmann suppression (X)-

However, it is. not clear that the Higgs interactions are sufficiently rapid, or the ensemble sufficiently large, for the extreme exponential suppression factor (2.23) to be operative. The safest way to avoid the overproduction of monopoles is to make the cosmic domain size much larger by arranging for a delay in monopole formation, perhaps by an epoch of exponential expansion before baryosynthesis driven by the Higgs vacuum energy V(0) in Fig. 7, which enables the <0|H|0> to be correlated over extended regions of space. We will return to this "inflationary Universe" scenario 7) '8 ) lilt)• in Section 2.4: in the meantime let us look at the phenomenology of GUMs. - 313 -

These are expected to ionize very strongly if they are relativistic, eg) and their ionisation should be detectable down to velocities v s = 0 (10~s or 10~"). The negative results of various searches tell us that the monopole flux F < O(\b h> ID" )wCV'ít«ö' ,2.2/()

~~as seen in Fig. 9. By looking for a flux jump in a superconducting coil one can be sensitive to all velocities v. A recent experiment gives an upper limit -1 (2.25)~~

and reports one candidate event. Because of the constraint (2.24) the mean velocity of the monopoles must be very low if this event is real and corresponds to flux close to the limit (2.25). There are limits on the monopole flux of

~~F< (2.26,~~

from the mass density of the Universe if the monopoles have a mass of 101' GeV and are evenly distributed throughout the Universe. On the other hand, if they are confined to the galaxy, its missing mass density restricts us to

~~3<50vr .„ „ _ (2 27)~~

How plausible is it that GUMs would be confined to the galaxy? It has been estimated that the galactic magnetic field would accelerate a GUM of mass 10" to 1017 GeV to a velocity of about 10"*, ample to eject it from the galaxy whose escape velocity is about 10~*. The galactic magnetic field would lose energy in ejecting GUMs: from the persistence of the galactic magnetic field one can infer ' an upper limit on the flux which is somewhat more stringent than (2.26) for monopoles with mass 0(10'«> GeV and v = 0(10"s to 10"2), and somewhat less stringent than (2.26) for v = OdO"1 to 1). Looking at the compilation of limits in Fig. 9« we see that astrophysics does not exclude monopole fluxes close to the present direct experimental limits. - 314 -

Recently an exciting possible5' signature of GUMs has received renewed attention ' ' namely the suggestion that GUMa may catalyze baryon "decay" at detectable rate3. It seems ' that GUMs should be surrounded by clouds of fermion pairs with ÜB i 0 and of radius O(l/m_) (~ 1 fermi for light quarks?). These ferraion condensates imply that GUMs colliding with nucléons may cause AP i 0 interactions with large cross- sections:

~~~" '- . - (2.28)~~

~~A AB i 0 cross-section would not wash out the baryons previously generated by GUTs as long as~~

~~% < OitO6) ,2.29)~~

~~and while o0 may be <1, it is unlikely to be much larger. The stability of the baryon (T„ > 3 x 10S0 years) imposes605f6A) a limit~~

~~(2-30)~~

Therefore a monopole flux close to the other experimental and astrophysical limits could give a rate of baryon "decays" detectable in forthcoming baryon decay experiments. To a neutrino physicist nucléon decays would be an unwelcome background to the search for cosmic ray neutrino events. How could one distinguish ordinary baryon decays from a backgound of "decays" catalyzed by GUMs? Clearly one would like to set up a monopole detector and a baryon decay experiment in coincidence . If oo really is 0(1), then the mean free path between "decays" could be so small that a chain of baryon "decays" might occur across the baryon decay detector. As "decay" modes one expects N •*• e+ + pions fnot v + mesons, u + strange particles suppressed by 0(m./m_)2i e + strange suppressed by Cabibbo angle factors^. Bubakov has also suggested that N •* e (u u ) •»• X might have an observable branching, ratio. It would be exciting indeed if baryon decay experiments were able to confirm the existence of GUMs as well as of baryon decays ! - 315 -

2.4 The Inflationary Universe There are several related mysteries about the scale, age and homogeneity of our Universe. Although the natural scale of gravitation is the Planck length of order 10~ cm, the Universe we now 3ee about us is very much larger. It is, of course, very much older than the Planck time: for a Universe to be old it must either be open or only very slightly closed (Í2 « 0(1)). For the Universe to be within an order of magnitude of the critical closure density as it now appears (0(1/10) < < fi < 0(10)), at earlier epochs its density can have differed from the critical one only in the umpteenth decimal place. It must have performed a very delicate balancing act to have survived to its present form. Another pu2zle is the remarkable homogeneity of the observed Universe, particularly of the microwave background radiation, over distances much larger than the horizon size at the epoch of recombination. We saw in the previous section that the low density of magnetic monopoles also presents a problem ' , which might be solved If there was a period 8) of exponential expansion before baryosynthesis . If this inflationary epoch were sufficiently prolonged, it could also solve the other problems mentioned in this paragraph.

Such an inflation could have been driven by vacuum energy. At the moment the cosmological constant is zero, or at least very small on the scale of high energy physics (its energy density A < 0(10"*7) GeV1*). Me now live in an epoch where many gauge symmetries are broken. Before they were broken when the Universe was at higher temperatures, the energy density A in the vacuum must have been positive as can be seen in Fig. 7, and the change in A can bs computed fromroicrophysJ cs :

i\ « s A ~~> • y (2.31 ? in a theory with Higgs fields H. Since the square of the expansion rate (á/a)2 is proportional to the energy density, one can expect an exponential expansion /-t - n j>ttn ( 0($f\ 14- l (2.32) - 316 -

while the vacuum energy density A is dominant. Large inflation could explain why the present Universe is very close to the critical closure density, and why it is apparently homogeneous on very large distance scales. However, this expansion should take place before baryosynthesis, otherwise the baryons generated in Section 2.2 would be drowned in entropy. On the other hand, if the GUT £SU(5)?3 symmetry is broken after the inflationary epoch, one does not solve the monopole problem because, by the very nature of spontaneous symmetry breaking, the directions which Higgses in the different domains of the Universe choose to point after inflation cannot be correlated. There is also the problem, well known to economists, of putting a graceful end to inflation.

Recently a new inflationary scenario has been proposed 7) '44 ) which avoids these two difficulties. Looking at Fig. 7 we see that there is still considerable vacuum energy for small non-zero values of <0|H|0>. It is therefore possible to have a period of exponential expansion after the Higgs field has started moving in some direction towards a minimum of the potential. This expansion after a non-zero value of <0|H|0> has been seeded not only solves the size/age and homogeneity problems mentioned earlier, but also avoids the problem of the graceful exit. It also predicts the existence of very few monopoles in the observable Universe because the directions of the Higgs fields are correlated. The new inflationary scenario may work in conventional GUTs with Higgs fields which are massless before symmetry breaking - the Coleman-VJeinberg hypothesis. In Section 4 we will make some remarks about the feasibility of the new inflationary scenario in supersymmetric GUTs. 2.5 Neutrinos GUTs suggest that neutrinos have masses. These are expected if lepton number is violated: one can write down Majorana masses such as K K. (2.33)

Vie believe that lepton number cannot be an exact gauge symmetry since there is no associated massless gauge boson analogous to the photon or gluott. Nowadays we all profess the dogma of the gauge age: "Every exact symmetry is a gauge symmetry", and therefore expect lepton nurober to be - 317 -

~~violated. Indeed lepton number violation and neutrino masses are found in 67 ) non-minimal GUTs. For example, in SO(10) GUTs one finds a mass of the form (2.33):~~

~~' **" ""^ (2.34)~~

which is much smaller than conventional fermion (lepton or quark) masses. 68) Non-minimal variants of SU(5) also yield neutrino masses in the general range (2.34), while even minimal SU(5) could yield neutrino masses 0(10"5) eV if one admits the existence of AL = 2 interactions at the Planck mass scale. Even such small masses could be detectable in the oscillations of solar neutrinos. The upper end of the range (2.34) extends to 0(10 to 100) eV, large enough to interest lovers of missing mass and theorists of galaxy (cluster) formation, as we saw earlier in 70) this meeting . However, one usually expects

~~so that the heaviest neutrino is likely to be the v (apart from small generalized Cabibbo mixing angles), and one is at a loss to explain the 71) large v mass reported recently .~~

Of interest to GUTters and to astrophysicists is the total number of neutrino species N . The best limits on N from particle physics experiments of order 105 come from the decays K+ •+ it+Z vv, J/<|» •* Z.. and perhaps T •»• Zw, wnile the success (2.3) of the b quark mass 33) calculation suggests to the optimists that N = 3. There is an oft- quoted bound on N from Big Bang nucleosynthesis:

~~Wv £ S 2 x 10~ ° as suggested by calculations of the abundance of D and He. However, as seen from Fig. 10, the bound (2.36) assumes that there are not more than~~

~~(2.37) - 318 -~~

If this were the case, the Universe would have expanded so fast that the combination of neutrons and protons into **He would not have been completed, and Y would have fallen below 0.25 again. Can one exclude the possibility that

~~vGOD ^ I^V ^ C/V.lC' ) < (2.38)~~

9) This can be done using constraints from the final stages of stellar evolution. During these the dominant rate of energy loss is due to the emission of neutrinos or other light particles. One can obtain constraints on W from the successes of evolutionary models for the following classes of objects:

Thus it seems that despite reasonable uncertainties in these models the gap (2.38) can be closed. We will see in Section 4 how similar arguments can be used to constraint the light particles expected in supersymmetric theories.

~~3. - SUPERUNIFICATION~~

3.1 What, why and how? This part of the talk discusses attempts to introduce supersymmetry into the framework of unified gauge theories. After this introductory section discussing what supersymmetry is , why one might want to use it, and how it could be realized in Nature, subsequent sections discuss its low energy phenomenology and the predictions of supersymmetric 18 (susy) GUTs for baryon decay ''> ' in particular. The modifications in conventional GUT cosmology induced by susy are taken up in part 4 of this talk.

Supersymmetry is a novel type of symmetry directly relating fermions and bosons. It is generated by fermionic charges 0 of spin 1/2. As one might expect of fermionic operators, they obey an anticommutator algebra which involves the momentum operator - 319 -

~~(3.1)~~

where the indices i,j = 1,...,N are internal indices while a,B are spinorial indices. Gauge theories can accommodate H <. A global super- symmetries . If one introduces local supersymmetry transformations, one must necessarily introduce gravity, and can then accommodate Ni8 local supersymmetry charges in a supergravity theory 73). However.many charges one introduces, one always has equal numbers of boson and fermion states if one wants to realize supersytranetry linearly:

~~(3.2)~~

~~In what follows we will deal almost exclusively with N = 1 theories, for which the only supermultiplets allowed in a gauge theory are the~~

~~(3.3) [ o )~~

The gauge supermultiplet has self-interactions which are completely specified by the gauge coupling constant and a possible 8 vacuum parameter. The chiral supermultiplets can have gauge interactions in the normal way accompanied by analogous interactions for the gauge fermions in (3.3). The chiral s.upermultiplets can also have self-interactions characterized by a superpotential P which is cubic in the chiral superfields and determines all the Yukawa interactions and the scalar fifeld potential .

Why should one be interested in a supersymmetry theory? First of all, because it is beautiful(?). Secondly, because it is the only possible type of fundamental symmetry which has not yet found a place in ele- \- ,3 mentary particle physics. Thirdly, because supersymmetric theories have f. many fewer divergences than conventional field theories. In particular, s it seems very likely that the N s 4 gauge theory is completely finite , £ while the N s 8 supergravity theory may well be finite up to seven loop j 75 ) ' K order . A fourth reason for liking supersymmetry is that it provides k.I - 32O -

a "home" for scalar fields which were hitherto the unwanted orphans of the particle spectrum. A related fifth motivation is that supersymmetric theories unify matter and radiation: they related gajge to spin 1/2 fields, the graviton to the gravitino and possibly to fields of other spins, and spin-zero (Higgs?) fields to higher spins as mentioned above. Sixthly, supergravity theories are the only existing candidates for unifying particle physics with gravity. Seventhly and most topically, supersymmetric theories offer some hope ' of alleviating or "solving" the hierarchy problem: why is

This major technical progress in the formulation of GUTs is a spin-off from the reduction in the number of divergences mentioned earlier. It depends in particular on the absence of quadratic divergences and on 77) "no-renormalization" theorems for the parameters of the superpotential P, as we will see shortly.

Before addressing the hierarchy problem there is one uncomfortable fact which must be confronted, namely that no supersymmetric partner of any known particle has ever been seen, which implies that supersymmetry must be broken. If it were exact, one would have bosons and fermions with equal masses, in the same way that isospin invariance would require m = m . How large could the breaking of supersymmetry be ? Since gravity has the energy scale of 1019 GeV, the Planck mass m , built into it, probably it only makes sense to invoke supersymmetry breaking on a scale < 0(m = 1019 GeV). The only other of -the motivations for super- ~ Pn symmetry mentioned above which also imposes constraints on the scale of supersymmetry breaking is the "solution" of the hierarchy problem. Let us suppose that God in her infinite wisdom fixes the Weinberg- Salam Higgs fields to have zero mass; we have no good idea how She does this, hence the quotation marks around the word "solution". The non- 77) renornalization properties of supersymmetric theories then guarantee that the Higgs masses m,. remain zero in an exactly supersymmetric theory. H In a theory with broken supersymmetry there are non-zero contributions to m„ due to imperfect cancellations among the various diagrams of Fig. 11, - 321 -

~~which reflect the incipient quadratic mass divergences lying in wait for non-supersymmetric theories. From Fig. 11 we get~~

~~In order to maintain the necessary lightness of the Weinberg-Salam H.iggs fields: |<5mij| < 0{l) TeV2, we see that Eq. (3.5) requires~~

The condition (3.6) does not necessarily require that the boson-fermion mass splitting in a given supermultiplet be 0(1) TeV2. It could be much larger141>78) if the supermultiplet in Fig. 11 is weakly coupled to the )' Weinberg-Salam Higgs fields, as is very likely the case for the electron, I for example. Because of the different coupling constant factors in Eq. (3.6) it could well be that the supersymmetry breaking mass splittings are not universal, but vary from supermultiplet to supermultiplet. Some >. superpartners may well have masses *0(l) TeV, but others could be split '*. much further away. 3.2 Low-energy phenomenology of broken supersymmetry The spectrum of light supersymmetric particles can be expected to include the following: - gluino g: spin 1/2 partner of the gluon, m- probably >0l2) GeV i 79) ~ "-'; deduced from its non-appearance in hadron-hadron collisions. -, - charged winos W~: spin 1/2 partners of the W", mr:+ 0(15) GeV because C ' 801 they have not been pair-produced at PETRAi - photino y and zino Z (or neutral wino W° and bino B): spin 1/2 partners of the Y and z° which may (or may not ) be mixed in the same way when tho Weinberg-Salam SU(2) x U(l) symmetry is broken. - 13) The photino Y could have a very small mass -squarks q: spin 0 partners of the quarks, two corresponding to the lert- and right-handed states of each quark flavour respectively, m~<0(15) GeV 80) ' since they have not been seen at PETRA. In general there could be mixing between the different squarks of the same charge, and also between - 322 -

the q^ and q^. There are significant restrictions on the spectra and mixing of the q from upper limits on flavour-changing neutral weak interactions (FCNI) and on parity violation in the strong interactions82*, - sleptons 1: spin 0 partners of the leptons, two per charged lepton flavour (cf. squarks) and N sneutrinos. mr+ > 0(15) GeV because of 80) ———— ^~ PETRA . In analogy to the squark case, there are restrictions on sl(=pton 81 ) masses and mixing from FCNI and from the anomalous magnetic moment of the muon13)>83). - shiggses H: charged and neutral spin 1/2 partners of the Higgs bosons, mg+>0(15) because of PETRA , whereas the H° could have (almost?) zero mass (cf. neutrinos). Possible variants of supersymmetry spectroscopy are shown in Fig. 12. The goldstino is the (massless) fermion associated with the spontaneous breakdown of supersymmetry. It is pr-escwnably eaten by the gravitino G and gigivev s it a mass which depends on the scale of supersymmetry breaking m

~~- O —*• ) *">/ (3.7)~~

If m is as large as the Planck mass, then m could also be as large 1 as mp. On the other hand, m = 0(1) TeV corresponds to m = OdO" *) eV, in which case it would be one of the lightest supersymmetric particles. Other candidates for the bottom of the spectrum are the photino and the neutral shiggs: these are referred to collectively as nuinos ' and show up as end products in the decays of other supersymmetric particles, e.g.,

thus usurping the rôle of neutrinos in conventional particle decays. Since some type of nuino shows up at the end of every sparticle decay chain one can imagine looking for them either as missing energy- momentum (cf. Pauli ) or else by direct detection (cf. Reines ). As compared with the old neutrinos, the problem is that one must first get - 323 -

~~above the threshold for producing their parent decaying particles, which are heavier than known particles, or else look for pair-production as in Z° •+ i.-jino pairs.~~

~~The gluino nay well be the lightest strongly interacting sparticle. It can combine with conventional quarks and gluons to form shadrons, e.g.~~

~~Vti (3.9)~~

~~whose spectrum should be calculable with lattice QCD. .Shadrons may have quasi two-or three-body decays via~~

~~ö ' o y- T- (3.10)~~

with the latter expected to be dominant if m~ < 0(l/10)ro . Detailed perturbative OCD calculations of the hadronic production cross-sections for gluinos (both total and differential) are now available87'. These should enable beam dump and other hadron-hadron collision experiments to establish upper limits on the gluino lifetime as a function of its mass: T~ may be 0{10"10 to 10"15) sec.13)'88) for m- « few GeV. S One can al30 get interesting limits on gluino production in heavy quarkonium decays and from the e+e~ continuum891. It seems likely on the basis of present experiments7^«87)'89) that the gluino mass has to be >0(2) GeV.

The W" and H can best be produced in e+e" collisions at LEP and elsewhere. They would resemble a conventional sequential heavy lepton in many ways, except1 that they have different neutral vector and axial couplings as seen in the Table below.

~~6V gA~~

~~w~ a -3/2 = 0~~

~~fl- = -1/2 B 0~~

~~•t- = 0 " 1/2~~

~~Table: neutral weak couplings of charged fermions. - 324 -~~

Hence their coss-sections and forward-backward asymmetries will be different from those of a conventional sequential heavy lepton. Heavy neutral fermions such as the W° and B° (or possibly the 'I? ) and perhaps the H° can be pair-produced in e e~ annihilation via the Z°. They can also be produced in association with a selec.tron in high energy e+e~ or ep collisions:

~~>(GV«V3Vs) o.m~~

~~Sleptons and squarks offer clear signals:~~

~~i« t (312)~~

when pair-produced in e+e" annihilation, which is why PETRA enables us to be sure that they weigh more than about 15 GeV. For future reference, it should be remembered that upper limits on FCNI and simple models of spontaneous supersymmetry breaking suggest that

~~I J • JL J Í~~

for the first two generations, and hence that their thresholds in e+e~ : annihilation should be essentially simultaneous, since the normal beam energy spread AE/E = 0{10~3) as well. The process e t q i» ë i q in high energy ep collisions is also a promising channel for the associated I 92) production of squarks and sleptons 3.3 Supersymmetric GUTs The hierarchy problem in conventional GUTs was our most topical reason for introducing supersymmetry, so it is appropriate to see how the standard predictions of Section 2.1 get modified. First a word about the construction of supersymmetric GUTs12 '7 '93': in addition to the doubling of every known particle to complete a supermultiplet, it turns \

out that one needs a doubling of the conventional light Higgses in an ' : SU(5) model. One therefore needs one or more pairs of (5+5) Kiggs .; 94) ' ' supermultiplets. The neutral weak mixing angle is increased so that - 325 -

~~/ _ (3.14)~~

the first of which is only marginally consistent with experiment, whereas the latter is too high. The situation could perhaps be improved by invoking isospin breaking among sparticles so that the neutral current strength parameter p i 1, changing the exDP'imentally preferred value of pinJ9 i or else by introducing oan^s into the supersymmetric 96) desert . This desert extends somewhat further than in a conventional GUT97),94)r18).

*lf > * *W (3.15)

if there is just one (5+5) pair of Higgses. Miraculously, although the formula for m./m changes in a supersymmetric GUT, the final pre- 18) Qi) diction for ID. is essentially unchanged ' at the successful mark of 5 OeV.

What of baryon decays? One might have expected on the basis of (3.15) that if T„ = niy, the baryon lifetime should be significantly longer in supersymmetric GUTs. This need not be the case, as Weinberg, Sakai and Yanagida have pointed out the existence of new diagrams (see Fig. 13) which means that Y_ « m^ in a supersymmetric GUT without 181 Q81 an extra symmetry. Careful calculations ' suggest that it is pos- 30 2 sible to have in > O(1O ) years if the gaugino masses are >O(1O ) GeV ~ 17T 18) as we expect. However," the nucléon decay modes are expected ' to be very different from those in a conventional GUT:

which is very different from the expected dominance by e+tt in conventional GUTs. There are, however, alternatives to (3.16) in supersymmetric 19 i GUTs. It is possible that the B-violating colour triplet Higgses in supersymmetric GUTs are significantly lighter than the vector X bosons - 326 -

~~(3.15). They might dominate nucléon decays in which case one would expect19''96)~~

~~P" "> (3.17)~~

to dominate. It is even possible to find supersymmetric GUTs in which + no) the old-fashioned e n dominates . Note, however, that the Kolar Gold Field events do not resemble N •+ \>K so much as e+ + pionr. or JJ + pions. The uncertainty in decay modes (3.16) and (3.17) points up the desirability of a highly flexible baryon decay detector such as a fine-grain calorimeter. Sasha Rozanov has proposed an amuning way of looking for the vK decay mode expected in some supersymmetric GUTs (see Fig. 14). His idea is to look for the monochromatic K° emer- L ging from nucléon decays in the rock surrounding an underground cave. The cave is lined with veto counters to pick up any entering charger) particles, and the interior contains a detector able to pick up K? decay modes such as ir°n ir~ or ir e" v and discriminate against the neutrino background by determining whether the kinematics are consistent with the monochromatic K° expected from nucléon decay. Perhaps baryon decay will provide our first limit for the relevance of supersymmetry to particle physics ? 4. - SUPERCOSMOLOOY

4.1 Introduction Part 2 of this talk briefly reviewed some of the key interfaces between 'conventional GUTs, astrophysics and cosmology. In this final part we will see how some of these interfaces may be modified in supersymmetric GUTs. The rrinciPal subjects discussed will be Big Bang baryosynthesis in Section 4.2 and nuino astrophysics in Section 4.3.

4.2 Superbaryosynthesis There is no problem of principle here, but some new "technical" difficulties may arise in supersymmetric Ol'Ts. One problem is that such theories tend to havf> several almost degenerate minima ' as seen in Fig. 15, and the Universe may not be able to choose the correct SU(3) y SU(2) x U(l) invariant vacuum until a temperature T « nu - 327 -

(T * io10 GeV)19)"21). In this case it is difficult to generate a baryon asymmetry unless the "superheavy" bosons whose decays generate the baryon asymmetry are somewhat less than the canonical 10ls GeV, perhaps 0Í101*) GeV themselves 9 ' . One can give triplet Higgs bosons such light masses more easily in supersymmetric GUTs than in conventional GUTs. There is, however, another difficulty, namely that even if the SU(3) x x SU(2) x U(l) invariant vacuum is energetically preferred, parts of the universe which fall into the wrong minimum may take too long a time to tunnel into the true minimum . However, one can enhance the tunnelling 21) rate by choosing a small self-coupling for the scalar fields . A final remark concerns the possible connection with the neutron electric diDOle moment mentioned in Section 2.2. It has been shown 22) that the vacuum parameter 6 is not renormalized in a supersymmetric theory, although baryosynthesis is still possible ' ' .If supersymmetry is already broken at a scale >0{1010) GeV then a connection between n_/n and d may exist, but there is no direct connection if the supersymmetry breaking scale is <<0(1010) GeV or starts in a sector of the theory far removed from the particles generating the baryon asymmetry. Inflation seems possible in principle in a supersymmetric GUT. However, since the vacuum energy vanishes in an exactly supersymmetric theory, it would be useful if the scale of supersymmetry breaking was >0'1010) GeV in order to have a large enoußh vacuum energy to drive inflation before the epoch of baryosynthesis. Although the Coleman-Weinberg mechanism of spontaneous symmetry breaking used in the new inflationary Universe scenario is not available in a supersymmetric GUT, it may be possible to ape its effects by postulating small scalar self-couplings or a runaway O'Raifeartaigh Higgs ' . Certain approaches to the estimation of the rate of tunnelling which initiates inflation, and the length of inflationary epoch itself, suggest that supersymmetric GUTs may have some advantages over conventional OUTs.

4.3 Nuino Astrophysics The astrophysical constraints on nuinos exhibit many similarities and some important differences with those on neutrinos. From Big Bang nucleosynthesis one deduces that there can be at most one nuino species - 328 -

weighing less than 0(1) MeV - if it decouples no earlW than th« nou- trjnos. However, in many theories the photino and/or the gravitino may decouple somewhat earlier and therefore not conflict with Big Ban?; nucleosynthesis . There are interesting constraints on the mass of the gravitino coming rrom cosmology ' . Because they live until the Universe has cooled to a temperature far below its mass, gravitino decays generate a large amount of entropy. They should therefore either be heavy enough to have decayed before nucleosynthesis - in which case the gravitino mass and the supersymmetry breaking scale m (3.7) should be large :

~~or else the gravitinos should be light enough not ' to weigh down the j. present-day Universe~~

But there is another important constraint on the gravitino mass from particle physics considerations . In the absence of radiative corrections all scalar masses must be larger than that of the gravitino:

~~and since some of these scalars have masses 0(100) GeV one infers that~~

~~O(i«>)~~

The particle physics constraint excludes the domain (4.1) and one concludes that the interesting mass range for the gravitino is light (4.2). However, there is a loophole in this argument: the bound (4.1) does not apply if there was an epoch of inflation, because gravitinos made previous to this epoch are drowned out or decay, while very few gravitinos can be created subsequently. Thus superinflationary models can use all the range (4.4) permitted by particle physics. - 329 -

There are some weak constraints on the scale of supersymraetry break- king rrom the late stages of stellar evolution * . In much the same ways as the neutrino pair emission discussed in section 2.5, photinos and gravltinos can in principlp e contribute significantly to stellar cooling, and one can establish limits ' on the supersymmetry breaking parameters :

~~from yG emission: "*5 > ^ID)*^/,^ ^tfW (4.5)~~

~~from YY emission: 1^^ ^ 0(40)íí^V (4.6)~~

Note, however, that these constraints only apply if the photino and gravitino weigh less than 0(10) keV. It is worth noting that nuinos might even be useful in astrophysics. Analogously, to massive neutrinos, massive y and G could aid in the formation of galaxies or galactic clusters. Indeed, they have certain advantages because they can condense over a wider range of mass scales from galaxies- to clusters, whereas neutrinos tend to gather on cluster scales only . Finally, it has been speculated that the photino could be responsible for some photoionization observed in the intergalactic medium through its decay y •*• y + G with E - 50 eV. The photoionization could equally well be due to boring, old-fashioned v1 •+ v + y decay 11*5 ), but many more prosaic explanations are possible !

5. - CONCLUSIONS We have seen that GUTs have phenomenological successes in particle physics, despite having technical problems with the arrangement of the gauge hierarchy. Conventional GUTs also offer enticing cosmological pros- pects: Big Bang baryosynthesis and the inflationary Universe. The most plausible solution to the technical aspect of the hierarchy problem seems to be supersymmetry. Supersymmetric theories offer much interesting low energy phenomenology and suggest the existence of new light neutrino-like particles called nuinos. Supersymmetric GUTs offer new ways for baryons to decay, but they may complicate the conventional GUT scenarios for baryosynthesis and inflation. Nuinos are constrained by cosmology and by the late stages of stellar evolution, but the masses of the photino - 330 - and gravitirio are still very uncertain. If nuinos exist, nuino physics and astrophysics will have much in common with present-day neutrino physics. Perhaps the next conference in this series will be

~~NUINO '84 - 331 -~~

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~~FIGURE CAPTIOUS~~

~~Fig. 1 : Lowest order diagram for baryon decay via superheavy X and Y boson exchange in conventional GUTs.~~

~~Fig. 2 : Lowest order diagram contributing to Big Bang baryosynthesis in non-minimal GUTs.~~

~~Fig. 3 : Illustration of the development of a baryon asymmetry Yn from the decay of superheavy Higgs bosons, taken from Ref. 38): see also Ref. 39).~~

~~40) Fig. 4 : Lowest order diagram contributing to Big Bang baryosynthesis in the minimal SU(5) GUT. Fig. 5 : Lowest order diagram contributing to 6 renormalization in non-minimal GUTs.~~

~~Fig. 6 : Illustration of the "hedgehog" configuration of Higgs vacuum if) expectation values around a monopole~~

~~Fig. 7 '• A generic Higgs potential, exhibiting a non-zero vacuum energy V(0) when || = 0, and finite temperature corrections ŐV(4>,T).~~

Fig. 8 : As the early Universe cools, causally separated domains of the Universe may have Higgs vacuum expectation values pointing in uncorrelated directions. Will a monopole be formed in the middle of the picture ?

Fig. 9 : A compilation of experimental and theoretical limits on the flux of monopoles as a function of their velocity v. The baryon decay constraint (dashed line) only applies to GUMs and is somewhat uncertain. - 339 -

We note that the most recent limits on the monopole flux from the persistence of the galactic magnetic field are not significantly stronger than the limit from the mass density of the Universe. We have omitted them from the figure for reasons of clarity.

~~Fig. 10 : The primordial helium abundance as a function of the number of neutrino flavours N . The lines BBN show ranges allowed by Big Bang nucleosynthesis. Also shown are the constraints~~

~~on Nv obtained in this paper from the consideration of .stellar evolution from Carbon-burning stars (CB), neutron stars (NS) and Red Giants (TO).~~

~~Fig. 11 : Contributions to 6m£ which are individually quadratically divergent but cancel (approximately) in (spontaneously broken) supersymmetric theories.~~

~~Fig. 12 : Possible variants of the spectroscopy of supersymmetric . particles fa) from Ref. 13), (b) from Ref. 14).~~

~~Fig. 13 : Example of diagram contributing to baryon decay in supersymmetric GUTs. Contrast the elegant simplicity of Fig. 1 !~~

Fig. 14 : A. Rozanov's idea for an experiment to detect supersymmetric baryon decay. A neutron in the rock decays emitting a monochromatic K.0 which penetrates a veto wall and decays into a detector in the cavern which can make a kinematic reconstruction of the decay.

~~Fig. 15 : Illustracon how SUÍ5), SUM) x U(l), SU(3) x SU(2) x U(l) and other supersymmetric minima of the Higgs potential may be degenerate.~~

~~\; - 340 -~~

~~X,Y~~

~~Fig. 1~~

~~Development of number densities~~

~~Fi*.~~

~~10 10" 10-* io"5 10" 10" Temperature (GeV)~~

~~Fig. 3 - 341 -~~

~~b /|\~~

~~Flg. 5~~

~~Fig. 6~~

~~Fig. 7~~

~~Fig. 8 - 342 -~~

~~i i r-TTinTT-]~n--r-| - r~r i-rrrr DENSITY LIMIT A ' \ \ \ \ ), VEIOCITY ill GAINfcO FROM GALACTIC MAGNETIC FIELD \h M.. : 10ft GeV~~

~~NUT~~

~~DENSITY LIMIT IF UNIFORM IN UNIVERSE~~

~~10 VELOCITY v Fig. 9 - 343 -~~

~~NS R6 1 A 0.5 H~~

~~CB =l9 10 nY ' OÁ - H HV BBN Y H \ BBN u f 0.3 H / H \ ^ \ • i i 0.2 - H h H 0.1 - H TT T H h~~

0 1 1 101 10J 10*

~~fig. 10 - 344 -~~

~~- (..~~

~~Bosons Fermions Fig. 11~~

~~Hass~~

~~1 TeV .~~

~~2«. .100 GeV- . z* M*- ... 40 GeV~~

~~B s*. .IT~~

~~- 10 GeV-~~

~~- 1 OeV -~~

~~H'7. Y.6 Y.e Gaure Hlggs Ouarks Leptons Gauge Hlggs Ouarlo Leptonä Mass~~

~~(a) (b)~~

~~Fift. 12 - 345 -~~

~~Fig. 13~~

~~Fig. 14~~

~~)A Ref.~~

~~FiR. 15 - 346 -~~

~~THE STANDARD ELECTROWEAK MODEL EMPIRICAL STATUS AND ALTERNATIVE POSSIBILITIES~~

~~J.J. Sakurai* Max-Planck-Institut für Physik und Astrophysik - Werner-Heisenberg-Institut für Physik - Munich (Fed.Rep.Germany)~~

The present empirical status of the standard electroweak gauge model is reviewed with emphasis on results obtained in the past two years. Also discussed are possible alternatives to the standard model.

~~Review of the standard model~~

It is hardly necessary for this audience to be reminded of the elements of the standard electroweak gauge model of Glashow, Salam, Ward and Weinberg . I just summarize here the testable features of the model, which 2 can be divided into two classes - the low energy (or low q ) predictions 2 and the high energy (or high q ) predictions. Needless to say, only the low-energy limits of the model have been verified experimentally. Everything that has been tested so far in weak interaction physics is contained in effective Lagrangians of the 1932 Fermi •type:

~~for the charged-current interactions and~~

~~cc for the neutral-current interactions. Here the charged current J can be written explicitly as~~

* U.S. Senior Scientist Awardee (Alexander von Humboldt-Stiftung), on leave from the University of California, Los Angeles. - 347 -

~~_i. j / \/ -» -w 1 W I A# I (3)~~

~~where~~

~~etc. (4)~~

and U„„ is a 3x3 unit; ry matrix that characterizes the mismatch between KM the weak-interaction ei.genstates and the mass eigenstates. If the neutrinos turn out to be massive, it is also necessary to insert an analogous 3x3 matrix in the lepton sector. As for the neutral-current interactions, the current J (where the superscript 3 stands for the third component.of weak current J (where the superscript 3 stands for isospin) that appears in (2) can be written as 0

~~where .... stands for the contributions from the second and third genera-~~

~~tion quarks and leptons obtained by~~

~~In contrast to these low-energy predicitons, there are yet-to-be-tested~~

~~high energy predictions:~~

~~(i) The masses and the decay widths (total and partial) of W- and Z°~~

~~including electroweak radiative corrections, (ii) Thé existence and the decay branching ratios of the Higgs boson,~~

~~(iii) Non-Abelian trilinear couplings among the gauge bosons.~~

Many people maintain the view that the striking low-energy successes of the standard model achieved up to now imply that the high-energy predictions listed here will also be fulfilled with certainty. This majority opinion is confidently expressed in the following remark of Gleshow at the LEI" Summer Study (September 1978):

~~"Since the low-energy limit of the unified theory is so well confirmed, few can doubt the truth of its central prediction: the existence of W^ at /v 80 ÇeV and of Z° at ^90 GeV." - 348 -~~

One of the main purposes of my talk here is to convince you that, on the contrary, the successfully tested low-energy predictions should be regarded as being independent of the yet-to-be-tested high-energy predictions (i), (ii) and (iii). But first, let me present the experimental evidence in favor of the effective Lagrangians (1) and (2) with emphasis on recent results.

~~Empirical support~~

In order to see where the standard model has been tested, it is convenient to use the Michelin star system invented by Bjorken at the Äkäslompolo Summer School two years ago. See Tables 1 and 2 for the charged- and neutral- current interactions, respectively. New stars acquired since 1980 are under- lined. I am pleased to announce that, unlike the Michelin evaluation of Paris restaurants, no star has been dropped since Bjorken's 1980 evaluation. Let us first look at the charged-current sector. There is a new star for (y u) (u i? ) ; this star is due to a recent observation of "elastic l> |i scattering" by the CDHS Collaboration, reported at this conference by B. Pszola. s-Je also see that the entries related to X decay are in extremely

good shape. Even the Cabibbo-suppressed strangeness-changing decays (K v.r, K yij ) have now been identified with branching ratios in rough agreement with 4) the. theoretical predictions. The only reason taht these •£. entries do not yet enjoy the status of three full stars - one of the stars is in parenthesis - is that the absolute lifetime is known only within a factor of two :

~~= (4.6 + 1.9) x 10"13 sec, (Mark II)~~

~~T (theory) = (2.8 + 0.2) x 10~13 sec.~~

As for the interactions of heavy quarks, the most significant advances in the last two years have been made in the area of the b quark interactions. From CESR data (CLEO and CUSB) we know that the b —»c transition is considerably stronger than the b ->u transition for two reasons: (i) the observed number of K's In B decay is "large", and (ii) the observed lepton spectrum in semi- leptoriic B decay is relatively "soft" . unlike the D° case, ths semileptonic branching ratio for B - being about 12% - does not appear to exhibit a large departure from the spectator model prediction of about 15%. The new - 349 -

~~lifetime limit of B reported by the JÄDE Collaboration constrains Ucb provided the spectator model can be trusted:~~

~~Z (6) 6 •/D~' Sec (9S%CL) ^=P fUj~~

while in the Kobayashi-Haskawa scheme |(J .{ is expected to be of order 0.2. Let us now turn to the neutral-current sector. Here the most significant advances in the past two years have been made in the area of neutral-current interactions not involving neutrinos. Especially important is the angular asymmetry in

~~(9)~~

No longer are we talking about upper limits on weak-electromagnetic interference. The "combined" PETRA data, as reported by P. Söding at this conference, give a conclusive (nearly 7 standard deviations 1) effect for the presence of neutral-current interactions in (9). The observed angular asymmetry, -11.5 + 1.7% at fs - 34 GeV, is in excellent agreement with the standard model prediction, -9.2%. At the same time we continue to see no deviations from the QED prediction in the integrated cross section; this feature is actually expected in the standard model at this energy with sin 9 ~ 1/4. In terms of the (ëe)(uu) coupling parameters h and h the data imply ktfv ^''AA' w*1^cn v*a ^ne factorization (single Z) hypothesis forces us to choose the axial-vector dominant solution in t?e scattering, a conclusion obtained solely on the basis of purely leptonic reactions. Similar information is being accumulated for

~~(10)~~

~~but the errors here are substantially larger. As for~~

~~(11) there does not seem to be any deviation from the QCD corrected parton-roodel pediction for R. This again is understandable because in the standard model - 350 -~~

the (ee) (qq) is expected to be weak for sin 9 'JC 1/4, where q can now stand for s, c and b as well as for u and d. No discussion of recent progress in the neutral-current interactions would be complete without mentioning the CERN SPS charge-asymmetry measurement (Bologna, CERN, Moscow etc.) in P~ + C * }*+ (125

~~reported at this conference by C. Zupancic. The q range explored in this experiment is up to <\> 100 times greater than that involved in the SLAC parity experiment~~

of four years ago. As a result, the asymmetry seen in (12) is of the order -4 of 1% rather than *v 10 as at SLAC. It is also important to note that the weak interaction effect detected here is primarily due to the parity-con- serving A A interaction while the SLAC effort primarily explored the parity-violating A V interaction. Even though this is a conference devoted to neutrinos, I actually have not much to say on neutrino-induced neutral-current interactions. As we heard from several speakers this morning, high-statics data on y e scattering are being accumulated on both sides of the Atlantic, and we expect a significant Improvement on the precision level of the data by the next neutrino conference. "Hie "elastic \> u scattering" process I mentioned earlier is relevant also to Table 2 because both neutral and charged currents contribute here. As is well known, the most quantitative studies of neutral currents are made in the deep-inelastic y N interactions, which are predominantly due to the (f>0 (uu) and WY) (dd) couplings. However, recent data here are sufficiently precise that the effect of the strange quark-antiquark "ocean" — — 8) coupled via (yy)(ss) should not be totally ignored In Table 2 only the diagonal neutral-current interactions are shown. Flvaor-changing neutral currents, which have no place in the standard model with GIM generalized, can be looked for in B meson decay - 351 -

~~The present experimental limit of -v 8% seems to rule out most topless models . It appears that the "standard" ((t,bt ) doublet is needed barring~~

~~pathological possibilities such as (c,b)R.~~

~~Parameter fixing~~

Let us not forget that the standard electroweak model is a many-parameter theory. By "many" I mean 17 or 24 depending on whether the neutrinos are massless or massive. First, there are 3 parameters, e, G and si»9 (or, equivalently, g, g' and v) all of which are known with accuracy. Then there is the Higgs mass n^, on which we have no information. In the three-generation model with m = 0, there are nine masses, m , m , R , m , m,, m , m , m. and m. , all known with the exception of m. . Next we have the quark c fc t c9) mixing matrix W , characterized by four real parameters 6., 8 , 6, and 0 KM 1 t.O S The present status of these parameters is summarized at this conference by K. Kleinknecht. One of the three angles, 9 , has been known accurately for some time through beta-decay-muon-decay comparison, and the allowed ranges for 9_ and 6, have been determined using dilepton production in VN collisions, D decay, B decay etc. As for the CP violation parameter $ , the size of CP violation in the K°-K° complex restricts it to be either near 0 or near W . If we relax m . = 0, then -there are 3 masses, m{y ), m(y ) and m(V ), and 4 parameters, 8 ', 9 ', 8i, and $', connected with U, . , the leptonic analog uf U . He have non-zero Information on only one of these KM 7 parameters; m(/ ), which is believed to be between 14 and 46 eV, at least in Moscow . To sum up, with m set equal to zero, we know 12 out of the 17 parameters fairly well, and, in addition, some information is available on 3 of the 5 remaining parameters. On the other hand, with m y ^ 0, all but one of the 7 additional parameters needed are completely unknown. Out of the 17 (or 24) parameters of the standard model, the single 2 parameter that attracted the greatest amount of attention is sin 9 . Pre- cision determinations of this parameter are of great interest for two reasons. First, the simplest grand unification scheme based on minimal SU(5) predicts a value of sin 9 tantalizingly close to the current experimental - 352 -

~~value, a point discussed by J. Ellis at this conference. Second, the weak 2 boson masses are predicted in terns of sin Ö via the celebrated mass 1) relations of Weinberg :~~

~~To show the sensitivity of the boson mass predictions to sin 9 , let us note for example~~

Now these are "uncorrected" predictions based on the original formulas of Heinberg (15). I should mention here that the electroweak radiative corrections at one-loop level lead to upward shifts of *v4 GeV for both W and Z . So the radiative corrections are as important as precision deter- 2 minations (now typically within + 0.01) of sin 8 . After these corrections the best estimates, according to the "experts", for the weak boson parameters are

~~±3 kV,~~

~~rw cr rz * 2.~~

~~Possible modifications~~

One way to test the standard electroweak model is to examine the "stability" of the model against possible, theoretically motivated modifications. He may first try to alter the model by making the absolute strength of the neutral-current interactions arbitrary: - 353 - )(J3- with O left as a free parameter. He expect J> t 1 in a model with a complicated Higgs mechanism where some of the scalar bosons have weak lsospins greater than 1/2. The O parameter may also depart from unity if there is a superheavy charged lepton forming a doublet with a massless or nearly massless neutrino, resulting in a large violation of weak lsospin symmetry. 12) Two-parameter analyses lead to

~~/ = 1,00% ± Ô.Û/S'j (19) J"«*^ = 0,13+± O.Oil~~

~~As another modification on the standard model we consider~~

~~" 7e" (20)~~

~~This structure is expected in multiboson models based on SU(2)~~

~~(21) C < o.ol, (9f/t CL)~~

~~Another way to characterize the neutral-current data is to use para- metrisation suggested by right-left symmetric models:~~

~~(22) - 354 -~~

~~Recent fits show~~

~~=I.03±6.0<, ?R=-6.*< ±ö.)l ,~~

So the parameters obtained are perfectly consistent with the standard model predictions P = 1, f = P = 0; generalizations to right-left symmetry are not required by the data. From the above value of f we can deduce that -J R the second Z boson mass of right-left symmetric models must be at least- three times as heavy as the standard Z mass. Actually the most stringent constraint on right-left symmetric models is obtained by considering higher-order charged-current interactions, to wit m(Kr) " m(K )• When we have a current-current type coupling of the (V-A)•(V+A) form, we can transform it à la Fierz into a linear combination of scalar and pseudoscalar interactions for which the well-known helicity suppression argument becomes inoperative. As a result, it is possible to obtain extremely stringent limits on the parameters of right-left symmetric 14) models. In this way, several months ago, Beall, Bander and Soni deduced for the second W boson mass

~~a result valid independently of whether right-handed neutrinos are heavy or light.~~

~~Interim summary~~

Our belief in the correctness of the low-energy limits of the standard model has, if anything, been strengthened in the past year or two. With the observation of weak-electromagnetic interference at PETRA the q 2 region where the standard imdel has been tested now extends beyond 1000 GeV 2 in the timelike direction. But this q range is not high enough if we are - interested in discriminating m_ = 90 GeV from m_ =tX?(four-fermion). - z z - 355 -

~~Despite these low energy successes, it is worth emphasizing that none of the high-energy predictions of the model have been tested. In particular, as yet there is no evidence for:~~

~~(i) The quark and lepton masses are generated by spontaneous breakdown à la Higgs - to confirm this we must find a scalar boson with the right coupling properties.~~

~~(ii) The weak interactions are accounted for by renormalizable gauge theories - for this we must study trilinear gauge boson couplings and check higher order corrections.~~

~~(ill) The weak and electromagnetic interactions are unified In the sense of Glashow~~

~~e n0 (25) - 9 *' u/. íi~~

~~To verify this we must know gj so far all we know is the big G, not the small g. Recall~~

~~In other words we don't yet know m^ !~~

~~Conservative alternatives vs. radical alternatives~~

Because only the low-energy limits of the standard model have been successfully tested, it is still possible to contemplate viable alternatives to the standard model. Crudely speaking, there are two classes of alternatives - conservative alternatives and radical alternatives. By "conservative alternatives" I mean alternative models in which the weak interactions are still described within the framework of a unified gauge theory of some kind. Such models arc based on higher groups - SO(2) U(l) £> U(l), SO(2) £> SU(2) & U(l) etc. and characterized by a richer weak-boson spectrum. In most mode J. s proposed along these lines, one - 356 -

of the Z(H) bosons has a mass close to the standard Z(W) mass. Because this sbject is adequately reviewed by V. Barger at the Wisconsin pp Workshop last December, I'll make no further comments on this class of alternatives. In contrast to the conservative alternatives which stay within the ideology of unified gauge theory, what I wish to call "radical alternatives" are characterized by more extreme views: W and Z need not be elementary gauge bosons; the weak and electromagnetic interactions are not necessarily unified. An example of this is a composite model of W and Z where the weak interactions are to be regarded as indirect manifestations of some basic dynamics in much the same way as the interactions of p and cO are now regarded as indirect manifestations of QCD.

~~/-W° mixing~~

Before discussing the composite model option let me show how the low energy limits of the standard model can be reproduced equally well within a more phenomenological framework based on global SU(2) broken by /-W mixing. In this written version I'll be brief on this subject because it was covered recently in my Schladming/Moriond (Les Arcs) talk, now available in preprint form Suppose the history of weak interaction physics were different. Imagine that we had known of the existence of neutral currents before the birth of electroweak gauge theory. How might the subject have been developed ? Given the existence of neutral currents with parity violation the most natural thing would be to extend the V-R (pure left-handed) interactions of charged currents to the neutral-current case by writing down current- current interactions that satisfy global SU(2):

~~(27) where J stands for a triplet of weak isospin built up of left-handed fermions~~

~~j -J -h U , J ~ (28)~~

~~The structure (27) is so natural; in fact it was actually written down by Bludman as early as 1956. - 357 -~~

But we now know that (27) Is not quite right. For one thing the observed neutral currents are known not to be of the pure V-A form. But only a slight modification is needed; the correct interactions are obtained by just letting

~~(29)~~

in the interaction Lagrangian (27). If the JvJ interactions are originally due to W-' exchange, this modification suggests some kind of / -W mixing where / is the old fashioned photon, not the B boson of the standard electroweak gauge model. Indeed it was shown four years ago that SU(2) symmetric couplings of W-'° to left-handed weak isospin, when supplemented by a gauge invariant Y-V° interaction of the form

~~- _2 Xtyh/uV (30)~~

are sufficient to reproduce the entire low energy phenomenology of the 18) standard model . Both the observed strength ( 0= 1) and the observed J - sin 9„J structure of the neutral-current interactions are accounted for with sin 9w identified as

~~(31)~~

~~But Weinberg's mass relations are, in general, not valid; instead 18) we expect a weaker mass relation~~

~~(32)~~

These considerations show that the low-energy successes do not guarantee the correctness of the weak-electromagnetic unification idea. We must still rely on Rubbia to see whether Weinberg is really right I - 358 -

~~Composite models~~

Recently several people have speculated on the possibility that the H and Z bosons, as well as quarks and leptons, are bound states of more fundamental objects - preons, rishons, haplons ... . In such models the weak interactions we observe are not fundament1; rather they are residual manifestations of a more basic dynamical framework. In particular, authors 19) such as Greenberg and Sucher, Abbott and Farhi, Fritzsch and Mandelbaum have considered a superstrong and confining dynamics characterized by an unbroken local gauge symmetry. The conventional W and Z, being composite, are not gauge bosons, and the basic dynamics is due to hypergluon gauge fields somewhat analogous to the octet of gluon fields in QCD. Weak interaction vertices such as Wfr->e>> are to be regarded as residual manifestations of the new fundamental dynamics - known as QHiD (quantum haplodynamics) in the Fritzsch-Mandelbaum version - in much the same way as the hadronic vertices of the 60's - j> ir^Kti , TtU <-> A etc. - are now believed to be residual manifestations of QCD, the basic underlying dynamics of the strong interactions. So weak interaction forces we observe in nuclear beta decay etc. are effective forces somewhat like van der Waal forces. Perhaps some historical analogy may be of interest here. In 1960 I thought that the particles which later came to be known as J>, oj and a> are the gauge particles of strong interactions ; by 1970, most people came to believe that f> and Où are not fundamental gauge bosons but rather quark- antiquark bound states. In 1980, right after the originators of the standard electroweak model were canonized at Stockholm, the physics community almost unanimously believed that W and Z were the gauge particles of weak interactions. Perhaps by 1990 most people will be inclined to believe that the W and Z are composites of more fundamental objects.

It is not my purpose here to present a detailed account of some particular composite model. I just wish to discuss some general features., common to the various composite models proposed, which are relevant to our understanding of weak-interaction dynamics. As mentioned earlier, the weak interaction vertices are not to be regarded as fundamental. Take, for definiteness, - 359 -

~~<33) ve 19) - In the Fritzsch-Mandelbaum version the y and e are bound states of a scalar boson (y) and a spin 1/2 fermion ( 7,2"), and the W itself is also a bound state~~

~~W°'-4= (34)~~

~~much like the J> meson. The vertex (33) that joins the three bound states may look pictorially as follows:~~

At the same time the photon itself is still to be regarded as an "elementary" gauge boson. Clearly there is no motivation for unifying the fundamental electromagnetic interactions with phenomenological weak interactions that are nothing more than bound-state rearrangements. Because vertices like (33) are not fundamental, we need not insist that they be renormalizable. If the mass scale of the underlying dynamics is of the order of TeV, the composite structure of leptons and weak bosons will dampen the vertex before we reach the energy at which unitarlty violation is expected to take place for pointlike leptons and bosons. The vertex (33) need not be reormalizable any more than the hadronic vertex

~~(35)~~

To obtain the observed properties of the weak interactions the underlying confinement dynamics must satisfy certain conditions. First, in the absence of electromagnetic couplings, we must have the global SU(2)_ of weak - 36O -

isospin at the level of composite leptons and quarks. Interactions of right- handed leptons and quarks w. th H must somehow been prevented (on highly suppressed). Second, to obtain the observed neutral-current structure we take advantage of the /-W° mixing mechanism discussed earlier. Fortunately this mechanism is naturally present in any composite model for W as long as «•.ne W is made up of electrically charged objects:

Ät first sight the value of sin 6 may appear to be of the order of -v 1/137 2 in such models. However, it has been shown that sin 9w as large as --v/1/4 is quite possible provided in is much smaller than the mass scale of the 21) underlying confinement dynamics The lack of weak-electromagnetic unification implies that Weinberg's mass relations are not, in general, expected. The weaker mass relation (32) may still follow if the excited W's play a relatively minor role in weak- interaction dynamics at low energies. In addition it has been shown that if the composite W initiates the p meson dominance idea of the 60's in the sense of complete W dominance of the isovector form factors of composite leptons and quarks, then Weinberg's mass relations may be approximately 22) recovered, say within 'v20%. Apart from a possible failure of Weinberg's mass relations^composite models at high energies are expected to exhibit many striking features - excited W's, a continuum of weak quanta, lepton interactions becoming strong, etc. The composite model scenario would be much more colorful than the standard model scenario where nothing but a grand desert is expected between 100 GeV and 10 GeV. A breakdown of the standard electroweak gauge model at high timelike values of q would promise us many exciting developments which will keep us busy until the dawn of the 21st century. - 361 -

~~References~~

~~1) S.L. Glashow, Nucl.Phys. ^2, 579 (1961)» A. Salam and J.C. Hard, PhyS.Lett. JUÏ, 168 (1964)i S. Weinberg, Phys.Rev.Lett. JU», 1264 (1967).~~

~~2) S.L. Glashow, Proc. LEP Summer Study, CERN Yellow Report 79-01 (1979).~~

~~3) J.D. Bjorken, Fennilab-Conf-80/86 THY (1980).~~

~~4) CA. Blocker et al., Phy s. Rev. Lett. 48, 1586 (1982) i J.M. Dorfan, Phys.Rev.Lett. 46, 215 (1981).~~

~~5) G.J. Feldman et al., Phys.Rev.Lett. 48, 66 (1981).~~

~~6) A. Brody et al., Phys.Rev.Lett. 48, 1070 (1982).~~

~~7) W. Bartel et al., Phys.Lett. 114B, 71 (1982).~~

~~8) F. Büsser, Neutrino '81, Proc. 1981 International Conference on Neutrino Physics and Astrophysics (University of Hawaii, 1981) Vol. 1, p. 328.~~

~~9) M. Kobayashi and T. Maskawa, Prog.Theoret.Phys. 49, 652 (1973).~~

~~10) V.A. Lyubimov et al., Phys.Lett. 94B, 266 (1980).~~

11) F. Antonelli, M. Consoli and 3. Corbd, Phys.Lett. 91B, 90 (1980); M. Veltman, Phys.Lett. 91B, 95 (1980); W.J. Marciano and A. Sinlin, Nucl.Phye. B1891, 442 (1981); C.H. Llewellyn Smith and J.F. Wheater, Phys.Lett. 105B, 486 (1981).

~~12) J.E. Kim, P. Langacker, H. Levine and H.H. Williams, Rev. Hod. Phy s. S3_, 211 (1981). - 362 -~~

~~13) N.G. Desphai.de and R.J. Johnson, University of Oregon preprint OITS-188 <1982).~~

~~14) G. Beáll, M. Bander and A. Soni, Phys.Rev.Lett. 4£, 948 (1982); J. Trampeti& (private communication).~~

~~' 15) V. Barger, University of Wisconsin preprint, MAD/PH/36/1982).~~

~~16) J.J. Sakurai, MPI-PAE/PTh 22/B2 (1982).~~

~~17) S.A. Bludman, Nuovo Cim. !), 443 (1958); See also Y.B. Zel'dovich, JETP 9> 682 (1959).~~

~~| 18) P.Q. Hung and J.J. Sakurai, Nucl.Phys. B143, 81 (1978); \ related ideas are discussed by J.D. Bjorken, Phys.Rev. D19, 335 (1979).~~

~~19) 0. Greenberg and J. Sucher, Phys.Lett. 99B, 339 (1981)» L. Abbott and E. Farhi, Phys.Lett. 101B, 69 (1981)i n. Fritzsch and G. Handelbaum, Phys.Lett. 102B, 319 (1981).~~

~~20) J.J. Sakurai, Ann.of Phys. Jil^ 1 (1960).~~

~~; 21) H. Fritzsch and G. Mandelbaum, Phys.Lett. 109B, 224 (1982); 't_ P. Chen and J.J. Sakurai, Phys.Lett. HOB, 481 (1982).~~

~~r 22) R. Köger1er and D. Schildknecht, TH 3231-CERN (1982)? H. Fritzsch, D. Schildknecht and R. Köger1er, TB 3264-CERN (1982). - 363 -~~

~~ev TV ud U3 ub cd es eb e •% T~~

* *** **(*, *** •** ** eV /

• • *£) •*• *** ** *

~~TV **(D V Y y /~~

* ** V * ** V ud

~~7 7 7 ? HI 7 7 ub f / cd~~

* chei to some extent cb y can checked in future

~~? very difficult, but maybe not hopeless~~

* new addition since 1980

~~Table 1: Michelin system for checking the standard model - charged currents - 364 -~~

~~6 V T *M~~

* • * V

~~* *~~

~~** ** ****~~

~~** ** *** *~~

~~* f ** * m ** **~~

* checked to some extent

~~V can be chocked in future~~

~~? very difficult, but maybe not hopeless jj_ new addition since 1980~~

~~Table 2: Michelin system for checking the standard model - neutral currents - 365 -~~

~~QUARK AND LEPTON MASSES AS ELECTROMAGNETIC SELF ENERGIES~~

Harald FHtzsch**

~~Max-Planck-Institut fir Physik und Astrophysik, HUnchen and~~

~~Sektion Physik, Universität München, Germany~~

Abstract: Bound state models of leptons and quarks are discussed. The weak Interactions are Indirect manifestations of tht bound state dynamics. The lepton and quark masses are electromagnetic self energies.

Neutrinos, the subjects of this conference, are particles, which lack many of the properties other particles have. Neutrinos are electrically neutral, and are colorless; their masses are (if present at ai) exceedingly small. He know, however, from experiment that neutrinos take part in the weak Interaction - they are weakly charged. And they must participate in the gravitational interaction, for they have energy and momentum.

~~Invited talk given at the International Neutrino Conference, Balatonfüred, Hungary (1982) Supported in part by DFG contract Fr 412/4 - 366 -~~

In this talk I would like to discuss a few ideas developed during the recent years and months, which, if true, imply that the neutrino and in addition all leptons and quarks are far more complicated objects than previously thought. We can compare the neutrinos with the neutron. A neutron is a neutral and colorless object. However an observer able to penetrate deep inside the neutron will discover objects, which carry electric and color charges - the quarks. The picture I would like to advocate is one in which the neutrino likewise has an internal structure. Once we penetrate deeper than about 10~ cm inside a neutrino, we will discover electrically charged and (perhaps) also colored objects inside it.

Recently a large number of authors has been interested in constructing composite models of leptons and quarks " '. The idea is that the leptons and quarks are composed of several constituents which are bound together by superstrong forces. There exist various constraints on the sizes of leptons and quarks, e.g. the agreement between theory and experiment of the anomalous magnetic moment of the electron, which imply that those sizes are less than about 10 cm.

In this talk I shall discuss a specific approach. We shall suppose that the W bosons and the fermions are bound states, while the massless bosons (photon, gluons) are elementary '. The masses of the W bosons are generated dynamically by the binding forces in much the same way the 9 meson mass is generated in QCD. In this approach the weak interactions are indirect manifestations of the strong binding forces inside the W boson.

In the absence of electromagnetism the global symmetry group of the weak interactions is SU(2) (weak isospin). The observed structure of the neutral current is obtained if one takes into account the mixing between the photon and the neutral SU(2) boson W,. This mixing arises dynamically, due to the electromagnetic annihilation of the W, constituents^).

We shall assume that the underlying gauge symmetry is given by the group SU(3)C xG^x U(l)e (c: color, e: electric charge). The group Gh is the hypercolor gauge group describing the confining forces responsible for the binding of the hypercolored constituents. - 367 -

The corresponding gauge theory is called QHD. 'For simplicity we shall use the hypercoior group SU(n), where n is yet unspecified. The extension to other groups 1s easily made. For illustration we consider the following scheme, in which the fermions are composed of (pseudo) scalar and fermionic constituents (hapions). The gauge theory QHD based on the group G^ (hypercolor gauge group) describes the dynamics of the haplon constituents bound together by the superstrong hypercoior forces. The QHD confinement parameter AJJ is supposed to be of the order of a few hundred GeV ( ) )• The gauge group G„ is not specified, but taken to be SU(n).

~~spin charge color hypercoior a 1/2 1/2 1 n e 1/2 -1/2 1 . n~~

~~X 0 1/6 3 n y 0 -1/2 1 ii~~

The simplest QHD singlets one can form are fermions of electric charges (2/3, -1/3) = [(ex), (ex)] and (0, -1) • [(ay), (By)] identified with (u,d), (v , e") respectively. The other families are interpreted as dynamical excitations of the first one (see ref. (5)). (For another scheme, in which all haplons are color triplets see ref. (3)). In this scheme exist vector bosons composed of the fermions (as, 6a, ...). Those are interpreted as the carriers of the weak interactions. The global symmetry group SU(2) generated by the haplon doublet (ß) is identified with the weak isospin.

~~The observed parity violation of the weak interaction can be accommodated in two different ways:~~

~~1. The bound state structure discussed above is assumed to be valid only for the lefthanded fermions.~~

2. Both the lefthanded and righthanded fermions are bound states, however the Ajj parameter of the righthanded fermions is larger than the AH parameter of the lefthanded ones, i.e. two QHO group are needed (GL/L', Gu^)- In - 368 -

~~this case the global symmetry groups of weak interactions is SU(2), x SU(2)R; the W-bosons coupling to the righthanded fermions are heavier than those which couple to the lefthanded fermions.~~

Both in the schemes A and B the weak interaction is an effective interaction of the Van der Waal s type, generated by the superstrong QHD force. The universality of the weak interaction between leptons and quarks follows from the global SU(2) symmetry in the a-e-space..

It is assumed that the spectral functions of the weak currents in QHD are qualitatively similar to the ones in QCO. At low energies they are dominated by the lowest lying pole, and at high energies (energies large compared to \i) they can be described by a continuum of haplon pairs.

It is interesting that many aspects of the bound state models can be derived from a local current algebra of the weak currents ' '. We observe that the left-handed leptons and quarks form doublets of the weak isospin. The weak isospin charges FV (i = 1, 2, 3) obey the isospin charge algebra

~~tFM]=i £ijkFk~~

~~We shall assume that these charges can be constructed as integrals over local charge densities F"-(x), i.e.,~~

~~Furthermore we assume that the charge densities obey at equal times the local current algebra~~

~~i = o = ie- -JF*1 6 {jt-y).~~

The local algebra is trivially fulfilled in a model in which leptons and quarks are pointlike objects and the weak currents are simply bilinear In the lepton and quark fields. However, if leptons and quarks are extended objects, the situation changes drastically. Currents, which are bilinear in the (composite) lepton and quark fields would not obey the local algebra, just like the currents, which are bilinear In nucléon fields, do not obey - 369 -

~~the local current algebra of QCO. Thus the local algebra becomes a highly non-trivial constraint. It is fulfilled in the napion models discussed above, in which the currents are bilinear In a and e.~~

It 1s not known what the spectral functions of the weak Isospin currents look like. It could be that they are dominated at low energies by a single pole (like the spectral functions of the ûu or 3d currents in hadron physics), by several poles (like the spectral functions of heavy quark currents« e.g., cc), or by a continuum of states. We shall suppose that the first case 1s realized, and that the weak spectral functions at low frequencies are dominated by the lowest-lying pole (W dominance). Of course, at higher energies, higher excited states as well as the continuum will become relevant.

The spin 1/2-fields a and ß are in the simplest version represented by inassless Weyl fields. Thus in the absence of electromagnetism the weak isospin is exactly conserved, implying è.g. m = m , m • m., m * m .... The question arises whether the observed quark and lepton spectrum is compatible with sucii a scheme. The masses of the observed leptons and quarks are small compared to K.. For this reason it looks promising to assume that in the limit where all interactions besides hypercolor are turned off, the leptons and quarks are massless bound states, i.e. the symmetry of chiral SU(2)W is realized by massless states, and not (as in QCD) by massless Gold- stone bosons '.

The picture which emerges is as follows. There exists a very strong confining interaction - the hypercolor interaction, which binds all haplons into hypercolor singlets, the "observed" leptons, quarks, W-bosons etc. In the absence of QED (and probably QCD) the leptons and quarks are massless. Introducing the QCD interaction lifts the quarks from mass zero to some mass level which is still SU(2) invariant (i.e. mu = m^, m * ms ...). If we introduce the QED interaction, the SU(2)W is broken. The mass splitting inside SU(2) doublets is .interpreted as a QED effect, like the weak Interac- tion mixing (Cabibbo angle etc.).

Before I enter a more detailed discussion, I would like to point out a possible analogy between the pions in QCD and the leptons or quarks. One aspect of weak interaction physics which seems puzzling is the fact that the apparent violation of the weak isospin inside the weak doublets - 37O -

(e.g. {v ,T~), (t,b), ...) is rather large. The mass difference bttween the two partners inside the (v ,T~) - doublet is about 1.8 GeV, the mass difference inside the (t,b) - doublet is even larger than about It GeV. Yet the weak isospin remains a good symmetry which is indicated for example by the fact that the so - called p-parameter (see e.g. ref. (9)) is measured to be very close to one. This indicates that mass ratios lika m(t) - m(v ) / m(-r) + m(v ) are by no means reasonable measures of the quality of the w^ak isospin symmetry. This is, of course, realized in the conventional SU(2) xll(l) gauge theory, where the masses of the ; armions are given in terms of the Fermi constant and a (very small) Yukawa coupling constant, describing the Interaction between the "Higgs" bosons and the fermiris. The large violation of the weak isospin manifest in the Yukawa coupling constants does not imply a large violation of the symmetry in the weak interaction dynamics.

If the weak interactions are a manifestation of hypercolor dynamlr.s, the question of SU(2) breaking is again open. One may wonder why the large violation of the weak isospin in the lepton - quark spectrum dees not imply a large breaking of the symmetry in dynamical parameters like the W- fermion- coupling constants.

We should like to study the violation of the isospin in the pion dynamics. It is well - known that there exist two different sources of the violation of the isospin in strong interaction: the difference of the quark masses m and m., and the electromagnetic interaction. Only the second source contributes to tho n - *° mass difference. If we set m = m- = m and let m go to zero, the pion mass approaches zero as well, provided we neglegt the electromagnetic interaction.

~~Following the laws of chiral symmetry breaking, one finds: '~~

~~H* = (% + fflj) * B + O(tn In m )~~

~~B • - - -~~

~~where u, d denote the light quark flavors, mu> md the quark masses,|o> the QCD vacuum, F the pion decay constant. Typical values are 10) (mu • md) - 14 MeV, B - 1300 MeV . - 371 -~~

The electromagnetic self energy of the *° vanishes in the chiral limit. The electromagnetic self energy of the charged pion can be calculated to order a in terms of the vector and axial vector spectral functions ':

~~2 3« „2 V A (AM +) . = — y- / ds • s In (--) [p (s) - p (s)]~~

~~(PV, p.: vector - and axial vector spectral functions). Saturating the integral above with the p- and A,- poles and using the spectral function sum rules one obtains:~~

Using the measured values F = 132 MeV and ? = 204 MeV, one obtains 3 o n nP M2 +) . = 36.4 MeV , which is close to the observed mass difference AMM2 ~35.6 MeV2. Combining the two relations, denoted above, one finds ':

~~M^o = (% +md) • B + ...~~

~~2 2 M += (mu + md) • B + a • M • 0.31 + ...~~

In the chiral limit m = m. = 0 we obtain M „ = 0, M + «36 MeV. As an U G It« n illustration we consider the case m = m. = 1 KeV. One finds M 0= 1.6 MeV, M + = 36.4 MeV, i.e. the neutral and charged pion mass differ by a factor of about 23. We have just found a situation in QCD, which resembles the one in the lepton- quark- spectrum, namely a large isospin breaking despite the fact that for m * m. the isospin is an exact symmetry of QCO. In the chiral limit the «-mesonsare particles, which in the absence of electromagnetism have zero mass, but have a finite size. Their inverse size Is of order A (A: QCO cut- off parameter). - 372 -

Including the electromagnetic interaction has the effect of lifting the charged pion mass from zero to the finite value M + « 0.16 • e • Mp « 36 MeV. The neutral pion stays massless. The charged pion mass is of order e * A[QCD], i.e. e-(inverse size of pion). We note that the *+ - mass is of electromagnetic origin. The self energy diagram consist of a charged pion emitting a virtual photon and turning itself into a massive state (p, A,, ...). Due to the chiral symmetry the sum of all these contributions is finite and of order e • A(QCD).

With these preparations in mind, we are ready to consider the lepton- quark spectrum. Let us assume that the leptons and quarks are massless bound states in the limit e = 0, 'like the pions in QCD in the limit m = in. = 0 and e = 0. Introducing the QED interactions means in particular introducing self energy diagrams where a lepton and quark emits a virtual photon and turns itself into a massive fermion with a mass of the order of A„ (analogous to the p or A^ mesons in the case of the pion self energy). The result will depend strongly on the mass spectrum of states at the energy of Aj,, about which very little is known. In general one finds:

2 M(fermion) S*|l • Q (fermion) • K • Ah where Q is the electric charge, and K is a constant depending on details of the intermediate states. Using as an illustrative example A^ = 100 GeV and K = 1 one finds the mass spectrum

~~M(neutral lepton) = 0 M(u-type quark) = 77 MeV M{charged lepton) = 174 MeV M(d-type quark) = 19 MeV.~~

Of course this mass spectrum is not very realistic, however it displays a number of interesting features, which are also fulfilled for the real lepton and quark masses: a) The neutrino remains massless {in the first order of a) b) The up-type quark is heavier than the d- type quark. c) The mass splitting Inside the weak doublets is large compared to the lepton or quark masses. - 373 -

Property b) is not fulfilled for the u-d system (the u-quark is lighter than the d-quark), but for the second and third family. Probably this is a consequence of the weak interaction mixing between the various families neglected here.

The example discussed above shows the possibility to interpret the lepton and quark masses as electrodynamic self energies. The self energies are finite since a real cut-off given by Ap enters in the calculations. Using definite bound state models for the leptons and quarks one may be able to develop an actual theory of the lepton and quark masses, and of the weak interaction mixing parameters.

~~Acknowledgement:~~

~~I would like to thank P. Minkowski for useful discussions about the electromagnetic self energy of the pion. - 374 -~~

~~References~~

1. J. C. Pati and A. Salam, Phys. Rev. £_10 (1974) 275 0. W. Greenberg and C. A. Nelson, Phys. Rev. D 10 (1974) 2567 H. Harari, Phys. Lett. 86 B (1979) 83 M. A. Shupe, Phys. Lett. 86 B (1979) 87 H. Terazawa, Phys. Rev. DJ2 (1980) 184

~~2. L. Abbott and E. Farhi, Phys. Lett. 101 B (1981) 69~~

~~3. H. Fritzsch and G. Mandelbaum, Phys. Lett. 102 B (1981) 319 and Phys. Lett. 109 B (1982) 224; Proceedings of the Europhysics on Unified Interactions, Erice, Italy (1981)~~

~~4. P. Q. Hung and J. J. Sakurai, Nucl. Phys. B 143 (1978) 81 J. 0. Bjorken, Phys. Rev. D 19 (1979) 335~~

~~5. H. Fritzsch, R. Kbgerler and D. Schildknecht, CERN-TH 3264 March (1982), to appear in Phys. Lett. B.~~

~~6. 0. W. Greenberg and J. Sucher, Phys. Lett. 99 B (1981) 339; R. Casalbuoni and R. Gatto, Phys. Lett. 103 B (1981) 113.~~

~~7. H. Terazawa, Progr. Theor. Phys. 64 (1981) 1763~~

~~8. G. t' Hooft, in: Recent developments in Gauge Theories, Plenum Press, N. Y. (1980), p. 135.~~

~~9. See e.g. tfie contribution of J. J. Sakurai to these Proceedings.~~

~~10. For a recent review see: J. Gasser and H. Leutwyler, Bern preprint (1982), to appear in Physics Reports.~~

~~11. T. Das, G. Guraluik, V. Mathur, F. Low and J. Young, Phy.- Rev. Lett. 18 (1967) 759.~~

~~12. Similar considerations have been made by P. Hinkowski (unpublished). PROTON DECAY IN SU(5) MODELS~~

~~V.S. Berezinsky • Institute for Nuclear Research, Moscow, USSR Abstract~~

~~Review of proton decay in SU(5) models ÍB given with an emph,i3Í3 on supersymmetrical (SUfiY) MU(5) models.~~

1. Proton decay In minimal SU(5) model» The content of minimal SU(5) model is well known: it compri- ses 5p- and 10-^- plets of fermions, by one in each of three generations, Hicgs 5-and 24-pleta and 24 gauge boaons among which X- and Y- bozons provide proton decay. Among many attractive features of this, mo.it economic, model tho impressive agreement between the predicted 4 value of '..'einberg ancle si-n 9w(mw) = 0.217 + 0.006 In 100/Afjs a and it/3 mpiir:urcd value' Sm 0w(TV\w) = 0.215 - 0.014 must be men- tionod. Tho .cost serious problem met by the model is the hierarchy of raasti.

~~Proton lifetime in *"'"'(5)nill model in Riven by conventional formula~~

l/l l 30 Cp » up (rV//5.1O )' .10 yr, (1) v/hoiT- :;i,, U: unification mana and a in a numerical coefficient of P order i-K). j'rom the; calculât Lonr; oT latent yearo it follow:? that pi-ûcticaliy two uneertainl.ierj iiPfcct the proton lifetime given by Uq. (1). 7ho "I'irct is connected with experimental value of strong interaction conűtont ^3(1^) '-'t »mail energies or, cquivalently, vfith ri,:ul:\r:l::.ation conntant Aj^é, • One nan approximatelyIT1X~/V — and hence "Cp^Apf^ • The cccond uncertainty ia caused by calculation oi' líiíitrii: element of qunrk trnüHxLion inside of the nucléon and included in a .

~~Unification ntaco in.~~

In tin» review« t!ic uwccrtainly in 1^, derived by different authors, if) found to bo donoribed by a factor 2-3. Such the figure co- v.o.zi from nuchanioai quntatjon oi" diJTurcnt reuultij. In fact to compare the re£;ull,T one- i.'iuüt «heck wJiai. value of ei.jtQ*',) v/as ftcoepted and taon use the correct i'ori-.iila for calculation of Aj^è from the adopted value; of ck^(cC') . At Q^"> L| rvi^" in two-loop approximation - 376 -

~~with the threshold behaviour taken Into account the following formu la can be used 1~~

~~where T(Q / is the threshold correction~~

To illustrate the possible error we just mention that using one- loop formula for the calculation of Af^ from £^(0.48^1^ )«• - 0.158'^' one obtains A^ a 38 MeV instead of the correct value ^ MS " 10° MeV. In Table 1 the results of the latest advanced calculations of nx_ are listed. The values of m^ are given for the value

~~A (íj, " 100 *"eV using the relation W^ «v f\ —& . When normalisation~~

~~to ck^(.mr) or d, (mT ) was originally used, we recalculated the value of Ap£ , using Eq.(2).~~

~~Table 1~~

Unification mass m^ at Aj^s » 100 MeV Ellis et al/4/ 1980 1.6.10UGeV Binetruy, Schuker/5/ 1981 1.6.1O14GeV Goldman, Ross/6/ 1980 1.1.10UGeV Marciano, Sirlin/7/ 1981 1.3.1O14GeV Llewellyn Smith et al./8/ 1981 1.3.10UGeV Berezinsky, Ioffe, Kogan^9^ 1981 1.1.1014GeV According to Table 1 the value of m^. can be given as

~~m^ = 1.3.1.2 * 1 - 1O14( Aj^/100) GeV (3)~~

~~The values of Apjj taken from different experiments and calculations are listed in Table 2. - 377 -~~

~~Table 2~~

~~Mackenzie, Lepage/3/ 1981 531^ 149~~

~~Voloshin/9/ 1981 80 many authors 1980-1982 50-250~~

Prom Eq.(3) and Tables 1 and 2 we conclude that central value of m^ at Affj =100 MeV is 1^= 1*3.1O14GeV, while the upper limit at AKTC^300 MeV can be safely taken as m_ < 5-1O14 GeV. r.'atrix element calculations in SIT^ and bag models GUT Lagrangian describes the transition of three quarks into antilepton at very small distances. To calculate the proton decay one has to know the probability of finding two quarks in one point, i.e. the wave functions of quark3 inside of nucléon. Many calculations of this type were performed in SUg and bag models . The range of values of a is shown in the following figure

~~O.7 M.O 3O 1 1 .I ^r>~~

The bi-anchin/3 ratios were calculated by many authors (see review* and references there). In Table 3 the ranges of values formed by the results of the different workers are shown*

~~Table 3 Branching ratios (%) according to different calculations •eV ey e,\ e+to %ir+ \f yi<0 ^K* SUg 33-41 2-17 1-12 18-26 9-17 1-4 O.3-19 0-0.3 bag 9-31 20-32 0.1-5 6-56 3-11 7-12 0.7-7 0.5~~

Prom the values of a_ and branching ratios listed above one can P -i-i derive the upper limit for proton decay Tp< 3«10 yr and conclude that branching ratios are predicted with great uncertainties. - 378 -

Matrix element calculations idependent on quark model of proton The calculations in SUg and especially bag models are unreliab- le since they involve the description of quarks in the nucléon and cannot provide any numerical method of uncertainty estimation. In ref. a method of matrix element calculation independent on quark model of proton was suggested. The essence of the method is a use of constant which describes a transition of proton into a 3 quark state. The constant was calculated from QGD sum rules in ref. . There are two 3-quark currents with proton quantum numbers,

~~^^w.pys^aK (4)~~

~~where i,j»k are colour indexes. The matrix elements of proton transition into the currents b and h are governed by the constants AN and AN :~~

^% , ^()> ANP (6), where M^p is a wavave function of proton. In ref.' for the constant it was found >v^ = 1.2.1O~3GeV6 , while )^N remains unknown, though considerably less than Xu , probably XN £.(0.2-0.3)AN • Fortunately Lagrangian relevant to proton decay in SU(5) J^J^ does not include b current. The problem than consists in calculation of matrix element ^M|b^,(0)\p> using the known matrix element (6), where M is one-meson state (H= 3T.J, ^ ,b , The calculations were performed in ref by two independent methods: by algebra of currents technique with use of PCAC and nonvanishing pole diagram contribution and also by dispersion relation technique. Por P-»€.'Ü3r<>both methoda agree within 10& of accuracy for matrix element. The uncertainties of the method were also estimated numerically in dispersion relation method. The value of a in Kq.(1) was found to be a = 1.0 with uncertainties described by a factor 2. The matrix elements were calculated independently for different decay modes. Minimal S_tJ(5). model: regulto and conclusions. The branching ratios of proton and neutron decays relative to P-» e^pr° decay are giv^n in Table 4 for model independent calculations'8' and SUg model. Tt.ble 4 Branching ratios of protcn decays f(P-^X )/F(P-* &+3T°J)

~~ref /13/ 0-10 0.10 0.01-0.08 0.03-0.10 4/5* 0.04~~

~~SU6 0.05-0.52 0.5-0.7 0.01-0.36 0.01-0.6 0.27-0.4 0,03-0.12 Branching ratios of neutron decays~~

2* 0.20 0.02 0.002 By asterisk are shown the branching ratios derived from isotopic symmetry. The ratio of neutron to proton width is Ip/lp =1.2. For an average nucléon in Fe-nucleus the probability of decays obeys the weak hierarchy s (N-»e#): (N-»^)'. (N->^K) - 1:0.20:0.10. The central value of proton lifetime calculated with A f^ = a 100 MeV (ra^a 1.3.1014 GeV) and a =1.0 is

27 TJp = 4«6.10 yr. (7) Th>3 upper limit for a nucléon in Pe calculated with the values ACT i 300 MeV (ji < 5.1O14GeV) and a„ é 2.0 is 30 rN(Fe)<2.10 yr (8) The contribution of three body decays and nuclear effects, e.g. |M +- N/ -> JL + mesons, can further lower the upper limit (8). Comparison of the central value (7) and upper limit (0) wi.h the measurements of proton lifetime in Kolar Gold Field' ' ( Co ^c 10 *x,6.10J yr) reveals the conflict of minimal SU(5) model wifh observations. 2. Hodifûcationa of minimal SU(5) model

There were suggested three ways of increasing Tp in SU(f5) models. (i) The increasing of unification mass m^ by introduction of new coloured quarks lighter than their lepton counterparts in multi- - 380 -

plets/13-14/. (ii) The increasing of nu due to new Higgs coloured particles, in particular, due to Higgs 45-plet/15/ (iii) With the help of mixing and permutations of right components of fermions the proton decay can be "rotated away" up to lifetimes 1 1 of order 10^*-10^yr/ °- 7/ # Sucn jnixiugg (permutations) being im- 1 possible in SU(5)min can be provided with help of Higgs 45-plet' . All the discussed modifications are introduced ad hoc for increasing Vp , in contrast to SUSY SU(5) models which were created to solve the hierarchy of mass problem. 3. Proton decay in SUSY SU(5) models The essence of SUSY models is the symmetry between fermions and bosons. Untill this symmetry renains unbroken the light Higgs particles are defended against acquiring the superheavy masses through radiation corrections. Then the natural scale of supersymmetry breaking must be of order 100-1000 GeV. Supermultiplets of SUSY models contain bosons and fermions. The supersymmetrical partners of usual pariteles in the supermultiplets are called nuinos. Nuinos are associated with the partcles of minimal SU(5) according to the following scheme.

~~n SUSY S(A5)Wm SUSY SW5)mm SUSY u% o Hx. V*. 0 Vx. *'*- °,~~

where 5u and 5H are Higgs 5-plets (the minimal number of Higgs 5- plets in SUSY SU(5) is two) and A^ are gauge bosons. The supersymmetrical partners are call-ed: squark (sq), slepton (si), higgsino or shigga ( H ), photino ( y ), glulno ( ? ), wino ( W ) and zino (Z }• - 381 -

~~a. Unification maag in SUSY SU(5)~~

It ia usually concluded that unless sin 0W ia too large the unification masa in SUSY SU(5) increases up to ni/v10 GeV, resul- /18—19/ ting thus in too large proton lifetime' '. The calculations of /19-20/ m_ in two-loop approximation were performed in ref. Accor- /19 dins to / the results are: = 6 oo) .005-In

Thus sin ©vu1 •'•s no* ^ a S°°d agreement with experimental value (0.215 - 0.014) and proton decay is practically unobservable. If to increase the number of Higgs 5-plets from minimal number 2 to 4» then:

~~= 3•'I O.OOS~~

In this case sin ©w is in obvious conflict with experimental value« v.'e will return to the problem of large unification mas3 in SUSV GU(5) in subsection d). b. Past proton decay in SUSY due to d =5 operators In ref.'s Z21"22' it was discovered that in SUSY SU(5) with two Higgs 5-plets there are operators of dimension d =5 which violate barion number (Fig.1)

~~H, H,~~

~~Pig.1 - 382 -~~

~~Here sUv and BD are up and down squarks (spin 0) from b and a generations respectively (a,b,= 1,2,3 ) and H^, Hg are superheavy shiggses. The constants of interaction and are proportional~~

~~to the masses of D and Ub (usual) quarks respectively.~~

~~(9)~~

where g is a gauge constant, liVi is W-boson mass and 2. w Since squarks are heavier than proton the diagrams of Pig.1 cannot produce the proton decay. But if W * W B and/or "g have a Majorana mass nu. proton decays via one of the diagrams shown in Pig.2a.

~~"M str~~

~~Pig.2.~~

As was found in réf.' 4-fermion constant Gt,F is on one hand strengthened by proportionality GHF ~ 1/rn^ (instead of Vni^. in the case of gauge boson exchange), by the masses of t- and b-quarks (as an example see Pig.2b), and on the other hand it is suppressed by Kabayashi-Maskawa angles 3-, Sg S., (see Pig.2b) and 4-fermion renormalization factor A TCO.Z ((i n SU(5() A) In the case oi" heavy wino one obtains - 383 -

There are also additional suppression factors in matrix element, namely, the supp—session due to Lorentz structure (S of 4-fermion Lagrangian connected with the current ^ with small constant Xfj , Eq.(6), and suppression due to the decay to K-meson. The proton lifetime estimated according to diagram 2b, r can reach experimentally allowed region at V^)^ r^ 10 GeV and VYï ~ Kj 3 TeV. The decay modes are strongly dominated by P-»"^« •

The case of small Majorana masses of winos and gluinos was considered in some details in ref.^23^. If K\ÇJ , tnrw^tt^the 4-fermion constant G^p^^M/f^R' ffli, ) » where m^ is Majorana mass of wino or gluino. The lifetime of proton is "Cp^iO-3 yr if Majorana masses Inris < 13 GeV and mJ»<5 GeV. This values don't contradict experimenr- fcal limitations. The decay modes are again strongly dominated by p_>^) )<•* for gluino exchange and by P-> V^ K. for wino exchange. c. Himts mediated proton decay The proton decay in SUSÏ models can be mediated by Higgs exchange if masses of coloured Higgs particles from 5-plets are im /v 10 GeV. The case is quite analogous to the corresponding decay in the usual 3U(5) models.Since the coupling constants of Higgs particles with fermions are proportional to fermion masf:os the decay . .. o modca are strongly dominated by the channels P ->J-*> V^ and p —> "vL K « The V/einberg angle and Vr^/VYx.^ ratio can be brought in agrrement with experiment . d., SUSY SU(5)Adiminished unification na33 The SUSY models discussed till now predict the strong dominance of P-» V K. or p-*M+K.°in proton decay. Menwvhile, as the results /ip/ y of ref. suggest this feature wa3 not observed. A question then naturally arises: do the absence of strong p-»vK , P-*/**K dominance reject SUSy models? /OR/ In ref. a SUSY model with diminished nu was constructed. There were introduced two additional Higgs 10-plets, ao that the symmetry between Higgscs and usual matter becomes more complete a3 illustrated by the following scheme. - 384 -

~~matter (5f)R) wherec /' :^: HÍ* H"1'" (24,,) (10 HJL. I~~

~~The 1O-plet Higgs masses can be produced by the interaction with Higgs 24-plet through its vacuum expectation value Vo, and by the usual mass term:~~

Prom (12) one obtains the masses of four Higgs particles from 10- plet (11); V (13) Consider first the ext?ems case of smallest unification mass m^.. It occurs when M -x. 2hVQ and Higgs singlet H| is light whereas the coloured Higgs particles H2i» H-^^ and H.^ are superheavy and don't influence the evolution of constants. Since H.+ is incoloured singlet» P^~ and ^-functions remain unchanged in comparison with the usual SUSY SU(5), while A^ gets from H^ , the additional contribution (-6/5): (14) Then in one-loop approximation one obtains

where m x and are the unification masses in the SUSY models with Higgs 1O-plets and without them respectively. Weinberg angle and mass of b-quark are in excellent agreement with the experiment. 0.220 > 4.8 GeV (16) Consider now proton lifetime. With the 4-fermion renormalization constants taken into account» - 385 -

~~i > .G ^o O ' A~~

~~one obtains for the central value of Up ( Kf^% = 100 MeV, a = 1.0) and for its upper limit ( Nf^a 300 MeV, a = 2.0), respectively: "Dp = 3.7.1029yr , T^ < 5.9.1031yr (17)~~

Of course nu (and hence ~Cp )can be increased by the diminishing : the masses of coloured Higgs particles in Eq.(13)» 4« Conclusion : predictions and signature of different SU(5) models --=: (a) Minimal SU(5) X Short lifetime T^Fe) < 2.10^ yr, weak hierarchy of decays! "^ 1:0:20:0.10 (18) ]

~~(b). Modified SU(5) models with mixings or increased mJC» j~~

~~31 34 ~C?~ 10 - 1O yr ' weak hierarchy of decays (18). (c). 3USY SU(5) v/ith diminished m (no box diagram decays, no Higgs / mc-áioted decays) "Up > 1030 yr v/euk hiernrchy of decays (18). ;i-,~~

~~(d) . uUSY SU(5) with cl = 5 operators (box diagram decays) :~~

~~31 32 ÍJhort lifetime ~C? < 10 - 1O yr, vory strong dominance of p -> ^ K (o) SUC Y StT(5) v^ith Higg3 mediated decays 30 34 1O ^r < Xp < 1O yr , '.\ tho ntronc hierarchy: - 386 -~~

References /I/ Georgi H. and Glashow S.L. Phya.Rev.Lett 32, 438, 1974 /2/ Marciano W.J. and Sirlin A. Weak Interaction Probes, Workshop, N.Y.1981, p.107. /3/ Mackenzie P.B. and Lepage G.P. Phys.Rev.Lett 47, 1244, 1981« /4/ Ellis J., Gaillard M.K., Nanopoulos D-.V. and Rudaz Nuclear Physics B176, 61, 1980. /5/ Binetry Pc and Schucker T, N.P.B 178, 293. 1981 /6/ Goldman T. and Roes D.A., N.P. B171. 237, 1980 /7/ Llewellyn Smith C.H., Ross G.G. and Wheater J.F. H.P.B177» 263, 1981. /8/ Berezinsky V.S., Ioffe B.L. and Kogan Ya.I. Phys.Lett. 105B, 33, 1981 /9/ Voloshin M.B. Preprint ITEP N 21, 1981 /10/ Xangacker P. Phys.Rep 72C, 185, 1981 /11/ Ioffe B.L. N.P.B188, 317, 1981 /12/ Miyake. Report at this conference 1982 /13/ Smirnov A.Yu. ZhTEPh Pisma, 31, 781, 1980 /H/ Ellis J. et al preprint LAPP-TH-14, 1980 /15/ Cook G.P. et al Phys.Lett 90 B, 298, 1980 /16/ Jarlskog G. Phya.Lett 82B, 401, 1979 /17/ Berezinsky V.S. and Smirnov A.Yu. Phys.Lett.97B, 371, 1980 /18/ Fradkin E.S. and Pradkina T.E. Preprint P.M. Lebedev Physical Inscitute N 246, 1981. /19/ Ellis J., lianopoulos D.V. and Rudaz S. preprint CERN TH 3199, 1981. /20/ Einhorn M.B. and Jones D.R.T. University of Michigan preprint Uli HE 81-55, 1981 /21/ Sakai N. and Yanagida T. N.P.B197, 533, 1982. /22/ V/einberg S. Harvard University preprint HUTP-8I/AO47, 1981

~~/23/ Aliev T.Ma and Vysotsky M.I. Preprint ITEP N 77, 1982. /24/ Nanopoulos D.V. and Tamvakis K. Preprint CERN TH 3255, 1982. /25/ Berezinsky V.S. and Smirnov A.Yu. preprint INR lï 32, 1982. - 387 -~~

~~PROTON LIFETIME~~

~~Dubravko Ta die" Zavod za teorijsku flziku, Prirodoslovno-matematiöki fakultét, University of Zagreb, Croatia, Yugoslavia~~

~~The main purpose of this note is to discuss a calculation~~

~~of the decay made p -» ir°e performed by the Zagreb group~~

~~\1\. We are concerned with the hadronic effects encountered~~

~~in the calculation of the p -• TT transition induced by the~~

~~Grand Unified Theories (GUTS). As far as these theories are~~

~~concerned we direct the reader to review articles |2-7|.~~

~~The calculation is based on the effective three-quark hamiltonian~~

~~Gu//2 = g2 ç /8M2~~

~~»vith g as the unified coupling constant, M the heavy boson mass and £ the normalization by strong, weak and electromag- notic interactions.~~

~~The direct contribution has been calculated previously~~

~~18 - 15 I - 388 -~~

~~G —— + + c <ïï°e IHGU|p >= -2 (1 + 3Y5) (2)~~

~~There is also a pole contribution |1,16-181 (see fig.l) where~~

~~a weak vertex~~

~~|HGüiNj >- -%~~

~~is determined by a three-quark fusion mechanism. Here N.~~

~~symbolizes either a proton or a resonance. The strong vertex~~

~~for the proton pole is determined by the strong pion-nucleon~~

~~coupling while for the resonance the effective coupling~~

~~constant is determined from the decay widths.~~

~~. Our calculation was finished before we were aware of the~~

~~results obtained in the ref. |16|. It has been prompted by~~

~~an analogy with the non-leptonic decays of hyperons. There it~~

~~seems that pole terms are essential for the theoretical calcu-~~

~~lation of the decay amplitudes. They might be even more im-~~

~~portant for a better understanding of the z*+ pv decay and~~

~~other radiative decays.When such pole contributions are used~~

in the framework of the empirical model |19,20| one has to warry about the possible double-counting. There is no a priori answer to the double-counting question as the answer actually depends on the determination of the model's parameters. Hadronic poles, at the quark level, can be understood as gluonic exchan - ges between quark lines (see fig. lb). Thus, in a sense, hadronic poles Improve results based on the straightforward application - 389 -

~~of quark models of hadrons. Some additional strong-interaction~~

~~effects appear that were not adequately represented by the~~

confining bag or potential.*

~~There is no exatr; procedure for choosing how many poles~~

~~to include. In non-leptonic decays dispersive argument was~~

~~used to retain only the intermediate states with the lowest~~

~~masses.~~

~~Our proton-decay calculation employed MIT bag model to~~

~~estimate hadronic matrix elements. Proton-pole term yielded~~

~~values comparable tc the direct contribution, while the con-~~

~~tribution of heavier 1/2 resonances was an order of magnitude ** smaller. Before presenting final results we will briefly~~

~~discuss certain difficulties and technical problems arising in our estimates in order to indicate theoretical uncertainties *** underlaying our numbers.~~

~~The main problem in the calculation of the hadronic matrix element~~

~~ip r = Fp(P)lY5uA(p)|a e~ ' (4)~~

~~is that the bag-model states are static. A straightforward~~

For comparison: in the nuclear shell model additional effects are referred as residual interactions. ** — 1/2 resonances are very thoroughly studied in the MIT-bag model |2 0|. *** There are additional uncertainties connected with the GUT's symmetry-breaking dynamics |6 | - 390 -

~~calculation gives~~

~~bag < ° l°l„lp >bag " ' d^lr) ^SVL' V°~~

~~g(r) •-1Í/2 |u(u2 + v2)| (5)~~

Here u and v are large and small components of the static cavity solutions. In units t» m I, c « 1 their dimensions are L~3^2. Thus the overall dimension of the result (5) is L~3^2 * and it is wrong as the dimension of F (0) has to be F (OH L , A way out is to relate |21,22| bag state to the superposition of the momentum eigenstates

~~F fx" (6) P~~

~~This relates F to the nucléon wave-packet x~~

~~3 2 |Fp(0) |= | / d x g (x)| (7) which at least gives a correct dimension for Fp. Alternative approximation 2 is found when X (p) is calculated using the Peierls-Yoccoz projection |22| :~~

* This follows from the effective hamiltonian

~~ff Hw* (pole) = 1 ^ !E!IÎÎÎL ~ (i+ 3 y,) * • , fl Mp e+ 5 p n~~

~~Dim | (Gu Fp g - 391 -~~

~~F_(P) - a —^-T / e1 F'r 9~~

~~3 p = / d p I3(p) | p | (8)~~

~~2 2 3 I,(p) » 1 ? / d 3r e -1 r-F D |exp( r -~~

~~X(P) " {* -*—•* m (2ir)J~~

~~In the expression for I~(p) the gaussian approximation for the~~

~~quark wave functions was used.'~~

~~The original four-fermion hamiltonian contains the inte-~~

~~gration over quark and lepton fields. In the integration over~~

~~the sphere in which quarks are confined the lepton space,~~

~~carrying dimension \T ' , is actually factored out. This is recovered by introducing momentum elgenstates (6). On the other hand this suggests approximation 3~~

~~3 F (0) 2 -i— / g(r) d r (9) /vbag~~

~~All three approximations agree within 5% for the proton state.~~

~~The agreement among approximations is much poorer when 1/2 resonances are studied. We have included the following l/2~ resonances~~

~~N = £L' (1S35)~~

~~Nb = sn (1650)~~

~~In table 1 overall effective strengths |A| and the form factors F we listed. For the approximations 2 and 3 we have - 392 -~~

~~found overall sign of A by using the LSZ reduction and~~

~~PCAC in order to estimate the sign of the strong pion verticies.~~

~~The results appearing in table 1 should be compared with the~~

~~amplitude from the direct contribution (2) (l4|~~

~~2 AD = 0.1472 (Ge V) (10)~~

~~The value (10) should be multiplied by the high momentum sup-~~

~~pression factor n ^ 2-5 |14,15|. Simmilar factors should~~

~~multiply the results presented in table 1.~~

~~It turns out that the contributions comming from l/2~~~

~~resonance poles are negligible in approximations 2 and 3.~~

~~Their contribution is most likely overestimated in the approxi-~~

~~mation 1. An analogous approximation overestimates the pion~~

~~form factor by a factor of five.~~

~~The inclusion of the pole term increases the probability o + to the p •* ïï e decay by a factor t 6 (approx(2 and~~

~~3) in comparison with the older bag-model calculations |14,15|.~~

~~With approximation 1 this factor would be -\. 25. This signi-~~

~~ficantly shortens proton lifetime T and brings it in much~~

~~better agreement with different approaches 116—IS J- Assuming~~

~~that the total lifetime is simmilarily influenced one finds the results shown in table 2. They were calculated by using the parameters of ref. |6 |, i.e. x—r = 0.16GeV and M =~~

~~2-1-10 GeV. For reader's conyinience we have also given~~

(in table 2) some other values listed in ref. \6 j. The inclusion of the pole terms in the bag-model calculations obviously improves agreement with other approaches. However the comparison with the calculations based on the harmonic - 393 -

~~oscillator models requires additional study of the plon form~~

~~factors (i.e. n mentioned above), the behavior of the~~

~~harmonic oscillator wave functions at the origin and the~~

~~perturbative vacuum inside the bag |13| . Comparison of the~~

~~various theoretical methods may eventually lead to definitive~~

~~acceptance or rejection of the minimal SU(5) GUT . There is~~

~~no doubt that the eventual experimental measurement (if any) ,~~

~~and especially the study of the decay branching ratios, will lead~~

~~to a much more thorough theoretical understanding. It will~~

~~allow clear distinction among various theoretical models.~~

~~Some existing experimental evidence |23| might be interpreted |6| as corresponding to the bound T-î& 6.10 yr - 394 -~~

~~Table 1~~

~~Effective strengths and weak vertices~~

~~Approxijiaticn 1 Approximation 2 Approximáción 3 Baryons 2 3 2! 3 2 3 |A 1 (GeV) |F| (GeV) |A| (GeV) |F| (GeV) | (GeV) |Fj (GeV)~~

~~2 P 0.2317 1.61:ao" + 0.2259 1.57xlO~2 + 0.,2072 1.44xlO"2 N 0.2485 34.18,~~

~~Table 2~~

~~Proton lifetime~~

~~v«.»yr, Ref. Remark~~

~~4 16~~

~~120 14~~

~~123 15~~

~~108 10 According to | 13|, y (0) from p-wave decay~~

~~172 10 According to |l3 | f (0} from CA, F parameter~~

~~432 10 1 (0) from CA, D parameter~~

~~18 Recent work Approx 1, p pole 4*6 n I, p+R poles 19 it 2, p pole~~

~~20 ii 2, p+R poles 20 n 3, p pole 18 H 3, p+R poles - 396 -~~

~~References~~

~~|1| S.Meljanac, D.Palle, I.Picek and D.Tadid University of~~

~~Zagreb preprint (October 1981). Nucl.Phys.B, to be published. |2| P.Langacker, Phys.Rep„ 72 (1981) 185~~

~~|3| J.Ellis, Gauge theories and experiments of high energies,~~

~~eds. K.C.Bowler and D.G.Sutherland (Edinburgh University,~~

~~Edinburgh, 1981) p.201~~

~~|4| T.Goldman, Progress in grand unification, preprint LAUR-81-~~

~~2675~~

~~|5.| H.Stremnitzer, Baryon decay in grand unified theories,~~

~~Proc. of Visegrád 1981 symposium~~

~~|6| W.J.Marciano, Proton decays 1982, preprint BNL 31036~~

~~|7| D.V.Nanopoulos, GUTS versus SUSY GUTS, preprint TH-3249-~~

~~CERN~~

~~|8| T.J.Goldman and D.A.Ross, Phys.Lett. 84B(1979)208. Nucl.~~

~~Phys. Bljl(1980)273~~

~~|9| M.Machacek, Nucl.Phys. B159(1979)37~~

~~|}0| M.B.Gavela,A.Le Yaouanc,L.Oliver, O.Pene and J.C.Raynal,Phys.~~

~~Rev. D23(1981)1580~~

~~|ll| A.M.Din, G.Girardi and P.Sorba, Phys.Lett.91BJ1980)77~~

~~|X2| G.Kane and G.Karl, Phys.Rev. D22J1980)2808~~

~~|13| J.F.Donoghue and G.Karl, Phys.Rev.D24_( 1981)230~~

~~|14| J.F.Donoghue,Phys.Lett. 92B(1980)99~~

~~|15| E.Golowich,Phys.Rev. D22 (1980)1148~~

~~|16| V.S.Berezinsky.B.L.Ioffe and Ya.I.Koqan,Phys.Lett.105B(1981)~~

~~33 - 397 -~~

~~1171 J.M.Fernandez de Labastida and F.J.Yndurain, Phys.~~

~~Rev. Lett. 4J (1981) 1101 f~~

~~|18| Y.Tomozawa, Phys.Rev. Lett. 45(1981)463~~

~~jl9j A.Chodos,R.L.Jaffe,K.Johnson and C.B.Thorn,Phys.Rev.~~

~~DIP (1974) 2599» T. De Grand, R.L.Jaffe, K.Johnson and~~

~~J.Kiskis, Phys.Rev. £12 (1975) 2060~~

~~|20| T.A. Oe Grand and R.L.Jaffe, Ann.Phys. (N.Y.) 100 (1976)~~

~~425, T.A.De Grand, Ann.Phys. (N.Y.)101 (1976)496~~

~~|21j J.F.Donoghue and K.Johnson, Phys.Rev. D21 (1980) 1975~~

~~J22[ K.F. Liu and C.W.Wong, Center-of-mass correction in the~~

~~MIT bag model, University of California preprint)~~

~~C.W.Wong, Phys.Rev.D24(1981)1416~~

~~123f M.R.Krishnaswamy et al- Phys.Letters 106B(1981)339 - 398 - n e P.N,~~

~~(a) (b)~~

~~Fig. 1~~

Baryon poles in p-decay and their quark content. Circle and box in /la/ are the strong and weak vertex, reapertively. Full lines in /lb/ are quarka, while wavy lines symbolize some of the numerous possible gluon exchanges. - 399 -

~~LOCAL CONFINEMENT OF CHARGE IN MASSLESS QED~~

~~V.N. Gribov* Central Research Institute for Physics, Budapest~~

~~ABSTRACT~~

It is shown that raaesless electric charges cannot exist in nature as they are completely locally screened in the process of formation. The possibility that this mechanism leads to a vacuum which underlies the Weinberg-Salam theory of eleccroweak interactions is mentioned.

The possibility that massless charged particles exist has always been doubted • Vet, no detailed analysis of the problem has ever been performed. It was not clear what would happen if such particles were introduced in the theory.

The introduction of massless charged particles in the theory occurs permanently and it is a very attractive approach since the introduction of particles with bare masses different from zero leads to the problem of eigenmass of particles for the solution of which we have so far no ideas. If bare particles have no masses, the mechanism of spontaneous symmetry breaking (condensate formation) can possibly provide a reasonable explanation of the appearance of mass of the observed particles.

To understand the essence of the problem associated with the massless- ness of charged particles it is sufficient to recall what problems were encountered in the thirties in the description of massive particles and how they were solved. In quantum electrodynamics there exist bare massive particles before the interaction is switched on. The amplitudes of creation and scattering of such particles are easily calculated in the Born approximation and have a simple and beautiful structure. However, the calculation of photon emission amplitudes in such processes leads to infrared divergencies which show that the number of created photons in these processes is large. This has been interpreted as the creation of the particle's classical field.

*0n leave from the Landau Institute for Theoretical Physics, Moscow. '^Folklore - 400 -

»«•ides, it has been found that this classical field polarizes the vacuum. As a result now every student knows that an electron is created with a definite charge distribution and a classical field around it.

The difficulty of the problem associated with the massleisnesa of charged particles becomes evident if one remembers that the probability of photon emission for the time t in a process with sufficiently high momentum 2 transfer q at m t/q>l is determined by

2 In Sj lnqt m 2 which at m •+• 0 tends to °°. That means that the number of photons appearing it» the creation process of massless particles is essentially larger than that for massive ones. This leads to the fact that the classical field of massless particles is rather singular, which would not have been terrible, had it not resulted in a strong vacuum polarization.

In this talk* we show that a massless charged particle created (in pair with an antiparticle) in a region of the size of the order of 1/q will be screened due to vacuum polarization for the time t determined by the condition

~~a •£ lnqt ~ 1 (1)~~

~~2 where a - a(q ) is the charge of the particle.~~

As a result a massless neutral object (a pair of neutral objects) of the siae of the order of 1/q will be formed. This result seems natural from the point of view of the analysis of the zero charge in quantum electrodynamics.

The phenomenon is the following. Let us study the creation process of two classical particles with charges e and'-e moving in opposite directions. Thti current corresponding to this process is of the fora

~~j Xt 2 U " n tvu6(vx)-v^5(v'*)]6(x )«(x0> (2) where v , vf are light-like four-vectors of the velocities of the charges.~~

*For details, see V.N. Gribov, Nucl. Phys. B., tc be published. - 401 -

~~The electromagnetic field created by this current is the following*:~~

~~v.. v.' (3)~~

~~2a (A) vx~~

~~The strength of the field is different from zero only on the light cone or on the sphere of radius t where t is the time from the moment when the charge was created (Fig. 1).~~

~~Fig. 1~~

~~Thanks to this simple form of the field it is possible to calculate exactly the current appearing in the vacuum of free massless fermions. It proves to be equal to~~

~~(5)~~

"Í vu' (6) where n is a light-like vector normal to the cone in the point x. The current is oriented along the meridians on the sphere the poles of which are determined by the instantaneous position of the charges. The charge density on the sphere equalb zero. In the points where the charges are positioned there is a 6-1 ike diverging contribution to the current (T •+ 0)

~~2a •5?*! (7)~~

*In this paper A denotes eQA. ; j is the density of the number of particles. - 402 -

necessary from the point of view of charge conservation. The divergence is due to the fact that the value of the charge transferred from one pole to the other during the time t is proportional not to t but to lnt and is infinite at any finite moment of time. It implies that physically it is impossible to create two charges instantaneously and it is necessary to introduce at least an infinitely small duration of the formation process T. This is done when the final expression (7) is derived.

So far we have described the result for vacuum polarization in a pure Bremsstrahlung field of two massless charges created for an arbitrarily small time T. In fact, this it not the solution of the problem of what happens in the creation process of two massless charges since vacuum polarization changes the field of the created charges. To get a correct answer it is necessary to solve a self-consistent problem, inserting into the Maxwell equations» the current in the form of a sum of external and polarization currents. This problem can also be solved and the result for the total current on the sphere j = jeX + jV is the following. The current on the sphere outside the points where the particles are positioned, is equal to

~~.o i = JU,1 3 " r-J where j . is the current in a pure Bremsstrahlung field (5), Y "• O /3n. The local contribution in the points where the particles are positioned is~~

~~jext (x) « U . (9)~~

~~The field on the sphere is of the form~~

~~F - —J^-— . (10)~~

~~This means that massless charges created during the time T will completely be locally screened in a sufficiently large time when~~

~~Y In | »I. - 403 -~~

~~In the self-consistent field, apart from the currents and field on the sphere (8), (9), (10), there are also currents and fields inside the sphere which we shall not discuss in this talk.~~

Let us consider how this classical approach is connected with the quantum description of the creation process of massless charges. The field A (x) of the charged particles created by the external field (for example, e+e~ annihilation) and observed in the points x.,x. is determined by the .two diagrams of Fig. 2. It is not difficult to show that the contribution of these two diagrams leads to Exp.(3) multiplied by the amplitude of Fig. 3 everywhere inside the sphere of Fig. 1 with the exception of the shaded region. The width of this shaded region is of the order of 1/q if the external field is a packet of the size 1/q.

~~Fig. 2~~

~~Fig. 3~~

The Bremsstrahlung field corresponds to the limit q -»• ». Calculating the vacuum polarization in the creation process of massless charges in the first approximation (diagrams of Fig. 4) and doing it in the formal limit q •* <*>,

~~Fig. 4 - 404 -~~

one gets the current different from zero in the shaded region., This current has the same structure as (5) differing only by the replacement of v-*- by -v . This replacement implies that the density of the charge on the sphere is non- zero; its distribution is determined by the denominators vx ~ -r- (l-cos&) and v'x ~ y (1 + cosS) and is singular near the charges.

However, as it is shown in the text, the charge distribution in the shaded region is defined by the details of the behaviour of the external current during the early stage of the particle creation (t < 1/q). This means, that the formal calculation in the limit q -* <», i.e. the replacement of calculations of the real diagrams by the calculations of the current in the singular Bremsstrahlung field is not correct. The structure (5) of the vacuum current is not due to higher order corrections but is a result of more thorough calculations of the integral features of the singular current. In the region near the external charges (black, region) one can use the Brems- strahlung approximation. The result (7) literally coincides with the perturbation theory.

~~Fig. 5~~

Higher order corrections (diagrams of Fig. 5a) are very essential if one wants to calculate the detailed behaviour inside both regions, but they do not influence the integral features of the singular current. Both results (5) and (7) are analogous to the sum rules for inclusive processes, but in the coordinate space. The self-consistent solution (8)-(10) comes from summing the diagrams of Fig. 5b. The described result is interesting from the point of view of the zero charge problem ' and the possible features of the 2) quantum electrodynamics at small distances. According to ' the «normalized charge as a function of the cut-off X and the mass m of the particle can be written in the form 2) L.D. Landau, I.Ya. Pomeranchuk - 405 -

~~a(iO~~

2 a(m ) is going to zero when either A. is going to infinity or m is going to 9 zero. The zero value of a(m ) in the limit X •+•<*> means total screening of the particle's charge by the vacuum polarization charge distributed in the region from I/A. up to 1/m. This means, that charged particles we are talking about and the masses of which enter the formula cannot exist. The above result was considered as a contradiction inside the theory due to its local structure.

It was not rlear how to handle the limit m -»-0 because of difficulties connected with the infrared divergencies of the theory. These difficulties can be avoided considering the process for a finite time t and introducing the classical field instead of the photons. Finite time considerations of the process are preferable also because in this case one does not need any hypotheses about the character of the stationary states existing in the theory. The statement in the present paper on the total screening of the charge in the limit in + 0 is in accordance with the idea about the equivalence of both the limits m •* 0 and X •*•<*>. The essential difference is due to the fact, that in our case the screening charge is distributed not over the region I/A. < r < 1/m, but over that of r of the order 1/A.. At the same time, from the point of view of this limit no reason is seen to suppose a contradiction in the theory. It is more natural to assume that the neutral objects which appear in these considerations and have the velocity of light are really massless, almost pont-like particles (their sizes are of the order of 1/A). Such an interpretation of the zero charge problem is not in contradiction with the equivalence of the limits m -*• 0 and X •*• », since the charge distribution from 1/A up to 1/m, which appears in the usual approach is in fact the charge distribution inside the stationary state (charged particles) not existing in the limit X •*• «\ In our approach it is quite natural that pointlike neutral particles are created in the limit A. •+ % too. Indeed, applying the calculation described above not to the creation of massless charges but to that of massive ones, the only difference would be that (instead of being valid for an arbitrary t) the formulae would be correct only for a time t 2 less than q/m where q is the momentum of the charge. At times less than this q/m the masses of the particles do not figure at all in the calculations. If the momentum q of the particle is of the order of X, then at the moment 2 t - A/m the changing charge of the created object becomes, acording to (9), - 4O6 -

~~which is going to zero as A. ->•«>.~~

From all what we have said it looks natural to suppose that the solution of the zero charge problem is the following in both the massless QED and the massive one in the limit A. •*• °°. In the theory there appear massless neutral point-like particles (of size of the order of 1/X) which are "bound states" of bare charged particles. If one proposes such a hypothesis, it is interesting to discuss what happens with these particles because of the existence of vacuum fluctuations which we neglected up to now. It is quite natural to have among these particles scalar ones. However, scalar massless particles must condensate and create an average field in the vacuum. Since the time these particles require for their formation is of the order of ~ 1/A.e , we do not see any reasonable equations for the density of the condensate except the equations of the type «(*•) ,_ hi „ ,

The interactions of massless neutral particles with this condensate would give them a mass probably of the same order as u> If the bare charged particles of the theory are massless they also can obtain a mass m, but of the order of a u because of their coupling constant a. The value of n depends on the details of the mechanism which produces the mass. The result would be the usual QED with massive charged particles plus with heavy neutral particles of the mass of order'— m. This theory vwould be very similar to the standard theory of the electroweak interactions.

In conclusion we should like to stress, that independently of the hypothesis about the existence of neutral massless particles in the theory, the formulae (8)-(10) describe in the framework of the usual QED the early stage 2 + - (t < q/m ) of the processes like e e annihilations into leptons. From these formulae it is clear, that if •=— In ^j £ 1, the states which are formed at m this stage differ essentially from the usual electrons and positrons (the charge of these states is much less than the electron charge). Therefore it is natural to expect, that the decays of these states would produce jets analogous to the jets in hadronic processes. - 4O7 -

~~OUTLOOK~~

~~V.N. Gribov* Central Research Institute for Physics, Budapest~~

I was asked to give some outlook of the theoretical situation in particle physics and it was very difficult for me to choose the topic and especially for this conference, because the main direction of this conference is to go far beyond our usual space scale, from 10 -10 cm. To go far to the neutrino mass, to proton decay and so on. I certainly agree with Lobashev that now it is very important to search for new particles, new phenomena connected with the smallest distances. Of course this is true for the experimentators, who have done so much for exploring the world o£ the distances from 10 -10 cm. But for theoreticians the situation is not so clear, because the world of smaller distances was not explored by the experimentalists, and dealing with it we must predict the structure of this world. Unfortunately, the possibility of such a prediction looks doubtful from the point of view of our previous experience. It is obvious that nobody would be able to predict the existence of quarks, gluons etc. without experiment. In this sense the theoreticians now are in a new situation: they can wonder about the new world, or chey can try to understand better the world which is already explored for us. Of course, work has to be done in both directions. In the new range of distances we can rely mainly on the symmetry approach asking ourselves how the symmetry of the observed world can be derived from more fundamental symmetries at small distances. In the old range of the distances the situation is the opposite: this symmetry approach was very successful, much more successful than the dynamics. But it gave its results and now, in this old range there is a problem of dynamics: how do things happen? In this situation I decided to talk about an old problem and only after that to connect this problem with the problem of the smallest distances. In order to be understood, I would like to remind you what kind of problem we had in the beginning of the exploration of the world of the elementary particles. The first discovery was that there exist strong and weak interactions, leptons and hadrons. What is the main difference between them? Leptons

*0n leave from the h,D.Landau Institute for Theoretical Physics, Moscow - 408 -

are pointlike within our accuracy. Hadrons have a size, of the order of -13 10 cm. How did we start to deal with these objects? For leptons, the situation was in a sense clear from the beginning. The man who first recognized this was Fermi. He undertood that if particles are pointlike, the only thing which can happen is that they come freely to a point, at this point they scatter or they produce something, and we can write this interaction phenomenologically in a simple form. After that we will discuss what is the structure of this interaction, what is its true form, what is the amount of the created particles and so on. This is what people call a field theory, but in fact it is a simple thing: pointlike particles can interact only in a point. The situation with the hadrons was very difficult from the beginning. First, in the sense how to write the interaction, second, how to imagine that something has a size? From the relativistic point of view, if something has a size, one can divide it. From this point of view one had the first puzzle: if two hadrons collide, we would expect from classical intuition that they can be divided, that we can find the things from which they consist of. However, in any hadronic collision we are producing particles, perhaps new ones, each of which has the same size. This means that it is impossible to divide them. As a reflection of this, it was absolutely impossible to write the true interaction of hadrons. There were attempts in the fifties, like the bootstrap, to try to find a theory without considering the constituents of this big objects. But these attempts practically failed. They failed not only theoretically but also experimentally because people started to investigate the spectrum of these particles, their quantum numbers, and came to the idea of the quarks. After that, in deep inelastic the experimentators could see precisely these quarks. So, the situation is that some constituents in some region really do exist. After the successes in different fields, we pretend to know what these constituents are. These are quarks and gluons. In many respects they are very similar to leptons. They enter the weak interaction in a very symmetrical way, and so on. They are almost like leptons, but the strange thing about them is that they are always living together, they can never go free: they were never observed to be free up to now, and this is a puzzle. Not only in the sense that they always arrange themselves in some volume, but also that the objects they form have quantum numbers which are different from the quantum number of the constituents. The constituents have color, non-integer baryon and electric charges, while the directly observed particles are colorless and have integer quantum numbers. How can this be? How can it be that quarks and - 409 -

gluons are so similar to the leptons, and at the same time they are living in very different conditions? The former answer to the question why they are living together was that they are interacting strongly. But now we know that for a short period of time after we create them they will interact very weakly, just like leptons. This is just a contradiction. People said that of course the interaction depends on the distance. If the particles are close enough they interact weakly if they are far enough, they interact strongly. But this seems to be a meaningless concept, literally speaking. If they interact weakly when they are close to each other, how can they know that they will have to interact strongly when they will be far from each other? This seems to contradict the causality. What we know is that the system is very simple for a short period of time, and something happens with the system if we leave it alone for some time. This idea existed even before quarks and gluons were introduced. This is the old story which was the essence of Regge pole theory, parton model and so on.

Suppose we have some constituents. There is a probability of their decay. A quark can emit a gluon. If we wait a little bit, it can emit again and again. This means that in the relativistic situation if we have some constituents and if they can interact at a point, after some time we have a bunch of the same constituents and we have the situation which we expected. The problem is, why they do not blow up, and not, how to produce a sufficiently large amount of the constituents. In the old theory we supposed, that the probability for the decay is of the order of unity and supposed that after some time the constituents will fill some volume and their configuration will become stable because of the interaction. This led to successes of the Regge pole theory in multiple particle production, in scaling, and so on, but all these successes were very qualitative. If you come to quantitative calculations and try to adjust the parameters to agree with experiment, you find, that the' pure asymptotic behaviour of cross sections occurs at very-very high energies. What is the reason? We did not know then, but now the situation seems to be the following. Putting the decay probability of the order of 1, you immediately produce this stable situation, and should expect that the asymptotic behaviour is reached very soon. After a few GeV everything will be very simple. Taking a very small probability, the obtained object will be very diluted, what will have nothing to do with experiment where the cross sections - 410 -

are still large, so this is also bed. What is the concept which comes now? It is that the probability for decay depends on time. For small times the probability for decay is small, for larger times the probability is increased. How to understand this? Here the new concept comes. The essence of the situation is that this process of decaying and creating the parton is not taking place in the empty space, but in the vacuum. In the vacuum a very striking phenomenon was discovered. Creating two charged objects which are receding from each other, at the same time the BremsStrahlung field is also created. If we created a pair of quarks, we create also gluons; in the electromagnetic case, we create photons. If the particles are massless then the field created together with the particles is smeared on the same sphere where the particles are located, and the field creates in the vacuum a vacuum polarisation current. Due to this current the charges of the original particles will change. It turns out that in QED the vacuum current decreases the charge ot the particles. But in QCD the gluon current has the opposite sign, and it increases the charge. The value of this current in the vacuum depends only on the magnetic moment of the particles in the vacuum and their statistics. For the given type of particles it is defined by a simple formula

where a is the coupling constant, n - the number of spin states of the particles, y - their magnetic moment; sign + stands for bosons and - for fermions. For the spin 1/2 fermions n = 2, p * 1/2, j = - -^-. For the gluons n « 2, 11 » -2 - i = ÏÎF V The value of this increasing local charge defines the probability of the emission of new gluons and quarks and plays the role of the coupling constant, growing with the time. If the particles have a mass, the picture is a little bit different, but the result is the same. This phenomenon explains the pecu- liar feature of gluons and quarks which makes them different from leptons and which can be important for the understanding of hadron interactions, but does not explain the confinement in the sense, that only colorless states (confinement of color) with integer baryon numbers (quark confinement) really exist. The progress in the solution of the confinement problem is at the moment rather modest.What I describe upto now looks even opposite to the color confinement, because the color charge is increasing due to the vacuum polarization. In order to have a confinement we need first the mechanism for screening - 411 -

the color and second the mechanism for screening the baryon charge of the quarks. The first mechanism exists in any gauge theory; it is the following. The Bremsstrahlung gluon field, emitted during the time of creation of color charges and producing the vacuum polarization current has his own color charge.

This charge can screen the color charge of the created colored particles4 and, as it can be shown, it really does it. The situation with the screening of the baryon charge of the quarks is more difficult. In order to screen the baryon charge of the created particles the gluon field must produce a colorless baryon current in the vacuum. Such a current can not exist in e.g. SU(2) gauge theory, because here the fields of quarks and antiquaries are the same. In theories in which the number of colors in more than two (e.g. SU(3)) such a current exists. However, in order to screen the baryon charge of the quarks completely or to make it integer this baryon current must be large enough. It can be shown, that for quarks in the vacuum with bare mass much less than the characteristic mass of the strong interactions (about 150 MeV) such a current can be sufficiently large, but if only heavy quarks exist it is small. This suggests, that, maybe, the confinement in the real world is not a feature of any color interactions but the particular feature of the gauge theory with light quarks and with a number of colors more than two.

The problems of confinement and of the structure of the hadronic states look very difficult at the moment, but I believe they can be solved. The main reason for this belief is the fact, that, as it is known from experiment, this problem has a simple answer. It is very important, that it is impossible to avoid the solution of this problem even going to the physics of short distances, because in this physics we are facing the same problem. Indeed, we have a very good theory of the weak interaction and it is in fact a phenomenological îheory for distances much larger then the characteristic size of leptons. For example, if we look at the electron it looks simple: a small charge, emitting a small radiation and so on. However, from the point of view of bare particles it is simple because its charge is screened very well. If we created two bare electrons with very high Momenta they will have very big charges and they can produce anything. This means, that if we go to the smallest distances we shall find the same problem. A manifestation of this problem phenomenologically is a bad feature of the Weinberg Salam theory in the sense of the mass of the particles. The problem of the mass in the Weinberg Salam theory is unsolved. The masses - 412 -

are introduced as free parameters and one does not understand how they appear. The reason to this is just what I said. The masses come from the shortest distances due to some dynamics and in order to understand this we have to solve a problem similar to that of confinement. In order to make contact with the topic of the conference, I would like to say a few words about this mass problem. During the last ten years our uderstanding of the notion of the mass changed very strongly. Some time ago, one thought that the mass is some intrinsic property of the particles. Like in the old theory of the electron, where some additional forces hold the charge together inside the electron. This idea may be not so bad but it gave us nothing up to now. Another idea about the mass is that the mass is just the scattering amplitude of the particle on the vacuum fluctuation: on some Higgs field or on something like that. There is no intrinsic property which we call mass, but of course it has the intrinsic property like a coupling constant; the particle interacts with the average field in the vacuum, it scatters, its velocity becomes smaller, and it gets a mass. This concept is more fruitful. When people start to discuss the possibility of the different neutrino masses, it is clear that without solving the dynamical problem we shall not be able to say much. For example, if on small distances we have some unperturbative phenomena, and we say from the beginning that we have right and left neutrions, due to this unperturbative phenomena left neutrions can become right. What would be the amplitude for this transition? It can be quite large in the sense that it can be q /A where A is a momentum where the charge is large and if we put this into the calculation we shall find that left and right will oscillate into each other, and we shall get two states: one will have a mass of order X, the other one will be massless. Then it will be impossible to have a massive neutrino. Only two components survive. This is just to show that our expectations could be quite different if we knew a little bit more about relativistic dynamics. ISBN 963 371 958 5 (összkiadás) ISBN 963 371 959 3

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