E+ E~ ANNIHILATION Hinrich Meyer, Fachbereich Physik, Universitдt

Home , Annihilation

- 155 - e+e~ ANNIHILATION

Hinrich Meyer, Fachbereich Physik, Universität Wuppertal, Fed. Rep. Germany

CONTENT

INTRODUCTION

1. e+e~ STORAGE RINGS

.1 Energy and Size

.2 Luminosity

.3 Energy range of one Ring

.4 Energie resolution

.5 Polarization

2. EXPERIMENTAL PROCEDURES

.1 Storage Ring Detectors

.2 Background

.3 Luminosity Measurement

.4 Radiative Corrections

3. QED-REACTIONS

+ . 1 e+e~ T T~

.2 e+e"+y+y~

. 3 e+e~ -»• e+e~

. 4 e+e_ •+y y

4. HADRON PRODUCTION IN e+e~ANNTHILATION

.1 Total Cross Section

.2 Average Event Properties

.3 Two Jet Structure

.4 Three Jet Structure

.5 Gluon Properties - 156 -

5. SEARCH FOR NEW PARTICLES

.1 Experimental Methods

.2 Search for the sixth Flavor (t)

.3 Properties of Q Q Resonances

.4 New Leptons

6. YY ~ REACTIONS

.1 General Properties

.2 Resonance Production

.3 £ for e,Y Scattering

.4 Hard Scattering Processes

.5 Photon Structure Function

INTRODUCTION

e+e storage rings have been proven to be an extremely fruitful techno• logical invention for particle physics. They were originally designed to provide stringent experimental tests of the theory of leptons and photons

QED (Quantum-Electro-Dynamics). QED has passed these tests beautifully up to the highest energies (PETRA) so far achieved. The great successes of the e+e storage rings however are in the field of strong interaction physics.

The list below gives a very brief overview of the historical development by quoting the highlights of physics results from e+e storage rings with the completion of storage rings of higher and higher energy (see Fig.1).

YEAR RING MAIN RESULT ON

1966 STANFORD, ADA e~e~ QED

1967 ACO, VEPP p,w, vector mesons

1970 ADONE R M 2 at 2 GeV

1973 CEA R i 4 at 4-5 GeV

1974 SPEAR (ADONE DORIS) J/ii, \|/' cc resonance

1975 SPEAR T -lepton DORIS, SPEAR P , Y -states of cc 1975 c 1976 SPEAR 2 jet structure

1976 SPEAR, DORIS charm particles

1978 DORIS Y,Y' bB resonances

1979 PETRA 3 jet structure

1980 CE SR Y" Y'" bb resonances - 157 -

Planned storage rings with energies larger than 40 GeV are bound to give

completely new physics results this time probably mostly in the field of weak interactions, provided the basic machine physics problem for higher

energy storage rings - low luminosity - can adequately be resolved.

The first lecture will give information on properties and limitations

of storage ring machines and about the basics of experimentation. Then the

results of QED tests in the purely leptonic channels are presented.

In the second lecture I try to cover information on hadron production

at higher energies where jet-phenomena are important with emphasis on three

jet events and their relations to some basic properties of QCD.

In the third lecture the recent searches for new particle thresholds

are reviewed and an account is given of some of the decay properties of

heavy quark antiquark resonances.

Finally(fourth lecture) the new field of photon-photon collisions where

very little was known until very recently is briefly covered with discussions

of C=+ resonance production and hard scattering phenomena.

In recent years a large number of excellent reviews of e+e annihilation

physics have appeared which the reader should consult for those parts of

the field that I have been unable to even touch upon and also for the de•

tails of the earlier important developments^. Since most of the very recent

new results do come from the four experiments at PETRA (JADE,MARKJ,PLUTO,

TASSO) I will frequently refer to those without trying to carefully follow

up the historical development of a particular field of e+e physics. For

some parts of the written version of the lectures updated information is

given as it has appeared during the time just after the summer school took

place.

1. e+e~ STORAGE RINGS

The two most important parameters of an e e collision ring are the

total collision energy E^M and the luminosity L, they will be briefly dis•

cussed below.

1.1 Energy and Size

The total energy is given by ( for head on collisions)

Z Fcl = (Z£) = S (ßtV)*-

where E (GeV) is the energy of the e- beams.

Starting with the construction of the first storage rings in the early

1960th machines of ever increasing collision energy have been build and

this trend is continuing with future projects presently very actively pur•

sued2. The main goal of the new projects is to get to the mass of the Z°

expected near E^ = 100 GeV. Fig. 1 shows the maximum energy E^ (max) reached

in the various colliding beam machines vs. time indicating also the anti- E+E- COLLIDERS "i i i i i i i i i i 1 1 r T-.—IT—i—i i i 111 1 1—j—i—i M 11 1 1—r i I I I I I 1 1 1 1 1 1 1 1—7 E (GEV) 1 1 V CM / |_ p'(NRI) » 1 J - .../ í *.

(LEP)^'" / (LEP)O 100 P (SPC) / (HERA) O / / / / / PETRAO/ / / (HERA)p / / / / / A. PETRA 10LR / O DORIS CESR O/ O SPEAR / /o / / / PEP O VEPP-4 CEA O/ / / / SPEAR / P ADONE /^DORIS

/ ; ADONE / /

_ /O ACO : 1 y DCI /

/ YEAR VEPP -/2M E (GeV) H ADA, STANFORD , . ^ i ' i i i i 1111 i i i ' i 1111 i t i 1960 1970 1980 1990 10 100

+ Fig. 1: Emax vs. time for e e~ storage Fig. 2: The bending radius p vs. E — —+ _ max rings. Also shown (dotted circles) are for e e storage rings. The line is the new projects under discussion. E2 max - 159 -

cipated completion dates for some of the new projects. Surprisingly enough

an exponential dependence emerges

with Y measured in years and (A = 0,5 GeV in 1960).

To keep energy loss by synchrotron radiation low enough the machine radius

goes approximately like Erfiax (see Fig. 2). By simple minded extrapolation

to the year 2000 a required diameter of 1.500 km would not fit into europe.

Clearly this is a rather unsafe and unrealistic extrapolation.

The relative sizes and geometries of e- storage rings can be easily

illustrated with a site plan of DESY (Fig.3). Electrons and positrons are

produced in the 400 MeV linac (1) stored and rebunched in PIA (2) transfered

to DESY (3) accelerated and then transfered either to DORIS (4) or PETRA (5)

the two machines used for physics programms. DORIS is a double ring structure

now used in a one ring mode with two interaction points and 1x1 bunch ope•

ration. PETRA has eightfold symmetry, with maximum 4x4 bunch operation now

however used only in the 2x2 bunch mode with 4 interaction points. As a

further illustration of the development of e+e storage rings the little

ring PIA (2) is compared in size Fig. 4 to the first e e storage ring rea•

lized in Stanford (1962) and in Fig. 5 PETRA is compared to LEP,most likely

the largest ring ever to be realized.

1.2 Luminosity

The colliding positrons and electrons are contained in rather short

particles bunches (*>~(1,5 - 30) cm long the precise value depending on the

accelerating Rf structure) circulating in opposite directions in the vacuum

pipe of the storage ring. With n- the number of positrons and electrons in 2 the bunches of crosssection F (cm ) and a bunch revolution frequency _ -I f(sec ) the luminosity L is defined as

i ~ sU+ M* -£/ F 0

+ 11 2 Typical numbers are n- = 3.5 • 10 , F = 41T-0,1 • 0,01 (cm ) and

f = 105 (sec-1) which leads to L~103° (cm-2 sec-1). As an illustration Fig.6

shows the maximum luminosity L , as function of E_„, for some of the e- 1 peak CM

L storage rings. peak. is the luminosity just after the filling procedure is

terminated and the bunches are colliding. The luminosity decays rapidly with

time due to loss of particles from the bunches. This effect on the luminosity

is in general somewhat balanced by a decreasing bunch crosssection F(see 1.3).

A refill of the ring is therefore necessary every few hours as can be seen

in Fig. 7 which shows the e- currents in PETRA over a twelf hour period.

From general experience with all e- storage rings so far one obtains

L for the integrated luminosity per day in terms of pea]t 160

Fig. 3; A site plan of DESY

PIA

•5m

Fig. 4; A size comparison of Fig. 5: A possible site plan the storage ring PIA with the LEP with the PETRA ring for first e_e~ storage ring in parison. Note the factor of Stanford. ^ 1000 in scale to Fig. 4 - 161 -

4 Z r Lotir ~ LPJT/TK • M** ' /S- (c*~ ) 14 where the reduction by 1/5 takes account of the many factors that decrease the luminosity. It was always known and has recently become even clearer

+ (PETRA) that Lpeak is strongly limited for all e e~ storage rings due to 'beam beam effects'3. In practice this means that the bunch cross section F increases very rapidly with the bunch intensities n- and finally leading to complete disruption of the bunches in the moment of collision. This behaviour is not understood. At PETRA two modifications of the machine are prepared to still increase luminosity. The cross sections F of the bunches at the interaction point are decreased by stronger focussing of the beams (low ß-insertions) with an ex• pected gain of factor of 3. Secondly through the action of an 1 GHz cavity an effective bunch lengthening is achieved with the possibility of signifi• cantly increasing n* avoiding however a simultaneous increase of F (see 1.3).

1.3 Energy Range of one Ring The event rate N for a specified process of cross section a in terms of L is given by

hi = L (xi'1) 1 .5

A few events a day can be considered a minimum acceptable event rate for a process to be studied. This requirement defines the energy range over which an e± storage ring of given geometry can be operated. The maximum energy loss per turn due to synchrotron radiation that can still be replaced by the accelerating Rf determines the highest energy an e± storage ring can run effectively. Roughly near this Rf limit the luminosity L goes down as L Installation of more Rf power can shift this limit to higher energies, this procedure however is very costly, ultimately the limi• ting energy may be given by the synchrotron radiation power dumped into the machine components and into the detectors at the interaction points. On the 4 low energy side the luminosity goes like E due to 'beam beam' effects. 2 Changing the tune of the magnet structure a dependence ~ E can be achieved. -2 Since the basic event cross sections to be studied behave like E (leaving aside the effects of resonances or new thresholds) the event rate on the low 2 energy side goes down ~E . From this consideration it follows that in prac• tice the operating energy range of a given storage ring is only about a factor of 3 (see also Fig.6) - 162 -

1032!-

PETRA 103 1

tfio30 VEPP-21

o io29

/VEPP-2 10®

Al ît 1ft 10* i 10 100 ECM(GeV)

Flg. 6: The peak luminosity as function of E^M for some of the existing

e+e storage rings. The position of prominent qq resonances is also indicated.

31. 3. 80 6 : ¿9 : 57 ENERGY [GeV] I" ImAJ I* [mA] PETRA 17 . 580 U. 09 3. 96

j i i i i i i_ -12 [HOURS] -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 NOW

Fig- 7: Electron and Positron currents (mA) in PETRA as function of time in the 2x2 bunch mode. - 163 -

1.4 Energy Resolution

For a given storage ring at energy E the energy spread AE within one e- bunch is ~ fVrr 1 .7 2 where p is the bending radius of the magnet structure. Because E ^ p max (see Fig.2) this means AE/E A/ const, for all rings. For a narrow reso- IC13.X nance with natural width /** AE the counting rate on top of the resonance is ^ 1/AE. Up to now five such resonances are known the ^/"/| Y, Y'¡ Y" and at least three more containing the top quark are expected to be found in 1 /2

(planned or operating) storage rings. Since Emax scales as ^ p the rate on top of narrow resonances located near E goes down ^1/E max max

The same resonance however will be more narrow at the lower energy end of

a high energy machine than at the high energy end of a low energy machine.

Therefore it is for the same luminosity more favorably to study the reso• nance at the higher energy machine (e.g. Y (9.46) at DORIS and CESR).

1.5 Polarization

Energyloss through synchrotron radiation polarizes the e- beams with the polarization direction parallel to the magnetic field in the bending magnets, as defined below

The rate of polarization depends on the geometry of the ring and on the beam energy (E) to the 5th power - 164 -

with c= velocity of light, a= fine structure constant,*f^= electron radius

p= the magnet bending radius, R= the mean bending radius of the machine and

E Y= /me with me= electron mass4.

The time dependence is explicitely given by

PC*) = <* 'f*fc X [A - «P(-t/c) ) 1 . 10

For PETRA (in the absence of depolarising effects) r lu

Since E2 going to higher energy machines T increases as E and there- max = 3 J-1 max fore may be prohibitively long compared to typical beam lifetimes (see e.g.

Fig.7) at the highest energy machines planed (LEP). Because of the de• pendence radiative transverse polarisation is sizeable for practical pur-

purses only near Emax of a given machine. Furthermore depolarising effects

limit the maximum polarisation approximately given as

1.12

with TjjgpQ^ the depolarising time. There is a large number of discrete ener•

gies where Tjjep0i is very small and no polarisation possible. In storage rings the e- spin motion is just Lamor precession about the field direction with the number precessions "f" in advance of the orbital motion given by

, s M v - v- ilz - °^zi *i* *'- -rfccv) = £C ) 1.13

with y = /mg and g = gyromagnetic ration of the electron. This means com• plete depolarisation at integer values of f. At very high energies however due to increasing AE the resonances may finally completely overlapp. Further details on polarisation phenomena may be found in Ref.5.

Let us now write down the differential production cross section for

some elementary two body reactions taking account of a certain degree of trans• verse polarisation P_¿ with the geometry of the event defined as below: - 165 -

In the one photon exchange approximation one obtains for particle pairs with spin 0, 1/2 ( in the limit S •*• 1 ) .

and a' = + 1 for spin 1/2 and a' = -1 for spin 0.

This applies in particular for y- , T- and any quark pair (spin 1/2) or e.g. for ir-, k-, D-, D° ÊT^spin 0) . If t-channel exchange is allowed in addition

like for e+e pairs the differential cross-section reads

1.15

and for electron exchange (YY annihilation)

1.16

+ whereof the ^(Çcross-section/J^(ij y ) si s duthe e tocas e fois r maximuy + y~ m inatl? formul" =90°a . (14)This. This e of dependencgreat e perimental importance since (with acceptable values for P^ ) the spin depen• dence of the pair cross sections appears as a^dependence near ^ = 90° 2 2 (with maximum ratio of 1+Pj_ /1-Pj = 12,6 for the counting rates) where the detectors are very uniform and also have complete acceptance. Fig.10 shows

the (jí distribution for e+e ->• e+e and y + y for the case of 70% (E=

3,7 GeV) and no polarisation (E=1,5 GeV)6.

En =1.55 400 1 1 1 1 1 I 1 1 1 11 11 [ 1 • 1 1 1 l II 1 1 350 (O) ee 300

250

200 An

; 150 (C) ee Fig. 10: Azimuthal angle distributions

1 1 ' 100 1 1 1 1 1 1 1 1 1 for muon pair production (yy ) i (b) fj.fi ii>

40 20 • ' : lililí 0 1111 0 90 I 80 270 0 90 I80 270 360 $ (degrees)

The same information is of course contained in the cos^dependence of the

cross sections, which is however much harder to measure since most detectors

are very nonuniform in The YY annihilation channel provides an optimum

monitor reaction for polarisation effects since it has the largest cross-sec•

tion ^ f/Jf ^¡if' anâ it """s not affecteâ by weak neutral current effects

at higher energies (LEP)7. - 166 -

Continuous on line monitoring of the degree of polarisation can be supplied by shining laser light onto the e- bunches and measuring an up down asymmetry of back sacttered (^180°) compton photons with respect to the beam plane. Electron-Beam-Polarisation has been carefully studied using this method at 8 9 SPEAR and has recently also been observed at PETRA . If the polarisation vector is turned parallel to the e- beams directions qualitatively new weak interaction effects can be observed at higher energies (LEP, HERA 1C):

2. EXPERIMENTAL PROCEDURES

2.1 Storage Ring Detectors The typical event rate for hadronic annihilation events at e.g. PETRA running near 35 GeV presently is

/^Z ~ _Q ¿j oit OC 2 O X*M*J*/oUy 2.1

with

30 -2 -1 This requires L 6" 10 (cm sec ) using(1.4.) p 30 -2 -1

L As another example with peaK ^ 10 cm sec at 3.6 GeV the event rate for T- pairs (just above threshold) is again only <^ 25 a day, a very low event- rate for a very inteiesting process. Since there are so few events a day one has to try to store and measure as many details as possible for each event. One simply can not afford to loose information. The main design critérium of e- storage ring detectors therefore is completeness. From the construction of many e- storage ring detectors a kind of 'standard structure' has emerged as shown below.

Fig.11 'Standard' radial detector structure for storage rings.

tracking shower counter

In radial direction the charged particle tracking region is followed by par• ticle identification or neutral particle detection. For lepton identification electromagnetic shower counters identify electrons,and muons are required to - 167 -

penetrate a hadron-absorber (iron). Photons are detected in the electron iden• tifying shower counters. Some detectors 'see' neutral hadrons inside the hadron absorber and charged hadrons are separated either by time of flight counters (at low momentum) and Cerenkov counters or specific ionisation loss at high . 11a energies Charged particle momenta are measured in the tracking region using a solenoidal (magnetic) field structure with field direction parallel to the e- beams.A cylindrical coil required to produce the magnetic field is uni• form in |» and a very reasonable approximation to a 4 li detector as illus• trated below

A 9/47r = vi* * %+mf - "

Fig. 12

Fig.13 shows the detector JADE as an example of a 'standard' detector for e+ e physics. For the very forward direction highly specialised detectors are developed with the main purpose to detect e- at small angles that are surviving from 11b 2 photon exchange collisions . As a typical detector combining many of the above mentioned features Fig.14 shows PLUTO in the improved version to study 2 photon reactions presently under construction. The table below lists most of the detectors installed in the various e- storage rings and some of the more characteristic features of them. Al• though for all of them it has been tried to optimize in a specific direction they all apparently follow the rule given above "that one can not afford to throw away events". - 168 -

Fig. 13

Side view of the JADE detector at PETRA

PLUTO

j i i i i i i i i i i i i i i i 87654 32 Im 0 Im 23 45678 Fig. u PLUTO, with improved forward detection - 169 -

E magnetic Detector Ring NO.of IP Design max field (GeV)

DM I DCI 1 3,7 Sol. multipurpose

MARK III Sol. multipurpose SPEAR 2 7,8 CRYSTAL BALL low energy photons

ARGUS DORIS 2 10,2 Sol. multipurpose

CLEO multipurpose CORNELL 2 16,0 — LEAD GLASS low energy photons

MAC Sol. total energy,leptons MARK II Sol. multipurpose HIGH R.SP. Sol. charged hadron iden• tification mass resol. PEP 6 36,0 S. DELCO Sol. leptons TPC Sol. hadron identification 2 ^-reactions

CELLO Sol. multipurpose JADE Sol. multip. ,charched had• PETRA 6 38,0 rons ,leptons TASSO Sol. hadron identification MARK J mag.iron muons,total energy PLUTO Sol. 2photon reactions multip.

TABLE 2.1

2.2 Background Several sources of background contribute to the trigger rate in typical storage ring detectors. The four most important are

a) Beamgasinteractions (BG) b) Particles from comic rays (CR) c) Lossof e- from the circulating bunches (BL) d) Synchrotron radiation (SR) a) The trigger rate for BG events is proportinal to the number of electrons and positrons in the bunches and to the residual pressure in the vacuum pipe at the interaction point times the effective detector length. BG events very often have charge unbalance (> 0) due to the protons from nuclear breakup, they always have visible energy

dinate along the beam) and Fig. 80 below. b) Cosmic ray background consists mostly of single muons and occasional large particle showers. They come uniform in time while the bunches cross for a few n-sec only with a frequency of order ysec.A bunch crossing gate provides some suppression at the trigger level. In the later event analysis cuts in *tj^ and z and more stringent timing cuts with time of flight (TOF) counters usually reduce it to a negligible level and, most important, also in the + - 13 v y final state due to its unique kinematics c) Electrons and positrons lost from the beam usually enter the detector re• gion with very small angle with respect to beam direction and produce a 'cloud like' pattern in the wire chambers due to the development of electron photon cascades. This allows easy rejection in later analysis. However with bunch currents near the beam beam limit so many particles may enter the de• tector that either a high trigger rate or an overcurrent in the wire chamber or both require the detector to be turned off until the beam conditions have improved. d) The effects of synchrotron radiation photons on the data taking procedure is similar to the case of beamloss. In addition however it may produce ran• dom wire hits in the tracking detector which finally can influence the track pattern recognition programs. Careful shielding and 1/10 field last bending magnets before the interaction point help reducing the problem. The SR from the final focusing quadrupols however:is a more difficult problem, the detec• tors simply have to stand it.

2.3 Luminosity Measurement Small angle Bhaba scattering with both the e+ and e detected in identical detectors left and right of the main detector set up in angular regions be• tween 1° - 5° provides a very adequate monitor (see table6.1, page85 ). In de• tail a lot of work is required partly with the application of radiative corrections. After all it is an 'absolut rate' measurement. Measurements of L with Bhaba scattering however at present usually do not limit the precision of the experiments with e- storage rings.

14 2.4 Radiative Corrections The largest contribution to the radiative corrections comes from 'initial state' radiation 'before' the e+e annihilation takes place (Fig.15a).This leads to lower available annihilation energy e¿M^ECM anâ the Pr°duced final state moves with respect to the detector mostly along the z-direction. For

a the more general case (like a measurement of ^^ot) complete knowledge is needed of the cross section at all lower energies and the detection efficiency for the radiative events. This is treated in extended MC programs generating the apropriate types of events at E^ plus a photon with energy selected according to a bremsstrahlungsspectrum. Since cross-sections in e+e anni- 2 hilation increase at lower energies like (E' ) the measured cross-sections at - 171 -

ECM are to large (due to the detector acceptances down to rather low E£M). Furthermore vertex corrections (Fig.15b) and (e,u,t)and hadronic vacuum po• larisation terms (Fig.15c) have to be added.

Fig- 15 a Fig. 15b Fig. 15 c

One obtains: ~ _ \

and cíj^i/ evaluated from a dispersion intergral14? Typically the correction for^o^" in 2.3 amounts to M10 to 15)%. This procedure, formula 2.3 above, takes account of small angle radiation, in certain cases however also large angle radiation or radiation in the final state deserves special attention. As an example consider e+e -> y + hadrons with the photon angle ^"^.^30°, this means into the acceptance of most of the detectors. The cross-section for this process (initial state radiation, hadrons) =-1) is 15

2.7

with

and amounts to^2% of €T(ECM) at PETRA energies. Fig.16 shows one example for this kind of event16: - 172 -

Liquid Ar Shower Counters

As a final example let us discuss the shape of a resonance curve (e.g.

J/^,Y/Z°) in e+e annihilation which is strongly distorted due to initial state radiation, since radiation of only very low energy photons ontop of a resonance leads to a final state just below the resonance and from a posi• tion in E,.,. just above the resonance one comes back on top of the resonance.

CM J Qualitatively it looks like the sketch below,the reduction in peak cross- 14 section is of order factor 2. For more details see Ref.

Fig.17

Shape of a resonance

in e+e annihilation

with (full line) and

without (dashed line)

radiative correction

" reso. - 173 -

3. QED-REACTIONS Final states in e+e collisions with only leptons (photons) can exactly (so far with any required precision or a precision that matches experimental uncertainties) in the frame work of Quantum-Electro-Dynamics (QED). Whenever storage rings opening up a new energy range come into operation the processes + - + -> e e e + e - + e e y y + - -> e e Y Y due to its simplicity both experimentally and theoretically attain immediate attention. For PETRA energies measurement of the new QED-process + - + - e e T T helps establishing the point like nature of the only recently discovered x- 1 7 lepton and partly contains information on the possible appearence of even more 'sequential' leptons. A further motivation for the analysis of charged lepton pairs comes from the interference term due to weak neutral current inter• actions of leptons since it should produce measureable deviations from pure QED at PETRA energies. The final states are very simple see Fig.18below

[

Fig. 18: y y and e e final states as seen in JADE

which shows examples due toy+y and e+e final states. A YY event looks iden• tical to the e+e case with the charged tracks missing. The appropriate (first order in a) cross-sections have been given above formula 1.14,1.15. The effects of polarisation (including the build up with time, formulai.11) have been observed at SPEAR for e+e and e+e ,y+y~ and are shown in Fig. 10 (note the 90° phase shift between e+e and y+y ) . Radiative corrections are sizeable and follow the pattern of formula 2.3 - 174 -

where ou ^ at 30 GeV in the e+e final state is ^ 3 - 5% and the new term P had + weak ^ue to wea^- ~ e-m- interference is of order - few % (depending on the scattering angle Some checks of the radiative correction procedure are obtained from measurements of the acoplanarity or acollinearity angle of the 1 8 two final state charged leptons. Data (for Bhaba scattering) from PLUTO , 19 20 JADE and TASSO in Fig. 19 show very good agreement with the respective calculations including detector simulation giving confidence that the radiative correction calculations are reliable. 3.1 e e -> T T 1 7 Most of the decay modes of the T are well known . It follows that x- pair production appears as 2 prong (^ 50%), 4 prong ( ^40%) and 6 prong (^10%)

events with missing energy carried away by two C^,1^) i three Cfyyu. , i ) or four (K. , \7" . ,Y<-, V£ ) undetected neutrinos. Furthermore the Lorentzboost collimates the T decay particles into a narrow come around the T- flight direc• tions. Because of this the -r-pair events are easily identified by all detectors. Also the various decay channels can be separated and have been found to be in 1 7 good agreement with low energy determinations . The angular distribution in $ is compatible with $ toxv K and has been used to extrapolate into the region (generally | c©*» £ I > 0.75) - pairs are not measured. The total cross-section for T- pair pro• duction obtained by taking account of the know branching ratios into specific 21 decay modes is shown in Fig. 20 . It should followa 1 / dependence if the T were a 'pointlike' lepton. Usually, deviations from this behaviour are parametrized in terms of an ad hoc form-factor

2 + + where q = s for x- production and the - signs are pure convention. The size of./\. is of order swhere AC ref lectsthe errorbars of the data points. Values 2 2 for A of order 90 GeV at 30 GeV correspond to ¿36" of ^10% and an increase of s to ^ 1500 GeV would for the same4£~give^. <\<150 GeV. An increase in precision (e.g. reduction in4f^ factor 10) at PETRA energies requires carefull evuluation of radiative corrections (formula 3.1 above) and in this sense tests QED. So far the x- data from PETRA have further established the xtobe a'pointlike' QED particle like the muon (u) and the electron (e) down to a 'radius' of order 2- 10"l6cm. - 175 -

Acollinearity Angle Distribution

i i i , i i 0 10 20 30 40 Acollineonty Angle (Deg)

Fig. 19: Acollinearity distributions for Bhaba scattering from a) TASSO20 c) JADE19 and the acoplanarity distribution from b) PLUTO18 10p—'—1—1—1—i—i—i—1—i—i—i—•—i—i—i—i—r (J(nb) i

0.011 i i I i I , i i i 10 20 30 VTlGeV)

Fig. 20: The total cross-section for T pair

production vs. E_M - 177 -

3.2 e e -» u u 22 The most recent data from the four PETRA experiments are summarized in

Fig.22 (angular distribution) and Fig.21 (total cross-section). One finds very good agreement with QED calculations again expressed by quoting^y+ parameters of order 100 GeV.

Finite deviations from QED are expected to show up at the highest PETRA

energies due to interference of y and Z° exchange. Quantitatively the effects are only of the order of present experimental error bars. The differential

cross-section ( 1.14) is modified as

3.3

^ = /L + T^ZR +- (n?V«*) FC 3.4

C = — = H-LJL • /U"RÍG^'¿) 3.7

and v, a are the vector-, axial vector coupling constants. In the standard

model we have 2

a = -1, v = 4 sin 9w -1 3.8

Mz= 74.6/sin ( 26w ) 3g

The term 'Co°J-ftintroduces a forward backward asymmetry for the differen• tial u- cross-section. Again using the standard model one is essentially sen- 2 F — B sitive to a only and expects Auy = F + B <\. -6% while the present best

value is Ayu = -(0.9- 4.9)% combining the data from all four experiments23 2 + 2 From sin 8 = 0,228 - 0,015 we know V - 0,008 and the expected change in the

total u" cross-section is very small. If more data become available it should be possible to actually measure 2 2 + + a and v using e.g. combined data for w- and £- production alone. cos e cos e

15.0 -i 1 1 ' 1 1 1 1 1 1 1 1 1 r- eV-* MV W = 30.7 GeV "8 b)

•ü 10.0

JADE +MARK J*PLUT0*TASS0 combined 27< Ys" < 35 GeV i • « • I • i- - -1.0 -0.6 -0.2 o 0.2 0.6 1.0 0.0 J i_ -0.8 -0.6 -0Á -0.2 0 0.2 0Á 0.6 0.8 COS Q 31781 cos e

Fig 22: The differential cross-section for y pair production from a) JADE 22b b) TASSO 21 c c) PLUTO21d and a combined distribution - 179 -

3.3 e e -» e e Bhabascattering is more complicated than u- or T- production since in low• est order of a, t and s channel exchange amplitudes contributé. At very small scattering angles where luminosity is determined the cross-section is com• pletely dominated by tchannel exchange ("Coulomb scattering). The data (see 24 Fig.23 ) from all four groups is in very good agreement with firstoïQer QED calculations after taking account of the necessary and sizeable radiation corrections. Concerning/i^parameters the remarks made in the discussion of

+ e e -+ u+y , T+T apply here as well. It is more interesting however to again look for weak interaction effect. 25 In Bhabascattering, one obtains

(( B+x)& - x(/t-X) R)

í + ¿^«) ((^ru-R)"(v"4 tvV

»Ith Y - cos,?, and Q - j> • HI • -±_ , fx - ~U-0,P) and R,j^a,V as before (Section 3.2). At large values of the scattering angle one becomes sensitive to o (essentially)*^ in (3.10) above with effects of about -(2-3)% at the highest PETRA energies. Date from the MARK J group and JADE already seem to be suf• ficiently precise to resolve a twofold ambiguity left over in the most re• cent neutral current data from purely leptonic neutrino scattering26( see Fig.24

+ + The data on e e •* p+y ,e e ,T+T can also be used to provide tests of more complicated weak interaction theories involving more than one neutral 27 28 2 vector boson ' . The vector coupling v in the standard theory is replaced by COS-fr 2**80 C0S

Fig. 23a: Angular distributions for Bhaba scattering from MARK J22Cand TASSO io- -i—i—i—i—i—i—i—r—i—r e+e--*eV(JADE) e* e"—- e* e" • ~~= 1076 GeV2 Of 1000 E„mc = 30 GeV cms O A 500 PLUTO •C > 10a 200 OÍ o 100 XI c 50 QED 20 —i—i—i • • i i •0.8 -0.6 -OA -0.2 0 0.2 OA 0.6 0.8 T3 cos 6~~

~~10' T r e+e>eV JADE lcos6l< 0.82~~

~~J_j L__J L 0 8 •0.4 0 0A 0.8 cos e~~

~~j 1 i i_ Fig. 23b: Angular distributions for Bhaba scattering~~

~~22b 30 31 32 33 3A 35 36 from PLUTO18 and JADE . Vs [GeV] - 182 -~~

~~sirfow gv~~

~~1.00 T~~

~~(95% CD~~

~~Fig. 24: A plot of the allowed regions for the vector (g^.) and axial vector (g ) coupling from purely leptonic experiments 26.~~

~~Fig. 25 2 g 2 The weak vector (g ) and 2 axial vector (g ) coupling a constants as determined from PETRA experiments~~

~~-OA-0.3 -0.2 -0.1 0.1 Q2 0.3 OA - 183 -~~

Limits on C using sin = 0,23 have been obtained, (MARK J) < 0.027,(JADE) < 0.033,(PLUTO)< 0.06 at 95% confidence level. In case there are only two neutral vector bosons (M.. ,MJ the limits on C can be translated into limits 22 21 on the masses, the results of JADE and PLUTO are displayed below: two boson fit

~~0 25 50 75 100 M, (GeV)~~

~~0 10 20 30 40 50 60 70 80 90 (GeV/c2)~~

~~Fig. 26 - 184 -~~

3 . 4 e e yy In this channel weak interaction effects are absent in first order7. If found to be in agreement with QED calculations including the radiative correc• tions, it provides a unique monitor reaction at higher energies where weak interaction effects are large. The data from the PETRA groups are shown in Fig. 27 and are seen to be in excellent agreement with QED. The introduction of './Ylike' parameters to express limits on the deviations of the data from QED is more involved, for a rather complete discussion see Ref. 2 9 .

~~VJADE - APLUTO : (Ref.29)~~

~~- 12=s/s~2s31.6GeV~~

~~—i—i—i—i i i i ' • 0 0.5 1.0 COS 0~~

~~Fig. 27: The angular distribution for e e ->- Y + Y from PETRA experiments - 185 -~~

4. HADRON PRODUCTION IN e+e" ANNIHILATION + — Qualitatively many features of hadron production in e e annihilation can be understood in terms of the quark parton model. The further hypothesis that very energetic quarks form jets of hadrons leads already to a rather detailed description of hadron final states . The radiation of strong interaction field quanta - the gluons of Quantum-Chromo-Dynamics (QCD) - produces additional experimentally accessible effects. The gluon radiation becomes observable in e+e annihilation most spectacular in the appearance 31 of three jet events at sufficiently high energy . Furthermore the new ab- solutly conserved quantum number color also appears in many measurably quan• tities most notably in the total cross - section for hadron production2but also quark and gluon jet formation3\nd in decay branching ratios for heavy quark 34 antiquark resonances. Electron positron annihilation has then emerged as a prime testing ground of the new hadron theory 'QCD1. The partons of QCD are the quarks with spin 1/2 and they come in three colors (I take red (r), green (g) and blue (b))and five kinds of quarks (flavors) are know up to now and eight gluons with spin 1 and color combinations like r g etc.are expected. Table of Quarks

~~flavor d d d s s s c c c, bJa b, t t t, r g b r g a r g b r g b r g b r g b~~

~~charge - 1/3 2/3 - 1/3 2/3 - 1/3 2/3~~

~~mass small small 0,5 GeV 1 ,5 GeV 5 GeV >17 GeV~~

~~a /a 16 qq tot 67 16 10 40 10 40 (%) 9 36 9 36 9 7 26 7 26 7 26~~

~~TABLE 4.1~~

~~The t-quark in the last column remains to be discovered its mass however is known already to be >17 GeV from experiments at PETRA (see section 5.2 below)~~

~~4.1 Total Cross Section Since the photon couples to the charge of the quarks the total cross- section if all hadrons originate from quark antiquark production reads~~

~~2 (S;^ « H\z • TU • £ 3 4 • [P.-J (3 - pS)/2 n. - 186 -~~

with ß^ the velocity of the quark i and e. the quark charge. The factor 3 in the sum is from counting quark colors (r,g,b) and the term in is the threshold factor for pointlike spin 1/2 particles. The cross-section just after the threshold for a new quark however is usually modified by resonance effects. In the limit ß^ -»-1 we have

Above threshold for bb production the individual quarks contribute to the cross-section(as shown in the table above) with %27% due to 1/3 charge quarks and ^73% due to the up- and charm-quark. Formula ( 4.1) works very well and in particular is in good agreement with the step at charm threshold and al• so consistent with the expected small step due to the b-quark (see Fig.28 ). Radiative corrections due to gluons can be calculated reliably and 35 have recently become available to second order in a

~~4.3~~

~~with Nf the number of flavours above threshold and ag the strong (quark gluon ) coupling constant~~

~~4.4 a is determined to be % 0,17, see below. The corrections to order a and~~

~~¿ as for~~

with L the luminosity and N the number of events with hadrons in the final state. Small angle Bhabe scattering allows a pretty accurate determination of L with the various precautions discussed above (see section 2.3) and ~2% is not unreasonable. To determine N, subtractions due to background and corrections for undetected events and for radiative effects (see section 2.4) have to be applied as listed below: R = CT,°7a,

~~-4-- "T" if T~~

~~• Froscali~~

~~X SLAC-LBL~~

~~o PLUTO~~

~~• PETRA~~

~~-CM (GeV)~~

I • > • • I • • • i I i _I_ _l_ 1.5 7 10 15 20 25 30 35 AO 50 Fig. 28: The total cross-section for hadron production in e e annihilation. Not all measured points have been platted for clarity. In the PETRA 38a region data from 4 experiments have been averaged . The dashed line is the parton model prediction plus first order QCD correction. For more details see also Fig. 29. - 188 -

subtraction - YY collision correction - trigger (acceptance,electronics) of events - T+T~ pair for loss - event reconstruction due to - higher order QED of events - dead time - BG, CR (see 2.2) - wrong identification as background

~~Some of the more important corrections for an evaluation of a. .~~

At present the errors on N are of the order of 5-10% but with further work on detector and event simulation they probably can be reduced to 2%. A further limitation on accuracy finally is simply statistics (see section 2.1) At PETRA so far four experiments provide data on o. ., all based on compa- 37 rabie event numbers . The luminosities are determined individually in each experiment and also hadron event reconstruction and definition is quite different. Therefore the systematic errors in the various experiments can be of rather different source and it might be reasonable to average the 38 data from the four experiments as it is done for Fig.28 . The full line is

calculated according to ( 4.3 ) above with ag= 0,18. The agreement is surprisingly good. With further very detailed work as indicated above A a. ./ a. . ^3% might be achievable,in the near tot tot future. E (GeV) quark contribution Aside froCm M the flat regions with energy ranges as shown below: TABLE 4.3 1.5 - 3.7 u d s 5 - 10.5 u d s c 12 - >37 u d s c b

~~R has several outstanding features, the qq - resonances resonance quark content p, cu, 4> uu, dd, ss J/~~

and the structures just after the charm - (3.77) and various resonances between 3.95 and 4.6 GeV) and bottom - threshold (Y,N (10.52)) while the region after the cj> meson has. resonance structure probably only in speci• fic channels (like i nee -•TTTTTTTT) and not in ^tot • ^M ( 3.77 ) exclusive• ly decays to D°D° and D+D-42and for Y'" (10.52) one expects similarily B°B° and B+B~ decays only with indications from inclusive kaon and lepton produc• tion recently reported43. The structures in the 4 GeV region should have domi• nant coupling to charm, the detailed phenomenology however seems to be rather complicated?9 (Fig. 29) - 189 -

~~~i—i—i—i—i—i—i—i—i—i—i—i—i—r~~

~~Ref.39a~~

~~O i , i I I i i I I I I I I I 1 L~~

~~0 3.5 4.0 4.5~~

~~Earn. (GeV)~~

~~6J0~~

~~Ü.0~~

~~or 2.0 Ref.39b~~

~~0.0 Lu—. . . L _i i i I i i_ ¿.0 4.5 5.0 EcM~~

~~'HAD i í.: Fig. 29: i The total hadronic cross- section in the charm threshold region Ref.39c~~

~~J l_ -i i L 40 . . 4.5 Eck (GeV) - 190 -~~

~~Fig. 30: The average charged particle multiplicity in e e annihilation. The full line is formula 4.6 with the parameters in the table.~~

~~< nch >/D~~

~~QCD + hadr.~~

~~QCD (asym.)~~

~~LENA~~

~~PLUTO~~

~~ECM (GeV)~~

~~7 10 15 20 25 30 35 10~~

~~Fig. 31: The ratio of the average charged particle multiplicity ch divided~~

~~by the dispersion D vs. E^M. The QCD predictions are from Ref.48 (full line) and Ref.47 (dashed line). - 191 -~~

4.2 Average Event Properties The number of hadrons produced in the events and the momentum spec• trum of the particles provide a first and simple characterisation of hadronic events. Further insight should come from the fraction of different hadrons as function of the hadron momentum;one expects mostly pions and kaons and a smaller fraction of baryons. Many of the measured hadrons are expected to be daughter particles from primary mesons like the vector mesons (p,"),K*) and charm particles (D°, D-, D* etc.). An unfolding procedure however to get e.g. the primary pseudoscalar meson spectrum is not yet possible due to lack of knowledge of parent particle spectra. Comparison then to theoretical predictions is rather indirect and no strong conclusions can be drawn. Among the final state particles in the events one finds also leptons (e,u,v) which come from the leptonic and semileptonic decays of new particles. Since the respective branching ratios are known this involves rather certain (and small) corrections only.

Charged particle multiplicity The data on charged particle multiplicity from low energy and the new 44 PETRA data is shown in Fig. 30 . The particle multiplicity rises rather rapidly + - 45 with energy a trend not only observed in e e annihilation but also in pp and v p collisions46. A simple parametrisation = a + b In S en can be fitted to the data only over limited energy intervalls. If the hadron multiplicity were directly related to parton (quark gluon) multiplicity than 47 calculations suggests a dependence like (with c^ 2.4)

~~which describes the data pretty well. The parameters a,b,c have been determined 44 by PLUTO and TASSO and are shown below~~

~~a b c Experiment 2.38 - .o9 0.04 - .01 1.92 - .07 PLUTO~~

~~2.92 - .04 0.0029- .0005 2.85 - .07 TASSO~~

~~2.5 0.007 2.4 Parameters for Fig.30~~

~~Fixing the coefficient c at 2.4 however also gives an adéquat fit.~~

~~/—Ó —T~~

~~< Also the ratio of the dispersion D = / nch> - cj1 to the average~~

~~< 47 charged multiplicity nch> has been calculated from QCD parton branching . The result of D/= 0,61 does not agree with the data one finds ^ 0,36 almost independent of energy (7 GeV~~

49 Koba, Nielsen and Olesen suggested to present the data as - PR versus n/ where Pnis the probality for a n-particle final state and pre• dicted this distribution to be energy independent. This has indeed been veri• + - 50 fied for many rreaction« s and seems to be true also in e e annihilation (see Fig.32 ).

The momentum spectrum of charged hadrons In magnetic detectors this is an easy measurement in principle. Many corrections have to be applied in practice, those related to loss of events and background have been mentioned in the discussion of the total cross-section. Furthermore there are losses and gains of tracks in individual events through absorption and decay, reconstruction and acceptance and photon conversion. At

~~low momenta say less than ^300 MeV/c the corrections become large and below~~

'vlOO MeV/c essentially no information is available. The scaled momentum spectrum in x = P/Pbeam where P^eam i-s the mo- + P mentum of the e- beam and P the momentum of the hadron is shown for several 51 energies (ECM) in Fig. 33 . The energy dependence of the total cross-section 1/S is taken out plotting S- da /dx (y b GeV2). Above X = 0,15 we find the P P scaled momentum spectrum to be rather independent of ECM within -v-40% on in• dividual points in general shape however probably ^10%. At lower momenta

Xp<.15 there is no scaling at all with ECM we rather see a very strong rise factor 10-20) . Complete scaling ibr O = a+b-ln S while a much stronger rise is observed (see Fig. 30 )-The rise in multiplicity therefore is related dominantly to low energy particles. Information on fractional particle multiplicities is still very in• complete. Separation of IT- K- and p- is done by time of flight which works

only up to fixed particle momenta.With increasing energy ECM the maximum xp below which particles can be identified decreases as 1/E. Recently some data has become available at higher momenta using cerenkov counters and dE/dx in- 52 formation . The data shows (Fig. 34a) an increase with energy ECM at low momenta not only for pions (which dominate in number) but also for kaons o 53 and protons. A study of K<, production has a similar result . At higher par• ticle momenta(Fig.34b) one finds more protons and kaons with the correspon• ding decrease in the number of pions. Baryons as leading particles come as some surprise and have so far not been taken into account in particle produc• tion models. 54 Neutral pion production has been studied in several experiments one finds do /dx (TT°) ^ da /dx (TT+ +TT-) as expected (see Fig. 35 ) . From the vector mesons (p , üj,,K*) only for the neutral p-meson (see Fig. 3 6 ) some measurements are available. They confirm the assumption of strong vector me• son production, a fact taken into account already in the models (see nage below). Inclusive charm particle production is not easy to do, because of the large number of decay modes of the D° andD¿ "*6. At lower energies - 194 -

~~W = 30G~~

~~1 » 1 I 1 1 1 1 « r -T , i Fig. 34b: Particle frac•~~

~~+ i l I tions in e e fît annihilation vs. the particle mo• i mentum. \ • • —)>—i— i 0 1.0 6 8~~

~~29880 P(GeV/ci 305J6 - 195 -~~

~~t TT"~~

~~— I/2(7T++7T")~~

~~Cr(7r°) = 0.48 ± 0.05 1 - criir* + TT~) CVJ 0.5 - O i JO ¿ 0.2 b| x~~

~~co 0.1~~

~~0.05~~

~~0.02~~

~~o.oi 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8~~

~~XE=2E7ro/Ec>m.~~

~~Fig. 35: Inclusive production of neutral pions in e+e annihilation 54 The shaded area is the charged pion cross-section for comparison.~~

~~Corrected X(| of p°s~~

~~10' L I I I 1~~

~~100' r-~~

~~10"~~

~~10,- 2~~

~~10- 3 0.0 0.2 0.4 0.6 0.B 1.0~~

Fig. 36: Inclusive momentum spectrum of neutral p mesons (k) at 7.3 GeV,5 5 . The I en histogram shows the prediction of the Field-Feynman model Fig. 38: An example of a two jet event. Charged particles are shown as full lines, neutral particles as dotted lines. - 197 -

E-, = 5.2 GeV where large data samples exist measurements however have been 57 done . The result is shown in Fig. 37 . It should be mentioned here that many more detailed measurements of this kind have do be performed before a really meaningful comparison to theoretical predictions can be made.

4.3 Two Jetstructure • Visual inspection of events at high energies reveals 2 jetstructure as the dominant phenomenon (Fig. 38 ). Qualitatively it calls for determination of an axis for each event and a measurement of the transverse (Pj.) and long- itudiual momenta (PJJ ) of the particles with respect to this axis. One way to do this is by determining the eigenvalues (and vectors) of the momentum 58a tensor 4.7

~~Ordering the eigenvalues > \^ > *3 one obtains~~

~~2. 4.8~~

~~o called sphericity and~~

~~4.9~~

~~and their expressions in terms of P, and P.. measured with respect to the 58b sphericity axis . A characteristic feature of jet formation is limited~~

~~> independent of energy and small ( %300 MeV) and Pj( ^ E. The data shows~~

59 this behaviour (Fig. 39) however there is a slight rise in Pj_ with ECM and PII rises not quite as fast as -vE the latter effect dominatly caused by the rapid increase of the fraction of low momentum particles with energy E^ (Fig. 30 ). The sphericity then should fall with energy E if jets continue fiO to be the dominant eventstructure. This is indeed the case see Fig.40 The success of the quarkmodel for the total cross-section (see section 4.1 above) easily connects to the observation of two jet structure assuming the quarks to "shower" into hadrons similar to the formation of electron photon cascades in matter30. The jet direction then on average should follow the ori• ginal quark direction and the distribution infr and ^) of the jet axis (e.g. identified with the sphericity axis) would be given by formula (1.14 ). With no transverse beam polarisation only the 1+a cos dependence can be fi 1 looked for and one finds values for a somewhat less than one . Actually a=1 is a limiting case only since quark mass effects as well a gluon radiation introduce corrections such that a becomes <1 . This could be used both to Fig. 40: The average sphericity vs. ECM from experiments at DORIS and PETRA60. - 199 -

find values for the masses of heavier quarks (c,b,t) and to determine the 62 63 strong coupling constant OQ/TT ' . With transverse beam polarisation moni• tored injA- pair production and Bhaba scattering the dependence allows a much better determination of a (see Fig.10 ). There have been more variables proposed to describe the jet behaviour most of them have actually been tried but no new conclusions have been obtained 64 that way . Finding a jet axis on an event by event basis certainly intro• duces a bias towards two jet events since even for random particle distri• butions always an axis is found by construction. To avoid the determination of an axis it was proposed to measure just the correlations between particle energies .A further motivation for mea• suring energy energy correlations oomes from 'leading log' QCD calculations that predict their shape and energy dependence65. The calculations are done for the partons of QCD (quarks and gluons)and the final stage of hadron for• mation is usually ignored. One measures the opening angle 0 for each narticle pair of an event multiplied with the scaled energies Z=P/E of both particles and defines 4.10 £-z2\A-i» *****

~~The prediction from LL QCD calculations have been given separately for same side correlations^ and opposite side correlation~~

~~4.11~~

~~for the same side 65 and a 'form factor' result for the opposite side 65'66 - 200 -~~

Fig. 41: Energy- energy correlations for different energies (2*E). The fi 7 fi ft full lines are from the FF model ' . The dashed lines are the QCD predictions (ignoring fragmentation effects) for de• tails see Ref. 66. - 201 -

These predictions are compared to data from PLUTO (Fig. 41 ). It is seen that at low energies the correlations are much weaker than the QCD LL cal• culations would predict however with increasing energy the data rapidly approach the predictions. This is expected since in the calculations the effects of hadron formation from the QCD quanta has been completely neglected. Formation and decay of the hadrons will considerably widen up the correlation. This effect on the QCD jet structure should become less important at higher ener• gies as observed. Further improvements in the QCD calculation should result in better agreement.The influence on the correlation from hadron decay is how• ever always left to be put in by hand and can be supplied easily once the primary hadron spectrum is known. Energy-energy correlation at larger angles is treated in section 4.4 below.

Jet Simulation Simulating the detector response to real events is a major task of experimentation in e+e~ annihilation. Since two jetstructure is dominating in the events the 'standard jet' algorithm of Field and Feynman67 is widely used for this purpose and briefly described below. A qq is generated with beam momentum each and further qq (uü,dd,SS only) are added. The q and q pairs form mesons which constitute the primary hadrons. Only the lowest lying pseudoscalar-and vector-mesons (v) are genera• ted with longitudinal momentum distribution independent of energy E (scaling)

~~4.13~~

The ratio W=P/P+V is a further parameter usually taken to be 1/2. The primary hadrons get their transverse momentum from the qq pairs forming them.The trans• verse momentum of the quarks (q,q) is generated according to a gaussian dis• tribution

~~with *Oq <\, 250 MeV. The light quark pairs are generated with some SU 3 symmetry breaking - 202 -~~

No primary baryons are generated also heavier mesons (like mesons from the tensor octett) are ignored. With only three parameters to be fixed once (afWjS^q), the model is simple (also fast on the computer) and very success• ful in describing the data. It only needed an extension to include the effect fi Q of occasional generation of three jets at higher PETRA energies . Also the influence of heavier quark production like charmed mesons and particles con• taining the b-quark can be successfully simulated69. In the model quantum numbers are conserved automatically. Momentum and energy is conserved only approximately due to the use of the scaling variable z. Other jet models have been proposed and are equally successfull in describing the data. Final results from the various experiments seem to have only very little dependence (if at all) on the specific models used. 4.4 Three Jetstructure Multiple jet events (3 or more) are expected to result from field theoretical descriptions of e e~ annihilation. For QCD as a rather well defined example many details for experimental signatures have been worked out for 3 jet events31'68. It is assumed that the basic colored quanta of QCD the quarks and gluons appear - if sufficiently energetic (>2 GeV) and well separated (>30°) - as jets of hadrons. Jet kinematics directly corresponds to parton kinematics in this picture. The color compensating mechanism then is assumed to be soft such that the basic parton structure is preservedby the jet structure. Events in e e annihilation in this picture are due to single gluon bremsstrahlung - 203 -

~~and E(q,q) the quark (antiquark) energies. 0O is the cross-section for two jet events. The gluon (xg) energy distribution can be obtained because of the constraint~~

~~x + x- + x q q g~~

~~Ordering of the parton energies (x^) such that x1> x2> x^ and integrating over leads to~~

-1 ÍS Ä 1 A 71 x1 is usually called thrust and is the scaled energy of the most energetic parton (sometimes the gluon) in a given event. For soft and collinear partons the differential cross-section for x three parton events diverges. This means that in such events one parton pair can not be separated into two well de• fined jets and the three parton event appears as a two jet event. For a mean• ingful experimental comparisons with (4.15) on an event by event basis one has to require for each parton a minimum parton energy typically of order 2 GeV and angular separtion of two partons of about 30°. Four jet events result from the parton graphs shown below: - 204 -

Their kinematic properties have been estimated recently be various authors The general conclusion is that only very few events 1%) with distinct four jet topology are to be expected at higher (>30 GeV) PETRA energies. As an immediate consequence of the gluon bremsstrahlungsprocess

~~jet axis~~

flat events are expected with large transverse momenta Pj^ in the event plane. Furthermore the jet character of the events requires the particles to cluster in three well defined regions. More quantitive evaluation of the expected effects in various experimental distributions have been obtained using the 6 8 3 jet models discussed above

Transverse momentum distributions In simple two jet models the average transverse momentum Pj_ of hadrons w.r.t the sphericity (thrust) axis is essentially constant (P^^ 0.3GeV) with energy. Observations show however a very definite increase with energy 2 (Fig. 42) which is due to the development of a very long tail in the Pj. distri• bution (Fig. 43 ) . In order to see if this is due to flat events one defines using the sphericity formalism (see section 4.3 ) for each event a plane. The average momentum (squared) out of the plane is given by

~~an in the plane by~~

2 v 2 < Pj_ out/ is observed to be small while< Pj_ in V again has a very long tail for the high energy data and cannot be described by two jet models. Higher^P^ in ^ can be enforced in two jet models by increasing the transverse momentum spread aq in the fragmentation process. However this cannot describe all data in par• ticular -

1 1 1 1 2 )0 (b) ° W = 12GeV • 274£Ws31.6GeV \ x 35.0=W s 36.6 GeV 101 0$ *

O 0 *

~~- 10° 0~~

~~0 0.2 0.4 0.6 0.8 10~~

~~2 2 •a * * PT (GeV/c) 1CT1~~

~~I z icr è t i i 1er3 -J 1 • I 10~~

~~2 2 PT (GeV/c) 10 20 W(GeV) 30 Fig. 43: The Pj. distribution for charged~~

~~Fig. 42: The average transverse momentum ?3b particles w.r.t. the event axis . 2 squared for charged par• ticles w.r.t. the event axis~~

vs. ECM. The full line indicates the predictio.. . . n fro- m a qq-g ÍÜ del the dashed line from a qq mo- model67. i i i i i i i i i ' i1 i1 i1 r~ T T- E 1 1 mjiT 1u—3 • W =12 GeV 12.0 GeV 17.0 GeV

~~10°~~

~~qq aq = 030GeV/c~~

~~o -i i ii i_ 4 0 4 GeV TT Iff* J__J ui i i i i i I i i_ ~1 r—i—r—11—i—i—i—|—i—i—i—i—i—r—i—I—r • 274~~

~~>out 1 -qq PLUTO - qq Oq=030GeV/c -qq aq=0.45GeWc J~~

I i -1 I I L_ 4 6 8 GeV 10-21 i il i I I—i i i i i i • ' • 0 0.2 0.4 0 0.2 0.4 06 08 10 12 14 0 6 8 GeV k 31770 (GeV/c)2 Fig. 45: The ^distribution (see text for de• 44: The transverse momentum distribution finition) for charged particles and for charged particles out of the event six energies 76 . The full line is a plane (left part) - and in the event parametrisation of two jet hadronisa- plane (right part) of the figure'4 . tion and the dashed line shows the contribution from gluon bremsstrahlung. - 207 -

hilation are more planar than to be expected from extrem fluctuations of hadron transverse momenta in the dominating two jet events. This effect can be demonstrated in other distributions as well. Take the thrust axis of an event and a plane perpendicular to it. One each side of the plane one forms

~~4.19 and the vector sum for the transverse momenta w.r.t the thrust axis runs only- over a halfsphere (see the illustration below in case of three jet events) A~~

Two jet events follow a probability distribution dP/dK1 derived in Ref.75 and shown as full line in Fig.45 • It has one free parameter only (for details see Ref.76 ) and describes the data very well for all energies however only out to a Kj of about 3 GeV. Beyond a value of K¿ = 3 GeV the data are well described (dashed line) by a term derived from the first order gluon bremsstrahlungs formula ( 4.15 ) above using

~~4.20 and~~

~~with - A-XI c4 * from y AH« 4.21 X - 208 -~~

~~Fig. 47: Two examples of clear three jet events. - 209 -~~

Fig.45 very clearly shows that a new hard process with high transverse momentum appears in the data for the upper energy range of PETRA and the shape in Kj_ is found to be in quantitative agreement with the form of formula 4.20 above. 77 A different approach was followed by the MARK j Coll . They analyse the flow of energy in the events. The main axis e^ of the events is defined using a thrust like variable

4 22 ~p = M*

A second direction e.^ (major) is found requiring the energy projected into the plane spanned by e^ and to be maximum and the third axis e^ (minor) is J_ to e^,e2. The energy flow1 in the direction minus the energy flow in the direction e^ is called oblateness O and is a measurement of the plana- rity of events. The distribution in oblateness is compared to 2 jet and 3 jet model calculations. At low energy the 2 and 3 jet models are both close to the data while at larger energies the additional contribution from planar events due to qqg final states is needed to explain the data (see Fig.46) Planar events need not to have three jet structure as it must be the case for an initial three parton final state. A further important step is a clear identification of events with three jets. Inspection of events with large Kj. , largejPj_| fat. The fat side is then checked for a two jet structure measured with the variable thrust T* in the rest frame of the fat jet. The distribution in T* is compared to the thrust distribution ob• served at lower energy (12 GeV) and found to be very similar to dN/dT (12 GeV) (Fig.48 ) where two jet structure of similar kinematics as expected at the fat side from a (qg) system at high energy is dominant. Dividing the planar events into three groups of particles using the triplicity algorithm 7- a study of particle distribution within each of the three groups shows jetlike behaviour. This was also the way followed by the PLUTO Coll. in their first publication80. The TASSO Coll.81 used an extended sphericity algorithm82 2 to define in planar events three groups of particles. The P distribution 2 w.r.t. an axis in each subgroup is compared to the Pj_ distribution in 2 jet events at 12 GeV as shown in Fig.49 . The cluster of particles around two axis at 12 GeV is found to be identical to the clustering around three axis in the planar 30 GeV events. The MARK J Coll.83 defines planar events using oblateness derived from the energy flow in the events. In the plane defined by thrust and major axis a three arm structure T $ T*broad jet>£ " aOGeV.Qj-Q^O.l T I T ví = 12 GeV all events o 2-Jets 12 GeV 60r i11 r t ; ill i i » i t* • 3-Jets 27.4 -31.6 GeV — MC 30 GeV

~~> O~~

~~Z.Q. -0|T3~~

~~-IZ'~~

~~0.1~~

0.01 0.5 1.0 Fig. 48: The thrust (T*) distribution in the 're in the 'rest frame' of the fat jet from clear 3 jet events Fig. 49: The P¿2 distributioPin of(GeV/c charge) d particles from two at (30GeV) compared to the jet events at low energy (12 GeV) compared to the thrust distribution at low Pj distribution w.r.t. three axis for clear three 78 81 energy (12 GeV) . jet events at high energy - 211 -

~~270°~~

~~Fig. 50: Energy flow plot for flat events at high energy (30 GeV). The full line _ g2 is the prediction from a qqg model~~

Fig. 51: The energy flow of flat events as function of the azimuthal angle in the event plane compared to model calculations. Note that all models give a three arm structure however only the qqg model describe the data 83.

~~r i—~~

~~X " ^—-^ :~~

~~ENERGY-FLOW 30 GeV PHASE SPACE Monte Carlo~~

84 Fig. 52: An energy flow plot in the 'event plane' from phase space - 212 - appears after superposition of many events ordered properly (Fig. 50 ). The distribution in the arms is shown to be narrower than expected (Fig. 51 ) from a random (according to phase space) particle distribution although the three arm structure itself appears even in the phase space model (Fig.52) - 8 4 a consequence of the strong ordering and superposition of the events . A careful quantitative comparison carried out by all four PETRA groups with two jet models, three jet models and phase space results in complete agree• ment with the three jet model while the two jet- and the phase gpace-model or a combination of both does not describe the data. More recently members of the PLUTO COLL. have presented a new way of ana- 8 5 lysing jet structures . It searches for particle clusters that will be iden• tified as jets if they contain a minimum number of particles (>2)and if the cluster energy is more than (typically) 2 GeV. Except for a minimum separation in space between each pair of jets no further correlations between the jets are required (like collinearity in sphericity and thrust analysis or planerity in triplicity and generalised sphericity analysis). The distribution in the number of jets (clusters) in events then is related to the number of partons in the events that give rise to jets. Some of the two parton events because of very broad fragmentation appear artificially in the three jet class and three parton events enter the two jet class for similar reasons. Two and three jet models help to disentangle this .The jet number distribution observed (Fig. 53) however can only be explained by a very significant sample of three jet events at higher PETRA energies. The four jet number is small and ex• plained by broad b-quark fragmentation events and spill over from real three parton events. Energy-energy correlation in the data can be used for a quantitative compari• son with the QCD predictions for sufficiently large angles between the par• ticles. One measures or 4. 23

where Z&, are the fractional energies of hadron a, b and 9a,b is the angle between them. First order QCD predicts 88 á*Z. - ií -0,(9) - T °" ^" ' 4-24 A ~ TT CT V. / where g (6) is an nfenergy independent function of e alone. At finite energies there is a further important contribution from parton fragmentation effects that may be parametrised as 88 • — - • *DlAi t7 4-25

~~À 0 Hc* 9 where C is a constant determined from = B + C • In E„.. and is the CM •* mean transverse momentum of hadrons in a jet. Taking - 213 -~~

~~20 Ecm iGeVl~~

~~Fig. 57: The energy-energy correlation at large angles vs. energy. The dashed curve is the QCD term (4.24) while for the solid curve the fragmentation term (4.25) is added.~~

Fig. 56: The forward-backward asymmetry in the energy-energy correlation at low (DORIS) and high (PETRA) energies. The solid curves are calculated using the standard jet fragmentation models67'68,69. The dashed line labeled EBEL is from Ref.88. - 214 -

~~one observes that the fragmentation term (4.25) vanishes in the difference~~

while the QCD term is quite asymmetric in 8 and 180 -8. The difference (4.26) 89 is shown in Fig. 56 at low and high energies .At low energy (9.4 GeV) both the QCD term and a simple qq MC describe the data, they cannot be distinguished. At high energy (30 GeV) and angles >40° the QCD term dominates and the simple

~~parametrisation (4.24;4.25) can be used to estimate ag. This is shown in Fig. 57 where the integral zy3~~

~~is compared to(4.25;4. 26) . A fit determines ag = 0.20±0.02 and C = 1.0Í0.2~~

~~in good agreement with other values for ag and also for C* from data in Fig. 30 and Fig. 39.~~

~~4.5 Gluon Properties The observed rate of three jet events should provide an experimental de•~~

termination of the quark gluon coupling constant ag through formula 4.15;4.16. In general this can be achieved by fixing the various parameters of the jet model (P/(P + V)a,a ) from a fit to distributions of the dominant 2 jet sample c¿ Going to the planar event sample then only one further parameter is left to

be fixed the coupling constant ag provided the structure of the jet distri• butions is given by formula4.15. Using the cluster formalism the PLUTO COLL. has compared the distribution as given by formula 4.16 to the distri• bution obtained from three jet events86. The experimental distribution is corrected for all instrumental and fragmentation effects and can therefore directly be compared to a parton level calculation . This is

shown in Fig. 54 for da/dX1 and in Fig. 55 obtained in a similar way for the Xj^ distribution (see formula4.20). The agreement with the first order calcu• lation is excellent. It therefore is very well justified experimentally to extract a„ using ( 4.15;4.16 ) from the planar (three jet) sample. 1 1 1 1 lili 600 PLUTO "

~~27GeV*Ecm<31.6GeV~~~

~~LOO —~~

~~200 —~~

-H

~~r-4- 1 1 1 -I L_ 1 1 2 4 6 8 Number of jets/event~~

Fig. 53: The jet number distribution at Fig. 54: The thrust distribution Fig. 55: The distribution in 86 ^ 30 GeV using the cluster forma- 86 of three events a ^30 GeV . transverse parton lism The curve is calculated using momenta w.r.t. the formula 4.16 X-axis in three jet events at % 30GeV95. - 216 -

~~The table below summarises the values for ag as determined by the various methods just mentioned~~

~~EXPERIMENT 83 0. 23 + 0.02 MARK J 87 + 0.02 TASSO 0. 17 + systematic 86 + 0.03 PLUTO 0. 15 uncertainties 89 0. 20 + 0.04 PLUTO 0.02 0.04 0. 18 + 0.03 JADE 90~~

~~TABLE 4.5~~

The results of the four experiments are compatible with each other and deter• mine to first order the quark gluon coupling of strong interactions. 91 9? There have been several attempts >-"-i?¿> to calculated the three parton final state distributions to second order in as- For a determination 2 of ag using formula (4.16 ) to make sense the (aj/ir) correction is required to be small. From the calculations this seems to be satisfied in one case 92 93 while two ' obtain the disturbing result that the second order contribution - although similar in shape - is of equal magnitude as the first order. This certainly needs to be clarified before the value for as obtained as described above can be generally accepted. Gluon spin Formally one can write down formula (4.15 ) with the spin 1 gluon re- 31 placed by a spin O gluon. One obtains

~~1 JÜ!L - 4.28~~

This is sufficiently different from ( 4.15) and allows a spin test. This has 94 86 been performed both by the TASSO - and the PLUTO-COLL. . The results are 94 86 9 5 shown in Fig. 58 and Fig. 59^ , Fig. 55 . In both analysis spin 0 is strongly disfavoured while spin 1 is in very good agreement with the data. Even more convincing test for the gluon spin may be obtained from 1.0

~~Fig. 58: The observed angular distribution of the X2'X3 jets directions with the direc•~~

~~tion in the rest frame of the X1 jet. The predictions for scalor- and vector-gluon theories are shown for comparison9 4~~

Fig. 59: The thrust distribution of three jet events compared to a prediction from a scalor gluon théorie8^. - 218 - a study of correlations of the event structure with the e- beams however the effects expected are small and the data samples obtained so far are just to small.

Further tests for the gluon spin are described in section 5.3. All spin arguments sofar rest on a comparison of the relevant experimentally determined quantity to the predictions of gluon spin O and spin 1 theories. While the spin 1 case is rather well defined - it is QCD - a similarily complete spin O theory is not described in the literature. Gluon spin 0 predictions can however often formally be written down from the corresponding expression in QCD. They are always found to be in disagreement with the data. This (probably, very likely) rules out spin O gluons. Effects from QCD gluons are always in very good agreement with the data. Therefore, "what else could it be than spin 1 gluons"?

According to QCD folklorev the gluon should fragment into hadrons in a markedly different fashion as compared to the quark. Qualitatively this has not been observed yet. The gluon jet in the three jet models is taken to be very similar to a quark jet and all the experiments are in good agreement 98 with this assumption. This is also observed in the decay structure Y Most likely the gluon jet energy simply is to low, I would expect marked differences for energies of the gluon >10 GeV where the gluon should have experimentally detectable probability to split into two gluon jets. In e+e annihilation in the continuum this is equivalent to observing the four jet 9 9 structure which therefore constitutes a crucial test of QCD - 219 -

~~5. SEARCH FOR NEW PARTICLES~~

5.1 Experimental Methods Pointlike particles of mass M and charge e (in units of the electron charge) can easily be produced in e+e annihilation, once 2*E > 2-M is reach• ed. The cross-section depends on the spin of the particle, for spin O we have for the differential cross-section

~~(ÁQ~~

~~and for spin 1/2 5.2~~

~~CAO, 7 v~~

~~with ß=P/E the velocity of the new particles. Integrating over the production angle one obtains~~

~~and~~

~~5.5~~

~~and~~

For quarks which come in 3 colors R (ß •* 1) is multiplied by 3. The threshold factor 3 (spin 0) and ß •(——) (spin 1/2) is a powerful handle to determine the spin of a new particle. So far no pointlike particles with spin O are known, the leptons and quarks have spin 1/2. In the threshold region ß«1 the new particles decay very 'non-jet-like' and can effectively be distin• guished from standard 2 jet events by methods that search explicitely for 100 3et structures .The sphericity method for example has been widely used for this purpose as will be discussed below. From experience above charm thre• shold (see Fig. 29) broader (^30-50 MeV)resonance like structures are expected also above B- or any other new quark - threshold. They have strong coupling to new particle final states which have very low ß and allow for precise measurements of masses and decay modes101. New particles should decay by standard weak interactions. For a new heavy quark Q one has - 220 -

with £, q the know leptons and quarks. Search for leptons (e,y) not coming from the decay of already known particles ( e.g.x , D) provides another clear signal for a new particle threshold. Just below the physical threshold bond states of the new particles PC — with J =1 exist.

~~The resonance cross-section observed in the final state f is given as~~

~~5.7~~

~~+ r is the total width and Tee, rf the partial decay width in e e pairs and the final state f of the resonance. The cross-section on peak of the reso• nance is~~

~~5.8~~

For cc and bb resonances (J/*f>, *f>, y , y', y" ) as observed in the existing storage rings (Adone,DCI, SPEAR, DORIS, CESR) the energy spread of the beams ^O* is much larger than the total width of the resonance r and in this approxi• mation ( - 221 -

5.10 >ta j which in DORIS amounts to a reduction of the natural peak cross-section by A- factor 10 on J/'f (3.1) and a factor of^ 200 on y (9.46). 2 *~ 2 SinceS" VE /JFp (formula 1.7 ) and E p (see Fig. 2 ) we roughly have 6* ^E which makes resonance hunting at high energy machines rather time con• suming.

~~RING ECM (GeV) a (MeV)~~

~~DORIS 3 0.7 TABLE 5.1 10 7~~

~~PETRA 10 2.5~~

~~30 21~~

~~LEP 40 10~~

~~100 60~~

~~Integrating over the resonance curve gives~~

~~rJt.JL ^4 5.11~~

~~The resonance cross-sections are even further reduced by radiative effects which are of order factor 2 ( see chapter2.4 ). New particles can also be searched for in yy collisions however only with M~~

(see chapter 5.3 below). At higher energies, beyond PETRA (e.g. LEP) the strength of the weak inter• action become comparable to the electromagnetic interaction and new particle production possibilities open up. For extensive discussions on this subject see RefJ02. On the Z°weak interaction of course dominates and Z° decay modes may be a very rich source of new particles. As a special example let me mention the process

e+e~ •+ y + Z° 5.13 neutrino pairs which will produce events of the kind shown in Fig. 16 however with only the photon observed and allows to count the total number of neutrinos in the world that couple the standard weak interaction . - 222 -

~~5.2 Search for the sixth Flavor (t) Let me group the known quarks and leptons as shown in the table below:~~

~~GENERATIONS~~

~~charge first second third~~

~~+ + + 3/3 e V T u u u, c c c, 2/3 r g b r g b d d d, s s s, Ebb, 1/3 r g b r g b r g . b~~

~~0 V v v e v T~~

~~TABLE 5. 2~~

Obviously there is a quark (in three colors) missing with charge 2/3 and unknown mass. Very many speculations have been put forward at what energy the new quark (top) is going to show up. From the discussion above one either searches for the narrow (tt) 1 resonances below top-particle threshold or for the new particles containing the t-quark (tü, td, ts, tc, tb) above the threshold (see Fig.60). The peak cross-section for a (tt) resonance is proportinal to Tee (see 5.10 above) which is not known. There is however a striking regu• larity observed for r of the known quark antiquark resonances. The ratio 2 1 ee

Tee/e is for the S-ground state, about 11 KeV independent of the resonance (see Fig.61 ). For the first radial excitationes (P',^',Y') ree/e is approxi• mately 5 KeV. This can be used to estimate Tee (tt) - 5 KeV. Furthermore a comparison to the experimental observation of theYresonance at DORIS leads to (using formula 5.10) R (tt) peak ^20 (15) at 30 GeV (40 GeV). A scan for (tt) 1 roughly proceeds in energy steps AE = 2

r =1 3 from a new resonance containing a new e =1/3 charge quark since one has ee * If M (tt) < 3 Ö GeV the scan would have missed the resonance. From cc and bb phenomenology the threshold for tq + tq particle production is expected about 1 to 1.5 GeV above the (tt) ground state. The new particles will add to the particle production cross-section an amount - 223 -

~~(tt ) resonances and threshold 20 ( hypothetical )~~

~~8 U~~

~~0 k 1 GeV >| ECM (GeV)~~

~~near a Fig. 60 A (realistic) sketch of R = ahadA>w hypothetical t(e = 2/3 threshold.~~

~~i—i i i i 1 '—I—I I I I 11~~

~~18 U)~~

~~16 - P U J/~~

~~^c u 8 XI Y' L_ i~~

~~J I I I I j i I i i i i I 0 5 1.0 2 5 10 20 30 40 50 H I GeV)~~

Fig. 61 The leptonic width of vector particles divided 5 by the average (quark charge) vs. the vector meson mass. i—i—i—i—i—i—1—i—i—i—i—i—i—i—i—i—i—i—rz R R - oley-httdmns) olcV— |iV) 14 JADE 4JM2 la) /T-. 29.9-31.6 GeV MARK J i.3i0.2 12 0.40 (JADE* MARK J + PLUTÜV TASSO)//. PLUTO a8t0.2 3/* Y TASSO U±Q2 10 Bhree^0.7KeV

6 0.35 4 K 2 CHARM \ Threshold \ V5~(GeV) 0_ \ CO \ 29.5 30.0 30.5 310 31.5 V t= 0.30 R i—i—'—i—'—i—i—i—'—i—-i—i—i—i—i—i—i—i—r1—r - (b) /s.- 35.0- 35.8GeV 12 CO (JADE*MARKJ*TASS0)/3 JADE 3.910.2 \ 10 Bh-ree<0.UeV MARKJ tu Q2 \ \ 6 TASSO 4.6¿0.3 6 0.25 4 v 2 V fs (GeV) _l i I • ' • 1 • I . I . I , |_i I i U 4.8 35.0 35.2 35.4 35.6 35.8 0.201—L_j i I i i_i L_j I_j I i i i i i i 0 20 40 , 60 80 100 S (GeV2) Fig. 62 Combined results from the PETRA experiments for the total hadronic cross-secticn at higher énergie. s 38a)

Fig. 63 The average observed sphericity in the DORIS energy range. Fig. 64 Plots of the shape of hadronic events a.) and b.) using the ' sphericity' formalism (see chapter 4.3). In c.) the results for the shape distribution of events from the decay of new heavy quark pairs is shown. The sensitivity of the experiments against the production of new hadrons cares from the lack of events with A > 0.2 and S > 0.6. - 226 -

~~2. 5.14 A R ~ 3 x jet = 3 • Ver = 4~~

The results of the scan (see Fig. 62) on R already render this possibility rather unlikely. An increase in sensitivity for new particles is obtained by searching for rather isotropic events, events that do not look 2-jet like. Just the average sphericity is sufficient for example to see the charm threshold al• though jet structure below charm threshold (3,6 GeV) is (almost) undetectable (see Fig.63 )105. In this figure the Y-resonance give a dramatic peak due to the very specific 3 gluon decay mode as will be discussed below. A plot of the sphericity distribution instead of the is of course more sensitive and a further increase in discrimination of non jet vs jet like events is obtained using the sphericity, aplanarity triangle as shown in Fig. 64 (see also section 4.3 above)or the cluster method (see Ref. 85 ). The data from all PETRA experiments exclude tq tq production up to an energy of 36 GeV. This conclusion is rather insensitive to the very details of the tq particle decay modes as has been shown by extensive Monte Carlo 106 studies of all experimental groups at PETRA The Monte Carlo model for heavy quark production in e+e annihilation is based on a paper by Ali. et. al. (Ref.69 ). The assumed decay modes of a new charge 2/3 quark predicts many leptons in the final states due tothe semileptonic decay of the heavy new quarks t, b, c (see page 66). A search 1 07 1 O fi therefore has been done for final states ' e+e -*-(]-+ hadrons The results shown in Fig. 65 do not require a new t quark^the data is well described by production and decay of c and b alone.

5.3 Properties of Q Q Resonances The properties of heavy QQ bound states have been reviewed recently 109 by many authors which should be consulted for the details .Some of the more interesting developments however will be discussed below with emphasis on new particle states as they can be reached in the formation and decay of - as well as and transitions between-heavy QQ resonances.The known quarks fall into two categories, those with masses lighter than the QCD scale parameter A ^ 1/3 GeV ( u,d,s) and the heavy quarks (c,b and hopefully one day a really heavy quark t) with masses ^ A (see table on page31 ). The heavy quarks may form rather stable (QQ) system where the quarks move essentially 1 in

~~nonrelativistically((v/c)* 1) . The masses of the bound states can then be estimated (calculatedfusing the nonrelativistic Schrödinger-equation,as - 227 -~~

~~M(GeV)ü M (GeV) • oooo 10.5 4.0~~

~~oooo~~

~~10.0 3.5~~

~~9.5 3.0~~

1 tîc j/* f?/x ( p,) lb Y Pb 0- 1" (2P) D 0"* 1" 2** 1- 0**

Fig. 66: The bound states of charmonium (cc) and bottonium (bb) . Dashed lines indicate the position of yet to be discovered states. The shaded boundary in the (cc) system is the physical threshold for charm par• ticles. In the (bb) system the threshold is not known precisely, it is however below the state indicated by OOOO and above Y" (1035) . The states are tripletts (not shown). - 228 -

where m^ is the quark mass and En (Q,V) the energy levels. The interaction is supposed to be characterised by a potential V (r) which is taken to be independent of the quark typ. There have been many proposals and ideas about 111 the correct potential to be used and very succesful descriptions of the mass spectra in the (cc)- and (bb) system can be obtained. At short distances QCD is the guideline and in a perturbative approach one gluon exchanges domi• nates which gives a 'Coulombic' behaviour ^ 4-/r while at large distances a linear potential is assumed. One has

The known mass spectra (Fig.66 ) can be well fitted by such a simple poten• tial model with three parameters A,a and the quark mass m^. However more trivial potentials (QCD counter examples) have been constructed which also 112 - fit the data rather well . Only a very heavy (QQ) resonance with > 20GeV could decide since there, because of the very short distance involved, the QCD part of the potential dominates. In Fig. 66 the position of still to be discovered bound states below open (Q-) threshold are indicated as dashed lines ^1 that can be mostly reached by y-transitions from the higher lying S states. The T^'ispredicted to be 65 MeV below \¡> ' however it should have a small y-transition rate and has therefore not been seen so far. In the Y-system one of course suffers from the very much reduced peak height of the Y',Y'' resonances ( see section 5.1) and not enough data have been accumulated to see

~~+ n n + the nb(0~ ) states. Note the small splittings M(Y (1 )) - M (nb (0~ ) predicted by the potential models which result in small Y-transition rates'1J¡~~

Decay into lepton pairs The decay width (QQ) -> l+l~ where A- are the charged leptons (e,y,T) 2 is proportional to the quark charge squared (e^ ) and to the square of the 2 wave function at the origin (r=0jJ divided by the square of the reso• nance mass

~~n = dèlf^~~

A flavor independent potential allows to calculate I|J (r=0) and leads to the regularity observed for rge (Fig.61). In a QCD guided potential one gets higher order corrections that give a further mass dependence which depends on the scale parameter A—. For a value of ^ 200 MeV r should fall with quark mass Mb _ ee ^ ^ providing an interesting QCD test on a new (tt) state One expects large corrections for r 115

~~- £ (d - "KM***)) 5.18~~

~~and further corrections not yet calculated are most likely not negligible. - 229 -~~

For a giveJ n m„ the ratio of r (D/r ( n ) is more reliable since some of Q ee ee the corrections cancel in the ratio. Although the absolut predictions for rge of ground states are quite resonable, it is seen (table below) that the ratios work even better.

~~STATE r (KeV) r /r (1S) (KeV) ee ee' ee Ref.112 Ref. 114 ggg~~

~~4.6 - 0.40 3.5 KeV 45 - 11~~

~~2.05- 0.21 0.446^0.06 0.35 0.45~~

~~4)' ' 0.26- 0.05 0.057-0.016~~

~~Y 1.29- 0.10 1.1 KeV 1.02± 0.10 Y' 0.45 - 0.05 0.43 0.45 < Y" 0.31 - 0.05 0.28 0.32~~

~~0.24 - 0.03 0. 20 0.26~~

~~TABLE 5.3 STATE M M-M(IS) Ref. 112 Ref. 114~~

* 3097 *' 3685 588 - 3 589 589 TABLE 5.4 *" 3768 671 - 4 705 715 Y 9458

~~Y' 553 - 10 (560) (560) 560 - 3~~

~~Y" 889 - 4 (890) 890~~

~~yin 1114 ± 5 1120 1160~~

~~Decay into 3 gluons In lowest order the QCD prediction for (QQ)-*- ggg is given by (posi- 1 1 fx tronicum analog)~~

~~5.19~~

~~Using (5.17) above this can be reexpressed as 5.20 - 230 -~~

~~r is determina from the area under the resonance curve (see 5.11 ) and ee using ( 5.20) the decay width should fall with resonance mass due to the~~

~~energy dependence of ac Measuring the branching ratio into lepton pairs~~

~~4-01" 5.21 and using n 5.22 ¿JL~~

~~a one r tne with R= a na¿ / yy determines ggqî results for J/iJi and the Y are~~

reported in table 5.3 above. Using (5.20) one finds ag (Y) = 0.17 - 0.02 and a (J/ii) = 0.19 - 0.02, however second order effects in a„ are most likely not negligible. The 3 gluon decay should lead to 3 jet final states. This follows from the basic assumption that the quanta of QCD,if sufficiently energetic appear as jets with (essentially) probability of 1. The matrix element has the following structure 117

~~^ 2 5.23~~

~~for gluons of spin 1. The average three gluon structure following ( 5.23) is shown in the figure below.~~

~~X, = 0.89~~

~~Fig. 67: The average three parton struc• ture on a heavy QQ resonance drawn to scale (relatively).~~

~~The scale energies are Xi=Pi/E where Pi are the parton energies 84~~

~~X3=0.39~~

~~X2=0.72~~

~~When should this structure become visible in the event shapes? - 231 -~~

1 1 1 1 1 i i Fig. 68: Comparison of Y(9.46) ggg MC • T direct dQta decay data with the three Phase Space MC: PLUTO pseudoscalar gluon model and phase _ 6 pseudoscalar/ vector mesons space models. x TD 2 4 / / \ \ " a) The distribution in the / A \ V - energy of the most energe• \ \. tic jet in Y (9.46) decays. / / \ \ \ \ v i/• i i i 0.6 0.7 0.8 0.19 \ 1.0

~~0.04 1 1 1 1 1~~

~~4 T•direcrtirerfdatt a — ggg mc Phase Space MC: PLUTO pseudoscalar 0.03 •V. pseudoscalar/ - vector mesons~~

~~CD 0.02 b) The distribution in the angle of the most - and second most energetic jets in Y decays. 0.01~~

~~PLUTO — ggg MC~~

~~Phase Space MC: — pseudoscalar — pseudoscalar/ c) The thrust distribution in vector mesons Y (9.46) decays. TJ~~

~~0.5 0.6 0.7 0.8 0.9 1, THRUST - 232 -~~

~~icos e i PLUTO: angular distribution of the sphericity axis on resonance.~~

~~The full curve is proportional to 1+0.39 cos29, the dashed~~

~~curve to 1-0.995 cos26.~~

~~25 ti i It » i i i i i i i i i i lit~~

~~Ib) y 'DIRECT 2 0 Fig. 69: The distribution for I cos $ I of the event axis of Y (9.46) decay data.~~

~~1 1 8 a) PLUTO~~

~~44d \ i b) LENA \ \ . \ 0.0 i i i i i i i I i » i I i i i I 0.0 02 0.4 0.6 0.8 1.0 Icos 0| - 233 -~~

The gluon energies at the J/I/J are simply not high enough and no significant distinction from other models (2 jet or phase space) seems possible (Fig.63). At the Y however the three gluon structure should at least be visible in the standard shape variables (see chapter 4.3). Very pronounced deviations from 118 the 2 jet case have been observed while phase space as another extrem can 118 also not describe the data (see Fig.63 and 68). 119 The Y decay data require gluons to be colored and provide a very interestina test on the spin of gluons. The decay matrix element for spin 0 , . Ï20 gluons is 5.24

118 This gives essentially 2 jet events which is ruled out by observation Furthermore the angular distribution of the most energetic jet (X^ is given as 5.25 with a= 0.39 (spin 1) and a- - 1 for spin 0. The data (Fig. 69) rule out • 118,44d the spin 0 case Hadronic transitions

~~The energy mass dif fence M(i|>') - M (J/*) and M (Y1) - M (Y) is suffi• cient to allow hadronic transitions the observed ones are listed below:~~

~~MODE B.R. %~~

~~^'-s- j/ljj TT + TT 33-3~~

~~0 0 TT Tí 17-2~~

~~n 3.9^0.3 TABLE 5.5 109b'121 2.18-0.14~~

~~2.5 -0.6~~

~~0 TT 0.09-0.02~~

0.15-0.06 + - Y'+Y TT TT 21-7 The transition rate Y'+ YTTTT can be estimated using reasonable assumptions on the relative decay properties of the Y and Y' although the total width of the 121 Y has not yet been directly measured .A comparison, with i>' -* J/\|> + TTTT gives

~~d = P(Y'-»Y+tt) = Q Oq ¿ O. OÇ 5.26~~

~~In QCD this transition results from a radition of two soft gluons a process that can be treated as a multipole expansion of the gluon radiation field from a (QQ) source122. It predicts - 234 -~~

~~in good agreement with the data. For spin 0 gluons one would have R^- -1 clearly in gross disagreement with the data.~~

~~The decay (QQ) -» y + gg~~

~~The decay of a heavy QQ resonance into 1 photon and 2 gluons is a poten- 1 23 tial source of very interesting physics. The rate for this process is~~

~~5.27~~

~~For a quark charge of 2/3 one has r /T - 0.13 for e_ = 1/3 only ygg ggg Q 1/4 x 0.13. The energy spectrum of the photon is given by 5.23 if one inte•~~

~~116 123 grates over X2 and if one integrates over X2 and using X1+X2+X3= 2 ' .~~

It rises almost linearity to the endpoint of X =1 however production of Y 124 resonances and higher order effects should give sizeable distortions Indeed several resonances have been observed in J/ty+y + hadrons as summa-

~~table below125:~~

~~MODE B.R.~~

~~0 J/t|i -+ y y 7± 5-10"5 + -4 Y n 10- 3-10 * 109b TABLE 5.6 Y n' ^ 50 -10"4~~

~~Y f ^ 15 -10~4~~

~~Y E(1420) ^ 50 -10-4~~

~~126 Also the inclusive y-spectrum has been determined recently and is~~

~~shown in Fig. 70. In the recoil spectrum (Fig. 71) the E(1420) appears~~

which comes as a real surprise since this particle is rarely observed in — 128 other hadronic reactions (it was discovered in pp annihilation ). It was then suggested that it may be a 'glueball' a particle not dominantely composed of a standard qq pair but rather of gluons. This will be not 1 ?<3 easy to prove .

~~It would certainly be extremely interesting to observe the inclusive~~

~~y-spectrum at the Y (9.46) and search for resonance effects in the final~~

~~state. This type of data could be coming in the near future from experi•~~

~~ments at CESR. - 235 -~~

~~I MARK H~~

~~measumeasurer d~~

~~\ —%~~

~~contribution r 'H~~

~~Fig. 70: Inclusive photon spectra 126 in the decay of J/if (3.1)~~

~~0.2 OA 0.6 0.8 1.0~~

~~X = 2P/m((l a) The measured y photon spectrum and the calculated contribution from IT0 + n decay o.~~

~~i 1 1 1 1 1 r MARKU~~

~~b) The photon spectrum with the IT0 + n decay photons subtracted. The line (QCD) is the lowest order prediction with experi• mental resolution folded in. - 236 -~~

J/4> —» YKsK- it*

~~Fig. 71a: Mass distribution for~~

~~+ 126 J/* r Ks K- 7T+ . The shaded histogram has an additional cut,~~

~~M (KSK±)< 1.05 GeV.~~

~~J/4»-*y+X~~

~~Fig._^71b: The recoil mass spectrum for J/ty •> y + X as mea• sured by the Crystall Ball127.~~

~~I i III I I 900 1100 1300 1500~~

~~Ev (MeV) - 237 -~~

5.4 Search for New Leptons Since there is no deeper understanding of the problem of particle gene• rations it may be assumed that further generations exist. The new 'sequentiell' lepton probably would be the lightest member as observed for the three known generation3 s (m < m,,m ; m < m ,m ; m < m, ,m.). The decay modes of the new e d n' ji s c T b t' •* lepton assuming standard (V-A) weak interactions can be predicted rather safely13Q The experimental search is based on the decay mode

~~and specifically also on~~

~~The cross-section for L+L production would contribute a fraction to R of~~

5 55 AR(L*ir) = ''M ?-' ) where ß = P/E is the velocity of the lepton L. The rather rapid increase of AR (L+L ) with ß allows for a sensitive search up to lepton masses close to the highest beam energies reached. No indications for a new lepton however 131 + have been found . Lepton masses M (L ) below about 10 GeV at beam energy 15 GeV give AR > 0.91 and events that would enter the T+T sample. The good agreement for the T+T cross-section with R (T+T )i 1 at 30 GeV excludes this possibility. Higher lepton masses M (L+) >10 GeV result in momentum unbalanced events due to >twoYl Per event with rather isotropic structure. Furthermore + - + they produce events of the type e e u hadrons that do not enter the T+T sample because of the higher multiplicity of the acompaning hadrons. The table below summarised the relevant results from the PETRA experiments.

~~131 + u + hadron event pattern Experiment PLUTO > 14.5 > 13.5 TASSO > 14.0 > 15.5 JADE > 17.0 MARK J > 15.0~~

~~TABLE 5.8~~

Finally I want to mention that here is also little room for any new particle produced in e+e annihilation below 35 GeV for two reasons: a) The event shapes of all events can completely be explained by qq + qqg events with standard quark (gluon) jets. b) The total cross-section is almost saturated by just the known quarks (u,d,s,c,b) and the additional contribution from qqg final states that lead to the first order correction of R ( see chapter 4.1). - 238 -

From Fig. 28 one estimates AR new < 0.25. Only in the region 6 GeV < E_,,.<9 GeV there seems to be a significant discrepancy of order AR new - 0.5 CM + _ * 132 It could be related to threshold effects from e.g. e e •+ J/ty + ct however no evidence of this kind has been reported so far. For other specu• lations see Ref.133.

~~Search for spin O leptons~~

134 In theories based on socalled supersymmetries each of the already known particles has a partner which differs in spin by 1/2 unit. One there• fore would expect spin 0 electron ( muon, tau) like new charged leptons (S1) Their production cross-section follows(5.3)and for each kind one has a depen• dence on energy 5.29

3 where 3 is the threshold factor. For electronlike spin O leptons t-channel graphs (with photino or goldstino exchanges) are possible in addition which adds to the 1 photon exchange cross-section . These new particles decay as ^5 S 1 + photino 1 with very short lifetime where 1 are the corresponding standard charged leptons. The experimental signature is two acoplanar charged leptons with large missing energy, carried away by the undetectable photinos. Corresponding distributions for the electron positron case have been shown in chapter 3, Fig. 19 however the missing energy and momentum always appears as photons seen in the detectors (PLUTO, JADE). Therefore no signal events have been found. The mass limits are 1 36 derived using the production cross-section5.29and one finds>13 GeV (PLUTO) at 31 GeV and >17 GeV (JADE) at 35 GeV. - 239 -

~~6. YY - REACTIONS~~

6.1 General Properties The e+ and e do not have to annihilate to produce further particles in a collision they may as well reappear in the final state together with other particles. This process is called 'YY collision'. The basic diagram describing the process e+e •+• e+e +X is shown below and defines the kinematical quantities used in what follows

~~F' P'~~

~~Fig. 72 The basic graph for two photon collisions and definitions of the kinematical quantities used.~~

~~For practical experiments three cases are distinguished depending on none of the e+e- (no tag) one (single tag) or both (double tag) being detected as illustrated below (Fig. 73): - 240 -~~

For PETRA energies events due to the 2y processes where expected to be rather frequent and very little was know fromearrlier experiments therefore most ex• periments did install electron detectors as close as possible to the beam pipe to tag 2y events.

~~Detector Tagging Acceptance Dead Region (mrad) (mrad) PLUTO 23-70 none CELLO 25-50 50-153 TASSO 18-60 60-207 JADE 34-70 70-240~~

~~TABLE 6.1~~

For the no tag condition both e+ and e are scattered at angles „ <. "1,2'*' mm here^/^^ is the smallest angle covered by the electron detectors. The produced system X then has limited transverse momentum Pj_with respect to the beam direc• tion of PL <

~~(o.(, UV od % E - ZO Ge-V CK^OI -fo-t o?^,^, =0.02.)~~

~~1 2~~

~~The longitudinal momentum PL may be large since EY and EY are rather different in general. The cross-section in the no tag condition is given in terms of the~~

~~scaled photon energies Z-\ = (E-E-,') / E and Z2 = (E-E2') / E -(E^ E2= E)~~

~~2 2 with W = (q^ + q2) the mass of the hadronic system and~~

~~L In the case of single tag events we have (since q-4rq..) with W2 — "M/i CM—0Í **vi^ (/I- coo-ft,) - 241 -~~

~~with Y = ~y%í~£y~~

~~The luminosity function r^- N depends very steeply on the ratio W/2E andW the mass of the produced particles X. Low mass particle systems are therefore strongly dominating the 2y processes.~~

~~Fig. 74 The relative luminosity dL/dz in photon photon collisions as function of the scaled hadron mass W/2E where E is the beam energy.~~

~~The double tag condition is more complicated and since up to now it does not play a role in experiments because of very small rates it is ignored.~~

~~6.2 Resonance Production Resonances with spin J, parity p in the series, Jp = 0+, 2 that de• cay to two photons may be produced in 2ycollisions notably the~~

~~T*,*,?', i-, Ai ,«Cc The resonance cross-section is given by - 242 -~~

~~O 2 2/ 22~~

with x_ (x) = (2+x ) M* 1/x - (A-x ) (3+x ) j Mr the resonance mass and Hv(M ) the decay width into two photons. Two resonances have been seen the ' + — o + — ri ' in the ir tí y decay mode and the f in i u , + - + - , e e •» e e n This reaction was observed by MARK II at SPEAR for energies 2.21<"Gev)«£.

13 E<3,7 (Gev) ?Final states with 2 charged tracks and 1 photon with total PA < 250 MeV with respect to the beam axis were selected. The invariant mass dis• tribution shows a clear peak at the mass of the n (980) (see Fig.75 ).

~~Fig. 75~~

~~The effective mass distribution for IT TT y in 'no tag' photon photon collisions .~~

~~2 mT*T-y{G«Vc )~~

~~The cross-section is 0,8 nb. Using is determined to be 5,9 - 1,6 GeV with additional systematic uncertainty of ^ - 20%. With BR ( n1-»- Y Y ) = 0,0197 - 0,0026 the total width of the n' is~~

~~r 300 90 eV The tot ^ 1 ' ) = ^ - value for ryY ( n' )=5.îil-/is found to be in good agreement with quark model calculations^-^~~

~~+ -.o + - e e f e e The data for this channel come from the no tag two charged particles final~~

E state with charge balance and visible energy ? 30% of the total energy cm^^®. The sum of the transverse momenta of the particles with respect to the beam is observed to be limited to < 0,5 GeV (see Fig.76 ). The invariant mass of the two particles (assumed to be pions) is shown in Fig. 78,79 .For most of the events the two particles are leptons (e,yU) from two photon QED processes. A clear separation into pions and leptons was not possible due to the dominantly low momenta of the particles. The QED processes however can be reliably cal• culated and with known efficiency and luminosity one arrives at the full lines in Fig. 77 ! For masses larger than 1,6 GeV QED describes the data very well. For part of the data (no tag condition) electron and muons can identified EVENTS per 0.05 GeV 1 i events per 0.1 GeV No tag PLUTO

~~1 3 4 5 W(GeV) Fig. 77 The mass distribution of identified lepton pairs from two photon collisions 14\~~

~~—i— —i 1— 0.5 1.0~~

~~_SUM r_ . ,~~

~~PL [GeV] Fig. 76 The distribution in the sum of the transverse momenta of two charged particles w.r.t. the beam direction140. - 244 -~~

~~EVENTS per 0.1 GeV~~

~~100-~~

~~2 3 W [GeV]~~

~~Fig. 78 The two charged particle mass distribution in 'no tag' 2 photon events. In the inset the contribution to the mass distribution from QED processes has been subtracted 140~~

~~-i 1 r TASSO 2Y"* 2 prongs Ino tag ) TASSO ^ data minus background 2 y -» 2 pr ongs (no tog ) 100 — f "simulated~~

~~-e*e--»e*e~*eV o in o n*if (Born) ci (adjusted) S 50~~

~~0 1.0 20 3.0 40 _i L 7760 30371 Invariant moss (GeV) 0 10 20 3.0 4.0 7780 Invariant mass (GeV) 31372~~

142 Fig. 79 The same as in Fig. 78 with data from TASSO - 245 - separately. For this subsample the invariant mass distributions are shown in Fig. 77 together with the prediction from QED which give a very satisfactory describtion of the data. Below 1,6 GeV there is an additional contribution with resonance like shape as seen in the QED subtracted mass plot Fig. 78,79. It can be fitted with a Breit-Wigner ansatz for the total cross-section and the mass and width of the f° taken from the particle data compilation!28. A special problem arises since the acceptance of the detectors is limited to Icos^l < 0,6. It is not known in which helicity state |x| = 2or X = O the f° is produced. They give very different decay angular distributions for the

+ 4 2 -1 2 FOR TT TT in the f° rest system, ^sin 6CM (|x|= 2) and ^(3 cos @ Q^ ) X = O. I XI = 2 is assumed to dominate and one obtains r YY= (2,3±0,5) PLUTO140, (4,1- 0,4) TASSO142 and additional systematic uncertainties of - 15%.

~~6.3atot for e,y Scattering~~

The total cross-section ayy(W) has been measured up to ^10 GeV using data in the single tag mode. This measurement is somewhat more difficult than a measurement of the total annihilation cross-section (see section above) be• cause a) the detection efficiency for the final state with present detectors is ^ 20% only and large model dependent extrapolations are necessary b) there is significant background at least in some of the final states from electropro- duction of hadrons on the nuclei of the restgas at the interaction point. Point a) can be improved with better model calculations and larger acceptance in the for• ward-back direction, point b) with better vacuum, however statistical sideband (in z) subtractions can probably never be completely avoided (see Fig. 80 ). 2 At -g =0 the cross-section is expected to follow a factorisation hypothesis

~~6.8~~

~~This can be understood in the framework of the vectordominance model (VDM)~~

~~is where the photon acts as a quasireal p-meson and aYy replaced by ap. times the Y - P coupling squared (up to known factors). In the single tag mode~~

~~Fig. 81 A graph for the~~

~~'p0p0' part of the total cross-section for hadron produc• tion in two photcn collisions. a, + e a, --I 1 1 1 1 1 EVENTS per 10 mm (nb)~~

~~800 PLUTO _ 1< Wv.s <35GeV ^ I -f :E=155 GeV_ 600 r^T 1 7.8 GeV. 400~~

~~200 -~~

~~1 1 1 1 1 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Q2 (GeV2)~~

~~I (nb) n 1 i PLUTO 400 3.5~~

~~-100 -50 0 50 100~~

z (mm) 0.7 Q2 (GeV:) Fig. 80 The z distribution for two photon event Fig. 82 The total hadronic cross-section for two photon candidates, z is event vertex coordinate collisions vs. the four momentum transfer 140 2 143 along the beam . squared Q of one of the virtuell photons Orr (W)|Q2a0

~~100 1 1—~~

~~(a)~~

~~VDM • l i 1.5 2.0 2.5~~

~~WYV (GeV)~~

W(GeV) Fig. 84 The total cross-section for e+e~ •+ e+e~ p°p° o oJ44 vs. M(p p ) Flg. 83 The two photon collision total cross-section extrapolated to zero rranantum transfer Q a* O. The shaded area indicates the uncertainty in this procedure. The dashed line is from the 143 naive factorisation hypothesis - 248 -

~~2 one of the p-mesons goes more and more off-shell and the -q dependence is expected to follow the p-propagator and one obtains~~

~~In the single tag mode W is determined only from observation of the hadrons which is somewhat incomplete, corrections are model dependent and the data 2 is shown only in terms of W .~~

two Wv^s bins and up to Q ^0,7 GeV is very well represented by the propa• gator. Relying on the model calculations for the hadronic system one is able to extrapoate from W . to W and using the p-propagator the cross-section Oyy (W,0) is determined see Fig. SS14-* . The systematic differences between TASSO and PLUTO can probably be traced to differences in the procedure (see Ref.141) used to extract ayy (W,0) from the measured cross-sections. At higher W the cross-section is not far from the factorisation prediction which at low W is very unreliable. The strong rise at low W is also seen in one single identifiable channel + - + - o o e e -»• e e p p as measured by the TASSO group^^ and shown in Fig.84 . There is however no easy explanation at hand for this large cross-section.

6.4 Hard Scattering Processes Although the bulk of the two photon events is explained by 'quasi-pp- scattering' as see in the discussion above some deviations from this picture are expected due to the pointlike coupling of photons to the constituents of hadrons. The relevant diagram has the following structure

o Fig. 85 Lowest order parton graph in two photon collisions. - 249 - which constituts a subclass of Let us consider two limiting cases: a) the production of two quark jets from the qq pair coplanar with the beam but non collinear and b) the scattering of one of the electrons into larger angle such that 2 2 Q 1 GeV . This measures the 'structure of the photon' in analogy to deep inelastic lepton scattering on nucléons. Both cases (a and b) are pictured below:

~~Fig.~~

While events from VDM like production generate very limited Pt of final state hadrons with respect to the beam the appearance of two-jet-like two photon events should generate a long tail in Pj . This has indeed been observed with about the expected order of magnitude(see Fig.87 ) . The two-jet-effect on the Pj^ distribution can be easily estimated in analogy to formula (4.2) however the quarkcharge enters like (eq)4. In comparison to lepton pair production we get in lowest order

~~R 6.10~~

Above charm threshold ( Wis 4 GeV) we have Ryy = 34/27 and the eq = 2/3 charge quarks (u,c) completely dominate. Examples of events with the correct topology have been found one of them is shown in Fig. 88 .

~~6.5 Photon Structure Function The general expression for the single tag cross-section formula ( 6.4 ) above can be reexpressed in terms of the familiar structure functions F_ and~~

~~2 F1 (x = Q /2Y)as~~

~~Aé Wot-E-'E 6.11 olxdy - 250 -~~

~~entries perOOOMeV)2 entries per(IOOMeV) • 1 1 i 1 1 r —i r i i PLUTO PLUTO 1000 O00 i *T2>75 / -~~

~~100 \ 3 < Wv,s<9GeV >- No tag+singletag 10 - -~~

~~1 1 i i i i~~

~~PT (GeV ) P/(GeV2)~~

~~Fig. 87 The transverse momentum distribution of charged hadrons 141 w.r.t. the beam axis for two photon collision events~~

~~13.8 GeV e: = 6.5 GeV~~

~~w = 8 GeV 1-6 = 3 GeV = 1.6 GeV~~

= 139*

~~Fig. 88 An example for a two-jet event from two photon collisions 141 - 251 -~~

~~and with F1 = F2 / 2x~~

~~For hadron like (p-meson) behaviour one expects in analogy to the ir-meson F2 ^ (1-x) while for pointlike constituents of the photon we get~~

~~6.13~~

~~This pointlike photon structure function rises with x •> 1 in contrast to~~

145 a hadron like F2 that falls like 1-x . There are preliminary data relevant çfor a measurement of from PLUTO 14 Hadronic events with one electron (single tag) in the angular region .07 < $ < .25 (see table6.1) corresponding to 1 = 2 5 GeV ) have been selected and the x dependence has been evaluated see FigJ89

~~The full lines show the VDM prediction and F2 according to 6.13) above. In Fig- 90 is shown for comparison data for the process~~

~~e+e ->• e+e 1+1 (and 1= e,p) which is a measurement of pointlike behaviour (leptons are pointlike particles)~~

of F2 (Y). It can easily be calculated since it is a pure QED process and good agreement is found. The shape of the hadronic photon structure function (Fig. 89 .) is very similar to the leptonic one and directly reflects the point• like structure of the photon constituents.Future data with higher statistics and more range in Q2 will allow the SM Q2//^2 term to be measured which pre- 14fi sents a strong scale breaking effect due to gluon radiation . For perfect 147 scaling one can showthat

~~6.14~~

~~The preliminary date from PLUTO covering the range 6 GeV <£< 15 GeV are shown in Fig. 91 . The VDM predition is far off while the quark parton model is in reasonable agreement with the data.~~

~~Note added:~~

~~The 'midnight' lecture on proton decay experiments I have not written up. Those interested can find reviews in Ref. 148 - 151. - 252 -~~

~~1 -F2(x)~~

Fig. 89: The structure function Fig. 90: The same as Fig. 89, but for of the photon at events with an observed lep• 2 2 <\. 5 GeV from ton pair instead of hadrons. large angle tag hadro- The line is the QED prediction. . 141 nie events

~~Fig. 91: A 'scaling' plot for the deep inelastic two photon cross section. - 253 -~~

~~References:~~

1) Review Articles on Electron-Positron Annihilation - G.J. Feldman, M.L. Perl,Physics Reports Vol. 19C, no. 5, 1975 - R.F. Schwitters, K. Strauch,Am. Rev. Nucl. Sei. 26- p.89, 1976 - J.P. Perez-Y-Jorba, F.M. Renard,Physics Reports Vol. 31C,No.1, 1977 - B.H. Wiik, G. Wolf,Springer Tracts in Modern Physics, Vol 86, 1979 - G. Flügge, KF Karlsruhe Report KFK 2995, 1980

2) Design Study of a 22 to 130 GeV e+e~Colliding Beam Machine (LEP) CERN/ISR-LEP/79-33 - A High Energy, High Luminosity e+e Collider Based on Superconducting RF Cavities, Cornell University May 19 80 - The SLAC Linear Collider, SLAC-PUB-2526 and 2549, June 1980 - TRISTAN- The Japanese Electron-Proton Colliding Beam Project, KEK Pre• print 80-15, Sept. 1980 - Study on the Proton-Electron Storage Ring Project HERA, ECFA 80/42, DESY HERA 80/01, March 1980

~~3) Results of Machine Physics Studies on PETRA in 1979, DESY Report 80/10 Febr. 1980~~

~~4) A.A. Sokolov, I.M. Ternov, Sov.Phys.Pokl. 8 1203, 1964~~

~~5) III. International Symposium on High Energy Physics with Polarized Beams and Polarized Targets, Argonne, October 1978, American Institute of Phy• sics New York 1979~~

~~6) I.G. Learned et. al. Phys. Rev.Lett. 35/688 (1975)~~

~~7) M. Capdequi-Peyraneyre et.al. Uni of Montpellier preprint PM/78/8 (1978) and PM/80/9 (1980)~~

~~8) R.F. Schwitters in Ref. 5 and SLAC-PUB-2258~~

~~9) H.D. Bremer et.al. First Results from the PETRA Polarimeter DESY 80/76 July 1980~~

~~10) I.K. Bienlein at the 1980 International Symposium on High Energy Physics with Polarised Beams and Polarised Targets, Lausanne Sept. 1980, DESY 80/126, Dec. 1980~~

~~11a) A. Wagner, Central Detectors DESY 80/83~~

~~11b) Ch. Berger, Forward Spectrometers, Aachen, Preprint PITHA 80/13 - 254 -~~

~~12) See e.g. PLUTO-Collaboration, Physics Letters 94B,254,1980~~

~~13) See Ref. 18~~

14) General References are: F.A. Berends et.al. Nucl. Phys. B 57/38, 1973 and Nucl. Phys. B 115, 114 (1976) and DESY Report 80/66 and 80/73 F.A. Bonneau and F. Martin Nucl. phys. B 27, 381 (1971), M. Greco et.al. Nucl. Phys. B 101, 234 (1975), J.D. Jackson, D.O. Scharre Nucl. Inst.S Methods 128, 13 (1975)

~~14a) F.A. Berends and G.J. Komen, Phys.Lett. 63B , 433,(1976)~~

~~15) T.F.Walsh, P. Zerwas, Two-Photon Processes in the Parton Model,DESY 72/77~~

~~16) S.L. Wu, TASSO Results on Jets and QCD DESY 80/106~~

~~17) Particle Data Group, Rev. of Mod. Phys. 52,1,(1980)~~

~~18) PLUTO-Coll. Zeitschrift f. Physik C 4, 269,(1980)~~

~~19) JADE-Coll. Phys. Lett. 92B, 206,(1980)~~

~~20) TASSO-Coll. Phys.Lett. 94B, 259,(1980)~~

21) For a summary of the most recent data: a) A. Böhm, Aachen Preprint PITHA 80/9 (Talk at XX.Int.Conf. on H.E.Physics, Madison, July 1980) b) MARK J-Coll. Phys. Rev.Lett. 43,1915 (1979) c) TASSO -Coll. Phys. Lett. 92 B, 199 (1980) d) PLUTO- Coll. DESY 80/116

~~22) See Ref. 21 and b) JADE - Coll. DESY 80/123, Dez. 1980 c) MARK J-Coll. Physics Reports Vol. 63,No.7,(1980)~~

~~23) A. Böhm, see Ref. 21~~

~~24) A.Böhm, see Ref. 21, MARK J-Coll. in Ref. 22, PLUTO-Coll. Ref. 18~~

~~25) R. Budny, Phys. Lett. 55B, 227,(1975)~~

~~26) MARK J- Coll. Phys. Lett. 95B, 149,(1980), JADE-Coll. see Ref. 22b PLUTO-Coll. see Ref. 21c~~

~~27) E.H. de Groot and D. Schildknecht, Phys. Lett. 90B, 427,(1980) - 255 -~~

~~28) V. Barger et.al. Phys. Rev. Lett. 44, 1169, (1980)~~

~~29) PLUTO-Coll. Phys. Lett 94B,87,(1980), JADE-Coll. Phys.Lett. 92B,206,(1980)~~

~~30) R.P. Feynman, Photon-Hadron Interactions (Benjamin, Reading, Mass. 1972) J.D. Bjorken, E.A. Paschos, Phys.Rev. 185,1975,(1969), S.D. Drell, D.J.Levy, T.M. Yan, Phys. Rev. D1, 1617, (1970)~~

~~31) J.Ellis, M.K. Gaillard, G. Ross, Nucl. Phys. B111, 253,(1976)~~

~~32) H.Fritzsch, M.Gell-Mann, Vol. 2, p. 135 Proc. of the 16th Int.Conf. on High Energy Physics, Chicago/Ill. (1972)~~

~~33) K.Shizuya, S.-H.H. Tye, P.R. D20, 1101 (1979), P.R.L. 4J_, 787 (1978) and 4±, 1195 (E) (1978), M.B.Einhorn, B.Weeks, N.P. B146, 445 (1978)~~

~~34) Th.Appelquist, H.D.Politzer, P.R. D12, 1404 (1975) M.S.Chanowitz, P.R. D12, 918 (1975) R.Barbieri, R.Gatto, R.Körgele.r, Z.Kunszt, P.L. 57B, 455 (1975)~~

35) M.Dine, J.Sapirstein, P.R.L. 43 668 (1979) W.Celmaster, R.J. Gonsalves, P.R.L. 44,560 (1980) and P.R. D21, 3312 (1980) K.C.Chetyrkin, A.L.Kataev, F.V.Tkachov, P.L. 85B, 277 (1979) and P.R. D2_l, 3312 (1980)

~~36) D.J.Gross, F.Wilczek, P.R.L. 30, 1343 (1973) H.D.Politzer, P.R.L. 30, 1346 (1973)~~

37) JADE Coll., P.L. 9_1B, 152 (1980), a9B, 136 (1979), 88B, 171 (1979) PLUTO Coll., P.L. 9_1B, 140 (1980), a6B, 413 (1979), 81B, 410 (1979) P.R.L. 44, 1722 (1980) MARK J Coll., P.R.L. 42, 1113 (1979), P.R.L. 43, 830 (1979) P.L. 85B, 463 (1979), P.R.L. 4_3, 901 (1979) TASSO Coll., P.L. 88B, 199 (1979), 83B, 261 (1979) Z.Phys. Ç4, 87 (1980)

~~38) a) D.Cords, DESY 80/92, U.Timm, DESY 80/70 b) C.Bacci et al., P.L. 86B, 234 (1979) c) J.Siegrist, SLAC - 225 (1980) d) Ch.Gerke, PLUTO 80/03~~

~~39) a) see 38c) b) DASP Coll., Nucl.Phys. B148, 189 (1979) c) PLUTO Coll., P.L. 66B, 395 (1977), A.Bäcker, DESY F33-77/03 (1977) - 256 -~~

~~40) D.Andrews et al., P.R.L. 45, 219 (1980) C.Finocchiaro et al., P.R.L. 45, 223 (1980)~~

~~41) F.Laplanche, p. 189, in Proceedings of the 1977 International Symposium on lepton and photon interactions at high energies, Hamburg 19 77~~

~~42) P.-A.Rapidis, SLAC - 220~~

~~43) C.Bebek et al., P.R.L. £6, 84 (1981) K.Chadwick et al., P.R.L. 46, 88 (1981)~~

44) a) TASSO Coll., P.L. 89B, 418 (1980) b) JADE Coll., P.L. 88B, 171 (1979) c) PLUTO Coll., P.L. 95B, 313 (1980) d) LENA Coll., DESY 81/008 e) C.Bacci et al., P.L. 86B, 234 (1979) f) J.Siegrist, SLAC - 225 (1980)

~~45) see Ref. 13 in Ref. 44c)~~

~~46) see Ref. 15 in Ref. 44c)~~

~~47) K.Konishi, Rutherford preprint, Proceedings of the Conference on Multiparticle Dynamics, Brügge 1980~~

~~48) S.Wolfram, CALT-68-778 (1980)~~

~~49) Z.Koba, H.B.Nielsen, P.Olsen, N.P. B40, 317 (1972)~~

~~50) see Ref. 44c and Ref. 44d)~~

~~51) DASP Coll., N.P. B148, 189 (1979), J.Siegrist, SLAC-225, TASSO Coll., P.L. 89B, 418 (1980)~~

~~52) D.Pandoulas, Proc. of the XX. Int. Conf. on High Energy Physics Madison/Wisc. 1980~~

~~53) TASSO Coll., P.L. 94B, 91 (1980)~~

~~54) A.Fang, LBL - 10389~~

~~_>5) S.C.Cooper, LBL - 11322 - 257 -~~

~~56) see Ref. 42)~~

~~57) M.W.Coles, LBL - 11513~~

~~58) a) J.B.Bjorken, S.J.Brodsky, P.R. in, 1416 (1970) b) PLUTO Coll., P.L. 76B, 243 (1978)~~

~~59) PLUTO Coll., P.L. 86B, 418 (1979)~~

~~60) a) see Ref. 38a), and b) PLUTO Coll., P.L. 81B, 410 (1979)~~

~~61) PLUTO Coll., P.L. 78B, 176 (1978), G.Hanson et al., P.R.L. 35, 1609 (1975) LENA Coll., DESY 81-008~~

~~62) G.Grimberg, Y.J.Ng, S.-H.H.Tye, P.R. D21, 62 (1980)~~

~~63) C.L.Basham et al., P.R. Dlj), 2018 (1979)~~

~~64) see Ref. 71), Ref. 79), Ref. 82), and~~

~~G.C.Fox, S.Wolfram, CALT-68-723 (1979), G.C.Fox, S.Wolfram, P.R.L 41, 1581, (1978), N.P. B149, 413 (1979), P.L. 82B, 134 (1979), G.C.Fox, T.-Y. TSE, S.Wolfram, N.P. B165, 80 (1980)~~

65) Yu.L.Dokshitzer, D.J.D'yakonov, S.I.Trojan, P.L. 78B, 290 (1978), and Physics Report 58c, 269 (1980), K.Konishi, A.Ukawa, G.Veneziano, P.L. 80B, 259 (1980), and N.P. B157, 45 (1979), and further references: in Ref. 66

~~66) PLUTO Coll., P.L. 99B, 292 (1981)~~

~~67) R.D.Field, R.P.Feynman, P.R. D15 2590 (1977), N.P. B136, 1 (1978)~~

~~68) P.Hoyer et al., N.P. B161, 349 (1979)~~

~~69) A.Ali, J.C.Körner, G.Kramer, J.Willrodt, N.P. B168, 409 (1980)~~

~~70) B.Anderson, G.Gustafson, C.Peterson, Z.Phys. CM, 105 (1979) P.Massanti, R.Odorico, Z.Physik C7, 61 (1980) G.C.Fox, St. Wolfram, N.P. B168, 285 (1980)~~

~~71) E.Farhi, P.R.L. 39, 1587 (1977), A. de Rujula, J.Ellis, E.G.Floratos, M.K.Gaillard, N.P. B138, 387 (1978) - 258 -~~

~~72) T.De Grand, Y.J.Ng, S.-H.H.Tye, P.R. D1j5, 3251 (1977) A.Ali et al., P.L. B82, 285 (1979), N.P. B167, 454 (1980) K.J.F.Gaemers, J.A.M.Vermaseren, Z.Phys. Ç7, 81 (1980)~~

~~73) see PLUTO Coll., Ref. 59, TASSO Coll., Ref. 81~~

~~74) G.Wolf, DESY 80/85~~

~~75) G.Curci, M.Greco, Y.Srivastava, P.R.L. 43, 834 (1979) N.P. B159, 451 (1979)~~

~~76) PLUTO Coll., DESY 80/111~~

~~77) MARK-J Coll., Physics Report 63, 340 (1980~~

~~78) JADE Coll., P.L. 9JB, 142 (1980)~~

~~79) S.Brandt, H.D.Dahmen, Z.Phys. CA_, 61 (1979)~~

~~80) see Ref. 59~~

~~81) TASSO Coll., 83B 261 (1979)~~

~~82) S.L.Wu, G.Zobernig, Z.Phys. Ç2, 107 (1979)~~

~~83) MARK-J Coll., P.R.L. £3, 830 (1979)~~

~~84) H.Meyer, Proc. 1979 Int. Symp. on lepton and photon interactions at high energies, FNAL 1979, p. 214~~

~~85) H.J.Daum, H.Meyer, J.Bürger, DESY 80/101, Z.Phys. C , to be published~~

~~86) PLUTO Coll., P.L. 97B, 459 (1980)~~

~~87) TASSO Coll., P.L. 94B, 437 (1980)~~

~~88) C.L.Basham, L.S.Brown, S.D.Ellis, S.T.Love, P.R.L. 4J., 1585 (1978), P.R. DT7, 2298 (1978), P.R. D19, 2018 (1979) C.L.Basham, S.T.Love, P.R. D2Q, 340 (1979)~~

~~89) see Ref. 66)~~

~~90) JADE Coll., P.O. 9VB, 142 (1980) - 259 -~~

~~91) K.Fabricius, I.Schmitt, G.Schierholz, G.Kramer, P.L. 94B, 431 (1980)~~

~~R.K.Ellis, D.A.Ross, A.E.Terrario, P.R.L. 45, 1226 (1980)~~

~~J.A.M. Vermaseren, K.J.F. Gaemers, S.J.Oldham, CERN TH-3002~~

~~TASSO Coll., Pi. 97B 453 (1980)~~

~~H.J.Daum, Thesis~~

~~K.Koller, H.G.Sander, T.F.Walsh, P.M.Zerwas, Z.Physik Ç6, 131 (1980)~~

~~see Ref. 33) and Ref.~~

~~PLUTO Coll, P.L. 82B, 449 (1979), PLUTO Coll., DESY 80/117~~

~~see Ref. 72)~~

~~see Ref. 63, 64, 71, 79, 80, 82, 83, 85.~~

~~R.H. Schindler, SLAC-219.~~

~~see G. Barbiellini et al. ECFA/LEP Study Group "Exotic Particles". DESY 79/27, 79/67 and 80/42.~~

~~E. Ma, S. Okada, P.R.L. 4J, 287 (1978) and 41(E), 1759 (1978).~~

~~TASSO-Coll. P.L. 88B, 199 (1979). PLUTO-Coll. P.L. 9JB, 148 (1980). MARKJ-Coll. P.R.L. 4_4, 1722 (1980). JADE-Coll. P.L. 9_1B, 152 (1980) and DESY 81-006.~~

~~PLUTO-Coli. unpublished.~~

~~see Ref. 38a.~~

~~PLUTO-Coll. P.R.L. 45 1533 (1980).~~

~~JADE-Coll. DESY 80/86.~~

~~a) K.Gottfried CLNS 80/465 C. Quigg, J.L. Rosner, FERMILAB-PUB- 79/22-THY, 81/13-THY. M. Krammer, H. Krasemann, Acta Phys. Austriaca, Suppl. XXI 259 (1979).~~

~~b) K. Berkelman, CLNS 80/470.~~

~~T. Appelquist, M.D. Politzer, P.R.L. 34 43 (1975).~~

see C. Quigg, J. , Rosner, Ref. 109a. E. Eichten et al., P.R.L. J3_4 369 and P.R. D17 3090 (1978), (1975), D21 203 (1980). J.L. Richardson, P.L. 82B, 272 (1979). w- Buchmüller, S.-H.H. Tye, FERMILAB-PUB-80/9 4-THY.

~~112) A. Martin, P.L. 9 3B 338 (1980), NP. B168 111, (1980). - 260 -~~

~~113) T. Appelquist, R.M. Barnett, K.D. Lane Ann.Rev.Nucl.Sei 28 387 (1978).~~

~~114) W. Buchmüller, S.-H.H. Tye, in Ref. 111).~~

~~115) R. Barbieri et al., P.L. 57B 455 (1975).~~

~~116) A. Ore, J.L. Powell, P.R. 75 1696 (1949)~~

~~and a collection of Ref. in Ref. 20 of Ref. 84.~~

~~117) e.g. K. Koller, T.F. Walsh, N.P. B140 449 (1970).~~

~~118) PLUTO-Coll., P.L. 83B 449 (1979).and Ref. 84.~~

~~119) T.F. Walsh, P.M. Zerwas, DESY 80/20.~~

~~120) K. Koller, H. Krasemann, P.L. 88B 119 (1979)~~

~~121) LENA-Coll., DESY 80/125.~~

~~122) K. Gottfried, CLNS/465 (1980).~~

~~123) see Ref. 34.~~

~~124) see e.g. S.J. Brodsky et al., P.L. 73B 203 (1978).~~

~~125) see Ref. 109b). 126) G.S. Abrams et al., P.R.L. 44 114 (1980). D.L. Scharre et al., P.L. 9 7B, 329 (1980). 127) D.G. Aschman, SLAC-PUB-2550.~~

~~128) Review of particle properties, Rev. of Mod.Phys. 52, No. 2 (1980).~~

~~129) see e.g. H. Harari, Proc. 1979 (see Ref. 84).~~

~~130) Y.S. Tsai, P.R. D4 2821 (1971) and SLAC-PUB 2105.~~

~~131) D. Cords, DESY 80/92.~~

~~132) K.-T. Chao, FERMILAB-PUB-80/70-THY.~~

~~133) R.M. Barnett, et al., SLAC-PUB-2475.~~

~~134) For a review see G. Barbiellini, DESY 79/67.~~

~~135) G.R. Farrar, P. Fayet, P.L. 89B191 (1980).~~

~~136) H. Spitzer, DESY 80/43.~~

~~137) see Ref. 131. 138) G.S. Abrams et. al., P.R.L. 43. 477 (1979) and R. Hollebeek SLAC-PUB-2517~~

~~139) M Chanowitz P.R.L. 44 59 (1980)~~

~~140) PLUTO-COLL. P.L. 94B 254 (1980)~~

~~141) W. Wagner DESY 80/102~~

~~142) E. Hilger DESY 80/85~~

~~143) PLUTO-COLL. DESY 80/94~~

~~144) TASSO-COLL. P.L. 97 B 448 (1980) - 261 -~~

~~145) S.J. Brodsky et.al. P.R. D 19 1418 (1979)~~

~~146) E. Witten N.P. B 120 189 (1977)~~

~~147) P. Zerwas P.R. D 10 1485 (1974)~~

~~148) Paul Langacker 'Grand Unified Theories and Proton Decay'~~

~~SLAC-PUB-2544~~

~~149) J.C. van der Velde ' A Review of Proton DECAY Experiments'~~

~~Univ. of Michigan Preprint~~

~~150) G. Barbiellini, R. Barloutaud 'Experimental Projects on Nucleón~~

~~Instability' XVth- Rencontre de Moriond, March 1980~~

~~151) M. Conversi 'Future Large European Underground Experiments'~~

~~CERN-EP/80-217 (1980)~~