PROCEEDINGS OF THE IV HIGH ENERGY PHYSICS SYMPOSIUM
E 1 S V W W S 1 ®
fiECEJVED by TIC OCT 18 1979
JAIPUR, RAJASTHAN December 5-9, 1978
Editors
S. N. Ganguli, and P. K- Malhotra
TATA INSTITUTE OF FUNDAMENTAL RESEARCH BOMBAY 400 005
ORGANISED UNDER THE AUSPICES OF THE DEPARTMENT OF ATOMIC ENERGY GOVERNMENT OF INDIA
s*THIB IOC ::' DISCLAIMER
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' Proceedings of the
IV HIGH ENERGY PHYSICS SYMPOSIUM
Jaipur, Rajasthan
December 5-9, 1978
E d ito rs
S. Nt Gang all
P.K. Malhetra
Tata Institute of Fundamental Research
Borpbay 400005
ORGANISED
UNDER THE AUSPICES OF THE
DEPARTMENT OF ATOMIC ENERGY
GOVERNMENT OF INDIA Request for copies of the Proceedings should be addressed to:
Head, Library and Information Services Bhabha Atomic Research Centre Central Complex T ro m b ay . Bombay 400085 ORGANISING COMMITTEE OF THE SYMPOSIUM
P. K. Malhotra C onvener
S. N. Gangnll S e c re ta ry
P. P. Divakaran
V.A. Kamath Head, Library & Information Services, BARC S. Lokanathan
N. M ukunda
Yog Prakash .
N. R am asw am y Under Secretary, DAE
M. V. Sreenivasa Rao
B. L. Saraf
K. V. L. Sarma
Virendra Singh
LOCAL ORGANISING COMMITTEE
S. Lokanathan 1 I C h a irm en B. L. Saraf . {
A. K. Arora
K. B. Bhalla
K. B. G arg
L P . Ja in
R. S. Purohit
M. P. Saxena
N. K. Sharma
S, R. Sharma THIS PAGE WAS INTENTIONALLY LEFT BLANK FOREWORD
The IV High Energy Phyaica Symposium waa held during s . December 5-9, 1978 at Jaipur - the 'pink city1, Rajasthan. It waa hosted by the Department of Phyaica, University of Rajasthan. It was organised by the Tata Institute of Fundamental Research, Bombay, under the auspices of the Department of Atomic Energy, Government of India. The
Symposium was inaugurated by Justice V. P. Tyagi, Vice-Chancellor of
Rajasthan University.
The Symposium waa attended by 140 delegates.' Out of 121 abstracts
(theory 85 and experiment 36) submitted to the symposium a total of 99 papers (theory 65 and experiment 34) were presented at the symposium.
Among the 14 invited talks, the talk entitled "Quark-Parton models for hadron-hadron interactions" could not be delivered, but is nevertheless included in the Proceedings.
There were two popular talks, one by Prof. L. K. Pandit On "A view of high energy physics" and the other by Prof. B. L. Saraf on "Some instructive experiments for physics laboratory". The first talk gave an overall view of the current research activity in the field of high energy physics in a simple language, while the second talk" stressed on a new method of doing experiments in college laboratories so that physical ideas become more instructive to students - the talk was backed up by imagina - tively designed experimental equipment.
-iii We weald like to thank oar colleagues. on the Organising Committee and the Local Organising Committee for their contributions towards success of the symposium. We are- grateful to the staff and the students of the Physics Department, University of Rajasthan, in particular
P rof. B. L. Saraf, for making excellent arrangements for accommodation, catering and lecture hall facilities.
We would like to thank Dr. V. A. Kamath and hie staff for-their kind co-operation in bringing out the Proceedings. Our thanks are also due to Mrs. M. Benjamin and Mr. V. S. Potti for their assistance in typing and secretarial help.
S. N. Gangull
P. K. Malhotra
-Iv - CONTENTS
Symposium Organising Committee 1
F orew o rd iii
Invited Talks
D.S. Narayan Jets and large P^, phenomena 1
Y. P ra k a s h Proton-antiproton interactions 32 (experimental status of baryonium s ta te s )
S. Banerjee Neutrino interactions - an 70 experimental survey
A . K h are New particles 132
L. K. Pandit Theoretical status of weak and 162 electromagnetic interactions
S. N . B isw as Thermodynamics of quark gas 186
K.B. Bhalla High , energy nucleus -nucleus 206 co llisio n s
S. R . C houdhury Instantona, CP -violation and 246 ax io n s
S. C. Ton war New results from cosmic rays 262
N. D. Hari Dass On supersymmetry 309
H. Banerjee Asymptotic behaviour in field 327 th e o ry
G. Bhattacharya Understanding of QCD through 343 solvable models
V. G upta Quark-parton models for 369 hadron-hadron interactions JETS AHD LARGE PHEHOHEHA
D.S. Harayan
Tata Institute of Fundamental Research Homi Bhahha Road, Bombay 400005, India •
1. Jets, their origin and importance.
He may define a j e t ^ * * 2* as a group of hadrons coming out of a collision, all of which are moving roughly along the same direction in the C.N. system of the incident particles. If p.(i * 1,2,... H) are the momenta of the particles in the jet and p = £ p., then the components * i=l of perpendicular to p are limited in magnitude.
Experimentally one may identify jets by using some criterion such as sphericity^2 2*. He define a variable S by the relation
c -*-2 3 I d.-, S * --- ^ ; 0 < S < 1 (1) 2 I ^i where p ^ is the component of p^ perpendicular to an arbitrarily chosen direction. The jet axis is that direction which minimizes S. The minimum value < S >m£n of S is called the sphericity. For an isotropic distribution S = 1 and for a parallel collimation of all particles
S * 0. The smaller the value of S, the greater is the jettiness of the particles.
Experimentally one finds jets in hadron production in e+« annihilation at high energies^9^’^2^, in deep inelastic lepton-hadron scattering^6 and in hadron-hadron collisions^ involving the production of particles with large P^. It is generally believed that
in all these interactions leading to the production of jets, one is
encountering sub-processes involving collisions between quarks and
gluons which are the constituents of hadrons.
The aechanima^10^ far the production of jets in different processes
is illustrated in figures (la) - (lcj. Fig.(la) shows the production of
jets in e*e” annihilation. A virtual photon formed by the annihilation
of o^e*, produces a quark and an antiquark which fragment themselves into
two jets of hadrons. In the deep inelastic lepton scattering in Fig.(lb),
the virtual particle emitted by the lepton is absorbed by a quark inside
the target hadron, which then fragments into a jet of hadrons. In the i . • collision between two hadrons A and B in Fig.(lc), two constituents a and b from the respective hadrons undergo a hard scattering and fragment
into two jets of hadrons having large transverse momenta.
2. Mechanism of quark-fragmentation.
From the examples of jet formation, illustrated in Figs.(la)-(lc), one finds that a quark tends to fragment itself into a jet of hadrons, whenever it receives a hard kick. . At present we do not have a clear understanding of how the fragmentation takes place. One believes that it is somehow connected with quark-confinement and colour confinement.
One reasoning^is as follows. Consider a proton at rest. It is rnqde up of three valence quarks (Fig.2), two of u-type uQ » u^ and one of d-type dQ and a cloud of gluons which confine the quarks. Suppose the uQ quark receives a hard kick, resulting in a large momentum transfer.
According to the present ideas based on Q.C.D., the struck quark uQ behaves like a free quark and starts moving away with a velocity .
approaching that of light. This results In a large separation between
uq and the remaining quarks (u^, dQ ). This separation causes the
confining forces to come into operation. Part of the energy of the
quark uq would be transformed into potential energy of excitation of
the confining gluon field. When the energy of excitation builds up to
something like 1 GeV, it can dissipate the energy through the creation
of a pair of quarks q^ and q^s such that q^ is created near the original
position of uq. This results in a situation in which we have three"” '
valence quark3 q^ u^ dQ , corresponding to a moderately excited nucleon
(proton or neutron) and a quark-antiquark pair q 2uc ul*ich may be regarded
as an excited meson. But the quark uq is still moving away and this
causes the separation between d2 and uQ to increase and hence also the
excitation energy. Once again, the energy of excitation can be dissipated
by creating another pair q^ q3 between dj and uQ . The process can proceed
in a string-like fashion until all the energy of excitation is dissipated
and we are left with a jet of hadrons.
The mechanism outlined above for the quark fragmentation is only one of several possibilities. We have imagined that the quark pairs are
first created near the original;proton and.spread outwards. It is, however, possible to imagine the process to be happening’ in the reverse (12) way. In either of these modes of fragmentation, one can see that (12) there would be certain correlations in charge and rapidity amongst the hadrons in the jet. We shall discuss the experimental evidence regarding these correlations in section (4.II).. It is also conceivable that the quark fragmentation can proceed in a manner entirely different from the string-like formation of hadrons.
An example of such an approach may be an extension of the quark (13) re-combination models , in which the re-combination leads to the formation of fast moving hot spots or fireballs, whose decay products constitute jets. In such models the correlations, which are inherent in any string-like formation of jets, can be expected to disappear and not detectable.
3. Basic concepts and assumptions in the study of jets.
There are a number of concepts and assumptions which are used in a phenomenological description of jets and large processes. The major ingredients in their description are the distribution of quarks and gluons in a hadron, the quark decay distributions and the transverse momentum distributions of quarks and gluons.
I. Distribution of quarks and gluons in a hadron; G (x), G (x). b*q b-*g A quark or a gluon in a fast moving hadron carries a certain fraction of the momentum of the hadron. We define the function^0^
G (x) dx to be the number of quarks of type q with a fraction of momentum h-*q between x and x ♦ dx within a hadron of type h of high momentum. He have a similar definition of G (x) for the distribution of gluons in a hadron. h*g The quark distributions in a proton are denoted by u(x) = G (x), _ p-»u d(x) = G.(x), S(x) = G (x), u(x) = G (x), d(x) = G (x) and . „p-*d— .. . p*s p-*u p-*d S(x) G (x). The distributions in a neutron can be expressed in terms p*s of the above functions by iso-spin symmetry. The quark distribution functions can be computed from the experimental information on the structure functions obtained froa deep inelastic lepton nacleow
scattering. Several" .authors^^) have given parsmetrixation of
.the quark distributions in a nucleon. The distribution functions as
determined by Field and Feynman^10^ (FF1) are sheen in Fig.(3). - '
One has no experimental information on the gluon distributions
in a hadron except that the gluons carry roughly about 50% of the
momentum of a fast moving hadron.
II. Quark and gluon decay distributions: D^(s), I>jj(x)
He define the quark decay distribution^10 D^(x)"as the
number of hadrons of type h which are produced in the decay of a quark
of type q such that the hadron h carries a momentum fraction s per unit
dz of the momentum of the fast moving quark. Similar definition holds
for the gluon decay distribution D^ix). The decay distributions are normalized such that
1 h I f z D (x) dx « 1 (2) h o while
1 h n. (z ) = / D (z)dz (3) ~ b o ' q o represents the multiplicity of hadrons of type h which carry a momentum
fraction greater than z . He have several of quart decay distribution ± ±° ± i functions like D1 , ... for pions and D* , ... for kaons. By “ u “ u h using iaoepio and charge eenjugatien invarianee,•the number functions for pious can be reduced to three and a similar number for kaons.
To further reduce these numbers to two, Field and Feynman^10^ assume w* * that De 8 D^ and choose for pions two independent functions
♦ o DCs) s d’ ♦ d* 8 2D* (0 )
and
■(*) 8 D*II ZD* tt (5) and two independent functions for kaons
V aDf tDf » K. aDf ♦<" • <6>
Since the total .charge of all hadrons from the decay of a quark should be equal to the charge- of the quark, we have the following relation:
Qo “ f k ~ Do * Do " Daldz (7) where is the charge of the quark q. In the above relation, we have neglected the contributions from the baryons.
The quark-decay distributions can be obtained using the experi mental, data on the inclusive hadron distributions in deep inelastic lepton-hadrdn scattering and in e % ~ annihilation. As an illustration, consider the inclusive pion production in deep inelastic neutrino scattering. The pacton model predicts.the cross-section completely in terms of the decay distribution functions of the quarks. The cross-
section^0^ is given by where the target H is an average over neutron and proton, H a (n * p)/2
and
Q(x) « x[u(x) * d(x)]
Q(x) « xtuCx) «• d(x)]
x is the sealing variable, x 3 - q2/2q.p, where q and p represent; the
four-.momenta of the lepton and the initial nucleon and z = E^/v, E^
being the energy of the pion and v the total energy of the hadrons
produced in the collision. Since the functions Q(x) and Q(x) are known ± from the data on structure functions, the decay distributions D can u be determined in terms of the observed pion inclusive cross-sections
as per, relation (8). Fig.(4) shows the data on the decay function D(z)
defined in (5), obtained by a suitable combination of'data, such as
N*1 til'1 and H*1 t N*1 where vp vp * - ♦ - r r e e e e h • h . , c (t ♦ H ♦ 1 ♦ X; x,y,z) N" (IN * I tht*; x.y.z) = ------,--- — ---- (9) °tot(lN * 1 ; *» y>
Ae e .<*> • ■ W~ tot £ “V * h‘ * ” <“>
The decay distribution functions have been parametrized in FF1 in terms of a finite number Chebyschef polynomials. The significant aspect of Fig.(4) Is that the data points, representing the function D(z) from totally different experiments, fall roughly on the same curve; lending support to the Idea that the decay of a quark is Independent of the process in which it is produced.
III. Quark fragmentation via a cascade process.
Field and Feynsan (FFl)^^2 ^ and independently Sukhatme^16^ have given a description of a quark decay in a cascade process. It is
illustrated in Flg.(S). A quark of flavor%a'combines with an antiquark b of a pair b b to form a seson a F, while the quark b combines with an antiquark e of a pair c c and so on. One assuaes that at each stage * a quark has a certain probability of becoming a meson and leaving a
fraction n of its momentum to the rest of the cascade. This, probability is denoted by f(n). One can then set up an integral equation for the quark decay function with-f(n) as a keraal. The equation can be easily solved for simple forms of f(n)• The parameters in f(n) can be so chosen that the solutions'for the decay functions agree approximately with those obtained empirically as described in the previous section.
The advantage of this approach is that it can be generalized to obtain correlation decay functions between two or more particles.
IV. Transverse momentum distributions.
One assumes that the quarks and gluons in a hadron have internal motions which would give them components of momenta perpendicular to
the direction of motion of the hadron. These components of momenta (17) (18) are sometimes referred to as primordial transverse momenta * of the quarks and gluons. One also assumes that when a quark decays into - 9 -
hadrons, all of them do not emerge parallel to the direction of the quark but have-small components of momenta perpendicular to the direction of motion of the quark. • The same assumption holds.for the decay of a gluon. The distribution of transverse momenta amongst •' o f the hadrons from the decay/a quark or a gluon is referred to as smearing(17)*(19).
4. Monte-Carlo methods;in the study of jets. (1.2) __ i) The cascade model of quark decay.has been used in FF2 to generate individual quark jets by a Monte-Carlo simulation of the
events. A total of 10,000 quark jets have been generated and they have been used to study the distribution of charge as a function of rapidity and correlations, such as the correlation between the fastest and the next fastest charged particles in the jet and several other features of quark jets. ii) Uncorrelated Monte-Carlo Calculations (UMC).
Bell et al*7* and Bossetti et al^20^ have given a simple Monte-
Carlo calculation, based on the longitudinal pahse-space, to study different distributions in a jet, with particular reference to the jets observed in neutrino-proton interactions. It is assumed that in the rest system of the hadrons, corresponding to a total energy H, there is one recoiling nucleon of energy E in the backward c.m. hemisphere and the remaining hadrons are in the forward c.m. hemisphere with a total energy V-E. The recoiling nucleon is chosen to be a proton or a neutron with equal probability, so that the hadrons in the forward hemisphere have a net charge (♦ 1) or (t 2) with equal probabilities. The recoiling nucleon has a flat distribution in
Xg « 2E/H in the backward c.a. hemisphere. The rest of the model incorporates a simple longitudinal phase-space approach with an exponential damping in P^.
It turns out that the bulk of the data on inclusive production of pions, kaons and identified protons can be reproduced by the simple
Monte-Carlo calculations.
5. Charge and rapidity correlations in a jet. - (1 2 ) The hypothesis of quark fragmentation as developed in FF2 has definite predictions regarding charge and rapidity correlations in a jet and these can be tested in the light of recent experimental results. (7) Bell et al have measured charged correlations of the fastest and the second fastest charged hadrons in a jet, which have momentum fractions z > 0.1. They have compared their results with the predictions (12) (7) of FF2 and the UMC model . Their results are shown in table 1.
A (>) or (-) sign signifies the charge of the hadron while 'none' implies no second charged particle with z > 0.1. One finds from table 1 that the data is in disagreement with the model of FF2. Between (♦ +),
(+ -) and (+ none), the observed correlation is greatest for (t +) and least for (+ none) while FF2 predicts the reverse trend. The UMC model correctly predicts the trend but it predicts too much (♦ +) correlation than what is observed. The strong (+ +) correlation in UMC is however, not a fundamental difficulty of the model. The strong (+ *) correlation is a reflection of the fact that the total charge (♦ 2) in the c.a. - 1 1 -
ferwurd hemisphere ia the BMC Mill, ■■aura as frequently as the tutol
charge (t 1). This in turn is related to n/p ratio of the recoiling
nucleon being equal to unity. This value for n/p ratio is, however, (21 ) unreasonable in view of the fact the same ratio in pp collisions
is of order 0.3/0.7, independent of the incident energy. If the value
of n/p ratio is reduced In UMC, the strong (♦ +) correlation would
decrease while (+ none) correlation would increase, and the model can
be expected to become consistent with experiment. He then face a
situation in which most of the data on hadron production, in deep
inelastic processes can be described in teres of a simple Honte-Carlo
approach based on longitudinal phase-space, while the quark-fragmentation
approach gives wrong predictions regarding charge and rapidity correla tions. If it 'turns out that the failure of the quark fragmentation model to explain the charge and rapidity correlations is fundamental, one may investigate, within the parton model, alternative approaches, such as the quark recombination model, where the correlations are expected to be weak.
6. Large phenomena in hadron collisions.
It is not our purpose here to give a general survey of the (9) (22)-(27) features * of large transverse momentum production of (16) (28)—(32) particles and the models which have been proposed to explain them. He consider only those features which are important as tests of the currently popular models.
A model which has been widely discussed is the Constituent (29) Interchange Model CIM , in which the basic hard-scattering sub-process - 12 -
involves a quark from one incoming hadron and a meson or a baryon emitted by the other incoming hadron.' The model predicts an invariant cross-section of the scaling form:
**o '71 b - t ,(V e) (13) d p PT
2PT where x^, = -p- , 8 is the angle of scattering and the value of n is obtained by a counting rule involving the total number of quarks in (22) the hard scattering process. In a recent ISR experiment, Angells et al have found that the scaling law is not valid when it is tested over a wide range of p^, values from p^ = 3 - 14 GeV/c. They found that the parameter n in (9) is itself a function of x^ and decreases with x^.
Another serious difficulty with the CIM model is about the relative cross-sections for jet triggers and single particle triggers. This ratio is more than 100 and keeps increasing with the transverse momentum of the trigger. In CIM model, this ratio is unity for a single sub-process like quark-meson » quark-meson; it can be somewhat increased by considering more sub-process but the model can not be stretched to get agreement with experiment. Besides there are other experimental results, to be mentioned, which are in disagreement with both the CIM model and the ’black-box' mode of Feynman, Field and Fox
(FFF1)(17) described below.
In the model of FFF1, the basic hard scattering Fig.(le), involves two quarks, one from each of the incoming hadrons. But the quark-quark scattering leads to an inclusive p^-distribution as p? , in disagreement with experiment, the quark-quark scattering has been modified by an
arbitrary.form factor (black-box) to get agreement with experiment.
Farther calculations however revealed two serious discrepancies of the
model with experiment. Since these discrepancies have Implications
which are fundamental to the methodology of quark fragmentation, we
point out below the nature of the discrepancies involved.
The beam direction and the direction of the trigger particle
define a plane called the trigger plane. The direction perpendicular
to the trigger plane is referred to as PQUt» (see Fig.6). If the quark
and gluons in a hadron have no primordial transverse momenta and there
is no smearing of hadrons In a quark decay, then all the hadrons with
large would have zero momentum components along Pout* The smearing
and the primordial p^ would however, give a non zero distribution of
components along pQut. But this distribution depends only on the amount
of smearing and the primordial p^ which has been put in the model and
does not depend upon p^1*1®. Experimentally, the p ^ ^ components
increase^®with the increase in p^1"*®, in disagreement with the (17) model of FFF1 . The second point of disagreement is that the model
predicted too many large pT particles On the away side (see Fig.6), (25) (27) a factor 3 larger than what waa experimentally observed.
The above discussion clearly shows that the disagreement of the black-box model with experiment is rather fundamental. Something new has to be inducted into the model to remedy it. In a second-model (28) proposed by Feynman, Field and Fox (FFF2) , there are new inputs, such as the introduction of gluons besides quarts in the hard scattering sub-processes, gluon decay distributions, D**(z) and a considerably larger - 14
value ef the primordial transverse momentum < k^. ■ 0.85 GeV/c, compared to 0.4 GeV/c in FFF1. The 'black-box' approach to the hard scattering sub process, has been replaced by a sun of cross-sections for different combinations of quark-gluon collisions as calculated in
QCD.
Too aany large p^ particles on the away side has been avoided by assuming that the gluons fragment into a distribution of hadrons of lower average momentum than does a quark. The gluon decays do not change things much on the towards side, since the trigger bias operates there in favour of quark jets. The Pout-distributions in FFF2 are also in better agreement with experiment, presumably due to the choice of a larger < k^. value.
Since QCD cross-sections are all scale invariant, one would expect an asymptotic p^4 behavior for the inclusive pT distributions.
But the presently available energies and p^ values are not yet asymptotic -8 and an effective p^ behavior has been reproduced at these energies. At still higher energies there would be a gradual transition to a p^4 behavior. In Fig.(7) the results of FFF2 for v° and jet. production cross-sections at fixed Sa • 53, 500, 1000 GeV versus p^ are reproduced. -4 A verification of pT behavior nay regarded as proof of QCD but not a confirmation of the picture of quark fragmentation, unless there (33) is also agreement regarding correlations. A recent ISR experiment by CERN-Columbia-Oxford-Rockfeller collaboration shows that the p - *out components on the away side keep increasing continuously with 2 __ and the value of < k ^ 0.85 GeV/c, used in FFF2, appears already to be inadequate to explain the data. If one has to invoke larger and 15
larger values of average primordial transverse ■omenta to explain
increasing values of pout-compenents, it would indicate that the eodel
lacks internal consistency and suffers free a defect in principle.
7. QCD effects in hadronization of quark jets.
So far us have been discussing quark fragmentation as the decay
of free particles. But in reality the quarks may interact with gluons
before decay, giving rise to features different from those of freely ( 3 * 0 - 0 7 ) decaying particles. Recently a number of authors have
considered the QCD effects on the hadronization of quark and gluon
jets. The basic approach is to calculate, perturbatively to a given
order in the gauge coupling constant »s> the cross-section for the production of a certain number of quarks and gluons and reinterpret these in terms of jets.
Steroan and Weinberg^35* have calculated in QCD the diagrams in
Fig.(8) for 6*6 and showed that fraction F of all events which have all but a fraction e of their energy in a pair of opposite cones of half-angle < (two jet events) is given by
e 2 , 1 - uf- (31og< +■ 41og6 loge ♦ -jj z- ) F « --- — ------2- i— (14) 1 * °sA
12 v vhere a * -• -— =* for four flavours, E Is the energy and 3 2 log E2/A A is a constant. The energy dependence could be put in a simple form:
* G(c* 4)( i f 1o« e 2/a 2 ♦ 1 ] (15) - 16 -
In a semi-log plot eq.(15) would give straight lines radiating from a common intercept at
log E2 * log A2 - (16)
Though the parametrization of eq.(15) is derived for jets in e*e~, it is reasonable to assume that it is also valid for jets in vH interactions; (3 0 ) The data of ABCLOS collaboration on jets in vN interactions are shown in Fig.(9) for a set of angles 6 and two values of e. The figures (9a) and (9b) correspond to two different ways of fixing the jet axis. The data seem to be consistent with the parametrization in eq.(5). Another
(3 7 ) 2 prediction of the QCD is that < pT > of hadrons in vN interaction 2 2 2 2 2 will increase with Q as Q /log Q /A , where Q is the modulus of the (20) square of the four., moment .mi transfer at the lepton vertex. The results of CERN narrow band beam (NBB) on vN and vN interactions and vp data is (?) (39) the wide-band beams'at FNAL and CERN are shown in Figs.(10) and
Fig.(il). Except for the data of CERN NBB on vN interactions, all 2 2 other data show no dependence of < pT > on Q and they are in agreement with calculations of longitudinal phase-space. It can, however, be 2 argued that the lack of dependence oh Q is due to a kihematical supression. The phase-space available for high p^, particles depends 9 2 2 2 on' W which is given by IT = M - Q + 2M E^y. As Q . increase the value of W2 decreases unless E and y are also increased. So there is need v J 2 to go to higher beam energies to get both the high W and high Q required to produce observable effects. (34) (37) QCB makes predictions not only about magnitude of
PT but also about the orientation of pT> i.e. the distribution of:
hadrons in the azimuthal angle The azimuthal angle * is defined
to be the angle between the vectors ?T and 7T . where 7^ and 7T are the
components of the hadron vector 7 and muon vector u respectivelyi--;.
perpendicular to the current vector $ =» 7 - 7, as shown in Fig.(12).
QCD makes the specific prediction that the" distribution of hadrons will
be flattened in the vp plane... More specifically, < cos 2* > is positive 2 "2 and falls as 1/log (Q /A ). Further, a greater fraction of the hadrons
will come off on one side or the other depending on the relative gluon/
quark fragmentation probabilities, so that < Cos + > f 0, ABCLOS (38) i ' collaboration have looked!for effects in < cos * > and < cos 2* >'
in neutrino interactions. From preliminary studies, they have not been
able to detect an effect in < cos # > 'while 2e effect is seen in 7 < cos 2* >. Bell et al ( ) have studied the azimuthal distribution of
hadrons in vp interaction using 15 ft. hydrogen, bubble chamber at 2 Fermilab. They find that the * distribution for high Q is peaked
near* = 0 or 180° in a manner.which may not be entirely accounted for
by UHC calculation,, although the departure from UKC is not large. Their
■azimuthal distribution of hadrons is shown in Fig.(13). Recently a test
of QCD by azimuthal correlations in e*e~ has been proposed by So-Young, (33) Jaffe and Low but it has not been tested experimentally.
8. Conclusion.
We have presented a large body of experimental evidence regarding
jets and large p^ processes which lend.support to the quark-parton
structure of hadrons, ' The exact link between quarks and gluons on one - 18 -
hand and the experimentally observed hadrons on the other hand Is,
however, not properly understood. The QCD approach does not even make
a pretense of understanding the link between them. All one has done
so far is a phenomenological description in terms of quark decay
functions. But it turns out that simple Honte-Carlo calculations
based on longitudinal phase-space seem to do equally well. Further
there is a vast amount of experimental information on partly hadronic
processes involving small" p^, which stand out side the scope of quark- (13) fragmentation models. Recently there have been some attempts to
.understand small pT processes in terms of quark recombination models.
Do we need two different descriptions to understand the large pT and
the small p^ processes? It is premature to venture an answer to the
question. - 19 -
Table 1
Charge correlations of the fastest and 2nd fastest charged hadrons
(see text). Numbers in table-are percent of events'.
FF2 Data UHC . hl > 2
+ 14~2'; 26 i 2 38
♦ - 20.1 24 ± 2 20
♦ none 26.1 20 ± 2 12 X - . + 16.2 ,21 ± 2 . 23
- - 4.4 3.0 ± .6 3.3
- none 9.4 2.4 ± .5 29
none none 9.5 3.8 ± .7 1.0 - 20 -
References
(1) For theoretical prediction .of jets in parton models, see
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(34) H. Georgi and H.D. Politzer, Phys. Rev. Lett. 40, 3 (1978).
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(36) So-young Pi, R.L. Jaffe and F.E. Low, Phys. Rev. Lett. 41, 142 (1978)
(37) A. Mardez, Oxford University theory preprint 29/78 (1978)
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(39) R. Hartman, Report at Oxford Topical Conf. on Heutrino Physics
at Accelerators, Oxford, 4-7 July 1978. - 24 -
(o) o' * — - c ^ f - j / X O N — (e*b-»c*d) dl t (e) -N t y - o ^
N
+ - Fig.l. (a) Quark-parton model mechanism for inclusive hadron production in e e annihilation, (b) Quark-parton model mechanism for Inclusive hadron production in lepton-hadron processes, (c) Illustration of hard scattering sub-process for the inclusive large P_ cross-section A ♦ B ♦ h ♦ X.
u ° /
Fig-2. Quark confinement and fetation of a meson let - 25 -
0-8 Quark Distributions in a Proton Fig.3. Quark distribution^10^ within 0 $ the proton.. Dashed curve stands for x d(x), dotted curve xd (x ) 0-4 for x u(x) and dash-dot curve XU (X) for x SCx). 0-2
i---- 1---- 1 Quark Decay Functions (1 0 ) zD„(z) Fig.4. The quark decay cunctions ' ' 7 X \ z D u ( z ) = z D 1 (z) z Dh(z) versus z. <1 X % . X \ x x zD \
zDicz) = zDj|"(z)^\ ■\ . \ 0 0 0-2 0-4 0-6 0-8 1-0
(dc) (cb) (be) PRIMARY MESONS Fig.5. Illustration of . , .(12) ARE FORMED cascade model for meson production when a quark of type NEW QUARK PAIRS •a* fragments into b b .e e ,..a ARE FORMED hadrons.
ORIGINAL QUARK OF FLAVOR V Beam loglo{Ed .+ (a) (b ) J ... . V ' - .'e • (c) Fig.8. QCD perturbation diagram for hadronic jets, in e e annihilation. - 28 - 6 € = 0-2 t 8 =36° 5 . ♦ 8=45° *8=54* 4 .3 2 0 0-1 10 100 Q2 GeV2 (a) 8 e =0-3 F * 8 = 27° 6 ♦ 8 = 36° ♦ 8=45° * 8 = 54° 4 2 0 0 1 10 100 Q2 GeV2 (b) Fig.9. 1/1-F as a function of c and 6 (see text for definitions F, e and 4). Figs.(a) and (b) correspond*38* to two different ways of fixing jet axis. I/N ,z > 0-2 Z > 0 :2 QCD 0-4 v 0-2 LPS T" 1/ N , Qtl z 0-3 0-2 LPS LPS 50 100 10 20 50 100 2 2 Fig.10. < Pj > vs Q for (a) vN Interactions with 2 > 0.2 (b) vH interactions for all z (c) vK interactions with z > 0.2. (Aachen-Bonn-CERH-Loridon- Oxford-Saclay collaboration^0^ ) (d) vN interactions for all z from BEBC NBB experiment. ' ' CM (p*}[GeV/c] 0 4 0 0-30 0-20 010 6 0 0-4 0-2 2 BEBC WBB vp 2 5 4 Ge /c]2 eV [G 2 0 Q 2 - 0 > z 10 2 QCD [GeV/c] ‘ 8 LPS 20 ~ P ' ■ 6 32 16 LPS 50 100 64 Fig.lib. >v with BEBC fros 0.2 > vs > z < up WBB experiment. WBB up IBexpforisent ; *'»■ > 0.3 firoa F8AL firoa 0.3 F8AL 9 .with (7) I ' • ■ -3k- Q a) b) Fig.12. (a) The current $ = v - n in the lepten plane, (b) The plane perpendicular to the current, defining as the angle between the perpendicular component of the hadron tf^) end the perpendicular component of the muon (p^). □ 325EVENTS:KQ<8 E3174 EVENTS:e 4 0 80 120 160 5o(deg) Proton-Antlarotoc interactions (Experimental Statu a of Barvonlnm States) 7 . Prakaeh Physics Department, Jemma University, Jasmm-180001 I, Introduction After the discovery of the narrow J/«j# resonances and its explanation as oc (charaonima) system, attention has been drawn recently that pp may also be a rich source of narrow resonant structures. These narrow resonances are being commonly called baryonium (or quarkonium). If one considers the picture in terms of nuclear Physics, baryonium are baryon-antibaryon (BB) structures which are bound by strong attractive nuclear potential. According to quark model and duality, these structures represent exotic diquark (q2)-diantiquark (q2) system which hacve strong coupling to (BB) rather than to mesons. Experimentally 3 th e s e states are expected to exist close (or above) to the nucleon- antinucleon threshold and w ill have narrow widths. Many experi ments have been performed in the last few years to search for these states. In this paper the present experimental situation of the baryonium states is reviewed. II. Theoretical relevence The existence of narrow baryonium states has been predicted in different theoretical approaches. A brief discussion is given below^-H"^. 1. Potential model The UN system differs from its equivalent HN system in two ways; firstly, that NN system can (++) large number of theoretical papers on these topics have appeared in the recent years. Only some prominent dhes are given in the article. - 33 - annihilate and secondly that rfff force nay he different. It is commonly beleived that the force between two nucleons la mediated by the exchange of some light boson (one boson exchange potential)# The h3 and NH interactions are related to each other through 0- conjugation^* K The r e s u ltin g HH fo r c e i s expected to be very strong (its depth may be a/1 GeV at a distance of^v0 . 5fm) and thus the hard core of M force is changed to strong intraction. This results in the formation of UN (or BB) quasi-nuclear resonant states. These states are much more strongly; bound as compared to the loosely bound deuteron. It is expected that large annihilation cross-section of O system (Ay 120 mb for about 200 MeV/c particles, in the c.m.) would not destroy or severely dieort the BB quasi-nuclear resonant structure because, .^the annihilation takes place at much shorter distance than the radius of the BB state. The annihilation is expected to take place through baryon exchange and its range should berv0.2 ftn. The t h e o r e t ic a l estim a tio n of annihilation widths of these states is 0.1-100 MeV depending on the angular momentum of relative motion of particles (widths are inversely proportional to angular momenta). . • * This concept is discussed in many papers [1-23 which predict a rich spectrum of quaai-nnclear bound states or resonant states. The posibility of existence of bound states like I? or YN is also predicted. The (+) This is in_analogy to the way that C-Parity connects e~e”and e“e+ systems. - 34 - spectrum of these quasi-xiucle&r states can range from / v i .7 GeV (below HB threhold) to^,7 GeV depending on the number of baryons included in the system. The widths of these resonant states depend on " the pp. annihilation potential. Some of these states can be very narrow (frvfew MeV). They are expected to be populated by radiative or pionic translations from atomic pp states [3]. Thus the study of these states would provide better understanding of nuclear force, nuclear potential and the exchange process. 2 . Quark Model i i) Bag version of QCD The quark model has successfully explained many • features of particle interactions in the recent years. It is now well accepted that quark dynamics ( or quark-chromo-dynamics-QCD) is described by a non- Abelian guage theory where interactions are mediated - by an octet of coloured vector gluons. Although this theory has not been tested directly.but it is now well known that many of its predictions with regard to the ordinary mesons and baryons have come out to be true. The colour guage theory predicts simultaneously the existence of certain extras ordinary states: like, 'glue-balls' (states without quarks)} ' exo£tic states' (states with peculiar . quantum numbers) and 'multi-quark states' (states with more than 3 q u a rk s). The existence of multiquark states has been discussed recently by Jaffa [4] and others £5—73• - 35 - The calculations are based on the description of c l a s s i c a l 1 bag-model’ considering that quarks are light and confined. The free hadrons are colour singlets. The interactions between confined quarks is weak and hadron spectrum is calculated using perturbation theory in colour coupling constant '*c=ga/4n. This explains satisfactorily the properties of (qq) mesons and (qqq) baryons. The absence of exotic hadronlc states m always been mysterious to the followers of quark m odel. Nambu [ 8 ] in 1966 indicated the saturation properties of SU(3)-colour forces, that two colour singlets do not exert strong force on each other, later Idpkin [9] showed that this may be the cause of the absence of strong attractive force in exotic channels. These discussions considered only colour-electrostatic interactions and ignored colour-magnetic force (i.e . spin-colour dependent interacting arising from one gluon exchange). The , justification for treating the problems of gluon- exchange through pertubatlon theory lies in the Bag-model where long range colour-confining forces are replaced by bag-pressure leaving only short range gluon-exchange. This interaction is attractive in antisymmetric flavour states and repulsive in symmetric flavour states. The result of such calculations [4] is that one can get exotic multiquaik states (qm qa with m+n> 3 ) from colour singlet baryons and mesons. One can also make 'Crypto-exotic* states, (i.e. states not in exotic flavour representation). The exotic states are - 36 - expected to be heavy and broad and crypto-exotic states, lighter and narrow. Similar calculations have also been recently done in quark gluon model with dual unitarization by Chan Hong Mo and Ijlassen [7j. If one considers the old quarks (u,d,s), the lightest (q 2 q”2) multiplet is a J^<'=0++ n o n et. Jaffe [4 j has calculated their masses and SU(3) structure. This is shown in P ig.l. The predicted masses of these states lie between 650-1100 I*ieV/c2. These are strongly coupled to pp channel. It is contemplated that the observed [ c( 1 3 0 0 )> S * (1 9 7 6 )j K(1400) may be related to these predictions. The bag model calculations have been extended [4,10] to explain (q 2 q~2) configuration which couple to BB (baryonium) by considering the deformed bags for high J-value. Thus one can predict the existence of various baryonium statesf e.g. states with mass (JPC, IG) = 2270(3", l +)» 2460 (4++,0+) and 2730 (5”"*,1+). These calculations have also been extended to.•=:study the (q*q) systems and q^- dibaryon system . One- of the predictions is that a ditarycn with JP=0+ and mass/v2150 MeV/c2 should exist as SU.(3) flavour singlet. ii) Dual-resonance model 'T Complementary discription of reactions by Hegge poles (or resonances) is commonly known as (+) For mass/'and other properties, see particle data Book-(1978). — TT — • duality.. I t provides simple and direct: relationa. between: low energy and high energy scattering mechanism. For inelastic, processes most t-^ channel. trajectories behave as if they are 1 built' throu^i direct channel resonances. Detailed discussions of duality have appeared, in many papers ( e.g.. see reference 1 2 ). •The existence of meson resonances with, strong coupling to. 2B. system was originally suggested, by Hosener [ll]. This is: represented by simple, planar, diagrams in. Fig.2. where for $IT elastic scattering the- meson, exchange in t-channel is equivallent to qq exchange in quark model, and. is sum. of the q2 q-2 resonances in the 3-channel. Thus baryonium is diquark- diantiquark system and is an exotic, meson. This has been further discussed by Chew [l3] and by Phillips and Hoy [12J. It is also shown that such exotic baryonium states w ill have 1=0,1,2. It is also shown/OZI-rule w ill suppress the decay of a. baryonium. to (qq)(qq) channels and decay to BB w ill be allowed. This is also shown, in Fig.2^ + ^. Chew [13X also, predicts Hegge trajectories for baryonium. Thus the experimental verification, of baryonium. states w ill be a good check on the predictions of duality and of QCD. I I I . BZP5HIH3HTAL STATUS The present review w ill, cover, first the. prominent resonances reported earlier (like 3,T,U enhancements) and then some further structures observed recently.. Three (+•) This is similar to the decay of recent reviews on the subject, by Montanet [14 j, Miller [15] and Kilian and Pietrzyk [15],have also given useful summary of the experimental data. The experiments conducted so far can be classified into the following three categories. a) pH formation experiments: These include measurements of total and elastic scattering cross-sections in the pp system. In these experiments one has to differentiate between true resonances and thrShold effects; hence, some times the interpretation of the data is not unique. We also include here experiments where BB (or pp) atomic structures are formed and their radiative transitions are measured. b) Experiments in which Bb states are produced in u-channel via N or A exchange. c) Experiments in which BB states are produced in t-channel which decay in states including (BB). 1. S-Meson resonance; Focacci [16] about 10 years back observed the presence of El-enhancement in a missing mass spectrometer experiment studying the production of charged bosons (X~) in the reactions Vp-+p+2T. The mass of the 3-resonance was inferred to be 1929+14 MeV and width T $ 35 MeV with prominent decay into 3 charged pions ( and possible neutrals). The first positive evidence of S-enhancement being a BB system came from the experiment 39 of Carroll et al [17], Kelogeropoulos iet al [18] and Chaloupka et al [19], The experiment of Carroll et al on pp and pd total cross-sections Indicated the presence of a structure at p momentum of 475 MeV/c corresponding to a mass of 1932+2 MeV with Breit-tiigner width, T = 9^ MeV. Chaloupka et al in an experiment with CBBH 2-meter bubble Chamber exposed to a separated p beam of 571+5.5 MeV/c observed a sim ilar structure between 1930-1940 MeV in the elastic channel. Their results are reproduced in Fig.3• ' The observed enhancement corresponds to a resonance w ith mass 1935.9+ 1.0 MeV and T = 8 . 8 2 ^ MeV. The 3 - enhancement has also been confirmed by Brtickner et al [20] where pp elastic scattering and annihilation cross-sections have been measured between 400-850 MeV/c using magnetic spectrometer. The mass of the resonance has been observed as 1939+3 MeV with 4 MeV. The prominent decay of S-resonance is through pp channel, with a branching ratio; ^20 percent. As phase space for the decay to pp is much smaller as compared to that available for the decay to pions, the decay translation prefers the elastic channel. There is no indication of this resonance in the charge exchange (pp-*nn) channel [19,21]. This may indicate strong Interference effect (i.e. interference of resonance with background or that of two resonances within the structure). The iso-spin (I) of the S-resonance is preferably =1 but 1=0 can not be excluded. Spin. (J)=0 and inelasticity (x)=l are consistant with the data, •’’he observed total and charge exchange cross-sections have been discussed by Montane.t [14] in the light of the theoretical arguments o f Dover, and Kalians [21,] and Kelly- and Phillips [22]., Pinal, interpretation is 'that 3 is a narrow resonance of. spin. I or 2 and with large elasticity.- There are • indications that «J^=2++ may he preferred for' this resonan ce. Table I gives the summary of the present status. — Broad resonances (i) Two further enhancements (called I,TJ-resonances-) were also reported, by Focacci et al [16] in the mass regionrv/2195 Met and~2382 Met. Abrams et al. [24 ] in a counter experiment measured the total cross-section f o r pp in t e r a c tio n s . The IN-enhancement a t mass ~ 2190 (1=1 ) and U-enhancement at mass-v 2350 ( 1=0 and 1 ) were observed. The earlier speculations that these enhancements may be threshold effects (pp-*ppn o r// etc) were found to be incorrect. Further experiments of Bisenhandler et al [25] and Coupland [26] confirmed the presence of T and U resonances as Baryonium states with mass in the same region as reported by Abrams et a l. The results of Bisenhandler et al are shown in Fig.4 and those of coupland et al in Fig.5. In. both the figures, the T and U structures are clearly observed. The summary of various experiments is given in Fig .6 which has been taken primarily from reference [26]. The sp in values of T and U resonances are estimated [14] to be 1» (x> 0.74) and J$2, (x)0.85) respectively being inelasticity. These predictions are again based on the theoretical arguments of references [ 22, 2 3 ].' 41 (ii) Further resonant structures representing baryonium states have been observed by Carter et al [27 ] in the differential cross-sections for pp-»«+ reactions in the C.M. energy range of 2020-2580 MeV/ca. The pp annihilations into s+ represent about 10 percent of the total cross-section and hence are not representative of the annihilation channels. However, their amplitude structure is rather simple and can be analysed in detail for the observed resonant structures. The results are summarized in Table II. These results are also shown in Fig. 6 . One wonders if the resonances at 2310 and 2480 are infact part of U-resonance. . The coupling of a ll these states to B B is much stronger than for pion decays. The low cross- section of the decay to nn (from pp->nn) to pp can be explained by involving strong interference with other resonant states or/the background as explained in the case of S-meson. Montanet [14] indicated that the prelinimary data of Bari-Brown-MIT collaboration indicates strong evidence of a' resonance at2350+60 MeV/c2 w ith r =190+60 MeV (J^=4*). The results of Peaslee et al [28] published, recently exclude this mass region. 3 . Harrow resonances (i) Benkheiri et al [29] studied the reactions iTp-»pfppiT(pf is fast proton with P>Pteam/2 and emitted in the forward direction within +150 mrad) w ith a tT beam at 9 and 12 GeV/c using CBHH^-spectrometer. It is a high statistics experiment using 1.65x10 events at 12 GeV/c (4-0 fit). The contamination of channels ( lik e $"p-» p i V iT) i s < 1 0 p e rc e n t. Bo enhancement is observed in (pfp) or (ppa) invariant mass distribution. The data indicate, the presence of A(1232) and B*(1520) in (Pf n~) and A (1232) in pi" channels. There is strong evidence for 2 peaks in the data (mass~ 2 0 2 0 and 2200 MeV/ca) in association with A and one peak (massa/2020 MeV/ca) in association with H*. The data also indicate that these resonant states are produced in the forward direction. The results are given in T a b le -I ll. The decay angular distribution in the Jackson frame of the resonances in the pp system shows strong forward backward asymmetry which is suggestive of meson or pomeroa-exchange in the production mechanism of pf P7i~ or pfp states. The angular distribution is quite different in pp resonance region. The results are show* in Fig.7. The two peaks are clearly observed. The peak at 1930 MeV can perhaps be interpretted with that of 3-meson. The production mecharlsm of these, resonances can be best explained by the diagram in Fig. 8- a . (ii) In another experiment Bvangelista et al [30] again using CEBU-0-spectrometer studied the following x~p interactions at 16 GeV/c: - 43 - where subscripts f and s represent faster and slower nucleons in the Lab. system. A narrow peak in the (PPf it- ) invariant mass was observed with mass, M=2950±10 MeV/c 2 and 32 MeV (1=1 or 2) with .production cross-section of^l pb. Pig. 9(a-) shows the results of the experiment. The decay spectrum of the resonance is shown in Fig. 9(b). It is indicated that the decay may go through other pp states with masses at 2200 or 2020 MeV/c2. If this resonance is confirmed^*), its production w ill be represented by diffractive dissociation of s as shown in Fig. 8 ( b ) . (iii) Prelinimary data of Toronto-York-Puzdue collaboration [33 ] of 1672 events of n+p-»pppn+ interactions at 11.5 GeV/c indicates a narrow resonance in the pp system. The experiment has been performed using the SLAG 40*' hybird bubble chamber f a c i l i t y . The co n trib u tio n o f x+p —* K+E”p*+ has been excluded from the data using appropriate trigger. The results of pp invariant mass are reproduced in Fig. 10. A narrow bump ( r v 4 .4 s.d. above the background) is clearly observed afc mass =1954+5 MeV, 10 MeV. The production cross-section is o=300+60 nb. This enhancement is not strongly associated with recoiling _ ^++ ( 1236) production at the other vertex. The decay angular distribution is consultant with J^C=l“” . The 1954 MeV/c2 enhancement is not obee1*ved in the backward produced pp pairs. Ho signal for a narrow resonace at 2950 MeV/c 2 as. reported by Evangelista et al [30] is observed in the data. The diagram explaining the production of the 1954 MeV/c 2 resonance is shown in Fig. 8 (c) and it is expected to proceed by either baxyon or baryonium exchange. (+) The prelinimary report of the results presented at the H.E. Physics conference, Tokyo indicates that the 2950 MeV/c 2 resonance has been submerged by the new data [31*32]. 44 4. Strange Barvonium States (i) First example of a strangeness = + 1 baryonium state comes from tne experiment of Apostolakis et al[34] The experiment was performed using Big European Bubble Chamber (BBBC) exposed to 12 GeV/c p beam. All events of &-prongs and associated 7 topology were studied. The effective mass distribution df (K° «£*+*”) is shown in Fig.11. The peak represents a 5.5 s.d. effect and contains 587 events including 52 events which are ambiguous between K° and A o r /\ . Bo evidence of the neutral state of this resonance (K°x+x+it0) or (K^#*+n"“) has been observed but the result is inconclusive because the mass resolution for s° events is small and the statistics for K— events is too low. Similarly it could also not tv established whether the enhancement is exotic (charge opposite to strangeness) or non-exotic For this, events from the reaction, pp->(K°K* s^*+*+ iT + neutrals) were studied where by strangeness conservation the identified K+(i”) corresponds to K°(K°). The mass of the enhancement with 3=^1 is 2600+100 MeV/c2| 18 Me7, a. BR=20pb where BE i s the branching ratio for the decay of the resonance into x” ) • ( i i ) R ecently whit#$more e t a l [4 0 ] have reported t h e ir results of a similar experiment in pp experiment at 14.75 Ge7/c using 80)• BNL hydrogen chamber. The data are based on 80,000 interactions in which they find 367 events of 6 prongs topology corresponding to pp-*K®s£ji+s” as compared to 587 events of reference [34 ]. Bo resonant structure a t 2600 MeV/o2 is observed. With - 45 - confidence level/about 95 percent, they quote o.BH<21nb. It is also indicated that the CEBU ■experiment of the Apeldoorn et al [40] fails to " confirm the 2600 MeV resonance. (iii) Montanet [14] has indicated that the prelinimary results from CBHS-n-spectrometer (T.Armstrong et al) indicate a broad resonance (mass^2200 MeV/c2) in the X U mass spectrum in an experiment studying K+p-»Q?f+ anything)at 12 GeV/c. There are also indications of other enhancements at in-2800 MeV and/v3050 MeV. Definite results are still not available [32], 5. Bxotic states E ffo r ts have been made fo r the p a st se v e r a l years to search for doubly charged meson resonances without any success. £wo recent jexperiments in this regard are of Boucrot et al [35] and Alam et al [36]. (i) Boucrot et al ueingflspectrometer studied the following reactions at 12 GeV/c. p-*pf + M~ (M~ being an 1=1 meson, K“-» pp s~) s"p-»pf -+M (M being 1=2'exotic meson, pp . In view of the fact that mesonic decay modes may become dominant if a central barrier suppresses the NH n(s) mode, 4« decay modes were studied for the search of M~ and M**~. The mass resolution for M in this experiment was 12-18 MeV. - 4 6 - Ihe results are shown In Fig. 12 where Invariant mass of (ppif if) aystan has been plotted from the reaction i"d-»p8pectpf (pp a~s” ). One event of the distribution corresponds to a cross-section of 1.7 nb. It Is clear from the figure 12 that there- is no evidence for a resonance. The upper lim it for the production o f M" or If*"" i s 10-50 nb for mass of these resonances between 2-3 BeV with f< 20,or T< 100 MeV respectively. ( 1 1 ) Alam e t a l [3 6 ] searched for doubly charged'“exotic mesons (lT~ ) In baryon exchange reactions. s*d-»(pB) + i +pf The experim ent was performed a t 13*2 GeV/c a t the SlAC 2-m eter stream er chamber with a s e n s it iv it y o f 240 events per pb per nucleon cross-section. Ihe results for invariant mass of (pp if) in (pp s“pf ) events and of (pp if if ) in (pp if if p^) events is shown in Pig. 13 for 4-c fits. Again there is no evidence of any enhancement in the mass range o f 1 . ^ 3 .2 GeV. Production of pp states below threshold (i) As discussed in section II. 1, antiprotons stopped in hydrogen can form bound states. An earlier evidence of/pn bound state was presented by Gray et al [37] in pd interaction;. Ihe experiment was performed in 30' * deuterium bubble chamber exposed to stopping p. Ihe resonance was detected in the study of the decay reactions. The mass of the resonance has been estimated as 1794.5+1.4 MeV/c 2, f ^8 MeV and binding energy of 83.3+1.4 MeV at 95 percent confidence level. - 47 (ii) In a recent experiment by Pavlopouloe et al [38] f-ray spectrum from pp annihilations at rest has been measured using a large Nal (II) spectrometer in the energy range of 30-1100 MeV. A total of (7+0.5)xl0^p were stopped in Hg. The back ground contribution from it0 decays and from neutrons produced from the interactions of charged pions of annihilation w ith surrounding h a s been suitably subtracted. The results are shown in Pig.14 and are also shown in Table 17. The (132+6) MeV Y-ray is from (ifp) radiative cap tu re. Thus th ree bound s t a t e s o f (pp) are c le a r ly established. It can be noted that 420 MeV line has energy which is/sum (within errors) of the otheVtwo lines at 183- and 216 MeV. These y transitions corresponds to states with masses 1684, 1646 and 1395 MeV respectively. The quantum numbers o f th ese s ta te s could not be ca lcu la ted in this experiment but assuming that initial state is a s-state, the observed y-transitions most probably corresponds to popular instates. 7 • 3iT-inuark states As already discussed in section II. 2, the bag model calculations of QCD predict the existence of a q6 dibaryon. Die lightest state is expected [4] to be stable except against weak interactions. It is predicted. to have J^=0+ ; SU(3) singlet, mass tv2150 MeV (i,e. 80 MeV less than/y\mass), strangeness = -2. In formation,it couples to m , z i and ST= in the ratio of 1:3:4. The most conven-ient method to produce these states is in pp interactions. The production mechanism 48 - in the reaction pp-»K+K+ X (X is dibaryon) _ is explained in Fig. 8 (d). Ihe production cross-section, however, is expected to be small. A.S. Carroll et al [39] searched for six-quark states in the missing mass spectrum of the reaction pp-»K+K+X in the mass range of 2.0 -2.5 GeV/c2 u sin g a double arm spectrometer at M l. Ihe beam .momentum was 5.1» 5.4 and 5.9 GeV/c. Fig. 15 shows the missing mass spectrum. Mo structure is observed. Upper lim it for the production of X is put 30-130 nb depending on the mass. 8 . Summary of the experimental data. , Ihe experimental data presented in the proceeding sections hast been summarized in Fig. 16. Excluding the resonance at mass=2950 MeV/c2 which now seems to have submerged in larger data,one can-observe the following. i) Marrow bound pgbtructures below the pp threshold are clearly established. However, their quantum numbers are not decided. ii) Ihe 3-resonance can be accepted as a clear evidence of a Baryonium. It should be regarded as well established. It is narrow and its elasticity . is large. iii) There are many narrow and broad (pp) resonances in th e mass reg io n 1950-2600 MeV/c2 . More data are required for their confirmation and for deciding their quantum numbers, though many of these are already on relatively firm footing. - 49 The resonance at mass=2600 MeV/ca which was supposed to he a good example of strange (3=1) baryonlum, has been placed In the doubtful categ o ry . iv) No state with 1=2 has yet been found. In addition to the states summarized in fig. 16, there are many unconfirmed resonances. For example,there are indications [15] of two resonances, one at (mass ~ 2850, 39 MeV) and the other at (mass ~ 3050, 15 MeV) observed in pp —>xX w ith c r o s s -s e c tio n s , 0 ^ 8 3 pb and and/>;22 pb respectively. There is. also^an indication [32j that an exotic state at mass rv 2500 Vie!/. This resoance has been observed in 'reactions (K+p-»'^piif’n) jn the ( Ap it ) system. The observed enhancement is/>>3-5 s.d. effect. If it is' confirmed, it may be an example of e x o tic resonance w ith Q=2, 3=1. The experimental uncertinties do not yet allow to establish whether states :separated from others by small mass differences belong to one state or/different states. It is likely that with better experimental precision some states.may submerge with others. The question of the existence of broad and narrow resonances is not yet clear. Jaffe [4], chan-Hong-Mo and Htfgassen [ 7 ] have discussed the problem theoretically. It is quite possible that some of these broad resonances ultimately may be observed to have substructures. 9. Conclusions i) The existence of baryonlum states is well established. Such states have been reported both below and-above the pp (or BB) threshold. Many narrow and broad resonances - 5 0 with strong coupling to pp (or BB) channels have been observed. ii) There are many resonances reported in references [14,15,32] which need confirmation and have not been included here. i i i ) There is no well-established example of strange baryonlum and no established evidence of any state with exotic quantum numbers. Similarly there is yet no evidence of q^ di-baryonium through there are some candidates [32]. iv ) Better experimental precision and more experimental data are required to establish these states and to decide if there are any substructures in some of these resonances. For example, if small charge exchange (pp-ron) cross-sections for S,T,U enhancements is really an interference effect, one would like to know their substructures. v ) Hore data are required to establish the quantum numbers of the currently observed bazyonium states. The picture of Baryonlum spectroscopy w ill be clear only after their quantum numbers are decided. v i ) One would like to know if baryonlum with 1=2 exists o r not? v l i ) Qualitatively one can say that the present experimental evidence is sufficient to accept the baryonlum states as exotic (qqqq ) system. Similarly the observation of bound pp system is satisfying to nuclear physicists. It is hoped that a better understanding of the mi cleon-antinucleon potential. - 51 - However, thla theory has s till to provide a satisfactory answer as to why the annihilation i s in h ib ite d in pp system . The quark model a ls o faces sim ilar problem. Thus further improvements in the theory are also Balled f o r . - 52 - BBFP.RTOTCB3 1. O.D. Dalkarov et al - Duel. Phys. B 21 (1970), 88. I.S. Shapiro - Sov. Phys. Usp. 16 (1973), 173. L.N. Bagdanova et al - Ann. Phys. 84 (1974),- 261. C.B. Dover and 3.H . Kahana - P hys. L e tt . 62B (1976),293* C.B. Dover and M.Goldhaber - Phys. Rev. D15: (1977), 1977. C.B. Dover and 1 , Trueman - BHD 22542 (1977) - p r e p r in t. FtMyers and A .G ersten - Nuovo Cim. 37A (1 9 7 7 ), 2 1 . 0.Dalkarov and F.Myhrer - Nuovo Cim. 4QA (1977), 152. 2. 1.3. Shapiro - Phys. Reports - 35C (1978), 129. 3. C.B. Dover - 4th International Symposium, Syracuse University, Vol. 2. (1975), 37. 1.N. Bogdanova et al - Ibid- (1975), 1. 4. R.L. Jaffe - Phys. Rev. D15 (1977), 267. R .I .J a ff e - P hys. Rev. D17 (1 9 7 8 ), 1444. R.L. Jaffe - Proc. of Summer Institute on Particle Phys. SLAC-204, (1977), 351. R.L. Jaffe - Proc. 'Particle and fields' 76 BNL-50598 (1976), G31. 5. C.Rosenzweig - Phys. Rev.; Lett. 36 (1976), 697. 6. A.V.Hendry and I. Hinchcliffe - Preprint-LBL-7597(1978). 7. Chan Hong Mo and H.H$/gassen - Phys. Lett. 72B(1977), 121 8. Y.Nambu - 'Preludes in theoretical Physics' Bd.A. Deshalit'et a l. North-Hoiland Pub.(1966). - 53 9 . H.J. Lipkln - Phys. Lett. 45B (1973), 267. Phys. Lett. 74B (1978), 399. 1 0 . K. Johnson and C.B. Thorn - Phys. Bev. D13 (1976), 1934. 1 1 . J.Bosener - Phys. Bev. Iett. 21 (1968), 950. Phys. Hev. Lett. 22 (1969), 889. Phys. Reports 11C (1974 ), 189. 1 2 . R.J.N. Philips and D.P. Boy. Reports Prog. In Phys. 37 (1974), 1035. 1 3 . G.F. Chew - Prof. 3rd European symposium on NB interactions, Stockholm, (1976), 51$. 1 4 . ' L.Montanet - CEHN/ BP/PHT3-77-22 . Talk given at tiie 71 international conference on. experimental meson spectroscopy, Baston, April, 1977. 1 5 . D-.H. M iller - Talk given at the 3rd international conference on Hew results in High Energy Physics at Vanderbilt UniveAty, March, 1978. E.Eilian «Tid B.Pietrzyk - Tilth International conference on H.B.Physics and nuclear structure, Ed. hy M. Locher. Birkhauser Terlog, Basel, (1978), p. 85. 1 6 . M.R. Pocacci et al - Phys. Bev. Lett - 17(1966), 890. 1 7 . A.S. Carroll et al - Phys. Bev. Lett. 32 (1974), 247. 18. I. Kalogeropoulos et al - Phys. Rev. Lett. 34(1975), 1047 - 54 - 1 9 . V.Chaloupka et al - Phys. Lett. 64B(1976), 487. 20. V . Bruckner et al - Phys. Lett. 67B(1977), 222. 2 1 . M. Alston-earnjost et al - Phys. Bev. Lett. 35(1975),1685. 2 2 . C.B. Dover and 8.H. Kahana - Phys. Lett. 62B (1976), 293- 23. B .l. Kelley and R.J.N. Phillips - HI 76-053 EL59 (preprint). 24. B.J. Abrams et al - Phys. Beg. D1 (1970), 1917. 25. B. Bisenhandler et al - Hucl. Phys. B113, (1976), 1 J. Alspecter et al - Phys. Bev. Lett. 30, (1973), 511. 26. M. Coupland e t a l - Phys. .L ett. TIB (1 9 7 7 ), 4 6 0 . 2 7 . A.A. Garter et al - Phys. Lett. 67B (1977), 117. A.A. Carter - Phys. Lett. 67B (1977), 122. 28. B.C. Peaslee et al - Phys. Lett. 73B (1978), 385. 29. P. Benkheirl et al - Phys. .Lett. 69B (1977), 483. 30. C. Evangelista et al - Phys. Lett. 72B (1977), 139• 31. CEBN Courier - September (1978), 284. 32. 0. Flugge - Plenary session (P5-a), XIX International conference on H.B. Physics, Tokyo, (1978). 33. A.VF. Key et al - Preprint. Paper presented at the 71 European Antiproton Symposium, Strasbourg, June (1978) and at the XIX International conference on H.B. Physics, Tokyo, August(1978). 34. A. Apostolakis et al - Phys. .Lett. 66B (1977), 185. 35. J. Boucrot et al - Hucl. Phys. B121 (1977), 251. 36. M.S. Alam et al - Phys. Bev. Lett. 40 (1978), 1685. 3 7 . L.Gray et al - Phys. Bev. Lett. 26(1971), 1491. - 55 38 P. Pavlopoulos et al - Phys. Xett. 72B (1978), 415. 39. A.S. Carroll et al -- Preprint-BHX. 24720, July(1978) 40. J. Whitmore et al - Phys. Xett. 76B (1978), 694. G.W. Avan Apeldoom et al - Phys. Xett. 72B (1978), 487.., - 56 TAB LB-1 Summary of the data on 3-meson r e f . (1^ (19) (20) Mass (MeV) 1932+2 1936+1 1939+3 P(MeV) o o+4.3 < 4 9 -1 • - 3 .2 - (TQB(mb) - = 1.6+ 0.7 - Iso-S p in = 1 (0 ) J 0 ,1 o r 2 (J*£ 2++ ? ) TABLB-II Bata from Carter et al [27] Mass (MeV/c2)W id th r(M eV )J * ’0 IG 2150+30 200+25 3 1+ 2310+30 210+25 4** 0+ 2480+30 280+25 5^~ 1+ - 57 - TABLB-III Result from Benkhieri et al [29] Mass P (MeV) : Cross-section (nb) (MeV/c2 ) * if p->A(1232),M I n~p-+H” (1520),M : A -»P*- , M-*pf : M-fpp, N>-»piT 1930 10 9+5 - 2020+3 24+12 16+5 (9 GeV/c) 30+12 (9 GeV/c) 10+4 (12 GeV/c) 26+8 (12 GeV/c) l6 +20 2204+5 i6 -1 6 . 17+5 (9 GeV/c) 21+5 (12 GeV/c) TABLB-1V Results from reference [38] Energy of Instrumental Confidence Yield per v-rays line width level 103 (MeV; (MeV) a n n ih ila tio n s 132+6 16 99 .3 5 .1 + 2 .7 183+7 19 9 9 .0 . 7 .2 + 1 .7 216+9 21 9 7 .5 6.0+ 1.9 420+17 34 9 8 .2 8 .5 + 2 .0 - 58 - Captions to Figures F i g .l . Ihe lightest 0+ nonet from reference [4] ■ calculated in bag mo'del. a) SU(3) weight diagram { (b) masses of the states. F ig .2 . Duality diagrams for baryonlum and diagrams for OZI-allowed and OZI-euppreseed decays. F ig .3 . Protoifr-Antiproton total inelastic' (0+2+4+6 prongs), elastic and 0,2,4,6 prong cross-sections (reproduced from reference [19]. F ig .4 . a) Behaviour of Total cross-section (from Bef.[24]) (closed' circles) and the partial elastic cross- section (open circles). b) Partial elastic cross-section after substract!ng the background. (reproduced from Bisenhandler et al [25]). F ig .5. a) pp total elastic cross-section. b) cross-section for pp-»nn (Data from D^Cutts et a l). The lower lines are the estimated background(reproduced from reference [26]). , F ig .6 . T-U resonances parameters from various pp experiments. The masses (MeV/c2) and widths are shown. F ig .7 . The pp invariant mass with cos6 <0(6 =Jackson angle) and 1175 P ig .8 . Diagrams representing the production mechanism of Baryonlum states. . a ) Production from i~p -> ( A o r H*M)-*pf pp Tfref. [29])* b) Production of pf p*“ (2950) from ref.[30]* c) Production 1950 MeV (pp) resonance from r e f . [3 3 ]. d) Production of a dibaryon in pp reaction as predicted by Jaffe [4]. Pig.9. Results of Evangelista et al [30] on (a) the"production of narrow resonance in (pPf<~) system at 2950+10 MeV and (b) the decay of the resonance. P i g .10. Results from ref. [33] for pp invariant mass in n+p-»ppp*+ in 20 MeV b in s . a) All pairs of pp { (b) All pp pairs with *(pp)<1.2 (GeV/c)a where t* = b-tmip and t i s 4-momentum tran sfer* ( c ) w ith condition (b) and p of pp pair not participating in £ + (Mpi±>1.4 GeV/ca). Fig.il. Effective mass of (K^ combination from the (6 prongs + v°) topology events. (reproduced . from ref.[34]• P ig, 12 . Invariant mass for .(pp*i) in reactions s"d-»P8p Pf PP«" . a) 26, fit with pf between 7-10 GeV/c* b) events in (a) with PBlow forward in (pp c) events in (b) with both h?(p*“ ) and ( a ) (p * ) mass (reproduced fi:om referen ce [3 5 ] )• - 6 0 - Fig.1J. Invariant mass of (a) (ppn) from (pp*pf ) events and (b) (ppiiit) from pp**pf events from 13.2 GeV/c tT d interactions. Ihe solid line is transverse momentum damped phase sp a c e . A ll events a re o f 4-C fit. (reproduced from ref. [36])• Fig.14. y-ray spectrum (true signal) from the transitions of pp bound system. Ihe solid line is the computer fit to the peaks in the spectrun (reproduced from ref. [38]). Fig.15. Missing mass spectrum (GeV/c2) in pp-»E+£+I at different beam momentum (reproduced from ref. [29]). Fig.16. Summary of the present experimental data on baryonlum states. Mass duus udds -^(uu+dd)ss VT -Lcuu-dd)ss = J udss,etc 1 GeV duss ^ udss — - = udds etc uddu *7^rtUU+dd)SS — uddu V 2 5 dusd udsu ta) (bl FIG.1- - 6 1 - (1) d u a l i t y d ia g r a m f o r b a r y o n iu m qqqq (2) 0 2 1 ALLOWED DECAY (3) 0 Z I-SUPPRESSED DECAY X F IG .2 . 2 6 0 n 2 2 0 - 90*1 200 8 0 180 70 160- 60 k 140 50/ 120 30- 100 20 - 1900 1920 1940 1960 1900 1920 1940 1960 1900 ^,1920 1940 1960 M(MeV) FIG.3.' ISO- 100 - 8 0 - 6 0 Oq 20* o0 10 - 0-5- 3 0 IENTUM Q eV/c 0*40-6 Q-8 1 0 1-2 2-0 2 2 2*4 2 5 - 20 E 20 2 2 2 8 E cm (GeV) FIG.S. 14 2 5 2-6 MASS GeV/c; F IG . 4.. - 6 3 - REF. 25 26 17 17 Cuts el til 27 °T o T •S h • pp-* n*n 2500- ' - 248*30 - ♦ 260*25 5 1 2400- 2385*10 I Q ♦10 80*30 2365-5 2345 ±15 2355* 5 2350*5 2335*6 160*10 225*160 u 135*150 185*20 - 75 132*15 ~ 60 2310*30 j_ _ ▲ 2300- 210*25 2200- 2185* 5 2189* 5t . 130*30 95*15 T 2150* 6 215St IS 2150*10 2150* 30 > 116*15 135*75 160*20 200*25 2100- 2000-I FIG. 6 - 30 e 20- t- > 2000 2200 2600 p p INVARIANT MASS GeV FIG. 7 (p) NO- OF NO- EV EN TS/20 MeV •8-9U [i'v) (IV) (P) cq ) d d" U. d U. u d• ‘ ‘ d * uu #d: ' eu ' d 111 - 10 X MASS(ppr n) GeV 1 » + + X (ZV)- F I G .9 + * NO-OF COMBINATIONS/O O l G«V/c* EVENTS/20 MeV > 111 o f\J EVENTS/25 MeV Z°T 10 0 5 2 2 - 0 5 2 - 6 6 '* AS GeV MASS FIG.13. . RG.12. 2 75 75 2 lb ) 34 ) lb 0 0 0 3 0 3 0 5 2 3 (b) 3-25 COUNTS o EVENTS/001 GeV/c* () - GVc A THRESHOLD IAA GeV/c 5-1 I (a) 100 200 300 400 500 500 400 300 200 100 z V) eV) (M ENERGY 1 . 4 FIG.1 o z V>- >ut v> DETECTION EFFICIENCY (X105) - 6 8 - s t a t e s p MODE COMMENTS (MeV) EXOTIC NO DEFINITE EVIDENCE 2950- < 3 2 1,2 NOT CONFIRMED WITH MORE 2950±10 DATA ? 2750- 2 6 0 0 ± 10 < 1 8 (P P )-* * S TT’S STRANGENESS = * 1 (ALSO AN 2 550- AT ~ 2200 ?) ___2480130_ 2 8 0 7 2 5 S“ 1 * ( P P ) - » n n PART OF U 7 234St15_ 8 0 ± 3 0 4 0 - ANOTHER RESONANCE OF 4 7 2350 2 3 5 0 * l V 160 ±2 0 5*? 0,1 210±2S 4 * * 0 .♦ **~2310±30' ( p p )-* n Ti 2 2 0 4 ± 5 T)p -* A*(pp)- -U-CMANNEL ® ^ 2 0 n b 2150- """iTioffo"" 9 0 * 2 0 51? nnSMALL 21SO t SO* 2 00*25 3 " (PP)~* 7777 2 0 2 0 ± 3 24±12 U-CHANNEL^77p)-KAo-N)+(pp) 4^,15nb 1 9 5 4 * 5 1950- < 1 0 t-CHANNEL,BEXCHANGE”-~ 300 193 6 ± 1 4 - 8 0 1,2 , 1 (0 ) ( p p ),(p n ) nnSMALL ( 2 *?) -pp THRESHOLC 1 7 9 4 1 1 4 <8 (p n )—HADRONS 1750- B.E.—83 '3 ± V 4 MeV 1 6 8 4 1 7 SMALL p p — y B.E = 1B3*7MeV SMALL 1 6 4 6 ± 9 ( p p FORMS = 2 1 6 * 9 MeV ATOM) 1550- 1395*17 SMALL = 420*17 MeV 1350 F IG .16. - 69 - DISCPSSIOB K.V.L. Sanaa: It should perhaps be mentioned that there Is evidence from polarisation experiments at Argonne tor a resonance (M - 2260 MeV, P»v 200 MeV, - 3~) in the two- proton system; see H. Hldaka et al.f Phye. Letters 7 QB. 4.79 (1977). Evidence tor resonances in other partial wares such as 1D2» also seems to be accumulating. Tog Prakash: I agree. Similarly Information tor Dib'agmn Is also gathering.. This *onld be IncJmgZd to update the available Information included In this surrey. Beutrino Interactions - an Experimental Surrey S. SanerJee lata Institute of Fundamental Research, Bombay 1. Introduction In the past few, years, enormous progress has been made in experimental V physics. With new results coming in from the SPS and the Serpukhov machines in addition to the Fermilab X facility, the studies have produced breakthroughs in a number o f f ie ld s . Before going to the results let me mention a few points on the precisions in these measurements. The CERH SPS and the Fermilab groups now u se a dichrom atic narrowband beam In addition to the wideband beams. The purity of the beams has gone up; th e wrong type X con tent ( P in V beam or V in V beam) is typically 2-32 and Vfi( Ve) contaminations are 1-2/. Furthermore the beam energy is fairly well, determined from the d ista n ce o f th e in ter a c tio n v ertex from a cen tra l beam a x is (for V 's from K decays, the uncertainity in this determination is •>» &X). The narrow band beam spectrum is much broader than the wide band spectrum and consequently the average beam energy is higher 75 GeV c f TO «v 30 GeV). However th e fluxes are reduced by an order of magnitude. The V -fluxes are determined by various techniques. The uncertainity in the absolute flux determination is 7? for V 's from n-decays and is 10-122 for V 's from E-decays. The detector systems used in the measurements can be broadly divided into two classes, the large bubble chambers and the electronic counter setups using huge hadron calorimeters and fx-spectrometers. The main features of these two detectors are summarised in table 1.1. The detector configuration in the * - 171- SPS beam line is shown in fig. 1.1. The kinematic variables used in the- subsequent sections are defined in figure 1.2. B = energy of the incoming V B = energy of the leading outgoing lepton {ji in th e case of charged.current interactions) V = E-E = energy transferred to the hadronic system q * 4—momentum transfer - at the leptonic vertex 2 2 Q = -q = mass squared of the off-sh ell VtUboson ' V A. y - B 9 0 dimensionless scaling variablfes _ Q2 X ' x M = nucleonic mass 2. Charged Current Interaction - Most of the recent results in charged current interaction come from deep inelastic scattering of with a nucleon target, i • 6# V N - p ~ jl . _ ■ + - 2.1 V N -* y. x There are also some new results in exclusive studies like quasi elastic process, single pion production etc. 2.1. Exclusive Studies A. Quasi elastic channel: Data on quasi elastic channels V n - u“p and V p - u+n have been used to study the axial vector r P ' form factor. All the analyses £2.13. assume CVC and dipole form factor for the vector component with = 0.84 GeV/c2. The axial - 72 coupling was taken to be 1.25' (froin p decay) and the axial form factor was also assumed to'be of dipole type. The: results'are summarised in figure 2.1. The reaction, v p--* ,A++ was also studied £2.2j in the frame work of Adler Model £2.3}. The value o f Ma is converging to a value slightly higher than M^. One should note that the current value of the coupling constant is slightly higher than ,1.23 and the dipole form of the vector component is known only within at low Q2 (even worse at large Q2). " . . . B. One nion prr-duction; The ANL groups £2.4] has studied single pion. production in deuterium from th resh o ld to E = 15 GeV. The reactions looked at are V p - p~p 7 t+ y n - ^"*n n+ 2 .2 Vn - ^i-p n° All three final states show strong £ -production suggesting a dominant isovector current. The analysis leads that the inter ference of the I = 1 /2 (A1 ) a n d .th e I = 3 / 2 (A^) components is needed to explain the data. However the data are consistent with a zero isotensor component. Assuming a zero isotensor current | A. I they obtained | - 0.57+0.06 and the relative phase 0 = 89.2+8.7 degrees. _ 2.2 Inclusive Studies- In a *V-A theory,- the differential, cross- section can be written in the absence of AS / 0 and AC- / 0 c u r r e n t as where P^' s are the nucleonic structure, functions. The relation is very similar to that in. the deep inelastic scattering of e or jx with nucleons. The extra term F^ comes from V-A interference and it changes sign from to V . At high energy one neglects M . " ^ terms and rev/rites 2.3 as ■ „ * „ e < & * > - — RV&a‘> * FLV:1,cx,eL) v There are several simplifying ideas involved in the analysis of the data.- The most important-ones'are listed below (1) Charge Symmetry: For inclusive processes, this leads (for. h S = 0,Zk c = 0 current) F/P = F^n and F.5? = F^vn- 2.5 ■ For isoscalar target this is simply ? ? = F^ • (2) Callan-Gross relation: Assuming th i spin-structure of the constituents, this relation gives 2xF1 .= F2 2.6 These two relations simplify 2.3 as d ^ VlV aV it d xd > - ~ T T Ck {1+ a -» zj F^ > \ In quark-parton model, the structure functiofi are related to the' parton distribution functions. (F2J^F^) gives the scatter ing of V on -quark (or V on q). ^(FgTxF^H 1-y)2 gives'the . scattering of V on q (or i> on q). F2(x,Q2) signifies the momentum distribution of all quarks and antiquarks in the nucleon and xF^(x,Q2) Signifies the momentum distribution of the valence quarks. Thus ^ ==5S [Q(X,Q2, *5U,Q2)(1-y)2:l ^ -5 ^ I8(i,a2)«X«.ii2)(i-7)2J. One other important notion Is the Bjorken scaling. This 2 V states that in the lim it of E — °°, Q — 00 and —* — finite, the . Q hadronic structure functions are only functions of x. The scaling leads that the total V (orP) cross section on nucleons would have a linear energy dependence like the V -lepton scattering. Now reverting to the experimental data, one can broadly classify the results into two categories ( 1 ) integrated quantities (e.g. total cross section, A. Total cross-section: New data [2.5] come from (1) SPS narrow band beam experim ents (2 0 -1 9 0 GeV) by CBHS and BE3C, (2 ) FNAL narrowband beam experim ent (2 0 -1 9 0 GeV) by CITiFR, ( 3 ) Serpukhov wideband beam experim ent (8 -3 0 GeV) by SKAT and IHEP-ITEP, ( 4 ) AN! 12' bubble chamber experiment. The D-data (fig .2.3) siqgsst a constant slope ((T/E) over the entire energy region. BEBC and CITFR data may su g g est a s lig h t in c r e a se above E = 80 GeV. The - 75 y-data at energy above 50 GeV have a constant slope. But lo.wer energy data indicate a decrease in slope, from 10 to 50 GeV. Fig. 2.4 shows the ratio of v to V cross section as a function of energy. The HPWP points show a systematic increase with, energy which is present on a much reduced scale in BEBC and CITFR data whereas it. is absent in the CDHS data. This discrepancy could be due to the different acceptance cuts in the different experi ments and the model dependent corrections to take into .account this effect. Gargamelle propane group (PS energies) and FNAL Michigan group (j2.6j studied the ratio ^ for P ' ~ At energies below one pion threshold, this ratio should be zero. Valence quark contri- bution.leads to a value 1/2. Correction from sea shifts the ratio to 0.6. It is difficult to'choose between the two with the present data (fig .2,2). B. Mean Squared Momentum; th is parameter aiid the value depends on the method _employed. The , ~ . v , v - CDHS group [~2.7] has filled the y-distribution ^ ------1-( 17-BV’ )y *(1+B^,5 )y^ assuming a constant B. The BEBC collaboration /xF *d x v obtains B = jygg- = ' ~ i • This method takes into account 2 6" ^ ^ y-dependence of B but assumes B = B (i.e . charge symmetry). The CITFR group [2.83 fits both zero and first moments of y to obtain B. The data are shown on.figure 2.7 for V . The HPWFOR group has reanalysed their data and their new results are consistent with other experiments. Bv is flat above E=s50 GeV. ,B. Differential distribution '(i) Test of Charge Symmetry: Charge symmetry for F ^ has been tested by looking at in H and V interactions /d6fiv / dS'i*'\ j _ 1 .0 5 + 0 .0 7 in CDHS experim ent ( $y' y=o I'3 6148 ^ 0.90+0.20 in BEBC experiment CITFR group studied this as a function of energy and it was found to be good within 5/. CDHS group .[2.6, 2.93 looked at the y-distribution for testing charge symmetry in xF^. The results of the analysis are shown in figure 2.8(a). and (b) at two different energies. Separating 2 — V the flat part from the (1-y) part at y=0, one measures Q whereas for 5 distribution, the cross-section at y=1 leads small Q2 and QV at high Q2. QCD suggests (fig .2.8c) for small x values antiquark content is more at large Q 2 .' So this • difference could, simply be a reflection of the scaling violation. (ii) Test of CalIan-Gross relation: Here one defines a-parameter f ] 2xF. dx A = -2 ------1 - 2.12 This parameter is expected to be 1 if the Callan-G-ross relation is true. BEBC-Gargamelle data have been studied in bins of x and q2 and shown in fig .2.9. CITFR extracts the information from the moments of y distribution,Mean values of 1—A is summarised' below 1-A : 0.1 1 + 0 .1 2 Q2>1 GeV2 BEBC 0.17+ 0.01 Q2>1 G’eV2 CITFR 2 .1 3 < 0.05 with 90X CL (iii) Sea contribution: The term XF^ ( aquation-2.3) in V and v interaction appears with opposite signs. This helps the separation of the sea from the valence quark. Also charm-changing currents can be used to estimate the strange sea contribution in the nucleon (i.e . from dilepton studies). The extracted values are summarised in table 2.1v It suggests the sea is probably not SU(3) symmetric. (-iv) Nucleon Structure Function: Assuming charge symmetry and fixing-a value for:-A*.,one can combine v and v data to extract the-nucleon structure functions. CDHS and 3EBC' "groups [2.6, 2.9, 2...1 Oj have studied this field extensively. lo cover sufficiently - 78 large range of x ,and Q 2 , the BEBC group combined their =data with GGM Freon data in wide band V beam at PS energies. Fig.2.10 shows, the structure function integral as a function of Q2. Both F2 and F^ show a strong 2 dependence suggesting the breakdown of scaling. The Fg's evaluated by the BEBC gtoup have a very similar Q2 dependence with the Fg's obtained from e-d and ^i-p scattering data [2 . 11 3, the absolute values’ differing ^y a f a c to r 5 / 9 . At large Q2, one finds that the integral / Fgdx- deviates sufficiently from 1 suggesting a significant gluon contribution. The more interesting aspect of the analysis involved a comparison of the higher moments of the structure function with the theoretical predictions. The Cornwall-rNorton moments £2 .1 2 3 are defined as Mjj(Q2) = /J xN~2 F1(x,Q2)dx 2.14 2 * The moments fall off at large Q . It is expected- that part of the decrease is due to mass correction terms of order M2/Q2 which are absent in the Bjprken lim it Q2 -* °°. So one redefines th e moment in term s o f a v a r ia b le ^ * * _ 2x 2 .1 5 ■ 1 ^ / q ' ^ to take into account, this effect. The Nachtmann moments ,[_2.153 can be written as p ■ ' O 4 £ B +1 Q M2(Q2) = fl F (x ,Q 2 ) X f(N 2+2N+5l+5(N+1 )7l +4M2x2/Q2-HT(H+2)4M2x 2/Q2Jdx (N+2) (N+3 j - 79 - g«»a) 2.16 x For 1T = 2 moments, the contribution from the low x - values "is significant and the correction for the experimental biases makes , the measurement unreliable. However higher moments do not suffer ftom this lim itation. The moments obtained have been looked in liglit of Asymptoti cally free gauge theories £2.143 for strong interactions. There . are 2 flavour singlet terms corresponding to sea quark and gluon distribution and 1 nonsinglet term for the valence quark. The function xF^ is a pure non singlet and so the predicted dependence is of simpler form MN(q2) = V SKA. 2-17 ■ ( InQ /A • - N—2 - where \ = D- nfir+1 j* I » m ='number of quark flavours. Fig.2.11 shows a plot for In against In M^, for a choice of N* and N". The linear dependence of the two function is expected from the theory. The slope is exactly predicted by the theory and it involves only the number of quark flavours and the gluon spin. Comparison .of the slopes from theory and experi ment is done in table 2.2. The agre'ement with the vector gluon type is remarkable. The Q2-dependence is studied in figure 2.12. Large Q2-data clearly show a logarithmic dependence. However higher order corrections £2„ 153 > change the shape of the predicted curve at small Q2 values. So evaluation of A,(obtained from the intercept of the curve) is not very precise. Including only first ordered correction one gets A = 0.74+0.05 OeV with - S O - the second ordered correction, put in, A = 0 .4 0 + 0 .0 2 5 GeV, 3. Neutral Current Interaction ' Since the discovery of neutral currents in 1973 [j.l3» much effort has gone into the understanding of the structure of the" neutral current. The related data come from four distinct types of experimehts (1) experiments using high energy ^u. ( ) hearns in the accelerator laboratories (2) experiments using low energy Ve beam in the reactors, ( 3 ) atomic physics experiments studying the parity violating effects ( 4 ) experiments studying, parity violating effect in electromagnetic scattering processes. In the analysis of all these experimehts, one starts with a framework given by Weinberg and Salam [3.2} involving a weak isospin and weak hypercharge in an SU(2)xU(l) model. The general form of the effective Lagrangian can be written as for pure lePtonic Process for semi leptonic proc.ess. The quark coupling constants u^, uR, dR are alternatively written (3.3) as 3 .2 In Weinberg-Salam model, ail these coupling constants' can be written in terms of a single parameter sin 2 0^ — 81 - uL- ±_|s;ni®w, dl=-5.*ss,ndw , - i +2sin% , 3,3 3.1 V-e Scattering: y-e scattering involves only lepton vertices and the analysis is relatively pure. However the low cross-section causes a. low event rate. The data £3.4,3.53 are summarised in table 3.1. The reaction is mediated only through neutral current. So the cross-section can be written as dy^“ = [(gv+SA)2-Kgv:?gA)2(l-y)2-Kg^-g^)Me I ] 3 .4 i-gg scattering can also go through charge current phenomenon. So in the coupling constants one should effectively have 1 -tgy and 1 -tgA instead of gy and gA respectively. The low energy 6 data from Gargamelle and Aachen-Padova have a strong sim ilarity with the high energy data from the Columbia-BNL . group. However the high energy Gargamelle data are inconsistent with these experiments. All these data are consistent with ( f i g . 3 .1 ) Sv = 0 .0 + 0.1 ; g A = - 0 .5 + '0.1 2 i.e . Weinberg-Salam model with sin 6W = 0.23^0.05 3.2 Inclusive, hadron production: The quantities measured in the reaction are: Rv = -CO^? • . D = 6^-N-^.) • 3.5 6"(^N-^a x ) er(3N-^u x) The bulk of the data comes from isoscalar targets and are . summarised in table 3.2 £3.5,3.63. Extraction of information from this process involves a quark-parton model' framework. The - 8 2 - analysis involves assumptions regarding the sea content in the nucleon and also QCD effects.. In fact the dependence of quark density function on causes the,disagreement of R„(Ry),in various-experiments (due to the variation in . averaged value' of Ry and Rjj , one obtains for the,quark coupling c o n sta n ts UL + dL = 0.29 > 0.02 •; 2 2 «r + 4 = 0.02 -2 o.ov . corresponding to sin%w = 0.23 + 0 .0 3 The BEBC group C3.7] has looked at the hadron energy distribution. They defined a variable y* in analogy with y, as R. y ' ' 3 ,6 where By(R) = the mean energy at a radius R. from the i) -axis, (the event occurring at that radius) y' is the same as y for events, whereas y‘ < y for ^ e v e n ts. Knowing the beam spectrum, one csin get a correspondence between y1 and y,distributions. Assuming the. tensor contribution to be zero, one finds the strength of PS and S contribution relative to that of V and A to be less than 0.12 at the 95X confidence level. The data are not yet sensitive enough to distinguish a tensor contribution from the V and A contributions., Using V and A type interaction and neglecting the AS = 1 . current, the y' distribution has,been.fitted in terms of 3 coupling constants u£+d£ = O.3 4 +O.O3, u^+d| =0.024+0.024; <*l^R ° * 19^ * 1 9 In terms of Weinberg-Salam model, this corresponds to sin^9w = 0.19+0.03. Inclusive scattering on proton [3.8l are summarised in table 3.3i This should in principle give the difference'of u and d couplings. But more precise measurements "are needed. 3.3 Exclusive Channels in y N scattering: Here the data exist mainly in elastic scattering studies [ 3 . 5 , 3.3 and single pion production [ 3,5, 3.1$ Elastic scattering has been studied in CERN PS energies by the Gargamelle and Aachen-Padova groups and by two counter groups at BHL. The results are summarised in table 3.4. The. data support a strong isovector component of neutral.current and the value obtained for sin 9^ = 0.22..Single pion production data come from Gargamelle propane experiment and the main feature in the data is a clear signal, of A (fig .3.2).. This supports a dominant isovector current. The cross-sections are tabulated in table 3.5. The difference in V.pit0 and V nit0 cross-sections indicate an interference of isoscalar and isovector c u r r e n ts. 3.4 Semi-inclusive measurements: The charge ratios of pions produced in neutral current experiments give a handle to the isospin structure of. the current. The data from the Gargamelle collaboration C3-1 "0 gives (x+/it~) = 0.77+0.14; =1.64+0.36 All the data have been systematically studied by Abbott-Bamett ^.12] and the solution for the quark coupling constants are summarised in table 3.6. 3.5. Atomic Physics Parity Violation Experiment: In presence of parity, violating current one. expects to observe small optical rotation of the plane of polarization of light passing through bismuth vapour at frequencies for which am interference■due to ..weak.neutral current is allowed. Three experiments have been done at Seattle, Oxford and Novosobirsk £3.12) . The value of the angle of rotation■of the plane of polarization have been compared with the theoretical'- expectation from Weinberg-Sdlam model (with siri^9w = 0.25) in table 3.7. Seattle group has a clear disagree ment' whereas 'Novosobirsk group agrees with th£ model pretty closely. The experiments are very difficult and one needs a inore careful study (both in experimental set-up and in"theory) before drawing any further conclusion. 3^6 Polarized electron scattering: SIAC-Yale group studied the asymmetry in longitudinally polarized electron scattering off deuterium target [3.14). ^he experimental set up is schematically shown in figure 3.3. linearly polarized light is produced from a dye laser and is passed through a Pockels cell to transform it to circularly polarised ligh t.’This circularly polarised light in its turn produces.longitudinally polarized electrons in Ga-As crystals mounted on the electron gun. Depolarization is negligible during acceleration and the magnitude and sign of polarization is measured from asymmetry in Moller scattering from a magnetised iron fo il. One' observes non zero asymmetries both in deuterium and in hydrogen. A/Q2)d = (-9.5+1.6) XIO-5- (GeV/c)-2 . A/Q2)h = U9.7+2.7) x IQ"5 (GeV/c)“2 - 85 - The re'cu^ts agree pretty well with sin^9w = 0.20+0.03. However the experiment has a limited coverage of and y. Variation in these parameters can settle the issue on Weinberg- •Salam model, is a conclusive way. All the data described here can be consistently fitted is with a Salam-Weinberg type model .with sin^9w = 0.23+0.02 ( see figure 3.4). 4. Final states The scaling violation observed in the charged current reactions has given.some insight to the structure to the nucleon. There the study was confined to the leptonic vertex only. Obviously one would get more information by studying the hadron vertex. The hadrons produced would be intimately related to those produced in eN,y N, and hadron-hadron collisions. Several Bubble Chamber groups £4.1J have#carried out analyses of these- hadrons in the light of the quark-parton model. 4.1 • Fragmentation Function The quark-parton model predicts that the differential distribution would factorise in the variables x and z (z is the fractional energy of an individual hadron -= E^/Ey) i.e . ' l i b * GNq,(x,q2:)i£(2) ■ ■ 4.1 where gives the distribution of quarks inside the nucleon and z) is the fragmentation function of the scattered quark q. The fragmentation function is normalised as f l B*(z)dz = and the fastest negative tracks, in V- and v induced reactions. Again the difference between IPS and FF model is- very little . . Only in v data, the' FF model has somewhat better agreement. The FNAL group did study the charge Correlation of the second fastest particle when the fastest particle is. a negative pion (class B) and a positive pio.n (class A). The charge density plotted as a function of the rapidity in the rest of the hadron system (fig .4.5) shows a good agreement with both the.IPS and FF model for class B; For class A, however, experiment gives an average charge of 0.19+0.04 whereas BPS gives 0.34 and FF model gives -0.15. The correlation existing in the data is stronger than mere charge conservation but much weaker than the FF-model prediction. 4.2 pT Distribution ' ' The prp distribution (Fig.4.6) cannot be well parametrised by a Gaussian (as in the FF model). Rather a fit of the type e"tmT (where m^ - transverse mass = >/m2+p^) with b = 6 explain 2 2 the data farily well. has been plotted as'a function of Q in fig.4.7. The v data and wideband ^ data do not.show any 2 2 significant dependence on Q . The phase space pulls down ■ 2 2 100 GeV and z at 0.2, one clearly sees a rise in This rise of spherocity,thrust variables £4.3j- Spherocity,-thrust are d e fin e d as . Z | p— . | p S = ( | ^ |^ X| -) fo r minimum £ IPyil lip.. . | (summation done .over- :T = 2 ( . ) " ^ Z |p^|m axim um one hemisphere) where^ p T ^ and p,*£ are transverse and longitudinal momenta of the hadron i. For two jet formation S would fall off whereas T goes from a value 1 in two jet configuration to a value 1/2 in spherical configuration. Fig.4.8(a), (b) show Sterman and,Weinberg [4.43 have defined a two jet event as an event that has more than (1- 4 ) of the energy within a cone of opening half angle 6 , They have ca lcu la ted th e fra ctio n o f such events in. the case of e+e” annihilation (1-F) would be by definition the fraction of three jet events. The energy dependence tak es th e form = Gfe ,6 ) [ y | In (^ 2 )+ 11 4-.5 Assuming a similar energy dependence to exist for the yN case, the BEBC group has plotted 1 as a function of Q 2 on a semilog plot for various £ and 6 (Fig.4.9). The data show an approximate linear dependence with a common intercept at A = 0.4. All these studies corroborate the earlier study of quark structure function. 4.3. Other studies There have also been several studies to look for resonance P * 6 » Aj etc. [4.5J in the charged current interaction. The AML-Carnegie-Mellon-Purdue group [4.5] has looked for all charged current events with a V° in 5 exposure at FNAL 15* chamber. The rate. of. V° events has been found to be large at small x-values. The.rate is very well explained by charm decays (fig .4.10). 5. Multilebton Production 5.1 Unlike charge dilepton Dilepton production by U was first observed by the HPWF group in 1975 £5.1J , in the dimuon. mode. Since then several groups have observed the dimuon final states (5.2]t Since muon identification utilises its long lifetim e and small cross section the observed muons have a large momentum cut off (at 4-.5 GeV/c). With the availability of the large sample one can now Ipek at' the energy dependence and various other distributions to study the production mechanism. The bubble chamber groups have observed the dilepton events'in yet another mode (namely ^ e - .mode). There the. electrons are observed with a larger momentum acceptance (momentum cu t o f f f s at 0 .3 G eV /c). C o rrela tio n w ith strange particles can also be observed. The observed dilepton events are smmnarised in table 5.1. Before going to the analysis,the various mechanisms to produce dilepton events are briefly discussed. The first mechanism (fig .5.1a) involves the production of intermediate vector boson which undergoes electromagnetic bremsstrahlung and decays leptonically to give rise to dilepton final state. The second process is the so called weak trident process and goes according to figure 5.1b. Here the typical rate is 10 J tim es the total neutrino cross-section. A third possibility is the production of a heavy neutral spin 1/2 lepton which subsequently decays leptonically (fig.5.1c). This characteristically has a - r * 90 ■ Pi bound £5.3j on the asymmetry of the two lepton momenta. ( .48< — 2 < 2.1). The fourth possibility is that at the hadron vertex a new particle is produced which decays weakly to leptons (fig.5.10) This is a process predicted by GIM model, in which a fourth quark, the charm,' is added to the u, d, X quarks. The charm production ■ - 2 off a Valence quark is suppressed by sin ©c with respect to the normal transition of its production off a sea quark. .XLso the number of'strarige 'particles produced along with the dilepton event is 1 when it is produced off valence quark and is 2 when it is produced off sea quark (see figures 5.1e). The first experimental observation is that both dimuon and ^te rate increase rather fast with energy, the rate being 0.5/'. of the charged, current interaction (figure 5.2). This rules-out the weak trident process as the main mediator of such events. The second lepton (with wrong sign) has,pn the average, much smaller momentum GeV/c fo r e le c tr o n s and -10—15 Ge-V/c fo r muons,, with p^ cut at 4.5 GeV/c), compared to that of the first lepton (pq~ 50 GeV/c). This rules out the direct production of inter mediate vector bosons or heavy leptons as the only source-of these events. The> most likely interpretation seems to be the production and subsequent decay of charmed particles in the GIM scheme. Some q u a n tita tiv e com parisons are made w ith a 1 0 X le p to n ic decay mode ,of charmed particles. This leads to a 5 / charm 2 production which is on the same level as expected from sin 9C. The second le p to n has a momentum t y p ic a l to t h e hadrons in th e shower, also it has a small p^ with respfect to the .hadron shower 91 d ir e c tio n , x and y -d istr ib u tio n s ( f i g . 5- 3A) of these events' closely resemble the'normal "charge-current distribution. 5 can produce charm from sea quarks whereas V can produce charm both from sea and valence quarks. So one1 expects . 5.2 Trinaion production " In 1976, the CITFR group C 5.4} first observed a trimuon event. Since then the HEWE group at and the CDHS group at - SPS have observed a reasonable sample of such events.. With this increased sample size f5. 5, 2 . 9J one can now study the origin of these events. Regarding its production mechanism, there are in principle two different models involving the production- of new particles: (i) Production and cascade decay of new heavy leptons at the lepton vertex (5.4a) (ii) Production and subsequent decay, of quarks with new flavour in the shower (fig 5. 4b) - 92 - . More conventional sources, for trlmuons are normal charged current ■ events with an ad dition al muon;p a ir . There the. two main p o s s ib ili ties involve (1) Internal br emsstrahlung of the leading muon ox of one of the quarks (IB-see fig. 5. 4c).. ( 2 ) Hadronic production of the muon pair in the shower (HMU-see fig .5 .4 d )., Y The increased sample s iz e comes from mainly two new experi ments at CDHS and HPWPOR. The dominant background to these events i s due to dimuon events with a decay. A fter correcting fo r such background, one sees a signal in mode for if and mode for 3 and the rates are summarised in table 5.3 and figure 5.5. The rate increases by a factor 10 from 30 GeV to 130 Gey. This is mainly due to the muon detection threshold of 4.5 GeV/c.The leading muon is chosen in a way such that the transverse momenta o f th e two other muons with resp ect to th e d irectio n o f W ( i . e . q) i s minimum. With this definition of the leading muon, one plots the effective mass of the remaining muons (figure 5.6). It has a low mass enhancement characteristic to the internal bremsshrahlung and hadronic muon pair production mechanism.. The transverse momentum of the pair with respect to the direction q again peaks at small values. The heavy lepton cascade cannot explain these two distributions simultaneously (see fig .5.7). The dominance of the HMU mode is. very clearly seen in fig .5.8 where one plots the azimuthal angle between the leading muon and the remaining muons in a plane perpendicular to the V direction. The peak at 1dO° is due to the HMU mechanism. However there is a cluster near 0-0 which is attributed to IB. Using this distribution one separates out th e contribution due to IB £r = ( ,8+.4)x10 5 from the contribution due to HMU (R = (2.2+0.4)x10~'’J, which agree —5 —5 reasonably well with the-predictions namely .7x10 <®ib<' 2x 10 . and Rhwt> 2x 1 O-^ fo r E > 30 GeV. Thus a ll the’ events in the trimuon production can be explained by charged current interaction with Internal bremsstrahlung and muon pair production-in hadron, shower. 5 .4 lik e sign dimuons like sign dimuons are of interest in the-light- of heavy lepton or heavy quark cascade models. One expects more like sign dimuon events than trimupn events. The. observed lik e sign dimuons [ 2 . 9 » 5* 2] sire summarised in ta b le 5 .4 . The main background to these events come from n/K decays in flight. The background has been studied by the CDHS group using Monte .Carlo technique whereas HPWFOR group studied the rate at various target densities and then extrapolated" to infinite .density. The calculated rates after background subtraction are also shown in table 5.3. The data s t i l l need more refinem ent before any fiirther conclusion can be drawn. 5.5 4-Iepton final state Three groups [ 5 . 8 , 5.91 have reported so far a candidate for 4 lepton events. They are summarised in table 5.5. A typical event is shown in figure 5.9. The most substantial background in - the 4-u events is due to trimuons with an extra x — p or K-p -2 decay in the shower. It would typically give ~ 2x10 events. 94 The, origin of such events could be due to the. process IS and HMU w ith an associated charm, production or charm production' as in . . dimuon events w ith an, associated charm pair production. There are obviously suggestions requiring new, particles (i.e. new leptons or new quarks).. The expected event rate from conventional sources _ 7 i s 0.2 event.for the 4—^ events and 10 event for the bubble •chamber experiment. One needs more statistics to get further - clarification^ 6. Direct Observation of Charm, heavy lepton etc. 6.1 Direct observation of charm . Charmed p a r tic le was observed in a hadronic decay mode by the Columbia BN1 group (jj. 6]. They looked for all charged.current events with a V° decay. The K° mass plot (fig.6.1} clearly shows a bump (4 standard deviation effect) at 1850 MeV (the region of D as seen at SPEAR), A ganssian of mean 1850+15 MeV and width 20^8 MeV fits the plot. The corresponding mass plot for neutral current does' not show that peik,indicating a suppression of. charm charging neutral current. 6;2 Charm-Changing neutral current CDHS group £6.13 has studied the wrong sign muon events to investigate the existence of the charm changing neutral currents. The Columbia-BN1 group studied events w ith an e + but no yc • in V ^ ■ sample to investigate similar effects. After correction for l^Cor .Vg)’backgrounds, no candidate was left over and both the groups have put an upper lim it. - 95 - CDHS upper lijmt Slch^ hagging^C l < 2i6Jf Coi-BH, Upp=, Unit < a.6Z 6.3 Heavy Lenton Production OIHS group €6.1} has used the single ^i+ events to put upper . lim its on charged heavy lepton production of muon type, the lim it being best summarised, by- figure 6.2. From single electron .events Oolumbia-BHl group f5 .6 j puts a 90£ confidence lim it on ’mass (l”) to be larger than 7.5 GeV and mans (1+) to be larger than 9 GeV. The coupling stren gth o f T to has been found to be l e s s than 2.53f to th e coupling by Columbiar-BNl and th e same lim it is put at 6% by the HEBC group. As regards to L° production, Aachen-Yadova group £3.53 has reported 12^i~e+ type events C.p > 2 GeV/c) at PS energies where 'charm background i s only 4+2< These p ~ e + pairs are not associated with hadrons other than recoil protons. The small angles between th e muon and th e elec tro n make charm as an u n lik e ly source. However a neutral heavy lepton of mass » 2 GeV can explain the events reasonably well. SKAT group at Serpukhov [5.7l reported a^t“e+ event having a lifetim e (5- 7)x 10-12 see (there is a visi ble gap of 4.8 mm between the ' f i vertex and the decay vertpx). la stly the BEBC wideband group (2 .S J in hydrogen has reported a 3 standard deviations btimp in n+ mass (fig . 6.3) which has been supported, by the narrow band group in neon. All these heed, to' be verified before any further conclusion can be drawn., - 96 - 7. Beam dump experiment 'y-beams are obtained in the accelerator laboratories from decays o f it and K. To Investigate any other sources of , i.e. from a parent with a shorter lifetim e, several beam dump experi ments were performed. The modification to a s.taindard set up involves the introduction of materials immediately when the. secondaries are produced (see fig . 7. 1 ). it and K would interact rather, than decay, and the flux of the .conventional' type of y 1 s. .would be reduced by a factor of thousand or more. 7.1 Observation of prompt The Spark chamber group at Serpukhov ( 7 .ij observed 195 p. events and 45 elec tro n type ev en ts. Prompt source was estim ated by subtracting backgrounds from ( 1) a study of the density of the target material ( 2 ) the measured V flux as obtained, from observed p. f l u x . The. mean value i s 12+10 which does hot exclude a zero effect. This corresponds to = (0.72+0.66) • Q . 10'5 In SPS, three groups (two bubble chamber and one counter) C7.. 2J simultaneously -lid beam dump experiment with an integrated 1 7 proton intensity of 3.5x10 on the target. The first observatioi was.the fact that the relative number of e-type neutrino, inter action has .increased significantly from the conventional runs. — + Expected ratio and •§— events from K, , E decays to be 0.06 }x and 0.1 respectively whereas the BEBC group observed the ratios as 11/29 and 4/5 respectively. The CUES group saw a sharp increase in the NC/CC ratio which can be consistent with the - ST - earlier measurement, only if one assumes a significant increase in th e V Q( A-'g) flux. The results are tabulated in table 7.1... Also there is a significant difference between the expected (.14-6+0.15) and the observed (.22+0.2) ratio of p i + to y T even ts. • Absolute event rates are predicted using the particle production spectrum from a thermodynamic model. This leads to an equal amount o f prompt v> » V , v , v in the source. There i s an ex tra r ■ r . __ - piece of information coming from the narrow band run with v where an excess of Vg type events were observed. This experi ment was carried out With th e proton h ittin g th e B e-target at • ' 15 arad (in the-other beam dump, proton hits a Cu target at 0 mrad). The prompt flux is better expressed as ^p/n ratio and shown in figure 7.2 together with other observations regarding prompt lepton production in hadron collision. These prompt j/'s could be explained in terms of charmed particle production and the cross-section needed to explain the observed event rates , vary from 20 to 400 pib (such wide variation is due to - the uncertainity in the production mechanism). 7.2 .. Universality in weak current The eVents observed in BSBC and G-argamelle also provide some indirect evidence on the issue of yU-e universality in neutral current interactions. From the observed v ( ^ ) charged r . r. current events, one expects to see 16 neutral current.events whereas th e observed number i s 26. The observed number o f e~ and e+ events would product an excess of 8, if.^i-e universality is valid. Thus the data not only gives evidence for neutral current events induced by and v e but also suggest the strength to * 98 - be compatible with p-e universality. 8 . Summary The important "results are summarised below: (1) The charged current studies have been refined to understand the nucleonic structure. Together with ed and pp deep inelastic scattering data, these studies establish a scale . breaking in these scatterings. This breaking has been, attributed to the 1st order correction of QCD and the quantitative checks seem to agree with the theory, rather well. (2) Data from a diverging set of experiments have been used to study the coupling constant in neutral current interaction. The coupling constants agree reasonably well with the SU(2 )x U(1) model due to Weinberg and Salam. Parity violating effect in e-d scattering has been experimentally demonstrated. There is some evidence of ^i-e universality in neutral current interaction. (3) The hadronic 'distribution hats been studied in the framework of Quark Parton model. The fragmentation functions aeem to agree fairly well with the theoretical expectation. However one finds the effect of first order QCD corrections to be important in the transverse momentum distributions. (4) Unlike charge dilepton events are well understood in light of the DIM model with charm. Trilepton events can be - accounted for from the production at the hadron.vertex’in terms of known quarks (+ some internal bremstrahlung of the leading - 93* - muon). The strange sea evaluated from the analyses indicates that the sea is not SU(3) symmetric. (5) There' is evidence of production of charmed particles in v interaction. However the evidence for heavy leptons is not that conclusive. (6) There is evidence of a prompt source of y ’s in hadron- hadron collision. This prompt source could very well be the produced charmed particles. ftf-Tmowledgernent: I am .thankful to a number o f persons fo r preparing this talk. It is impossible'to mention them all by name, nevertheless I would like to-mention Dr J. Muivey, Dr K.W.J. Barn ham and Mr P. Mitra for their kind help in this r e s p e c t. * - t o e - R eference [2.1] M.M. Bleed eft aa,,- Sbys, Sett. 1g (£4> 2S1 A, Otteen Seeomrtela eft a l,, Buov. Cto, 5&S ( 67) 927 H» Hold®? eft 65L., Knov, 0# i* 52. ^68) 39B It, S. SttCtas a# a l,, Btyrs, Rev* Sett. 3 3 (69) 1014 $, B u gaev eft a l . , 8 »sv. Cjja, Lett. £ (6 9 ) 699 S. Bonaefttl aft * 1 .. maoV. Cfea. ?8 A ( t o ) 260 Papers submitted Topio«tt Socfenettce on ^Pbyeiee-^Otford ( 19 ® ) { M l J- M 1 e* 90Li» $h5» . fie*. Eeftt. £ 2 (1 8 ) 1012 C2*S 3. Adler, Bby#, Re*. £)& (75) S544 {2.4| V,B. Barnes eft & 1918) z $•% P» Boseetti 9* al*„ Ptiya. Sett, 2g| (77) 275 B-.G, Banish eft a l , , Pbye, Rev, S ett.. 5 3 (7 7 ) 1595 S.d. Bariett eft s i., Phy». Setts* jg£B (77) 291 M. Holder eft at;* Paper submitted to Topical Coat, on V P hysics - Oxford (7 8 ) end Tokyo 'Conference (78) B .3. Baranov eft a t . . Paper subm itted to Tokyo Conference (78> A.B. -’yaaff'stiratan eft g l . , Pbys. S e t t . 76B (78) 238 (2.$ P. Seuilli, Pro®, of Topical Conf. on V ptiys. Oxfbrd (78) g.1| M, Hold®: eft al., Pfeys, Sett. (77) 577...... - B.C. BariSit eft a l . , Ways. Rev. S e t t . £ 0 (7 8 ) 1414 52.<§ K. Tlttel - Talk presented to Tokyo Conf. (78) £2.1(3 P.O. Bosett1 et al., Oxford University Preprint 16/78 £.13 E.M. Riordian et a l., SIX-PUB-1634 (75) H.S. Anderson eft aT., Phya. Rev. Sett. 3§, (77) 1450 H.L. Anderson et al., Phys. Rev. Lett. ^ (76) 1422 - 101 - £2.12} J.M.' Cornwall and R.E. Norton Phys. Rev. 177 ( 69 ) 2584 {2 .1 3 )0 . Nachtm.ann N u cl. P hys. B65 (7 5 ) 237 0. Nachtnann Nucl. Ph.ys. B78 (74) 455 (2.14} B.C. Cross and F. Wliczek PhyS.Rev. to (73) 3633 . D.O. Cross and F. Wjjczek Phys. Rev. IQ. (74) 980 8. Ceotgi aSd H.P. Politzer Phys. Rev. Bg, ( 7 4 ) 416 ( 2 .1 $ Bardeen e t a l . , FNAl 78-42 THY 13.13 F.J. Hasert et al., Phys. Lett. 468 (73) 138 £3 . 5 S. Weinberg Phys. Rev. L e tt. 15. (67) 1264 . . S. Weinberg' Phys. Rev. Djj (72) 1412 A. Salan 8tb Nobel Symposium ( Stockholm 69) 367 [>.3jf P*Q» Hbhg dtod J.J. Sakurai Phys. Lett. 63B (76) 2195 [3.§ J. Blietsehau et al., Phys. Lett. £2B (78) 232 H. F a lssn er e t al.» Phys. Rev. L e tt. 41 (7 8 ) 21.3 P. Alibran et al.„ Phys. Lett. 74B (78) 422 0. Ball ay et a l., Pt$ye, Rev. Lett. Jg. (77) 62 P. A libran e t a l . , CERN/BP/PHYS 78r.6 (1978) ' F. Reines et al., Phys. Rev. Lett. (76) 315 £3 . 5} C. Balt ay Talk given to Tokyo C-nf.' (’’h) (3.63 J. Blietsohcm "et a l., Nucl. Phys. B118 (77). 218 F.5. Herrit et al., Phys. Rev. D17 (78) 2189 P. Wanderer et .al., HPV7F 77-1 (July 77) M. Holder et al., Phys. Lett. 72B (77) 254 P.O. Bosetti et al., Phys. Lett. 76B (78). 505 [3.7] H. Deden et al., Aachen Preprint PITH.i-103 (78) [3.8/ F..Harris et al., Phys. Rev. Lett. gg (77) 437 H. Derrick et al., Phys. Rev. D18 (78) 7 J. Marriner LBL-6438 (77) - 102 [3*9\ W. lee et a l., Phys. Rev. Lett. 32 ('76) 186 D. Cline et al., Phys. Rev. Lett. 3X (76) 252 D. Cline et.a l., Phys. Rev. Lett. 3X.(76) 646 M.-Pohl et a l., Phya. "Lett. 22B (78) 489 (3«1 <3 W. Krenz e t a l . , N ucl. P hys. Bj 55" (7 8 ) 45 " D. Erriques et 'al., Phys. Lett. 75B (78) 550 W. Lee et nl., Phys. Rev. Lett..J8 (77) 202 (j.lflH . kluttig et al.; Phya. Lett. 212 (77) 446 [3.15) L.P. Abbott and R.M. Barnett Phya. Rev. Lett., £0 (78) 1303 L, F, Abbott and R.M. B arn ett SLAC-PUB-21 36 [3.13]L.L. Lewis et a l., Phys. Rev. Lett. 32. (77) 795 P.E.G. Baird etal.> Phya. Rev. Lett. 3 2 (7 7 ) 798 N„ Fortson Proc."of V-78 Conf. (Purdue 78) L.M. Barlov et a l., JETP Lett 26 (78) 379 (also Tokyo Conf. 1978) [3 .1 5 °.Y* Prescott et al., Phys. Lett. 222 (7 8 ) 347 (4.1} J. .Bell et a l., Michigan Univ. Preprint UMBC 78-6 A. Vayaki e t a l . , CERN/EP/PHYS 78-28 P.C. Bossctti et al., Oxford Preprint 58/78 V. Stenger Oxford Preprint 59/78 M. Derrick et al., Phys. Rev. D17 (78) 1 ^4.3 R.P. Feynman and R.D. Field Phys. Rev. D15 (77) 2590 (4.3j H. Georgi and M. Machacek Phys. Rev. D15 (77) 1416 |4.4] Sterman and S. Weinberg Phys. Rev. 52 (74) 3391 • * (4.5 Papers submitted" to Oxford Conference (78) Also see [2.63 / e .... C?.l 4. Benvenuti et al., Phys. Rev. Lett. 34 (7 5 ) 419 - 103 - [5.2) A. Benvenuti et al.,. Phys. Rev. .Lett. (78) 1204 B.C. Bsrish et al., Phys; Rev. Lett. J6 (76) 939 M. Holder et al., Phys. Lett. 625 (77) 377 J. BlietsohaU et ol., Phys. Lett; 533 (f5) 361 J. Blietschau et ol., Phya, Lett. 60S (76) 207 P.O. Bosetti' et al., Phys. Rev. Lett. J8 (77) 1248 O.E. Erriquez.et al., Phys. Lett.. 77B (78) 227 P.O. Boaetti et al,, Phys. Lett. £2§ (78) 380 . J. V.ankrogh et al., .Phys. Rev. Lett. ^8 (77) 1248 £5>3 Bais and S. Trieman Phys. Rev. Lett. 25, (75). 1206 [5.4) B.C. Barish et al., Phys, Rev. Lett. 28 (77) 577- [5.5 A. Benvenuti. et a l., Phys.,,Rev. Lett. 40 (78) 488 T. Hansl. et al., Phys.- Lett. 77B (78) 114 6 -5 C. Baltay et al.," BHL-24663 submitted to V-78 conference |5.7} D.S. Baranov Serpukov preprint I EVE 77-30 (77) [5.8) M. Holder e t a l ., Phys. L e t t .. 75B (78) 105 ,'R.J. Loveless et.al., Phys. Lett. 78B (78) 505 [6 . 1J M. .Holder et al., Phys. Lett. 74B (.78) 277 [7.l} A. . Soloviev Prc c. of 77 Int. Symp.. on lepton and Photon Interaction at high energies [7.5il P..Alibran et.n l,, Phys. Letts. 74B (73) -134 . T. Hansl et al., Phya. Letts. 243 (78) 139 P.O. B0s e t t i et a l . , Phys. L ett. J4B ( 78) 143 H. Wacksmutti CERH/EP/PHYS 78-29 - 104 - Table 1.1 Electronic•Detector Bubble Chamber. Target mass goes up to Target mass i s ty p ic a lly 10-2C 1000 ton s tons-so event rates are down. * by a factor of 50 p identification is * . It heeds an EMI for unbiased^ excellent (from range) identification Neutral component of Part of the neutral shower is hadron shower is well invisible and fudging is measured necessary It is blind to details It is excellent for details of the shower of the shower It has no electron, V° •. Electron, V° identifications detection capability are very gobd Angular coverage is not 4it angular acceptance always complete - T05 T able 2.1 5 S Canment - ■ Q + CDHS 0 .1 2 + .0 0 2 0 .0 4 * 0 .0 2 , Dileptori data 0 .0 2 + 0 .0 0 7 BEBC 0 .1 1 + 0 . 03 - - ■ HPWFOR 0 .1 4 + 0 .0 3 0 .04+ 0.015 Col-BNX - 0.015+ 0.01 Dilepton data Average 0 .1 3 + 0 .0 2 0.02+ 0.01 Table 2 .2 O bserved QCD QCD- . slo p e P r e d ic t P r e d ic tio n ion (s c a la r (v e c to r glu o n ) glu on ) d ln'M3(JJ=i6)/d ln M3(N=4) 1.29+ 0.06 1.290 • 1 .0 6 d In M ^N ^/d In M3(N=3) 1 .5 0 + 0 .0 8 1.456 . • i .1 2 - ‘ d In M3(S=7)/d In M3(N=3) 1..84+0.20 1 .7 6 0 1.0 9 - - - 106 - T able 3.1 Experiment Reaction C barged Events Back Cross-section current obser ground lO-4 2 ^ cm2 sample ved Gargamelle 1 0.3+0.1 < 3 (CERN-PS) v ’- y ~ Gargamelle . -3 0.4+0.1 1 o'*2 *’1 (CERN PS) -Of. 9 Aactaen- 32 ' 21 1 .1+0.6 Padova v p e ~-~yie~ (CERN-PS.) Aach en- T7 7. 4+1.0 2.2+1.C Padova (CERN-PS) Gargamelle 41000 9 0.4+0.4 (CERN-SPS) v F e~ ~ y ~ 4 ,3 - l l 5 t0 Gargamelle 4000 ’ , "0 < 3.3 (CERN-SPS) BEBC 7500 1 0.4+ 0.2 (CERN-SPS) < 3,5 Columbia- v e- —V e 100000 11 0 .7 1 0 .7 . 1.8+0.8 BNL ( FNAL)' ? ? FNAL-MICH-- 6300 0 : < 2 .9 IHEP-ITEP ( FNA1) 180Q MW (.87+25)6-^ '' V ~ 5e e’ fis s io n [_1.5 Oarga- 1-10 1 0.2 5 + 0 . 04 0 .5 6 + 0 .0 3 0.26+0404■ 0.3 9 + 0 .0 6 m e lle , CERN BUI 1-10 0 .4 0.25+ 0.05 7 'BO HP WE, 30-200 -"4 ' 0 .2 8 + 0 .0 5 0 .3 9 + 0 .1 0 0 .3 0 + 0 .1 0 Oi 38+0.09 FNAL 3ITFR,. 30-300 12 0.28+ 0. 03 0.35+0.11 0 .2 7 + 0 .0 2 0.40+ 0.08 FNAL ODHS, 3 0 -2 0 0 12 0.293+ 0.01 <0.3510.03 0.295+ 0.01 0 .3 4 + 0 .0 3 CERN BEBC 3 0 -2 0 0 15 0 .3 2 + 0 .0 3 0 .3 9 + 0 .0 7 Narrow band - CERN ■ 15'BC, 10-100 10 0.35+ 0.06 FNAL i— —— Table 3.3' R*1 = 6^( v -* ^ ) | Berkley -H aw aii-Michigan ! 6.4 8 + 0 .1 7 ■ V ' ■ ' 1 -p _ grP( jT _ V ) AML-3 arn eg ie M ellon- 0.4-2+0.1 3 Purdue (2-) LEL-ENAL 1.31+ 0.38 - > 0 8 - Table '3.4 - > p -..V E xperi- v > P ment Bv exits : Bgtck— vup - vup Events Back vuP - v up obser ;ground obser ground ved y - r ? ved VpP — p +n EPS 255 88. 0.11+0.02: . 69 28 0.19+0,05. (o ld HPW) CIR : : 71 30 0.20+0.06 Aacben- 155 110 0.1 o+o .03 Padova G arga-.. .100 . : 62. 0.12+0.06 m elle (PS) - 109 - Table 3 .5 Experim ent Ratio measured Experimental results (VX 1t°) CIR/Aachen Padova 0.21+ 0.07 2(ji~ X k °) VX it0 Gargam elle 0 .4 6 + 0 .0 7 2 { p + X it°) Vn it+ AM 12' deuterium 0 .1 3 + 0 .0 6 ^"*PTC+ V 131t° ■ 0.40+0.22- p ~ plt+ Vpit- 0 .1 2 + 0 .0 4 ^ ”P"+ Vnit0 +\> nit° Gargamelle propane 0 .4 5 + 0 .0 8 2(^Tpit°) — o — o • VT3lt + VnTt 0.57+ 0.11 ’ 2(^i+na°) V.. VpTtU 0.56+0.10 • jTpit0 1 J o . vnu 0.34+ 0.09 ^"pit0 • Vmt~ - 0 j 0.45+0.13 ^ pit v nit+ 0.34+ 0.07 - 0 - 110 - Table 3 .6 Coupling constant Evaluation by Abbott Weinberg Salam and. B arn ett s i n 2^ 1 /4 g V 0 .0 + 0 .1 0 .0 g A -0.55+0.1 . - 0 .5 UL 0 .3 5 + 0 .0 7 0 .3 3 dL -0 .4 0 + 0 .0 7 -0 .4 2 UR -0 .1 9 + 0 .0 6 - 0 .1 7 % 0 .0 +0.11 0 .0 8 Table 3 .7 Xin ran , WS-prediction Experimental value S e a ttle 876 - 23x 10- 8 .. (-.5. + 1 .7 )x10-8 Oxford. 648 -3 0 x 1 0-8 (-5.0+ 1.6)x10-8 . Novosobirsk 6 48 . -3 0 x 1 0 -8 (-49.5+5) x 10-8 - 111 - Table 5.1 Experiment.. Beam T arget Observed Obser r a te (%) FfieV) e v en ts ved v° i 1* HP WE V 350 l i q 160 p~p-+ - (0.40+0.08) s c i n t i llator, lro b f i l t e r 50 l i q 90 p +p ~ (0.27+0.09) V s c i n t i l l a t o r iron f i l t e r 0ITFR V 100 S te e l 67 p ~ p + - .1 V 100 S te e l . 28 p * p ~ — 1 CDHS V 100 Iron 257 p ~ p + - 0.49 Iron V 85 58 p y . -■ -0 .3 9 G argam elle ■ V 2-10 Freon 14 ^ir e + 3 0.3 1 + 0 .1 3 Wis-CERN- V 30 21X Ne-H 17 )i~ e+ 11 0 .8 + 0 .3 FNAL Col-BNI 30 64% Ne-H 204 u ~ e+ 43 0.5+ 0.15 LBL-Seat- V 30 64%- Ne-H 1 p ~ e+ . 1 0 .3 4 + 0 .2 3 Hawali - 0 .1 3 . + — 0 15+0 - 14- - LBL-Seat- V 30 .64% Ne-H 4 p e 2 -0 .0 8 Hawaii . FNAl-Hawaii- • y 30 64 % Ne-H 9 ^ ” e + LBL FNA1-HEP- V 30 64% Ne-H 6 p ~ e+ 1 0.21 ITEP-Mich - FNAL-HEP- V 30 21% Ne-H <1 p + e~ 0 <0.5% ITEP-Mich FNAL-HEP- ' y 30 •/ 64 % Ne-H 12 /p +e~ 7 . 0.22+0.07 ITEP-Mich ' BEBC ' y 75 ' 64% Ne-H’ 5 p ~ e + + ' 2 0 .7 + 0 .3 BEBC 1 y 75 64% Ne-H 11 p ' p •6 0 .8 + 0 .3 BEBC y 30 64% Ne-H 21 p ~ e + 6 0.41+ 0.01 C-W-B-LB1 y 50 45% Ne-H 40 p ~ p + 5 0.43+ 0.1 G argam elle V 30 . Freon 70 p p 8 0.62+ 0.18 skat V 2-30 Freon 8 p e 1 0 .7 + 0 .4 Table 5 .2 Gol-BNL CDHS HPWF' V .. . . HPWF V b-Quark/V alence Quark 3+ 2/ 5 + 2 / (9 .9 + 3 .5 ) (6 .6 + 6 .1 ) Table 5 .3 Experiment Beam Pp ^ t W en t a observed (BG) ... 6(3 p ) /6 ( 1 u ) 4 A ll E B> 120 GeV CDHS WBB 4 .5 GeV/c 76 (6 ) 4 ( 6 .6 ) (3.0+0.4)x10~^ ( 1 1 + 2 . 5 ) x 1 0 ~ 5 CDHS ‘ WBB 4 .5 GeV/c - • 6 (2.4+1 )x10~^ , HPWFOR' • . WBB 2 GeV/c 49 2 (6+2)x1:0-5 ( 1 2 + 5 ) x 1 0 - 5 Table 5 .4 Experiment Beam typ e in V Background r r r a tio ln^1 r a tio ... CDHS • , Narrow.band 47 30 8+5/ 9 CDHS Wide band 289 200 < 7 / 23. < 1 0 / HPWFOR- Wide band 38 18 12 + 5 / 2 Table 5 .5 E^GeV) Group,. • liver.t type ’ PX1(GeV/c) P12(G'eV/lc) P13( GeV/c; P14(6eV /c) EviS(GeV) — + c— in in cooo CDHS 9 11 - . 45 ' ". 9 71 289 HPWFOR n Y p .44 60 4. ■ 3 BFHSW ji+e“ e e~K°7Y .22 2.3 2 .0 0.9 32 Table 7.1 BEBC . • •’ CDHSB G argam elle e /f- 6+/h + NO/CO ( e + + e ^ )/ (/i+ + /U~) Eh>20 GeV Evis >1° GeV : W 20 Ev is> 5 ° W 10 6eV 0 mr 0 .0 7 0.09 0 .3 0.16 0.12 0.0 7 Expected 15 mr 0 .1 6 0 mr 0 .3 7 0 .8 0 0.86+ 0.08 0.0 2 + 0 .0 2 0.19+ 0.02 0 .5 6 Observed 15 mr 0.6 7 - 114 Figure Captions 1.1 Experimental set up at SPS 1.2 Deep inelastic scattering (see text) 2.1 Evaluation of from quasielastic CC' v sc a tte r in g 2.2" Charge current cross-section ratio on neutron aM protoil ta r g e ts . • ( - ) (-) 2.3 Cross-section for j) N ^1"X- as, a function of V energy 2.4 • Ratio of; V to ^ CC cross-section as a function of energy 2.5 Piot. Of • • - p • 2.9 Test of callan vross relation in x and Q Bins 2 2.10 Structure function integrals as a function of Q 2.11 Plot of log of F^ Nachtmann moments for various N-values 2 - 2.12 Q dependence of F^ Nachtmann moments 3.1 Evaluation of gA and gy from V-e elastic scattering data 3.2 pit0 effective mass plot in the reaction vp -* V p^° 3.3 Experimental set up for polarised e-d scattering experiment 2 3.4 Evaluation of sin ©w from various measurements 4.1 Average hadron charge m ultiplicities in ff and bins 4.2 Average hadron charge multiplicity as a function of W (with a cut in z) 4.3 Fragmentation function distribution from various experiments 4.4 z-distribution of fastest positive and negative hadrons - TT5 - A»5 "Charge particle correlation for negative, anil positive p a r t i c l e s .4*6 .Pj distribution of hadrons in charge current events 2 P 4 . 7 4.9 Probability of 3-jet production in CC V. interaction 4.10 ,; V°. m ltip licity as a function of x in CC v interaction. 5.1' - Various mechanisms for dilepton production. • 5.2 Dilepton rates as a function of V-energy 5.3 x and y distribution for the leading lepton in dilepton ssCmple 5.4 .. Various mechanisms of trimuon production 5.5 Trimuon rate as a function of ^-energy 5.6 Effective mass of two non leading muons in trimuon sample . 5.7 >pj distribution of . the non leading muons with respect to q 5 .8 Azim uthal d is t r ib u tio n o f th e n onlead in g muons w ith respect to the leading muon 6.1 Kitx mass distribution in CC sample of.Col-BNL group 6 .2 L im its on h e a v y .le p to n mass from-CDHSB group 6.3 . mass distribution for;the tv.o BEBC groups 7 .1 Beam dump experim ental s e t up a t 3PS 7.2 -Prompt lepton to n ratio observed in various experiments 116 - imuMip Mur iumi hadron (mass* W N (mass= m) Energy=EH) " (G e V /c 8) b e 1 - 117 - ay .a • - EC CSPSI 8E6C C1TPR(FNAU * v GGM • HPWF o C1TFR o CDHS o o o o o E GeV FIG 2/ as °O0o^ 0 *• !02 ’ e 4* v v oCD • A SKAT o Am 0 P'ANL * *» < • ■ CDHS oo GGM/BEBC 005 * 15FNAL e e o -a • o ► " ITEMHEP ox m*nox ci 01 o wO^tflaj-n 002 _j_ 1 100 10 E GeV FIG 25 E • 30-90 G«V £ • 90-100 GeV . I to) lb) * O 05 O' 0 0 0 -2 0 -4 0 6 0*8 1-0 0 0 02 0-4 0*6 0-6 t y . FIG. 2*8 * 0 5 ri5 M 0 -4 SO 9 0 0 0 3 * 00 0-2 0*4 0-6 0 8 10 K FIG. 2 8 1C) • Leg el momtM • IUMIQUI |0 6 o i FIG. 31 20 X 1-09 1-29 MASS (pv*) (OeV/c8) FIG. 3 2 121 - SEAM MONl TORS I CURRENT • ; ENERGY 1 POSITION a n g l e ______. * 3 q A s SOURCE}1 U COMPUTER TO ELECTRONICS TO ELECTRONICS Fig. 3.3 o, F I G . 3 - 4 w-e-to GeV W-6-8 GeV 4 :‘f" 1—*r—4----- W *4-6G #V ;y~*~j-- 3 c W« 3-4 G eV 2 4 ■W-2*»3GeV 9 2 « * - * « 2 4 8 l« 92 64 Q* GeV8 FIG . 4 ‘ l • Ivwlth Z 9*2 o h'w lth Z >*2 5 IO per e v e n t O-l W (GeV) L - 123 - ■ ‘■ps A V •2-1 A ISI or V FIG. 4 3 001 0001 o 2 4 6 8 10 Pf (CeV/O2 . FIG 4.6 2/N z> 0.2 1/ N 0.8 ® QCD - LP5 all z 0.2 ,2 FIG 4J - 124 - 0 6 (A) 0 3 0 (B) (O . W > 6 G fV /0 - L P S - L P S — L P S 0 4 0 20 »-.f.0CD v> blb V 0*2 0 10 01 001 2 0 20 0 8 1*0 W. GeV/C FIG. 4-8 *b 410FIG. 125 - T j h e d r o n s J hadrons (E) FIG. 5 I CDHS O-Ol Cd-BNL o-oos 0-01 00 0 0 0 5 0 0 0-0 50 100 150 200 E (GeV) FIG. 5 2 126 HPWF COL-BNL 100 100 60 80 60 60 40 40 20 0-9 i-0 0 0-9 10 o 0 5 10 0 0-5 X VIS Yvis FIG 3-3 (O) hadron h o d ro n (B) r (4£) • MPWF o CDHS -5 SO 100 ISO 2 0 0 Evig(Gev) FIG, 5-5 (CeV/c) — HMU 20 4 0 30 10 20 0 0 I 2 3 4 0 6 0 120 180 Moss (M2 M3 r (GeV) < degrees) . FIG. 5 6 FIG. S B 4 j »$3 ai P» q X NUMBER OF EVENTS EXPECTED - 831 - K B C GGM P, > GtV/c SPS — ,0- beam r f Yvls>0-5 (w b) r COS 0 > -0 8 CDHS beam ' FIG 7.1' OS 10 IS 2 0 25 3 0 3 5 2 10 Mass I/T 7r*)(GeV/Cz) 30 NB Ne P* > 2 GeV/c 10 20 VIS>0 S COS0>-O-8 5 10 6 10 IS 2 0 2 5 3 0 10 100 200 300 MASS(>i-ir*)( G eV /C 2 ) 0 E; GeV FIG. 6-3 FIG 7.2 ■ - 130 - BISCUSSIOH Probir Roy: QCD has a specific prediction for the Callan-Gross relation, at finite Q^, i.e. R a S ^ « Is there any v ■ - Q - verification of that in neutrino scattering? S. Banerjee: Violation of Callao-Cross relation gives rise to a linear term in y in the differential cross-section. Due to biases in the experiments, it is hard to obtain a reliable y-distribution. So the validation of Callan-=Gross relation can be tested only within a large uncertainity. As fa r as I know, no experiment has y e t managed to obtain p data senative enough to test the Q dependence of the v io la tio n . K.V.l. Sarmas"1) Evidence for Callan-Gross relation from V data assume the validity of charge symmetry, which itse lf may be violated. Perhaps the best evidence f*r this is /• 2 X F , - j j ' = 0.25+0.1 (g iv en in the recen t review o f Hand) coming from electron scattering experiments. 2) Regarding the observed parity violation in the e d experiment it is difficult to associate it unambiguously to neutral current or to electromagnetic interactions. What y all we can say for the present is that parity violation is observed in the scattering of ed experiment. v - 151 - I. Das: Ion presented charged current cross-section data for the proton and neutron targets separately. These would give the integrated distribution functions for the u- and d-quarks. I suppose these numbers are consistent with what one would obtain from the electro-production experiments. S. Banerjee: In principle, one could test that.I am sorry, I do not know how w ell th ese numbers t a l l y w ith the electroproduction data. e Hew Particles Avlnash Khar* Institute of Physics, A/105 Sabeed Hagar Bhubaneswar-751007, India I. Intrp.fafttlofl Almost every ohild ask a his parents as to where he/she has oome from? In his/her own way the child is worrying about the origin of life. After some more years he Starts enquiries about the mysteries of the universe and when be has somewhat matured he bothers about the constituents of Matter. These three' are probably the most fundamental problems which have been worrying human beings for oenturies. In this talk however my aim is modest, I will only concentrate on the progress that we have made in the last two years in understanding the third question. Since last few years it is widely believed that quarks and leptona are the constituents of nature and that their number is equal and atleaat four. Whenever I think about the status of quarks I yg reminded of the following quotation of T.H. Huxley 'It is the customary fate of new truth to begin aa heresy and end as superstition'. Undoubtedly, quark la no more heresy though probably not superstition as yet: In the.quark model the mesons are made of qq while the baryona are made out of qqq. All the hadronic systems can be divided into following 3 categories: 1. < ^ $ 2 ^i belog charm or heavy quark 2» Qt$ 2 q - u, d, s quark 5. All other combinations. - 1 3 2 - - 133 System (1) i.e. bE , cc etc. to atleast zeroth appro ximation can be described by two-body Schrodinger. eq. so that one .can extract a lot of information regarding quark- antiquark potential from a study of such bound systems. System (2) i.e. D ( cu ), F( cs ) etc. are not so in teresting as mg- ” mg so that to zeroth approximation it is equivalent to one-body problem that is almost indepen d en t o f mg. Thus such system s are alw ays r e l a t i v i s t i c . System (3) includes a ll Earyons,Baryoniums, old meso ns etc. This whole category is terribly complex and proba bly w ill not shed much light about strong interaction be tween quarks. Hence I w ill not talk about these objects any more, but w ill mostly concentrate on mesons belonging to category (1). Throughout my talk I w ill assume that the quark dyna mics is described by QCD, a non-Abelian gauge theory of st- fcmg interactions in which colored quarks interact via ex change of an octet of colored, massless, gluons."In parti cular I w ill make use of the following ingredients of QCD ( which are no doubt valid at the hand-waving level but a rigorous proof is lacking): (1) QCD is asymptotically fr ee (2) quarks are in 3 colors and are confined (3) all flavor dependence stems from quark mass effects (4) the interaction between stationary quarks is given by local, spin and flavor independent potential (5) OZI rule. - 134 - I w ill follow the. following plans In Sec. 11^. I w ill review the present status of the .charmonium model.In Sec. Ill, I w ill have a quick look at the " open charm " as re vealed by D ' and F mesons.' In Sec.IV, I w ill talk about the startling discovery of heavy leptoiy "C and. 2^ . Now that one has six leptons it is natural to expect that there must be six quark flavors too. Lo and behold fifth qua rk itbeauty) has already been found.’Fermilab and DESY both have seen bE bound states and I will devote quite a bit of time in discussing hidden beauty (sec.V). With so. much support for quark-lepton symmetry one is almost sure that the sixth quark t (taste) must be there. The proper ties of the tt bound system are speculated in Sec.VI. In last section I summarize our present understanding about tte constituents of matter. I I . Charmonium Just within four years, the -spectroscopy has bec ome one of the richest in hadron physics^. Fig. (1) shows the known charmonium levels upto 3;8 GeV. Qualitatively th is spectrum had been predicted just after and were discovered (but much before other levels were found) on the basis of a simple minded charmonium model. According to th is model T^i , y * , ...... are the bound states of charm quark-antiquark (cc) system which to atleast zeroth appro ximation can be described by nonrelativistic dynamics.The - 135 cc potential is assumed to be - Vf3z; = _ + VcCAl (2.1) where the fir st term is the one-gluon exchange potential which is expected to dominate'.at short distance while the second term is the quark confining potential which domina tes at long distance. Taking lattice gauge theory as a gu ide it is usually assumed thatVc(SU=09 t v/ith "a* being fla vor independent*. This model gives good qualitative fit to 2 2 the data not only for a t 0,2 GeV , K(m^,) "i 0.2, m =1.6 T GeV but also when K(m^ ) =. 0.4 0.5. A la QBD it is clear that the potential must generate spin forces by vector exchange. However nothing is known about the way sp in forces are generated by Vc(r) which can be considered to arise from multiple gluon exchanges.- Using 3pj data one can only shown that^ Vc(r) cannot be spin-independent. Further, if Vc(r) = ar it cannot gene rate spin forces by vector exchange alone**. Infact Vc (r) = ar can simultaneously explain 'sjty and 3p j It must be admitted that this choice of Vc(r) is not on the same firm footing as the one-gluon exchange poten tial .Even VG(r) = ar^ is consistent2^ with the experimentally observed ordering S(1S) ^ B (IP) B (2S) B (l$) ) . **Whether V (r) generates spin forces by vector exchange or 1 not can be decided by accurate determination of 1 p. mass i 5 3 as in the case of vector exchange M( p^) has been shown to be |(21M (l3px)-5M(l3p2)-7M(l3p0)) = 3562 + lO MeV. - 136 - splittings only and only if a fraction f ( ~ 6.1} of ar generates spin forces by vector plus color moment exchange and ( 1 - f ) by s c a la r exchange6^ ( fo r c o lo r moment —"A ~ "5 and a and mc as before). There is a serious problem for this model if one id entifies x(2.83) and x(3.45) with *t\ and »c c. respectively. One finds that there is serious disagreement 7) between theory, and experiment ; ( Table 1 ). Table 1 i Ml transition rates for charmonium P rocess Theory Experiment 40 % 1.7 % V —b “XCV^W V l) 9 % ' 2 .5 % 4 % 1 % fc(v '—)XCV«,s.)*T) X 8 x lO- 6 (6+4) xlO- ' This is really a serious problem because even for light mesons where nonrelativistic quark model is not expected to give good results, theory and experiment agree' within factor of 2 to 3. IWo solutions have been proposed to the Ml trouble * Cl) x (2.83) and x(3.45) are not "V\.c and and that the actual '*\c and are there within 100 and 50 MeV of T l'l' and 1 respectively. In this case detection of and is going to be quite difficult. But then what are - 137 - - 137 - < and x (3.^)2? .s65jJa£Et2 * ° W,£3 l;r-@i^^ialP);eeTh£i§<,-4-eVeihas been) detected- in » T/<|» -f-Y nd one iT-e-3 ‘dgEay-^natdneyhas experimentally i 'S c S. 6 } V ^(^124-yCCt. -C l-a ± t.2.)X\o T (2.2) (2,2) stfcax t»o-i S^fieti'thWff hand-theoretically we expect that —> 'M % - 7 ) x o-5 /• (2 .3 ) j/f t -£ & )<>-*-- 3 / > -I-Y) = \o k V V ' tig C2„s: ' ? donii?rting (2.2) and i(2.3) we predict that (*-€,) — ■* B(.X (3 i) -----* 7/vp-^Y) -&&}/• (2.4) 3 fci i lar& c which i s too large to be acceptable. In fact experimental (2=2) Andie-result (2.2)' indicates that ?x>(3;.-6)rist_a o * , 1 or 2 st- 3113,1 )«t:$ atie so that both radiative transitiops are El transitions. ' : Before finishing this, discussio^; of hidden charm let ‘sii ' ; me mention tht discoveiry of t"(3.77). Naively one would r-5ht feh«t ^ave''thought th a t x^/ ian d ;^ "• r(Bdth. being JpC = 1 ~ and va da I;-.* hote’. that-the data is also, consistent with a low mass >,-■ o s-t.at.e a t 3*18 GeV* - 138 - differing in. m afes ju st by 80 MeV) should have similar deo- ay rates, but experimentally Is narrow while U is broad ( £ 28 MeV) and decays almost lOOK to V °TP and d V even though i t is only 30-40 MeV above" the threshold for these decays. This Is a dramatic confirma tion of the OZI rule ( See F ig. 2 ). Thus even though we ha ve no rigorous understanding of OZI rule there is no~doubt- that it is a reality. III. Charmed Mesons ■ 3.1. Properties of D and D* s- If charm quark is present. then in addition to , one should also nave charmed mesons cq (q u>d,s ) possessing nonzero charm.By now pseudoscalar mesons b+ (cS), D°(cu), F+(cs) and vector mesons D*+, D*° and F*"*" have been detected. The masses of D* and D° are known very accurately11^ in V'(3.77) = 'VfeV3 ±o 9 y M y ■- ' i t V i i o g heY S -= ^ _ ■ = 50-to2» VNeV (3*1) 12) Theoretically, using N.R. quark model one finds 8 ■= 6.5 MeV. In the standard WS-GIM model, the charged weak curr e n t is g iven by V*- cosec( Qc being the -Cakibbo angle. This leads to selection rules PAGES 139 t0 140 WERE INTENTIONALLY LEFT BLANK - 1*1 - (2) 1V1-- ^ .0 .2 5 GeV, all data is consistent with 'Wl,, =o. ' • > -12 V (3) X ( f 1 C 3.5 x 10" Sec. which is consistent with the theoretical ^prediction at 2.8 x lo"33 sec. (4) Michel parameter ?= 0 .6 6 + Os 13 which strongly favours "C—^ coupling to be V-&. (5) S (. "C "*-» e ~ B C X ~ —9yW- ^ v ^ " ) - t&V- rules out that X is a pazalepton. Most likely "C is a sequ ential lepton with its own lepton number and hence own nu- etrino 7-^ . (6) Various semilptonic decay rates are in good agreement with the' theoretical calculations 19) as can be seen from Table 2 i ' .. .Thble 2s Semileptonic Branching Ratios of ~C Process Ebcpt1-. (%) Theory (%) (Branching ratio) -r —) tt v -z; . 7 .7 + .1.3 10 X —) K V j " < 1 ’.6 0 .5 -C - > 24+9 22 x A ,ur lO + 3 10 Now.that one has six leptons, the quark-lepton symmetry demands th a t there must be two more quark flavors.Remarka b ly enough, in last one year we have firm evidence for fi fth quark and we discuss it in the next section". -1*2 V. Bwuty , 5.1. Experimental situation!- Last year at Fermllab,Leder- 2 0 ) man group found strong enhancement, at. 9.5 GeV In the mass spectrum of dinuons produced In the 400 GeV proton- mcleus collisions: V* X ( Cuy T-fe) >yU4"/AA "X (5il) Their analysis shows that there are either two or three narrow peaks in th is region which they named as ~£ -£ z XT"). Recently kothf and ' have been seen at DESY in x _ 21) e e collisions . According to them 9 - z V>T/ =. )0 0 \6 t-oz ^eV ^ V\T , - w = => % a -t 10 < y \ y - $11- 4 V VCe(T) = vl + .ly Ve€( T Z) - 0 33t l« 'k«v (5-4) x A . T-5 keVMVA C-LO V/nr.) =. <=>0 keVv Vec A reunalysis of the Flax data with the above value clearly shows *r"as a fl 5.2. Analysis of the Datas- (l) The. most popular Interpretation of these new mesons *J*. " f ' and T " is that they are the ground and first two excited ^s^ bound states (J^c = 1~~) of fifth quark-anti- - 1*3 - quark(bE) system. It is a measure of the fantastic success of the cc interpretation of the 'V-family that , there is almost no dissenting note about, this interpretation. t jg (2) Since *T/"T > l are narrow enough to have appreciab l e f y *branching ratio, they must all lie below the thr eshold for decay into a pair of mesons Qq + qQ,- Thus where as ss just fails to have a narrow state ( -meson is Just above. KK), cc has two and. tb has 3 such narrow states i.e. as m^ rises the number of narrow ^s^ le vels below Zweig threshold seen to increase. (3) Hie story is similar to Nov,74 discovery of l/'V , ^^ except that unlike r j ' has never been clearly seen in pp' in te r a c tio n s. The reason fo r t h is is . that" whereas the *■£)'£*, production rates are T ‘ T/ • T " ® = V 0'3' 0 ,5 / ^ V > > > e , ( * (s.Cc) so th at / /; (4) Since T , "T,T are very narrow ~ 5 GeV. - 144 - (5) The charge of the beauty quark can be determined from which in the nonrelativistic approximati on is given by , e j t \vV_to))2- r ( V—^ e^" e- ) ^ ^ 1 M y (S,‘7) \4,<^0)l being the appropriate bound state wave function at the origin. Now from the leptonic decay widths of Tl.+ Jackson has derived an airpirical formula^ ± -)5 (5 .8 ) so that g(V) 1 6^ should be nearly independent of My.The plot of vs Mv (Fig.3) shows that the data cl early favours — ^ ahd not 4/9. (6) The. hadronicrwidths of ^ and 1 can be calculated from QCD a. la T A ’z'f* caseS. According to 0CD^^ VAT) T Vi-T- W > = v Y \ ^ (5.S) where O^s(,V\^,)l2:0-l5 is the quark-gluon coupling constant which is obtained from QCD by using the formula - L _ s T \ +^-«'s(n^)\vx(^/^) is.io) with = 0.19. Using the expression (5.7) tor V <7) 3 T ® - in (5 .9 ) we fin d th a t Vv(.T) = \9.5reA T) - -fc*.9 k«V •X e e - -',5.11) - 145 - which is somewhat smaller than the experimental value. 5.3. Potential Modelss— Since according to QCD, the quark- onium potential is flavor independent hence the popular charmonium p o te n tia l i£ co rrect should a lso exp lain the bE spectrum. Mi out 2 years ago the dependence of the qQ 26) spectrum was studied by using the potential (Z. 1)?. The predictions were (1) for m^ ^3 . 5 (6,10,14) GeV there will be 3 (4,5,6) narrow bound states below the Zweig thr eshold (Q V(T,T 1---^e.'^e*)=.(o-7vo-*i5) KeV Which are crudely in agr eement with the experiment numbers. (3) for 5 GeV,this model predicts that "YW-j./— 420 VWV which is badly in disagreement with the experimental mass difference of 558+ 10 MeV'. Thus it is clear that the conventional charmonium model is not correct1. Two alternatives have been suggested in the literatu re (i) it has been shown^8^ that if K(m^,) • is chosen to be 0.4 ~0 ^ 5 instead of 0.2 then is Qf the * This prediction is not a special virtue of the potential (2*. l) because fora wide class of potentials it has been y i ) #—* shown that YVrwhere n is the number of narrow 3 s^ bound states below Zweig threshold. For mc= 1.6 GeV we then get the desired results; i 146 rignt order of magnitude. Notice, that for this value of K one has also been able to explain 3pj /'j»"Ylc and 4,Z-Vl^ splittings^ It should be noted that whereaa , K(q2) is the quark-gluon coupling constant at space-like q2, 0^(q2) is - ' 2 2 the corresponding one at time-like q and at finite q the two eould in principle be different. Using data on Vy^CT) and V^C(T) it turns out that — 0.20 but data on scaling violations in deep-inelastic scattering indicates 2q) 2* that K(m^) could be as large as 04 ~ 0.5. However, r <3/f.,V> are now fco° larx3e unless mc - 1.2 which gives rise to states which are much more relativistic. similarly,for mbc:5 GeVz Pee(T z t ' ) also cane out to be too largef. (ii) Motivated by the apparent equality — 3o) has been suggested that QQ potential is C W ( | ) , 5 -1 2 ) for which the level spacings can be rigorously shown to be independent of For c=0.75 the chamonium spectra and 0311 be f i t ted approximately. However for 1 5 ( <»Vc1)cj is again too large so that the use of i,".R. approximation for charmonium is highly questionable*; Besides, this model is bit crude and has no theoretical ba sis in the context of QCD. In conclusion, there is no qua- rkonium potential which can explain bE and cc spectra simultaneously. My feeling is that we are missing some vi- „ tal-point ( may be N.R. appx. is bad for cc) and. that, isr 14 7 - why no model satisfactorily explains both cc and bb spec tra, 5.4, Model Independent Resultsr- The other approach which has atracted sdme attention in the literature is to derive results which would be valid for a class of potentials. Some of these results are (i) Relative Magnitude of Is and 2s wave functions at the origin* For cc as well as bb systems we find from the data on the leptonic widths that ^ Coj^ • 31) — Martin has shown that the su fficien t condition for (5.13) is " < o for a ll r. (5.14) j V, Notice that the quarkonium potential (2.1) satisfy ^ _ <;0 Vi for not only \ cC5i) - "O^'A ^ <, Needless to say that the logarithmic potential also satisfies this condition. From Martin * s sufficient condition it is clear that the QQ potential cannot be con vex. However nothing can be said about mixed potentials of the type V(?Z.j (o should suffice even for this case. This is because even for. large n Gupta and Rajaraman havti shown that V'V- -Co) \1 >, < \V1/ X^1x»yS Co) X \ (5.15) provided NCO) is finite and (5.14) is satisfied. What are sufficient conditions for \15.^Co)\ ^ \ R^(p)| ? This is relevant question for bE system as lp and 2p leve ls of it are expected to be below Zweig threshold and the decay rate for p-levels is proportional to Rp being the derivative of the radial part of the JL=1 wave 33) function. Unfortunately it turns out that sufficient conditions can only be derived* for p which is probably not relevant for the bE system. . 3 4 ) t.ii) Bounds on Decay Ratesi Recently Rosner e t a l. have derived the lower bound Vee ('T/T ) by making use of the inequality** ) ^/ ° (5.16) which is true for concave potentials (d^v/dr^ 0 for a ll i). i * Sufficient conditions, have also been derived for I < \ d v - 1*9 - Strictly speaking, their derivation is not valid for - f f . Besides, it is not clear if the quarkonium potential is rea lly concave or not. Infact even the class of potentials VC5>0 - “ fill. + agj\ ' otvic-L 1 ^ , ^ Z (5.17) are consistent with the ordering of levels. Using the fact that , for V(rj = ar® the dependence of \v^(o)^ is given by 3 and assuming that the m^ -variation of \ \^> to ) is smooth for the above potential, it has been shown that^^ > VeeCT/ T /') >, (2-07, \ \2.) keV (5 .1 9 ) L This again rules out 6 , -=. -L . UsincUsing similar similar technique technics it has also been shown that 3 rfx>— >,(&Ml) k«v (5,2 0 ) 5.5 Beautiful Mesons:- Undoubtedly the best way to detect beauty quark is to look for " beagtiful 0~ mesons “ B°(b3), B~ (bu?, 3° (bs) , ?(be) and their vector counterparts'. Since we have seen in Sec.Ill that as m- rises 9 VA _(.Gl5,) - V\ ( g >%, ) < v o _ V D ~ '' hence we expect that B*, G*, P* w ill decay dominantly by e.m. interaction i.e. p * ) — ) ^ C PJ -V Y . - 1 50 Infact it has been shown that the hyperfine splittings for all of them are nearly equal^ X 5.3 GeV and we expect to see them soon in PSTFX. The domi* nant decay modes of involve charmed mesons. The QCD 38) calculations indicate that the nonleptonic decays of 3°* are not substantially enhanced in comparison to the semileptonic decays which are expected to be about 2C $i The B° - 5° and — 5° mixing problems have been an alysed and it has been claimed that if "YV\^8 GeV ( "Tf\^ being the 6‘the quark mass) then this mixing is much lar ger than D° - D° and the CP-violating effects in B° - B° may be even Comparable;, to those in K°-decays 6. T este The situation as for today (Dec.6,78) is that there ' are 6 leptons and 5 quarks. What next 7 I am very confi dent that there must exist 6'th quark "taste" (after cha rm and beauty what elae '. ) as (i) Quark-lepton symmetry which has guided us so successfully demands it", (ii) If we want to build 317(2)^8)0(1) type of gauge theory then the cancellation of triangle anamalies require that no. of le ptons be equal to quark flavors, (iii) Natural suppression of &S-I and -1 effects to can only be retai ned in that case, (iv) CP-violation can be naturally - 151 - incorporated in SU(2)^® U(1) gauge theory only if there are six quarks. These arguments are so powerful that I am ready to bet for its existence*. Its expected charge is 2/3. Remembering that i GeV, tt 3 GeV, vvVp= 9.$GeV I conjucture that the lowest 3Sj state of the tE system w ill be around 28-30 GeV so that** ^ = (^>3st ~ 5eV (6-3) S- Using the analysis of the last section i t is then clear that 6 narrow 3s levels are expected in tt spectrum fcel- 1 _ _ ow the Zweig threshold % -V ^^/(q=u,d).. Using Jackson's phenomenological.formula \«\tojyL and ( vV,'V ) the leptonic and hadronic widths of ^ and can be estimated. I find that40^ k«V C J ( 6 .4 ) v/here 0.13 has been used. From here i t turns out that - ~ V ' c - \ A ,a..stC )\V ~ ^ (6.5) * Let us hope that "taste" w ill bediscovered by the time we again meet two years from now. I hope that the organ- . izers w ill reveal the same taste as they have shown in selecting this pink city to celebrate beauty. **In th is context i t is encouraging to note that dimuon d~.~ ta at Femilab in pp collisions does not find any peak upto 18 GeV. - 152 - (upte that V\ ^ - 3-2 ±-7 and p lation of mass splittings, decay rate etc. for tt system is therefore quite straight-forward. In particular a la po- sitronium one would expect that VV'"S _ !2 l . * 7 Concluslons There is no doubt that qualitatively the nonrelativi- stic quarkonium models explain the cc and bE spectra very well. However, at ,a quantitative level the situation is not so good and infact there is no model which satisfacto rily explains both cc and bE families. With lot of data expected in coming two years from PETRA and 8BP let us ho pe that the theory w ill be in a better shape by the time we meet next time. Anyway there is no doubt that by any standard, the success of the quarkonium model is phenome nal'. Infact our understanding of cc and bb families is much better than that of lighter mesons. The picture that emerges regarding constituents of nature is: we_have 6.1eptons and 5 quarks and—it-is almost - 153 certain that a sixth quark will be found soon. Is that the final number or the number of quarks and leptons w ill go on increasing ? Asymptotic freedom te lls us that there ca- 41) nnot be more than 16 quarks A better bound is obtained 42) from astrophysics which indicates that number of leptons cannot be greater than fourteen. The point is that any new neutrino (with YVt^lO KeV, ~CCv) few sec) would have increa sed the energy density during the early stages of the expa nsion of the universe. As a result the rate of expansion is 4 speeded up which affects the He abundance in the universe. The observed upper bound of 29% on the cosmic helium abund ance implies that number of neutrino types is ^ 7. At a deeper level I wonder if quarks are indeed small est constitutent of hadrons or not. It is quite possible that quark will turn out to be “Just yet an&ther sari of Draupadi**. Acknowledgements It is a pleasure to thank Virendra Gupta,and S.P.Kis- ra for constructive suggestions1. * In the classic Indian mythological epic " Kahabharatha" the story goes that once Dusyasan tried to take off the sari of Draupadi in front of everyone present in the co urt of his elder brother. She prayed Lord Krishna and the unbelievable happened i As Dusyasan took of one sari, he found her covered with another sari and i t went on and orf. Finally he gave up ■ 154 r.oturonces I. Some good reviews on charmonium are Y.Hara,Rapporteur talk at XIX International conference, Tokyo (1978);T, Appelguist et al. To be Published in Ann. Rev.Nucl.Sci; G.Feldman and M.Perl, Phys. Rep.33, 285 (1977);V.Gupta, Phenomenology of New Particles, TIFR (1978);K.Gottfri- ed. Invited talk at Humburg Conference (1977). A.Martin, Phys. Lett. 67B. 330 (1977); H.Grosse, Phys, Lett.68B. 343 (1977). 3. D.Pignon and C.A.Piketty, Phys. Lett.74B, 108 (1978) 4. A.Khare, Nucl. Phys. B14Q. (1978); Phys.Lett.73B, 296 (19 7 8 ). 3. V.Gupta and A.Khare, Phys. Lett.JOB, 313 (1977). 6. L.H.Chan, Phys. Lett. 7IB. 422 (1977);C.E.Carlson and F.Gross, Phys. Lett. 74B. 404 (1978). 7, G.Flugge, Rapporteur talk at XIX International Confer ence, Tokyo (1978). 3 . H.Lipkin, Fermilab Conf. 77/93 THY (1977). 9. A.De Rujula and R.Jgffe, MIT-CTP/658-77. 10. G.Flugge, Ref.7 II. P.Rapidis et al. Phys. Rev.Lett.39, 526 (1977). 12. K.Lane and S.Weinberg, Phys. Rev. Lett'. 32, 717 (197 6); H.Fritzsch, Phys. Lett.63B, 419 (1976). 13. G.Feldman, Repporteur talk at XIX International Confe rence, Tokyo (1978). - 155 14. J.B ills etal. ;:ucl. Phys. Bloc, 313 (1975) .-r.Cabi'cko and L.Maiani, Phya. Lett.73B. 418 (1978). 1 5 . P.Rapldls et al. Ref.(11). 16. R.Brandellk et a l., Phys. Lett.ToB, 132 (1977). 17". R.Brandelik et al. Phys. Lett.73B. 109 (197c). & good review Is by M.L.Perl, Invited Talk at Humburg Confe rence (1977). 19. N.Kawamoto and A.I.Sanda, Phys. Lett.76B, 446 (1978); F.Gilman and D.M iller, Phys. Rev. D17. 1846 (1978). 2 0 . S.W.Herb et a l., Phys. Rev. L ett.39. 252 (1977);H.R. Innes et al., Ibid 39, 1240 (1977). 21. C.H.Berger et a l., Phys. Lett. 7 6B. 243 (1978);C.W. Darden et a l.. Ibid 76B. 246 (1978);J.Blenleln ibid 78B, 360 (1978);C.W.Darden et a l., ibid 78B. 365(1978) L.N.Lederman, Paper presented at XIX International Conference, Tokyo (1978). 23. J.E llis et al., Nucl. Phys. B131. 285 (1977). 24. J.D.Jackson, Proc. S1AC Summer Institute, 147 (1976). 25. T.Appelquist and H.D.Polltzer, Phys. Rev. Lett.34,43 (1975); Phys. Rev. D12. 1404 (1975). 26. B.Elchten and K.Gottfried, Phys. Lett. 66B, 286(1977). 27'. C.Quigg and J.Rosner, Phys. L ett.72B. 462 (1977). 28. C.Quigg and J.Rosner, Phys’. L ett.7IB, 153 (1977);D.Pi- gnon and C.A.Piketty, Pnys. Lett.74B, 108 (1978). 29 . A.De Rujula et a l., Ann. Phys. (N.Y) 103, 315 (1977); R.G.Moorhouse- et a l., lJucl.Pnvs.B124. 285 (1977). - 1 5 6 - 30. C.huigg and J.Rosner,Bef.28, 31. A.Martin, Phys. Lett. 7QB. 192 (1977). 32. V.Gupfca and R.RaJaraman, Tb be published In Phys.Rev. D. 33. A.Khare, IP/BkSR/78-15. 34. J.Rosner e t a l. Phys. le t t . 74B. 350 (1978). 35. A.Knare, IP/BBSR/78-9. 36. A.Knare, IP/BtiSR/78-14. 37. A.Knare, Pnys. Lett. 79B. (1978). 38. J .B ills et a l., Ref. 23. 39. J .B ills et a l.. Ref. 23, A. A ll and Z.ZAydln,DE&Y 78/17. <0. A.Khare, Under preparation. 41. D.Gross and F.Wilczek, Pnys. Rev. Lett. 30.1343(1973) H.Polltzer, Ibid 30, 1346 (1973). 42. G.Steigmann e t a l., Phys. Lett. 66B ,202 (1977). - 157 Figure G aptioa Fig.1. Charmonium spectrum Branching ratios of Y* -decays; a = 7 +2% ,b = 7 + 2%, C = 7 + 2% , d = 16 + 3%, e = 23.4 + 0.8%, f = 3.3 + 1.0%, g <2.5%, h < 1.0%, ig £"0.5%, j <_ 1.7%, kl= 0.28 + 0.12%. Data are taken from ref.(7), Feldman et al.ref. (1) and Phys.Lett.75B. 1 (1978) . F ig . 2-; Feynman diagram (a) for OZI - allowed decay V (3.77) — >Dl$ (b) fo r OZI - v io la t in g decay — i T/if -f- 2 .T T F ig .3. V( V ie+e“)/eg versus r f id *4-0 * -0 3df XX P*H - 15! - F it. 31 (b”) so Q = 9 0.3 0.5 H /G .V ) Fi«. 3 - 160 - DISCPSSIOHS S.P. Mlsra s (i) When you take K = .4 to .45 and e.g. get oorreet splitting for ^ and H e, still eto. puzzle of electromagnetic transitions remains. (ll) For B compared to B " the ratios are probably different just because branching ratios are different. Can that be so? A. Share i Teal You are quite right. The puzzle of *1 transition rates still remains. Yesi As I mentioned in my talk probably it is b ecau se - jn"/u~) » B(V- S.R. Choudhury : 1. You said that the linear rather than logarithmic is more natural from the QCD point of view. Could you please elaborate on this. 2. You quoted the mass 5 GeV for the b-quark. But this in a continued theory is just a parameter and is therefore model dependent. What is the stability of this figure 5 GeV? A. Share i 1. What I had said was that V(r) m =j£ +ar is more natural than (leg(~) from QCD point of view. Prom QCD we expeot°that at short distance the potential should go as -1/r. At long distance ofcourse the only require ment of confinement and VQ(r) - ar*1 o<1 2. Certainly, m^ is a parameter In potential models. Humber of calculations have been done In the literature and they seem to Indicate that m^ lies between 3,5 and 5 GeV. R. Ramacbandran : 1) If X (2.83) Is baryonlum, we should expect it to be even more narrow than In view of its double forbiddenness, a la OZI rule. Is there an experimental Indica tion of this. 2) Is there a theoretical motivation for linear potential? A* Share : 1. Experimentally, I think, X (2 .8 3 ) appears to be broader than J /f . 2. There la no theoretical motivation Her pure linear potential. However, from QCD there is definite motivation for THEORETICAL STATUS OF WEAK AND ELECTROMAGNETIC INTERACTIONS L.K. Pandit Tata Institute of Fundamental Research Horn! Bhabha Road, Bombay 400005. Mld-1978 has seen a turning point In the theory of weak and electromagnetic interactions. While prior to that date numerous renormalizable spontaneously broken nonabelian gauge symmetry models, attempting a joint description of both these classes of interactions, were in the field; after it, due to dramatic develop ments in the experimental situation, most models have been ruled out. In excellent accord with most of the experiments is the simplest of a ll the models, namely the original SU 2 ® gauge model of Weinberg [l] and Salam [2] extended successively first by Glashow, Iliopou- los and Maiani [3 ] and then by Kobayashi and Maskawa [4]. In the present report this extended simple model w ill receive the spotlight. 1. The standard SU., Q gauge scheme with four leptons and four quark flavours. Let us very briefly recall the essential features of this, by now very w e ll known, scheme. (i) The left-handed components of leptons and quarks are arranged as doublets of the SUg , while the right-handed components are all taken as singlets: CL , , I ; etc. (doublets) (l) "l / eR ' ^R • UR ’ ^R ' bR ’ CR ’ e t c * (slnSlets) (2) - 162 - 1 6 3 - If the Ve aHd are taken strictly massless, and occurring only as left-handed particles, the above choice is strongly sug g e ste d . (ii) tie must certainly go upto 4 quark flavours, so that the above scheme has no strangeness-changing neutral currents (GIM[3]) when dZ and sz stand for the conventional orthogonal Cabibbo rota ted combinations of the quarks d and a. With fractionally charged quarks (charge + ^ for u and c and - i for d and s), each coming in three colours, another desirable property is then also present, namely, that axial-vector anomalies get neatly cancelled between the leptons and the quarks as pointed out by Bouchiat, Iliopoulos and Meyer [ 4 ]. The extension to six quark flavours (Kobayashi and Maskawa[5]} and six leptons (including 3)^ and x). w ill be discussed in some detail later. To begin with we ignore these additional flavours and leptons. (iii) On writing the SU2 & gauge invariant Lagrangian, we obtain interactions of the triplet of gauge vector bosons V^- (i = 1,2,3) coupled,with strength g to the currents of the SU2 generators T^ (i = 1,2,3), and the interaction of gauge vector boson singlet coupled to the generator TQ of with strength g7 . The e le c t r ic charge Q = T^ + TQ . The gauge symmetry is spontaneously broken down to the elec trom agnetic U^(Q) gauge symmetry, in the sim p lest manner th at works very well, by arranging to give (through choice of a suitable potential) a non-zero vacuum-expectation-value to the neutral member o f a complex s c a la r Higgs doublet ( Diagonalisation of the mass matrix of the vector bosons so gene- ± o rated gives the eigen-states , A^ . The field A^ is massless and couples to the (minimal) electromagnetic current of Q. W" are charged massive intermediate vector bosons and Z° is a neutral intermediate vector boson. Z® and A^ are orthogonal combinations of and : Z° = cos6v W + sin 6 v A^ = - sinev + cos6w Bg , (3) where tan6v = g'/g . my - i gana » = m y/cos26w . (4) (iv) For phenomenological purposes, it is useful to note + that the couple with strength g/f2 to the currents of T^+iTg . couples with strength e to the current of Q, where e = g sin 0 w ; (5) and Z° couples to the current of (T^ - sinJ8y Q) with strength g/cos6y(=e/sindy cos6y). The universal Fermi coupling constant G for the effective + four-fermion interaction mediated by V" is given by Q- = - s L = ^ - . ( 6) ( 2 8 mj . 4>i8 2 . Charged-current Interactions (Leptonic and Semlleptonlc) The theory has all the usual desirable properties in its charged currents, strangeness-preserving as well as strangeness- 165 changing. The Cabibbo universality has been built in. Properties of CVC, PCAC and current algebra are a ll present (assuming that the strong interactions are described by QCD). No second-class- currents occur. So all the conventional pure leptonic and semi- leptonic processes are automatically well described by it. The additional, comparatively new, feature is, of course, the presence of charm-changing currents with specific Cabibbo factors. The latest experiments on charged-current V,V deep-inelastic scattering experiments [6] find adequate explanation. No right- handed fermion couplings are required. There is no longer any 'high-y* anomaly, etc. The dilepton production by neutrinos, along with associated production of strange particles, is well accounted for in terms of oharm-changing pieces of the charged-currents [7]. The current- current interaction with these pieces also is in accord with the data on the weak decays of charmed p a r t ic le s . The trimuon production events are accounted for [6] in terms of conventional mechanisms: besides the usual p produced by the one has a p-pair by (l) internal bremsstrahlung followed by p-palr production and (2) hadronic p-pair production (from charmed hadrons). No new heavy leptons or quarks are required for these events. 3. Neutral-Current Interactions. (a) Neutrino-reactions. An immense amount of data on neutrino induced neutral current interactions (inclusive deep inelastic' neutrino scattering, elastic Vp scattering, single and inclusive n production) has. 166 - been accumulated recently [8]. Phenomenological analyses (avoid ing any specific gauge models) using these data have been carried out by several authors In the spirit first pursued here by Raja- sekaran and Sarma [9]. From such analyses the chiral neutral current V-quark (u,d) coupling parameters can be extracted [10]. We quote the Abbott and Barnett [10] fit:- Leff “ ~ (1+y5^ [ (0.33+0.0 7 ) u Y? (1+y5)u +(- 0 . 1 8 +0 . 0 6 )* * u y ^(1-Y 5 ) u + (-0 .40+0.07)d Y^(l+Y5)d +(0.0+0.H )dY?(l-r5)d] (7) For the standard SUg ® gauge model, the corresponding parameters are (for sin28w = 0.22): 0.35, -0.15, -0.43 and 0.07, respectively 5 the agreement is excellent. Theoretically the cleanest neutral current processes are (V^e) and (V^e) scattering. However, the cross-sections being very small here, their experimental study is more difficult. Here the picture had, for a while earlier this year, become disturbing for the standard model; but, soon after the clouds disappeared and the latest high statistics data (for review c£.[8]) agree with the standard model with sin2©w sz 0.22. (b) Electron-quark neutral current interaction. (i) Atomic Bismuth Three experimental groups [ll] have so far reported results on their searches for the parity-violating optical rotation in atomic bismuth close to the allowed Ml transition from the ground state. In a heavy atom the dominant parity-violating effective - 167 -- potential arises from the coupling of the electronic A-current with the quark V-current (the nuclear A-current matrix element is small, being proportional to the nuclear spin). The perturbation caused by the parity-violating potential permits al3o a small El transition. The interference of the ffl. and the El amplitudes leads to the optical rotation. For R 5 Im " R= 2.4+4.7 , ( X=6476A ) (Oxford) : 0.7+3.2 , ( X=8757A ) : (Seattle) (8) -19+5 , (X —6476A ) : (N ovosibirsk); „ At the Tokyo Conference (August 1978)> revised numbers (unpublish ed) from Seattle (-0.5+1.7) and Oxford (-5+1.6) were being, men-' tioned. The Standard model, with sin20y. Oi 0.24 leads to R= -(13-23). at 6476a and R = -(10-18) at 8757A .depending on the details of the atomic physics calculations (central field theory with shield ing). The theory disagrees with the Oxford and Seattle results, while not with the Novosibirsk result. The issue is. clearly unsettled both experimentally as well as theoretically. Complexity i " in the atomic physics calculations, having to deal with 83 electron^', bedevils the situation. (il) Inelastic scattering of longitudinally polarised electrons off deuteron. " ; While the atomic physics, parity violation experiments.are s till far from being in a position to pronounce on the validity of theoretical models, light on the issue has come from a different kind of experiment. In the middle of 1978, a result became avail able from an experiment at SLAC [12] measuring the asymmetry - 168 - param eter 'led 5 = , (9) aR+aL for the Inelastic scattering of longitudinally polarized (R,L) electrons off unpolarized deu.eron. At y a 0 .2 1 , Aed = ( - 9 .5 + 1 .6 )x 10"5 lq2l /GeV2 . (10) According to the standard model [13] (using parton model) we have A d= - ——— [(1- ^slnaev)-t-(l-4 sin2ew) ] (11) ea 20V2 ita 9 w w l + ( l - y ) 2 The first term in the square bracket corresponds to A@ (electro nic A-current coupled to quark V-current) and the second term to VQ A^ . For ein26y - ^ * the second term is negligible (also y is small s 0.21). The dominating first term corresponds to Ae7^ - the very combination ox relevance in the parity-vlolation in heavy atomer. For the standard model (for y = 0.21) Aed /1*1*1 * -(9-7 to 7.2)xlO~5/GeVa, (sin20w = 0.20-0.25). (12) Thus thd e-d experiment gives good support to the model, although the detailed y-dependende s till needs to be checked out. All the experimental support for the standard model cited above is clearly necessary but not yet sufficient for the model. The important thing is that the simplest possible gauge model is working so well. In this connection I may be permitted to mention that it is not entirely ruled out that in future a more elaborate gauge model may s till be called for. Recently I have advanced two - 169 alternative U^-gauge models [14] that agree quite well with all the neutrino-neutral current data as well as the SLAC e-d asym metry measurement; while on the s till problematic parity violation in atomic physics, they disagree among themselves and with the standard model. 4. Nonleptonlc decays of strange particles. An outstanding problem in weak decays has always been that of a quantitative understanding of the non-leptonic decays of strange hadrons - specially the observed large |AI| = i (or octet) enhancement compared to the jAlj = | (or 27) transition. Since strong interaction effects are present in their fullest complexity here, non-leptonic decays are not considered as effective as the purely leptonic and the.semileptonic weak processes in deciding between various models of weak interaction. With the advent of an asymptotically free gauge theory of strong interactions - QCD - there has been renewed interest and some progress and promise in dealing with non-leptonic decays. It is generally assumed that the dominant short-distance behaviour of the (W-boson mediated) current-current interaction may give most of the non-leptonic interaction [15] on account of the large value of the W-mass, and that the short distance structure of the quark operators involved (the currents having specific quark structures in a gauge theory) may be perturbatively analysed on account of the asymptotic freedom of QCD (assuming it to be the correct strong interaction theory). This idea was employed some years ago [16] with some qualitative success. The QCD correction gives an enhancement of the lA ll = i channel of the order a 4 , whereas one actually requires an enhancement of the. order of d 20. 170 - The above treatment takes care only of the short distance part of the gluonic correction. It is possible that the unmanage able long distance part (surely of great importance for hadronic structure) makes important contributions in enhancing [All = i or suppressing the |A l| = | part of the weak non-leptonic ampli tude. The SU(6) wave function of hadrons (including colour label for the quarks) can possibly play an important part here [17] (specially in suppressing the |Al| = | matrix element), although in such arguments the difference between current and cons tit u e n t quarks makes fo r some con fu sion. Recently a new QCD contribution has been proposed as a possible means of enhancing the |A il = i amplitude [18]. This arises by the process shown in the accompanying figure: X jv y J UL.J V describing the process of decay of s^ to dL and a virtual gluon which then goes into a uu or dd^-system. Since the gluon has 1=0, an effective [Alt = -i' four-quark operator is generated in the process. Note that the result is non-vanishing only because the u and the c quarks are non-degenerate. This term could, according to the authors [18], dominate the conventional four-quark terms. An interesting consequence, if the above mechanism is chiefly responsible for the |A *1 = i enhancement in the strange - 171 - particle non-leptonic decay, ie that, since a corresponding^term in charmed particle decay (operator (cu)(uu+dd) A 8=0 ) comes multiplied by sln 6c , no significant non-leptonic enhancement w ill occur in charmed particle decay. This would he in accordance with experiment. 5. Extension to 6—leptons and 6—quark flavours. (a) (t.V^-leptons. Since the discovery of the t—lepton [19], a good deal of data on its decays has been obtained by various experimental groups working a t BEST and SLAC (SLAC-LBL, DBLCO, PLUTO, HASP e t c . ) . The data is best understood by adopting (9 (13) as a new doublet of SU2 ® U^ , sequentially to the (Ve e^) and (V1^,p-l) doublets. Then the comparison of theory and experiment is as given in the accompanying table [20] , • Mode Theory Experiment 0 .098 0.073+0.013 0.006 < 0 .0 1 6 Ai 0..093 0.10+ 0.03 X e X 'I 0.17+ 0.13 0 . 1 7 - 0 . 1 8 X * X 1 { 0.16+ 0.03 - 172 - (b) Anomaly; Weed f o r new quarks Inclusion of the doublet in the standard SU2 ® gauge theory reopens the anomaly cancellation problem. The sim plest solution is to assume the existence of two more hew heavy quarks t ( Q = > - ) and b(Q = — ) , each in th ree c o lo u r s, and 3 3 introduce the doublets (one for each colour). (14) This w ill once again ensure anomaly cancellation. The introduction of a new quark* most likely the b-quark, has already been necessitated by the discovery of the Tf-states (bb- states) [21]. (c) New quarks for CP-violation An extremely elegant manner of incorporating CP-violation was proposed in 1973 by Kobayashi and Maskawa [22]. Consider first the standard model with 4 quarks only, arranged as usual in left-handed doublets. Then the usual Cabibbo mixing is all that is allowed. To see this we note that the most general charged weak current has the form: (5i V ^ u(^ ) ■ - (15) where u,c,d,s are quark mass eigenstates and U is a general 2x2 unitary matrix. In general U may be parametrised as i6 , _ 16. e 1 cos© e 2 sin© u =1 1 6 . 1 6 . I , . ( i s ) -e 3 sin© e 4 co s© / x * 3 4 - 173 - The current (15) is invariant under a common phase transformation of all the four quark field s, but not under independent individual phase changes of the fields. Without change in the physics, we can thus introduce individual phase changes u -veiotu, etc., so that taking out the overall common phase we have 3 phases available to cancel out the 3 independent phases in U. What remains then is merely the Cabibbo rotation matrix: cos6 sin6„X - ® ° ) (17) (-sin6„ cos8„ / c c [Let us note parenthetically that a corresponding rotation among (Ve » 'space is physically meaningless if the neutrinos are mass-less, for the rotated as well as the unrotated combinations a. are equally eigenstates of the (zero) mass-matrix, and it isAmatter of convention what we call V and what X) . Once settled, there is "e * p separate conservation -of the electron and muon number.]. Thus it is clear that with 4 quarks and only left-handed quark doublets, no CP-violation can be introduced through a phase occurring in mass-diagonalisation. One way would be to also include right-handed doublets; but this possibility is not support ed by experiments relating to the charged current. Another'possi b i l i t y , suggested by Kobayashi and Maskawa, i s to introduce an a d d itio n a l left-h a n d ed doublet (t^.Tj^). , by in crea sin g the number of quark flavours to 6. Then in the standard SU2 ® gauge theory we have 3 left-handed quark doublets: ( 1 8 ) * - 174 - i t i Where d , a , b are related to the mass eigen-states d,s,b by a 3x 3 unitary matrix U t. d') M\ 8Z = U s (19) b'j \b / 1 How a general 3x 3 unitary matrix le specified In terms of 9 r e a l parameters. Of these 3 may be taken as (Euler) angles 6^(1=!,2,3) and 6 as phases-parameters. There are 5 nontrivial Independent phases which may be used In defining the six quarks (an overall common phase is trivial). Thus we shall be left with one non trivial phase angle, 6 , that may be used for introducing CP-viola tion . In terms of et = sind^ ., c^ 3 . cosO^ , 1 = 1 ,2 ,3 , and 6 we then have the weak-interaction left-handed quark doublets: Clearly now the usual Cabibbo universality, which Is good to 1 part in 1,000, [23], Is not naturally satisfied. It will be exact only fo r 9 2=6^=0 ; but then the lowest mass b-carrying particle would be stable - whereas experiments at FNAL [24] indicate that no new stable particles (v 55 10- 8a) e x is t w ith mass a 5-6 OeV. Prom universality considerations: s* a sinaec a 0.05 ; e1 ~ec czi30 s* < 0.06 e 5 < 16° . (21) Prom Am(K°-K°), one fin d s > 175 fg < 0.2 . (22) For the CP-violation parameter e in decay one finds e a2a^ ain 6 » 10”^ , (23) which implies that at least one of the parameters e2>®3 and 6 18 sm a ll. ~ The electric dipole-moment of the neutron is estimated [25] to be. Dn ~ 10”29 e cm. (24) The experimental lim it for D® is s till in the neighbourhood of -24 10 ecm, and so not-yet in a position to test the above estimate. For further material on the weak decays of heavy quarks in this scheme the review by Gaillard [18] may be referred to. 6. Comments and Speculations beyond the Standard Model. . The simple standard SU2 ® U1 gauge model of weak and electro magnetic interactions is, as far as the so far available experi mental results are concerned (save atomic physics parity-violation, where the situation is unclear both theoretically as well as experimentally), doing extremely well. However, it cannot be really considered as the final fundamental theory on account of the following reasons: (i) There are a large number of parameters in the theory, which have to be fed from outside. These are the various mixing angles (the Cabibba"angle ©c in the 4 quark theory or the angles ®1 , ®2 ,®3 P*1080 ® in the ® quark theory), as well as the various mechanical.masses of the feimions and bosons in the scheme. - 176 - (ii) While It Jointly describes weak and electromagnetic - - interactions with the bonus of giving the neutral current weak interactions, it does not represent a true 'unification’ of weak and electromagnetic interactions. For, it introduces two indepen dent gauge coupling parameters corresponding to the disjoint SU2 and gauge groups (equivalently, the two parameters g and s in 0w). To at least partially rectify the shortcoming (i)_ a-number of workers [26] have attempted to obtain the mixing angles in terms of quark masses, noting that all these parameters occur in the quark mass matrix generated through Yukawa couplings of the quarks with the Higgs fields and the spontaneous gauge symmetry mechanism. The trick lies in constructing Lagrangians with certain additional discrete symmetries. The difficulty in this approach is that in the presently successful minimal SU 2 ® gauge theory, with just one Higgs doublet, no such discrete symmetry exists [27]. Hence in all such attempts the minimal flavour group has to be enlarged, without any experimental-support for'such an.enlargement at present. To rectify the shortcoming (ii), one seeks a unified gauge theory employing for the gauge group a simple group (or a semi- . simple group with isomorphic simple pieces related by. a discrete symmetry) such that the SU 2 ® group of the standard model appears as a subgroup. Then there w ill appear only one gauge coupling constant and the parameter sin©w of the standard model w ill be deter mined purely through the group theoretical constraint implied by the above imbedding. The unification strategy outlined.above has, in fact, been - 177 - employed for grand unifications of the weak, electromagnetic and stron g in te r a c tio n s by a number of authors [2 8 ]. The sim p lest example of such schemes is the SU^ gauge theory of Georgi and Glashow [28]. The strong interactions are taken to be described by QCD, the SUj gauge theory. The (weak and electromagnetic) SU2 ® TJ^ group and the (strong) SU^ group are embedded in SU^ : SU5 Z> [SU2 ® t^ ] ® SU° . (25) The leptons and coloured quarks together are put in irreducible rep resen ta tio n s o f SU^. The SU^ gauge th eory, in v o lv in g 24 v ecto r gauge bosons, has to be broken suitably by use of appropriate Higgs f i e l d s , b a s ic a lly in two ste p s: M(X) „ M(W,Z) SU5 »"[SD2 @ t^ ] ® SU° ------> U-^Q) ® SD° . (26) At the first step characterised by a superheavy mass scale (M(X)) a ll the exotic vector bosons attain superheavy masses, correspond ing to 'hyperweak interactions' unobserved at present energies. At the next step the W.and Z masses are introduced to account for th e known conventional weak in te r a c tio n s . The embedding, im p lies the result [29] t r T2 sin28u = 2— . (27) t r Q2 For the assignments chosen by Georgi and Glashow [28], sin2©^= 2 . However this value applies in the SU^ gauge symmetric situation when the energies involved are large ^ M(X) . The strong in te r action renormalisation calculated a t th e much lower mass scale of M(W,Z) reduces it quite a bit to a value C: 0.2 (depending on the various.mass scales) [29]. MB - In a grand unification acheme, as the SU^ gauge theory, among th e many e x o tic hyperweak e f f e c t s im plied i s baryon number non-conservation,, which w ill make proton unstable. The presently available lim it on the proton life time Is [30]: x(p) > 2x10^° yr. (28) From this one obtains [29] on simple dimensional consideration that the superheavy vector boson mass M(X) 85 lO^GeV, The techni ques of the renormalization group equations are available in gauge theories to relate the effective coupling constants at different energy scales. At a scale characterised by a superheavy mass H 101® GeV for the SU^ scheme), one expects all the interactions, strong, weak and electromagnetic, to be characterised by the single unification coupling constant. At lower energies available to us today we see the differences in the effective coupling cons tants. Effects of renormalization of the highly symmetric values of parameters such as fennion masses, sina8y , e t c . , ob tainin g at unification energies ~ M, on coming down, to the present energies have been studied by various authors [29,31]• - Renorma lization group considerations of this, type lead in the SU^ scheme to a more specific value t(p) 2£ 10^-10^* yrs. So an improve ment of the experimental lim it on the proton life-tim e is a very worthwhile project. While the unification mass scale of of 10^ Ge7 will be essen tially inaccessible to us, there are certain unification schemes in which the unifying mass M is only 85 10*, [32], which may be accessible in the near future making many new effects open to ■** . experiments. - 179 Behind the elegance of the unification Ideas hide also some u g ly fe a tu r e s. The u g lie s t fea tu re i s the tremendous number o f Higgs fields that enter such schemes. Mass scale hierarchies as well as mass parameters and mixing angles remain theoretically unaccounted for. It could well be that the ugly features finally outweigh any real gains. It is possible that the requirement of .renormalizability is being overplayed [ 33] and that the present simple model of weak and electromagnetic interaction represents only a phenomenologically useful stage to be supplanted in the future by a framework unforsee- able today. . - 180 - R eferences [1] S. Weinberg, Phys. Rev. Lett. 12, 1264 (1967). [2] A. Salam, Proc. Eighth Rebel Symposium (Stockholm 1968), Ed. N. Svartholm. [3] S.L. Glashow, J. Iliopoulos and L. Maiani, Phys.- Rev. -D2 1285 (1970). , [4] C. Bouchiat, J. Iliopoulos and Ph.Meyer, Phys.Lett. 58B. 5i9 (1972). [5] M. Kobayashi and K. Maskawa, Prog. Theoret.Phys.49. 652(1973). [ 6 ] For a review cf: K. Tittel, Proc. XIX Intl. Conf. oh High Energy Physics, Tokyo (1978); and S. Banerjee, this Symposium (Jaipur, 1978). [7] For a review cf: C. Baltay, Proc.XIX Intl.Conf. on High Energy Physics, Tokyo (1978). [ 8 ] For a review cf: C-. Baltay, Proc.XIX Intl.Conf. on High Energy P h y sics, Tokyo (1978); and S. B anerjee, th is Symposium (Jaipur, 1978). [9] G. Rajasekaran and K.V.L. Sarma, Pramana 2, 62 (225B),(1974), and preprint TIFR/TH/78-44 (1978). [10] L.M. Sehgal, Phys. Lett.71B. 99 (1977); P.Q. Hung and J.J. Sakurai, Phys.Lett.72B. 208 (1977); L.F. Abbott and R.M.Barnett, Phys. Rev.Lett. 40.1303(1978) B. Paschos, Brookhaven preprint 1978 J.J. Sakurai, Proc. Oxford Neutrino Conf., July 1978. [11] P.E.G. Baird e t.a l., Phys.Rev.Lett-22,798(1977); L.L. Lewis et.al., Phys. Rev.Lett.22 » 7 9 5 (1 9 7 7 ); L.M.Barkov and M.C. Zolotorev, JETP Lett.26,379(1978). - 181 - [12] C.T. Prescott et.a l., Phys.Lett.77B. 347(1978). [13] For example see: R.N. Cahn and F.J.Gilman, Phys.Rev.D17, 1313(1978). [14] L.K. Pandit, TIPR/TH/78-43, paper No.1083 contributed to the XIX International Conference on High Energy Physics, Tokyo (1978). [15] K.Wilson, Phys.Rev.179. 1499(1969). [16] G.Altarelli. and L.Maiani, Phys.Lett.52B. 351(1974)? B.W.Lee and M.K.Galllard.Phys.Rev.Lett.33.108 (1974)• [17] R.P.Feynman, M.Klslinger and F.Ravndal, Phys.Rev.03.2706(1971): J.C . P a ti and C.H.Woo, Phys.Rev.DJ, 2920(1971); J.F. Donoghue, B.Holstein and E.Golowich, Phys.Rev.(to be published); C.Schmid,ETH preprints (1977). [18] M.A. Shifman, A.I. Vainshtein and V.I.Zakharov, JETP Letters 22, 55(1975); Nucl.Phys. B120. 316(1977); and JTBP -63 and 64(1977) (preprints). See also M.K. Gaillard, Lectures at 1978 SLAG Summer Institute, Fermilab-Conf-78/64-THT(August 1978). [19] M.L.Perl et.a l., Phys.Rev.Lett. 5 5 ,1489(1975). [20] For a review cf: G.Altarelli, Proc. of the XIX Intl.Conf. on High Energy P h y sic s, Tokyo (1978). [2 1 ] S.W. Herb e t . a l . , P h ys.R e v .L ett.2 2 ,2 5 2 (1 9 7 7 ). [22] M.Kobayashi and K.Maskawa, Progr.Theoret.Phys.49. 652(1 9 7 3 ). Phenomenology of CP-violation following this proposal has been studied by: S. Pakvasa and H.Sugawara.Phys.Rev.D14.305(1976); J_ Bills,M .K.Gaillard and D.V.Nanopoulos, Nucl.Phys.B109. - 213 (1976); L.Maiani, Phys.Lett.62B, 183(1976). - 182 - [23] A.Sirlin, Nucl.Phys.B71.29(1974). [24] For example, H.R. Gustafson e t.a l., Phys.Rev.Lett. 57. 474 (1978). [25] For a review cf: R.N. Mohapatra, Proc.of XIX Intl.Conf. on High Energy Physics, Tokyo (1978). [26] For example: F.Wilczek and A.Zee, Phys.Lett. 70B, 418 (1977); H.Fritzsch, Phys.Lett. JOB, 436(1977); 13B.317(1978): H.Terazawa, Tokyo University preprint (1977); H. H arari, H. Haut and J. Meyers, Weizmann I n s t, preprint WIS-78/22-Ph. A. Ebrahim, Phys.Lett. J6B, 605 (1978). T. Hagiwara, T. K ita zo e, G.B. Mainland and K. Tanaka, Ohio State Univ. preprint (1978). M. de Crombrugghe, to be published. A different approach to the Cabibbo angle problem has been pursued by P.P. Divakaran, TIFR-preprint (1978). [27] R. Barbieri, R. Gatto and F. Strocchi, Ph.vs.Lett.74B.344(1978). [28] H. Georgi and S.L. Glashow, Phvs.Rev.Lett.32. 438(1974); J.C. Pati and A. Salam, Phys.Rev. D8, 1240 (1973); for a review and more referen ces c f .J .C .P a t i, Univ. of Maryland Physics Pub.No.78-152, (1977); H. Fritzsch and P. Minkowski. Ann.Phys.(N.Y.)95. 193 (1975); F. Gursey and P.Sikivie, Phvs.Rev.Lett. 36. 775 (1976); P. Ramond, Nucl.Phys. B110, 214 (1976). [29] H. Georgi, H.R. Quinn and S. Weinberg, Phys.Rev.Lett. 33. 451 (1974). 183 [30] F. Reinea and M.F. Crouch, Phys. Rev.lett. J2, 493 (1974). [31] M.S. Chanowltz, J.B ills and M.K. Gaillard, Sud. Phys. B129, 5 0 6 (1 9 7 7 ); A.J. Buras, J.B ills, M.K. Halliard and D.V. Nanopoulos, Nucl. Phys. B135. 66 (1978); D.A. Boss, CEBIT preprint TH.2469 (1978) (Nucl.Phys.B. to be published); C.Jarlskog and P.J. Yndurain, CERN preprint TH.2556 (1978). [32] V. Ellas, J.C. Pati and A. Salam,•Univ. of Maryland preprint 78-041 (1977) ' See also H. Fritzsch and'P. Minkowski, ref.[28]. [33] For a very stimulating critique cf. J.D.Bjorken, Ben lee Memorial I n t l. Conf. .B atavia (1 9 7 7 ), SLAC-PUB-2062. - 184 - Discussions . H.D. Hari Daas : Even i f the Welnberg-salaxn models are verified experimentally it would aeem that unless we have an understanding of the mechanism by which spontaneous symmetry breaking take place we do not have a fundamental theory. L.K. Pandit The spontaneous symmetry i s Introduced through Higgs fields, with a suitable choice of the potential function. However, it is true that a more direct dynamical breaking, without use of such scalar fields, might be more satisfying. What would be the shape of a ’fundamental* theory is difficult to conjecture at this stage. A. Khare One unsatisfactory feature of the minimal SU(2) X U (i) model is that the Higg’a scalar mas a i s a rb itra ry . I t i s d if f ic u lt to believe that 'the theory1 of e.m. and weak interactions should have no prediction for Higg's scalar mass. Any comment? L.K. Pandit I agree S.P . Miara Could you elaborate on the Higgs sector, since thqy are theoretically needed in the ' standard' model? L.K. Pandit The Higga fields have very specific inter actions. However, as the^ mass of the Higgs particle is not fixed by the theory, very specific predictions about it are difficult to make. - 185 - R. Ramachandran • Can you comment.on cxurent status of Bjorken' a critique of gauge theories. L.K. Pandit Bjorken'e main criticism concerns the over-reliance on the renormalizability criterion. He has constructed a non-gauge theory model (introducing a charge-radlus for the neutrinos: SLAG-PUB-2062 (1977)) which can account for the neutrino neutral- current experiments. But his aim was only to stimulate alternative ways of thinking in this game, which is certainly a very healthy objective. Thermodynamics o f Quark Gas 3.H. BISWAS Department of Phyelcs and Astrophysics University of Delhi, Delhi-7 I would lik e to ta lk on th e ap p lica tio n o f quantum s t a t i stical mechanics to a system of particles consisting of quarks, now Believed to he the fundamental objects which constitute a hadron. The motivation for such a study stems from a remark by landau1 In 1932. With the discovery of neutrons, landau made an observation that stars with central density much higher than that of a white dwarf might be possible. White dwarfs have central density 10^ g/om^. Two years later Baade and Zwlsky2 confirmed that super dense objects do exist In the remnant of super-novae whose density could be as high as 101* g/cm^. In 1939, Oppenhelmer and Voikof^, starting from an equation of state of non-interact ing neutron gas and numerically Integrating the general relati- vistlo hydrostatic balance equation showed that neutron stars can exist whose central density is aA high as that pointed out by Baade and Zwlsky. Soon after and still today more realistic theoretical Investigations have been underway to understand these highly dense objects. Question immediately arises: What state of matters can arise If the density increases beyond 101^ g/cm^. Central density •» 101® g/cm^ can be seen In a neutron star core. The various possibilities have since been considered, for lnetancei (a) with the Increase of pressure when chemical potential of neutrons Increase, the residual electrons may be absorbed by neutrons with the formation of hyperons, thus forming a hyperon or a hadron1c resonance star, (b) neutrons may solidify with a possibility of crystalization (c) strong Interaction effects may generate plon field with the possibility of pion - 186 - — 187 condensation phenomena to occur and (d) lastly under high pressure if the neutrons come close and overlapp on each other then a very interesting situation can hapoen. It is now believed that hadrons are made of confined " quarks and when neutrons overlapp so closely that the constituent quarks do not remember in which neutron they belong to and as a result the core becomes a quark soup. It then seems more appropriate to consider t.he system as a gas of quarks and if quarks are point-like as we believe now- there can occur a state of quarks with arbitrarily high density. Thus many interesting questions arise, (a) Whether at such super density the matter can remain in quark phase? (b) Another interesting question whether a phase transition can take place from the neutron matter phase to quark matter phase; this is an important question from the thermodynamic point of view and (c) The Super dense system presumably occurs during gravitational collapse, as such the magnetic field strength increases and one now kncws t hat magnetic field strength as high as fo,3_ gauss is observed on the surface of a neutron star.' Thus collective property like spontaneous magnetization, superfluidity.and super-conductivity can also occur. I would like to report some preliminary results based on quantum chromodynamics and other phenomeaological models. . It is wellknown that interactions between quarks is realized through the exchange of an octet of .massless vector gluons satisfying S U ( 3 ) -color gauge theory in the Yang-Mills fashion.; An interesting consequence of this Yang Mills theory is that quark-gluon interactions satisfy asymptotic freedom; this implies in turn that at very short distance the - 188 - the quarks-gluon interaction is vanishingly small i.e . the quarks are almost free within a short distance inside a hadron. The masslessness of the gluons and the asymptotic freedom presumably also give bad long distance behaviour! the hypothesis is that it presumably gives confinement to "the quarks inside the hadrons. As a first aporoximation Collins and Perry assumed that in the super dense state the quarks are free. Assuming a strong degenerate system o.f quapks . at T = 0, they obtained the following expressions for the various thermodynamic quantities. Let be the fermi momentum for the quark with i-rf type of . flavour. Assuming the quarks as massless we have for the number density the wellknown result, Ni = * ~ Ult { W f • a where d stands for the degeneracy.factor and here it is equal to 6, A factor 3 occurs due to its color degree of freedom and an additional degree of. 2 due to the assumption that quarks are spin half objects; and of course stands for number of quarks of the t-<£ type flavour. Quark density denoted by B/V is expressed as §. = -L I t = _L .s b3 V 3 v 371*- »' Fl‘ The energy d en sity , jo i s given by y 4- t - 169 and finally the pressure P The summation is over i=l,2,3, if we restrict the flavour to be u,d,s, only. r Thus for a Quark density (assuming 10 quarks in a hadronic volume) (0 ^°^/Cw3 i . e . 1° we have — JL GeV which leads to a density^ f y g iv en by . a ; ? x i° % A?* •' 37 and "P cr 3. X 16 . ' ■ ' ii . 3 Since Central density— to is found inside a neutron star, it is indicative that central core may*exist in the quark phase rather than in neutron phase. .• This simple calculation sparred a numerous realistic calculations. First_it must be realized that the quarks inside the hadrons at short distances are almost free .but nevertheless they are not solitary objects. The strong interactions between quarks at such high density has to be taken into consideration. The first simple consideration in the thermodynamics of. a quark gas has been made on the basis of the phenomeaological MIT bag Model for hadrons by Bavm & C h in f It is wellknewn this model in its simple structure is- expressed by means of two parameters: (l) the Bag Pressure, B >0 which confines the quarks inside a given region of space and - 190 - (2 ) a constant coupling strength which signifies the strength of the gluon interaction with quarks along Yang-Mills fashion bbeying the color gauge group S0(3)c ; The parameters B and are obtained by f i l l i n g th e masses of nucleons and A -resonances and other quantities like magnetic momentum etc of the known hadrons. For T=0, we have for the number density, N _ A k 3 V ' T r pF For d=6 (in co lo r SU^) we have from above Thus the feral momentum of the ith flavoured quark i s ' - (T ^7 ) * Ukm i stands for the " flavour index. Putting -C. . . N i N We easily see, for neutron^ 'ST =3. t I f B= Bag Pressure then on dim ensional reasons We can easily write for the energy density O , the following! 4 • „ J ■ P - L V -r • • - 191 Therefore the energy per particle is ' ! = ■ : In above V stands for the volumetof the system and finally the pressure P is given by These equations do not contain any quark gluon interactions constant. At T=0 to order, the only interaction effect that comes into play is the exchange energy contribution; The exchange energy arises from two spin quarks interchanging positions in the Fermi Sea by exchanging one virtual gluon. •v r to order ; s — > > - f i ° When this contribution is added, to above, we get for E/N and P th e fo llo w in g . £ + t>c%f J : . . AJ N 4/? V£: P e - B 4 - ( N /v) ■ where D - - TT^ f) + ?*_ J 4 4" 6 r J 1 constant strength of the Interaction, Note that ”and f . “ from above we also find r = j (p - 4 b) Me now use the following values of the parameters B and namely? to obtain the eq Uation of state for the quark gas in MIT Bag mddel. With this quark equation of state and from the knowledge of neutron matter equation of state Baym & Chin investigated whether phase transition from hadronic to quark matter is possible: To investigate this we must , following Landau, find whether the phase-equilibrium conditions can be obtained of i.e . for the two phasesAmatter naxmakl namely neutron and quark we must have f TVessivre) and yL, : p - i • (Chemical Potential) To see t h is we p lo t 4i-c. <^vucWVAAd - 193 - 3.8 F i^ l d L Tk^rj GdCulJicn of Wxiu^o. v5 1+ V—> 1.1 ■ HiMjhns* fijtjiu'' — tt—- Va.Y ia.k&noJL s CaZcu&aJit* t£ Rt»w£kLV.p«^e ' The presence of phase transition between the two phases i s shown by th e e x iste n c e of a double tan gen t as shown by the dotted line. The pressure is negative of slope of th e common tan gen t i.e . P r . ^ / j y The chemical potential is the intercept of the common tangent on the y-axis. Thus both pressure and chemical potential are equal as is evident from the figure. We give below in a tabular form the various values of the relevant parameters for — 194 * the understanding of the phase transition. T h a S E T b AHUTJCV *?A f!A niETEKS r------TVansi-h cm CC'TV^TduL . P KnSJuLc (2A-. 1.6 1.3, Z 7.7 ( H Tk- S>vC huY*/'*V'af. t>» cv2 4-C 4 ./ \ 7 . S ; ■ 7 ; ' A. , J ; . . : e". .• Hence, th e phase tr a n s itio n d en sity in th e neutron m atter phase is much higher in both cases(of the nucleon models) than the maximum density available in neutron matter calculations; Thus if is unlikely that the quark matter be a stable one, L IN above we have.taken vanishing masses.for quarks. In general Mw and M^ (masses of up and down type quarks) are not zero. Thus one may expect some changes in our result if non-vanishing quark-masses are used. In this case - 195 - we have fo r E/N the follow in g % ' "V + TT ^ { U ‘ 1X1 , - j i & , i m 1 K - i *• where *%• = \ > 9 i j m c * 1; - Mi = quark mass of ith flavour » tMk = c; log MtV . The bag model parameters B and ^ " a rd th e same as we used earlier namely . o 3+ / 3 O - 0-5S1 The resultant phase transition density remain close to the massless quarks case. This question was re-examined in the context of 6 quantum chromodynamics by Chapline and Nauenberg. They h?ve considered the effect of the second order in coupling constant o ' 2a fI&T . It is shown using renormalization group equation that the coupling strength o(^ is subtraction dependent and is given by < . = - ! — ■ ' - v h - .%* » A1- Here K=3, • i f the flavour symmetry is S U (i) Q2 = momentum transfer carried by gluon T_ and /\ = Subtraction constant, which characterizes the Interaction strength. A can be fixed from other experimental data like deep inelastic electron proton scattering as an examole. However, in th e .present case o f th e many body system at T=0 we can choose t_ k . where \Pp i s th e ferm i momentum and A p is a suitable subtraction constant. Taking effect of the exchange energy contribution in which two quark interchange positions through the exchange of one virtual gluon inside the fermi sea, we can write e/ n . With and K=3 we can rewrite ^ as follows^ Ap J r 2 L _ L c 18 /»5 X Then the quark density, becomes for equal mixtures of u, d and s- quarks - 197 - Energy (~i - t - ±~) per particle is given by B/ and.-energy density .4 ,4 ^ £ - 3 r , . _ i _ n v 4T 2- . 3? Icy K- J 3 3 •n r ? * P .. 7TV At T= 0, Gibbs energy per particle, i.e. the chemical potential is ^ ^ 3 [ f .- t - fl - TT- „ and Pressure, P is P = t \ - 6 d.*' = 2 A 7* [/ + (' - T~x)J 4 7I1 - L 3 7 / 05 ^ , h 5 ^ J We can now plot P versus j. for ? given /IF for quark gas and compare it with F versus y£<_ for neutron m a tter. - 198 ~ = 4»oMev = 306 Mev 2 0 6 MtV A p - loo Mev TClo tJyrjsfCw') The curves for various A g denote quark gas case BJ, PS and CL are neutron matter ^A- P ) curve. BJ = Bethe-Johnson ! Repulsive core fitted to agree more c lo s e ly with the observed property of £3 -meson. PS = Pandharipande-Smith : includes tensor interaction. Cl = Causality lim it in whi'ch velocity of sound in neutron gas is equal to velocity of light. The parameters-in BJ are matched to obtain this result. ' For /ip '?£■ lo o MeV and belcw there does not occur any phase transition, as the P-yA- curves of the "tuo raitter phases do not intersect. - 199 - Phase transition can occur for values of Ap ~ 2 j?0 ffaend above. We give below various relevant values of the thermodynamic parameters indicating the possibility of the phase-transition. BJ PS Cl 1 300 400 300 400 300 400 24 36 4 .1 1 0 .S 3 .6 7 .3 hadron 2 .1 2 .6 0 .7 1 .1 0 .5 0 ,6 d e n sity r B/tf neutron m atter d e n sity 6 7 .5 2 . 3 1 1 .3 ?r 0 ° 5$/ c J ) Maximum 3 .3 1 .1 1.6 fe . from neutron equation of s t a t e and fo r maximum mass o f UiHg .Thus the ehase. transition density for neutron.matter in all cases except for the causality lim it case is nuite above the maximum density available from the corresponding neutron equation of state and numerical solution of Tov equation with a max-neutron star mass ~ |.6 83 « tip stands for the mass of the sun. Thus this calculation shows phase transition is not - 200 - entirely ruled out. It may be mentioned that the situation In 2nd order 6£6D Is quite similar to the result obtained In the Bag Model. For In Bag Model we have P = '/3 \_f- 4Bj where j> «r E/v and In fict> we find P= y3£f- it Comparing the two we have for B the following, g r ^ F ¥ ? I I an 1- i»^2X For A p ~ S&THeV SF the value of B becomes B « NtV/fJ which Is" close to the result, wed Lw. B+^rfojUl- M I T 6A«| OcD e z ♦ I r r/ 4 ' letow*. Bdu^ #(eAt V ClntiM Bynamirj This preliminary result motivated large number of a people to look into the problem of phase transition more closely in higher order of o(c in QCD . Let us discuss this below In a little detail. In particular, many authors have calculated the ground state (1=0) of a quark gas upto and including effects of fourth order In quark-gluon coupling constant in the framework of quantum chromodynamics. They have also vmd the renormalization group techniques to rewrite the e by gluon and ghost loops. Another new set of diagrams a r ise due to 3-gluon v er tex . The fie ld -th e o r e tic formulation goes as follows. ■ . ' ? In terms of Fermion field variable , we have for number density 71 rz TV Cx) where (•••• means th e s t a t i s t i c a l thermodynamical average and given by — ------ Noting that temperature Green's function can be written as c U < TV*) , One can write •H . - i fO± Tr[T«6(t,/./)] i-s "the fourir transform of > ft) where satisfies the following Schwinger-Dysen. integral equation:- 6 = !?{*,?,»* fF f - t i z ( y f i d - , / . ? ; and <• = io(- f£ -< X Y^Sp y ('*) *• c <) are th e w e ll known S U(3) - % matrices, and the temperature-dependent quark propagator is given by s*Ff t , F = — L - where. 'K p ( ^ y is the fermion distribution function. For T=Ot we have as usual ’ipW -' 1 > > < h - o'., and fo r gluons we use * f i_(L- &*!)• " V 1 ' 1(1- r Ka y as t he gluons . are not real, The thermodynamic p o te n tia l, U7« , i s obtained from ^ = - T V = - / ( / ) <=<> - «Q» and is given by •n = -1 jV f T^° ^ Grand Partition function Is ?f> e*f£-*UVA/^j . Using above one can find all the, thermodynamics quantities. Upto fourth order at T=0 for a one-flavour-three color quark gas, the thermodynamic potential is *J2. - (-% ./>) fl ' 2-5it4z - /. 62VcZ/0jc/e - 7, o? v /J - 203 - To explore the possibility of phase transition we consider the pressure .*■ given by T = t AW + ^ At low d en sity ^ W t :;'5A p ~ i!U )h ^ • Wc & . iixi-Yyr/f*? provided at a subtraction p oint of. 3 GitV The results support that super dense" stars may- e^i$t in 'quark phase rather than in the neutron, phase. The phase transition we talked about here diould be understood as a transition of a state of localized quarks in a neutron phase to a state of delocalization. The transition is characterized by.a change in the color-conductivity of the matter from zero in the neutron phase to a finite value in the quark phase, analogous to the Mott metal-insulator transition - 204 - phenomena. Before we conclude we must mention whether the discussion above suggests the possibility of a third family super-dense stars of quarks. A preliminary calculation in this direction e has been done by Itoh quite sometime ago. He used para statistics for non-interacting quarks to determine the equation, "of state of quarks. With this along with TO V - equation, he found that quark star with a maximum mass of ' can exist. He however took lo6eV_ for a quark mass with |>p i G»tV. . The heavy mass ~io R eferences 1. L.D. Landau, C ollected papers by L.D. Landau, ed ited by D. t e r . Haar (Pergamon, New York, 1965) 2. V7. Baade and F. Avicky, Proc. Natl., Acad, Sci, U.S. 20, 2599 (1934). 3. J.R. Oppenheimer and G.M. Volkoff. Phys. Rev. 55, 374(1939) 4. J.C. Collins and M.J. Perry Phys. Rev. Letters 34(1975) 1353 5. G. Baym and S.A. Chin. Phys. Letters 62 B(1976) 241 6.’ G. Chapline and M. Nauenberg; Nature 264, 235(1976) and Phys. Rev. D16, 450(1977) 7j B.A. Freedman and L.D. Melerran Phys. Rev.l6D, 1169(1977) V. Baluni—M.I.T. preprint CTP, 669, September 1977,’ 8. N. Itoh Prog. Theor. Phys. 44, 29 (1970) 9 . J.D . Anand, S.N . Biswas and M. Hassan, Phys. Rev. D(To be p ub lished-1979), P HIGH ENERGY NUCLEUS-NUCLEUS COLLISIONS* K.B. Shall a, Department of Physics, University of Bajasthan, Jaipur-302004 (India) 1. Introduction: During the past few years a considerable interest has grown in this subject, with the availability of high energy beams of heavy ions (upto Z = 26 and Energy 4.5 Gev/nucleon) v at Bevalac (Berkeley) and Syncrophasotrone (Dubna). New accelerators are being planned which will give us beams of high Z and or of high energy. For example, Numatron in Japan w ill contribute with very heavy ions at 1 Gev/nucleon. There is a good hope that plan for very ambitious machine w ill be realized at G.S.I. Darmstadt. This machine w ill provide 10 Gev/nucleon beams right upto 238^0 and in addition will have storage ring. If this plan is realized, we will be able t o study Heavy Ion R eactions a l l the way upto a c.m. energy of 5 Tev, after about five years. Many experimental and theoretical physicists are persuing their studies of nucleus-nucleus reactions at high energies. This can further be judged from the fact that symposia have been held exclusively for the heavy ion reactions (e.g. Darmstadt March 1978, Berkeley July 1978). Under these conditions it w ill not be possible to give a complete picture of the subject - 206 - - 2 07 - in one talk. I have tried to make this talk an introductory with an emphasis on emulsion experiments. Central collision studies have gained importance, as people are expecting to observe new phases of nuclear matter at high density and high temperature. On the other hand many theoretical approaches are being presented to explain the experimental data. I shall like to be excused by theoretical.physicists to devote less time to various theoretical models. Though simple picture of fireball model and extension of IPM for hadron nucleus to nucleus-nucleus collisions will be discussed very briefly. The following sections will deal with ( 2) Terminology^ ( 3 ) Peripheral Collisions, (4) Central Collisions, (5) Hadron- nucleus and Nucleus-nucleus Collisions, and (6) Conclusions.' 2. Terminology? (a) P eripheral and Central C o llisio n s - Heavy ion or nucleus-nucleus collisions can be divided into three types^Hev These are called peripheral, quasi-central and central collisions and can be understood to have large, medium and small values of impact parameter,Pig. 1 illustrates these three types quite clearly. We have b ^ (R^ + Rg) for peripheral ( 1 ) (R^+Rg) > b >, t R^-Rgl fo r q u asi-cen tral and 0 ^ b < | H^Rgl for central collisions where Rj and Rg are radii of the projectile and target nuclei, respectively. - 2 0 6 - In peripheral collisions the projectile and target nuclei.are far apart, so a small momentum is transferred between the wa interacting nuclei. Here one or both of the nuclei w ill disintegrate emitting fragments whose characteristics are determined by th e in t r in s ic fermi-momentum d istr ib u tio n s o f nucleus within the fragmenting nucleus The fragments of the projectile are emitted in a narrow forward cone while the fragments of the target are nearly isotropically distributed in the lab. system. These two parts will occupy two regions of pseudo-rapidity centred around and 0, as shown in Fig. l(a). For quasi-central and central collisions projectile and target nuclei are close and closer to each other. The difference in the two types could be understood on the basis of number of nucleons talcing part in the reaction. Ih'both cases whole kinematically-allowed rapidity space is available for produced particles, the difference being.in the degree of population of the central region. In central reactions we shall expect almost complete extinction of projectile fragmenta tion products and the rapidity space available for the particles is almost limited to the region between PF and TF (Fig. l(b) and l(c)). Fig. 2(a) and 2(b) show micro photographs of peripheral^^ and central^^ collisions. (b) Participants and Spectators - A very simple picture of a nucleus-nucleus reaction ( 1 ) is given by the nuclear fireball model of G.D. Westfall et alv in which the projectile and target nuclei are assumed to make 209 - clean cylindrical cuts through each other. This results into participants and spectjfatoAS as shown in Pig. 3. The fraction of nucleons which constitute projectile spectator, target spectator and participant- fireball w ill depend upon the impact parameter and size of the projectile and target nuclei (see Fig. 3(b)). Kuclear fireball model basically involves three concepts: geometry, kinematics and thermodynamics. The geometry and kinematics will tell us the forward velocity and the energy of the participant fireball. The thermodynamics assumes that this energy in the fireball is thermalized and that the fireball decays as an ideal gas. We shall discuss this model a little more, when we compare the p red ictio n s o f t h is model with the experimental results of Pe + CNO and Fe + AgBr central collisions (c) Cross Section and Mean Free Path - Relativistic nucleus-nucleus. reaction cross sections (57) have been measured by P.J. Lindstrom et al ’ . They have tabulated^®^ these cross sections for different projectiles. {^H1, C12, 0 16 and Ar40] and ta r g e ts £h , 0, Cu, Ag, Pb, u ). These results are reproduced in Table l(a). They have fitted the data to empirical expression of nucleus-nucleus reaction cross section proposed by Bradt and Peters ( 36 ) , i.e. G5 5 = rcrf (a|/3 + 4/3 - b')2 (2) where Ag and are the_mass numbers o f the beam and target n u c le i and b' is an overlap parameter. They fin d r0 = 1.29, b1 is not a constant, but the data can be fitted to b' = l - 0.028 Am1w i f th e minimum mass number A^^ = Min (Ab, A j)'< 36 and » ' = 0 i f 4nin >36* ( 6 ) H.H. Heckman e t a l v ' have measured mean-free-path lengths for %e, 12C, 14N and l60 nuclei at 2.1 Gev/n in nuclear emulsions. Their values along with values for p (8 ) , d ^ and Fe^10^ interactions are given in Table l(b). The data of H.H. Heckman et al of interaction mean free paths are well accounted for by Bradt-Peters expression (Eqn. 2) when r0&» 1.24 fin and the overlap parameter b' is dependent on p r o je c tile and ta r g e t. We can check, with Eqn. 2, the percentage of reactions with three constituents groups (H, CNO and Ag Br) of nuclear emulsions for Pe projectiles will be. quite different from proton projectiles (e.g. percentage of Fe-H reactions is “i 15 per cent where as for H-H reactions it is **4 per cent). 3. Peripheral Collisions: We have seen, in Pig. 1, that in peripheral collisions projectile fragmentation ( H. — rf\jp ) and target fragmentation ( = 0) products are well separated on the pseudo rapidity plot. In other words we can expect to observe pure projectile fragmentation and or target fragmentation reactions. Here we shall summarise very briefly the results of such studies. - 211 - Table 1(a). Cross Section in Bains (AA >, l ) ' Pro j 40. % 12c 160 Ar •Target H 0.25+0. OS 0.34+0.02 0.68+0.05 C. 0.23+0.01 0.81+0.02 0. CNO (i-oo7+;JJ|) Cu 0.78+0.02. 1.710+.030 1.90+0.03 2.85+0.08 Ag AgBr ( 2 .i8 : :| ^ ) 3.47+0.11 Pb 4.51+0.16 U 5.00+0.24 Table l(b). Mean free, path in Emulsions. P r o j e c t ile p d. ^ e 12c ‘ 14H l6 0 ' Fe Mean fr e e p ath w»35cm 26.9+.8 . 21.8+0.7 13.8+0.5 13.6+0.4 -13.0 *9Cf “ j<).5 - 212 - (a) Projectile Fragmentation - A systematic studies of projectile (beam) fragmentation were performed by D.E. Greiner et a l^ 1^ in Berkeley using a magnetic spectrometer system. .Charge and mass of fragments emitted with a velocity close to the one of the beam were obtained by measuring regidity* energy loss in solid state detectors and time of. flight. All fragnents with A/Z between .2 and 3.4 could be isolated. The angular acceptance was .7°; Some important results for *2c and induced reactions are*7’11’12): 1 . The isotope production cross-sections are to a high degree factorized: ^* " b t =. ^B ^ (exceptions for hydrogeii target and one-nucleon transfer), B, T and F in d ic a te a dependence on beam, ta rg et and fragment mass, respectively. Yg is independent of beam energy and targets Y^, the target factor, is independent of beam energy the beam and fragment m asses. Y$ 0#? 1 a£' / 4 fits the cross section data to + 10 per cen t. In a recent investigation, regarding fragmentation of ®6Fe at 1.88 Gev/n with H, Li, Be, C, S, Cu, Ag, Ta, Pb and U f 37 ) targets, G.D. Westfall et alv ' confirm the factorisation of (T fj (Eqn. 3). - 213 - 2. All fragments are emitted with parallel P„ and transverse Pj_ momentum'distributions which follow a Gaussian shape l-v, eXP(-^L) (4) w ith a ~ values between 50 and 200. Mev/c. 3. A comparison between cross-sections of mirror fragments shows that the neutron rich Isotope is always preferred CTff 1.0 < —=_< 4 .1 ° F = 'neutron Isotope production cross section1 = 'proton isotope production cross section'. These results can be understood, if we assume that target nucleus only acts as energy injector i.e . limiting fragmentation hypothesis. The Gaussian shape should be expected from statistical approaches to heavy ion reactions assuming small co rrela tio n s among nucleon momenta in the n u c le i, Such modes tell us essentially that the momenta of the fragments, in the beam rest system, are proportional to the internal fermi momentum. H.H. Heckman et al'(6) ' have measured projected angles for Z = 1 and 2 secondaries from the interactions of C, N and 0 in nuclear emulsions. They are able to represent the peaks observed in the projected angular distributions with gaussian o f o~~ = 1.65° and = 0.83° respectively for Z = 1 and Z = 2, For z = 1 the peak is superimposed on a broader distribution 0—= 7 .5 ° . For z = 2 fragments also there is a.large angle tail. These observations indicate the Z = 1 and Z = 2 fragments are produced with transverse momenta greater than is characteristic - 214 - of peripheral collisions. ■ The results of a recent experiment with Fe-emulsion Interactors at 1.7 Gev/nucleon have been reported by K.B. Bhalla et a l'( 13 ) . These r e su lts are shown in F ig. 4 (a ). Y/e can see that where as a central peak can be associated with a gaussian distribution, a significant large angle tail is observed. The experiments of B.Jakobsson et al^14^ and B. Judek^1®^, in which they measure fragments with greater-Z, -also confirm that He and Li fragments sometimes receive a large momentum t rans fe r. Results 3 above, which states that neutron rich isotopes are preferred in the final state is somewhat puzzling. The opposite result would in fact be natural if the fragments resulted from an evaporation chain or a normal stripping process of nucleus with a neutron shell beyond the proton surface ( 1 2 ) . This is another indication of a violation of the simplest statistical reaction models. A detailed ^ e fragmentation experiment of L.M. Anderson^®^ usin’g a double focussing spectrometer- is worth mentioning. His conclusion, based upon measurements of single particle inclusive cross sections for the production of protons, deutrons, tritons, ..?He, and ^ e at momenta from 0 .5 to 11.5 Gev/c and angles from 0° to 12°, is as follows. A sharp fragmentation peak is observed at the projectile velocity and in the forward direction for each fragment of mass less than that of the projectile. The production in these peaks - 215 - is predominantly peripheral and agrees with lim iting fragmenta t io n fo r beam en erg ies from 1-2 Gev/n and fragment momenta at least to 0.4 Gev/c in the projectile frame. :tl. The projectile frame momentum distribution is not isotropic, being broader in the transverse and backward directions • than in the forward direction. These distributions, at least; in the case of protons, appear to be composed of two distinct regions in both the forward and transverse directions with the break occurlng at p^10^ . 0.2 Gev/c. The momentum at which the cross section reaches, its peak value at p$ = 0 agrees well with what is expected from persistence of velocity, and this peak shifts to lower momenta at larger p^ He further points out that the experimental data from, such experiments w ill help us expand our understanding of •high energy/ concepts such as. lim iting fragmentation, particle : production mechanisms, nuclear structure, and hadxpn-hadrbn interactions in general. Cb) Target Fragmentation - Pure target fragmentation products "will be very slow i.e . 0. Normally measurements involve higher energy fragments in addition to slow evaporation like products. J. Gosset et al . 1 have made' very elaborate study of the" inclusive reactions /K:; ♦ . ' p ♦ x •• \ (s):/-, . Al " .. ■>/ - 216 - at selected bean energies Tn = 0,25, 0.40, 2.1 Gev/n. The fragments F detected were protons through nitrogen, produced at angles between35° and 150° in the energy range, 30 ^ Tn < 150 Mev/n. Based upon the measured differential cross sections for the production of the hydrogen and helium isotopes in the energy interval 30 ^ 50 Mev/n in the reaction ^°Ne + U - F + X at beam energy 400 Mev/n they conclude'. . 1. The angular distributions are smooth and forward peaked, tending.to an 'evaporation peak' at low energies. 2. The forward-peaking increases with mass of the fragment, so protons are predominant in the backward hemisphere. Similar behaviour has, also been observed at a ll other beam, en erg ies. Based upon their results of ^He production for different beam en ergies, ta rg et and p r o je c tile m asses, and the energy windows for the ®He fragment they further conclude. 1. Forward peaking o f ^He in crea ses as the energy o f projectile decreases from 2.1 to 0.4 to 0.24 Gev/n in the rea ctio n *^Ne + tf — ®He + X. 2. At 2.1 Gev/n, the production of ®He, from ^Ne projectiles on U and Al targets are different. 3. The production o f ®He (30-50 Mev/n) by *He and *®Ne projedtlles on U at 400 Mev/n is shown to be independent of the projectile mass. - 2 17 - 4. An increased forward-peaking is observed at high energy window (50-100 Mev/n). Simple'fireball sodel picture explains satisfactorily the proton inclusive spectrum at lower incident energies i.e . 250 and 400 Mev/nucleon. As it fails to reproduce the trend of the data in the 2.1 Gev/nucleon Ne + U reaction, an idea of two-fireball model with one fireball related to the projectile and the other to the target (for instance for ^Ne-U; = C.14 and 0.91) is brought in. In conclusion we can say that simple fireball model gives good description of comparatively peripheral events or perhaps all events at a comparatively low energy. 4. Central Collisions: Central collisions of heavy ions have become very important, as nuclear matter'at higher densities and temperature can be. explored by these studies. So many reviews talks have l) 2) been presented, e.g. I. Otterlund , B. Jakobsaon , A.M. Poskanzer on-the subject. Here in this section we shall try to give very recent results. Geometrical definition of central reactions, given in . Eqn. ( l ) , w ill g iv e very sm all cross se c tio n s, when the siz e . of the interacting nuclei are comparable (as extreme case the probability for central reactions will become zero, when R^ = Rg. Moreover, the interesting phenomena, like, high nuclear density and high plon m ultiplicities, "will not necessarily be realized - 2 18 - for 'b* < I - Rg|. By calculating the overlap density, B. Jakobsson^ev shows that we could expectorb = 7 fin. Ar + Pb reaction to be more ’central’ thanftb - ofta.reaction if we look for ^ signals in the experiments on Sentral reactions. So geometrical definition given in Eqn. (l) is not very strict. Looking at the photomicrograph (Pig. 2b), we can see that no projectile fragments are visible. Projectile frag mentation products will have pseudo rapidity - 0 , where is the pseudo-rapidity of the excited residual projectile nucleus and a ~ ~ is the dispersion of the distribution. I f - c r ~ corresponds to an emission angle 0Q in the lab system, we can regard a heavy ion interaction to be central if no charged fragments are emitted with 0 < 0Q. This criterion has been used by M.I. Adamovich"et al^18^ to select central 12C + Bn reactions at 3.3 Gev/nucleon. To select central reactions Heckman et al^^ use a 0Q value corresponding to 71 - 1.50” for protons in l60 +’ En and 40Ar + Bn reactions. / < ift V These criteria' •’ y could be regarded as to avoid peripheral reaction or selecting non-peripheral reactions. Degree of destruction o>f the target nucleus or the number of heavy tracks in nuclear emulsions (N^) can also be used to define central reactions. w ill Include all charged target fragments except singly charged particles having p > 0.7. ; K.D. Tolstov et al^8^ have used > 28 in. selecting central = 219 reactions with Ag Br targets. In addition they use Ng > Nb (number of grey tracks greater than number of black tracks, assuming that grey, trapks could come from participant nucleons. 56 In the studies of Fe + Em reactions at 1.7 Gev/nucleon it has recently been observed that central collisions with the li^ it nuclei CNO may be obtained by using the criterion Ng > 26 and N^.^ 5. K.B. Bhalla et al^®^ have reported many unusual events (Pig. 5 and 6). In one Fe-(c,N,0) event Fig. 5 we observe 45 shower tracks i.e . "the target is totally distinte- grated and. all but one particles have {5 > 0.7. The lightest possible target is C and therefore at least 5 protons are emitted from the target with momenta larger than 1 Gev/c. In another event 4 He and 24 singly charged particles with p > 0.7 are observed. Thus all the protons emitted from the totally disintegrated target nucleus have momenta >lGev/c. They have also observed central reactions with a comparatively large number of the particles (Pig. 6(a), 6(b)). The emission of fast protons (p >1 Gev/c) from the disintegration of target is an unusual result. Based upon the above mentioned considerations, lund University group (4) has recently studied central Fe®^ + CNO and ®®Fe + AgBr reactions at 1.7 Gev/nucleon. Reactions with N ^ =(Ng + > 26 and Nh 5 were chosen for central CNO collisions; since Pe + H reactions can give. N ^ > 26 at 1.7 Gev with very small probability. 10 per cent of the Pe +■ AgBr reactions with the highest m ultiplicity of charged particles were chosen as a representative sample of central Pe + AgBr a, - 2 2 0 - reactions. Pig. 7 shows u = -log tan 6/2 plots for.the two selected samples of central Pe + AgBr and Pe + OHO reaotions- The two distributions are very similar in spite of the targets which are quite different. An attempt is made to explain the data from the clean-cut fireball break up and spectator evaporation model. We have already given in Pig. 3(b) the number of nucleons in the overlapp ing and non-overlapping parts, of the interacting nuclei, as a function of the impact parameter (b) for Pe + CNO (b < 2.5 fm) and Pe + AgBr (b < 3.5 fin) reactions. These ranges of impact parameters are assumed to be representative for the selected samples of collisions. Central Fe + CNO and Pe + AgBr reactions are quite different from fireball point of view. In Fe + CHO reactions the number of projectile spectator nucleons are 75 per cent of the number of nucleons in the fireball. In Fe + AgBr reactions this percentage is much smaller ( ** 8 p er c e n t). For the target spectator the situation' is reversed ( ^ 0 per cent . and v« 20 per cent respectively). The emission of particles from the participant system follows -the outline of relativistic fireball model. The energy is thermalised in the participants before the emission of pions and protons. The number of emitted protons is assumed to be the same as the fireball proton number as the production of multiply charged particles is quite small. The pion m ultiplicity is calculated as the difference between the total charged particle m ultiplicity observed and the multicity given by the model i.e . 221 Sch ~ ^part ~ ®proj.spec ~ The decay of the spectators is treated in the spirit of the clean cut approach with isotropic emission from systems with v e l o c i t i e s ff = 0 and JT = f^,eajn- The u -d is tr ib u tio n s th u s calculated are shown as curves in Pig. 7. The dotted curve is from calculations based upon sequential evaporation of the spectators, where as the solid one is for isotropic break up ( P I ^ with Gaussian momentum distribution' . We can see that both calculated curves do not agree with the experimental results. We can see that only a comparatively small number of the 26 projectile protons are observed in the u-space where we expect spectator particles. In central Fe + AgBr reactions this is expected since the projectile is almost totally overlapped, and consequently, most of the projectile nucleons participate in the reaction. It is quite astonishing that a similar suppression is also observed in Pe + CNO reactions. The width of the two experimental distri butions are the same, but the centre! of the distributions are shifted A u = 0.51. Cascade evaporation calculations of V.D. Tonnev^Rev using the same criteria as in the experiment, also disagree with the experimental distributions. Prom this experiment we can conclude that the emission of particles from non overlapping parts of the interacting nuclei (Pe - CNO) in central collisions cannot be regarded the same way as the spectator break up in peripheral collisions. To explain the experimental findings, we must assume that the participant * 2 2 2 - ( poX volume is extended in the transverse direction. The fire-strea k ' broadening of the temperature and velocities w ill make the discrepancies less but hardly negligible. Now we shall mention very briefly the results of other experiments^, to study the central collisions of relativistic heavy io n s . H.H. Heckman et a l ^ have stu d ied th e angular and momentum distribution of fragments emitted from central collisions between emulsion nuclei (Ag Br) and heavy ion projectiles ^He, ^*0, and4®A at 1.8 Gev/n. For measurements they have used only those prongs with g >, 2 250 Mev for protons^ specially concentrating on fragments with R < 4 mm. Some general conclusions of the experiment are given below. 1. There is no unique particle-em itting system, characterised by a centre-of-mass velocity p„ and spectral velocity P0- = that accounts for the spectra of fragment ranges (momenta) and angles. 2. The distributors are broad, Maxwellian-like, with maxima that shift towards smaller angles as the fragment energy increases, and as beam energy decreases. 3. For each fragment energy range Ep < 30 and Ep < 250 Mev, the changes in the angular distributions are primarily due to increased forward-coning of the angles in forward hemisphere. 4. For Ep < 30 the angular and range distributions do not depend on the mass of the projectile. For E^ < 250 Mev the angular distribution depends on the projectile mass, the angular distribution for 40Ar + AgBr reactions is much " 223 more forward peaked than in reactions induced by light *He and l60 projectiles. .5 . Ho statistically significant structure, attributed to well defined collective phenomena, is observed in the range or angular distributions. Another worth mentioning experiment is of. B. Schopper's (23) group' '. They investigated the interactions produced by He, C and O-beams with energies from 0.1-4 Gev/n in Ag Cl mono crystals. The distributions of all particles with (^ ) > 8.5 are measured for events where more than 15 prongs (of the above kind) are observed. The authors claim that . the sharp peak which shifts its position in a characteristic energy dependent way is the signal of Mach Shocks with' a propagation velocity. Vshock ~ Vinc Co$ ®peak ^ They also claim that the peaks are due to the emission of high energy He nuclei among the highly ionising particles. A search for shock wave phenomena has also been made by J. Bakobsson eta l^ 24^ in central l60-AgBr interactions at 0.2 and 2.0 Gev/n. . They do not observe any significant sharp T|— JT1 dE peaks in the representation of tracks with ^ > 16 but the curves are shifted with beam energy in a way which agrees qualitatively with the AgCl results. They further show that the angular distribution of high energy He nuclei, emitted from the target in the central l60-AgBr interactions, are found to be highly forward-peaked at 0.2 Gev/n but almost 224 isotropic at 2 Gev/n. The angular distributions are in qualitative agreement with shock wave calculations, however, no narrow peaks are observed in the angular or energy distri bution of tie nuclei. (19 ) G.M. Chernov et al concludp that the role of collective phenomena such as nuclear shock waves and high angular momentum, tr a n s fe r i s very sm a ll in n u cleu s-n u cleu s in te r a c tio n s , based upon their study of interactions in nuclear emulsions at 2 .1 Gev/n. The n u clea r em ulsions and AgCl m o n o -cry sta ls can .b e classified into category of 4it detectors. Die advantage of emulsions are: event by event analysis, high spatial resolution and unlimited sensitivity to different rates of energy loss. Loading of emulsions with fine wires have been developed at Lur.d'1'15^. B. Jakobsson et al^26^ have studied ^Ne + VI reactions in wire loaded emulsions. Recently bubble chambers ( 2 7 ) and streamer chambers^2®^ have also been used for the study of heavy ion reactions. Apart from the magnetic field which makes it- identification easy here, such detectors can be triggered electronically and they are thus very suitable in exclusive studies of central events. Much technical advancement is seen in two elaborate experimental set ups^2’ The first one is a collaborative project^2^ between LEL (Berkeley), GSI (Darmstadt) and University of Marburg. The experimental set up consists of a telescope (used for measuring inclusive spectra) surrounded by.80 plastic scintillators (to measure, the associated multi- pliclty).(single^particljT). So with this arrangement they are able to measure^inclusive spectra along with associated m ultiplicity of charged particles of any kind above a low-energy th ereh o ld (>35 Mev/A). The plastic scintillators are arranged into three azimuthal rings-around the beam with a few additional scintillators at back angles. Thus the azimuthal correlation of charged particles can be obtained. (3) Fig. 8 shows 3 such events ' observed in the array of 80 plastic detectors. The other set up consists of 9 magnetic ( p 9 ) spectrometers , each capable of makiiiL. ^eoaration between pions and protons and energy separation (typically protons with energies higher than 200 Mev and lower than 200 Mev), to view the target symmetrically. This detector is very useful to" study two or more particle coincidences. 5. Proton-Nucleus and Nucleus-Nucleus C ollisions: Natural question which comes to one's mind i s ,how does the nucleus-nucleus data' compare with the hadron-nucleus data. In this regard two works are worth mentioning, one is of G.M. Chernov et al and the other which deals with analysis of very high energy interactions is by I. Otterlund and E. Stenlund^3 0 ). G.M. Chernov et al^ ^ . have studied multiple production induced by 2.1 Gev/n ions in nuclear emulsions. They have presented data regarding m ultiplicities Nfe, N ' etc. angular distributions and correlations of charged secondaries based upon the measurements of 1813 inelastic interactions; - 226 « and compared with the data of proton nucleus interactions at ( 3 1 ) 2.23 Gev' For comparison of multiplicities, see table 2(a). Fig. 9(a) shows that the angular distribution of S*# particles are: similar to similar distribution in FA reactions of the Y 3 1 ) same energy' . Fig. 9(b) shows that the mean multiplicity of S'-particles increases monotonically with and that < N '> • yj ° is close to the shower-particle multiplicity in P-Ba in t reactions at the same energy per nucleon ( Win t = A “ 2 En± Z± (7) where A is the mass of the incident nucleus, n^ and are th e number and charge o f p r o je c tile fragments. could ■ also be a measure of the centerality of the reaction. Like Fig. 9(a), they have also drawn angular distributions of black and grey tracks and compared w ith th ose from P-Bn interactions at 2.23 Gev. This comparison shows that there is. no dependence of these distributions on the atomic number of the projectile, ^hey further show that the angular distribution of g- and b-particles in + Bn reactions tire in good agreement with predictions from cascade evaporation c a lc u la tio n s performed by Gudima and Toneev' . It can be concluded that the observations of inclusive m ultiplicity, angular distributions etc. do not differ very much from PA •S' particles are the shower particles without non-interacting singly - charged projectile fragments. - 227 - Table 2(a) A comparison of the mean m ultiplicities in If A and pa interactions NA (19) PA (31) T=2.1 Gev/n T=2.23 Gev No. of events 504 702 Table 2(b) ' Interactions at V.H.B. P n T B V Nh ^s^N NT ■ ■ NP Gev/n 8 o a lcu l. Ca Pb *•'300 518 >10 8 .4 81-94 "*40 508-563 B Ag, >"300. 204 30 8 .4 25-33 "11 151-185 Br 0 11 "*3000 215 13 12.5 26-35 "12 238-294 He 11 "4300 95 23 13.1 11-17 ^4 98-138 B 11 "14000 179 24 15.2 25-33 "11 274-334 B 11 "*1700 193 20 11.4 25-33 "11 205- 251 2%=3775 ;3413—4155 15 15 - 228 - reactions if we take into consideration the increase in the cross section i.e. simple geometrical effects explain the observables^^ev ^ . ( 71 ) . The analysis of I. Otterlund and E. Stenlundxv , on the basis of extension of independent particle model for. hadron nucleus interactions, for heavy ion interactions at very high, energies is quite illustrative. The observed particle m ultiplicities' for hadron-nucleus reactions follow the relation. , V - i - H S (<0 ° hA where 5 ^ and are the respective inelastic cross sections and A is the target mass. Every scattering of the leading hadron inside the hit nucleus produces p s-particles. Associated with the leading hadron is a contribution of a of scattering of the leading hadron or the average 'thickness' of the target). This generalization is-based upon the following assumptions: 1. In A-A reactions a ll nucleons in the overlapping parts participate in the production "of s-particles, see Fig. 10. 2. When a nucleon has collided once, the repeated scatterings do not, on an average, change the number of s-particles associated with this nucleon. This is verified from hA-experiments where the m ultiplicity of s-particles in the projectile fragmentation region depends weakly on the. amount of nuclear matter transversed by the incident hadron. 3. Depending on the lim ited space-time development of hadronic reactions inside the hit nuclei, the pions are emitted first when the two nuclei are separated, i.e. any intranuclear cascading in the interacting nuclei is neglected. 4.. Consequently each participating nucleon from the projectile contributes, on .an .average, with a m ultiplicity o f a Eqn. (10) can further be generalised to following Eqn. (li) for nucleus-nucleus reactions: < ^s> = NP “ associated with the nucleons from the projectile that do not participate. NT and 6p are dependent on the impact parameter, b. For reactions where > Ap and b < iR^-Rpl , all nucleons in the projectile participate, and consequently 6p = 0. The data of a representative sample of very high energy heavy ion reactionsis given in Table 2(b). Calcula tions of m ultiplicities, calculated from Eqn. (il) are also given in the table. They have chosen a = p = -| (based upon h-A results). The upper and lower lim its of NT correspond to b = 0 and b = I R^-Rpl r e sp e c tiv e ly . The sum o f m ulti plicities in all the 15 reactions is also, given in table, which clearly indicates good agreement. For pseudo-rapidity, = - In tan e / 2, distribution the experiments of PA reactions agree with Ngtnr^) kR ) Projectile fragmentation ( 12) Ng(l^ ) iR ^^(Tj )v Target fragmentation Based upon the above model the pseudo-rapidity distributions for AA reactions will be N^(7| , Ap)j? 'u jfC ! ). np (13) Ns ( ,t ’ V * . Fig. 11 shows that the'predictions from Eqn. (13) are in good agreement with experi46ntal findings, tor'll-distribution of a Ca + Pb reaction at 300 Gev/n. In the Figure is also shown - 231 - protons emitted from projectile fragmentation = 71 Mev/c, we see all the protons have disappeared i.e. It Is a central rea ctio n . We have described the extension of one model, attempts are being made to extend other models also e.g.' Coherent lube Model of A Dar. In fact, as reported by I. Otterlund^®v ^ an Improvement of CTM has been caused by observations in very high energy heavy'Ion reactions. This Illustrates how heavy ion studies can also contribute to our understanding of more elementary reactions, e.g. nucleonrnucleon and nucleon-nucleus collisions. Conclusions: Before I conclude this discussion which I shall do with some very recent quotations, I shall draw the attention to some theoretical works, lot of information is contained in the review article of J.R. Hix^ev Some of.the models we have already mentioned i.e. fireball ( i ) model of G.D. Westfall et alv , extension .'of it to fire streak ( 2?) model by W.D. Myers , cascade evaporation model o f K.K. Gudima (3 P ) and V.D. Toneev' and extension of independent particle model by I. Otterlund and E. Stenlund^®^. Others worth mentioning are relativistic hydrodynamics by JR Nix group' (33 ', ) one dimensional cascade model by J. Hiiffner andJ. Knoll'(34) , and extension of coherent tybe model' ( 3 5 ) For conclusion I have selected two para graphs: - 232 - ( p ) A.M. Poskanger' ' w rites: ••The basic reaction mechanism of these complicated reactions (nucleus-nucleus) must be understood theoretically before we can search for any of the predicted exotic effects of high density and temperature nuclear matter. It may well be like searching for a flower in a field of tall grass. However, this background grass must, be understood first, and may be interesting in itself" . He later writes, "In this new field we are rapidly progressing throu^i the grass while the search for the flowers is just beginning? The other paragraph is written by J.R. Nix^33^. His imagination of possible phases of nuclear matter at high density and temperature are reproduced in Pig. 12. He writes in conclusion: (tAs we continue our study of hi ^-energy heavy-itin c o llis io n s , we should bear in mind th a t we are entering an unexplored realm of science. We may or may not find the nuclear phase transitions that we seek. However, like Collumbus - who set out to find a new route to the Orient and discovered America instead - we are likely to make far more important discoveries than we originally intended. Wherever we land, we are on one o f th e voyages o f th e country** - 233 - REFERENCES Review Articles Rev. l. I. Otterlund, Lund Univ. Report LUIP 7810 (1978) and Proc. of the 4th Summer Study on Higji Ehergy Nuclear Collialons Berkeley,(1978). Rev. 2. B. Jakohsson, NORDITA Report 78/28 (1978) and Proc. of the 5th International Seminar on-H.E. Physics Problems,' Dubna (1978). Rev. 3. A.M. Poskanzer, Lawrence Berkeley Report LBL 7762. Invited talk for Int. Conf. on the Dynamical Properties of Heavy Ion Reactions, Johannesburg, S. Africa, Aug. 1978. Rev. 4. J. Rayford Nix, Las Allamos Scientific Laboratory- Report LA-UR 77-2952. For publication in Progress in Particle and Nuclear Physics. 1. H.H. Heckman et a l ., Lawrence Berkeley Report LBL 6561 (1977). 2. A.M. Poskanzer, Lawrence Berkeley Report LBL 6586 (1977). 3. G.D. Westfall et al., H yto w • 4. K.B. Shalla et a l ., Lund Univ. Report LUIP 7809, to be published in Phys. Letts. 5.- P.J. Lindstrom et a l., Proc. of the 14th Int. Cosmic Ray Conf., Munich (1975) 2315. 6. H.H. Heckman et a l ., Proc. of the 14th Int. Cosmic Ray Conf., Munich (l975) 2319. 7. P.J. Lindstrom et a l., Lawrence Berkeley Report LBL 3650 (1975). - 23* - 8. K.B. Bhalla and I. Otterlund, Rev. of Experimental reoulte on Hadron-nucleua interactions(under preparation). 9. S.K. Badyai et a l., Private communication. 10. B. Askelid et a l., Univ. of Lund Annual Report of Institute of Physics (1977) 11. 11. D.E. Griener et al., Physics Rev. Letters 35 (1975) 152: 12. B. Jakobsson, Centre de recherches nucleaires de x strasboung report CHN/PN 77-3. 13. K.B. Bhalla et a l ., Lund Univ.■Preprint LUIP 7805 (1978). 14. B. Jakobsson, R. Kullburg, I. Otterlund, Lett Al. Nuovo Cimento 15 (1976) 444. 15. Leonard M. Anderson, Jr. (Ph.D. Thesis), LBL Report ■ 6769 (1977). 16. B. Judek, Proc. 14th Int. Cosmic Ray Conf.,Munich (1975). 17. J. Cosset et a l., Phys. Rev. 0 16 (1977) 629. 18. M.I. Adamovich et a l., JINR, El-10838, Dubna (1977). (Reference from Review talk of I. Otterlund - Rev. l). 19. G.M. Chernov et a l., Nuc. Phys. A 280 (1977), 478. 20. K.D. Tolstov et a l., Z. Physik A 284 (l978) 283. (Reference from Rev. 1 .of I. Otterlund). 21. For direct isotropic break up. We have used gaussian momentum distribution with . G^" = 71 Mev/C, and = 131 Mev/C (ll) which correspond to zero tempera ture internal Fermi momentum distribution. 22. W.D. Myers, N u cl. P hys. A 296 (1978) 177. 23. E. Schopper et al., Proc. of Meeting ott Heayy Ion Collisions, Fall Greek Falls State Park, TN, June * . 13-17, (1977), and - 235 => H.ff. Bamnbgart et a l., Z. PhysIk A 273 (1975) 359. 24. B. Jakobsaon, B. Kullbeig and I. Otterlund, Nuel. Phys. A 276 (l977) 523. 25. B. Lindkrist, Nucl. Ihstr. and Methods 141 (1977) 511. 2 6 . B. Jakobsson, B. Lindkvist and I. Otterlund, HO EDITA Preprint 78/17 (1978). 27. Alma-Ata-Budapest-Bucharest-Cracow Colliboral Report given at the Int. Oonf. on High Hiergy Physics, Tokyo (1978). (Ref. from Rev. 2). 28. S.Y. Fung et a l., Phys. Rev. Letts. 40 (1978) 292. 29. S. Hagantlya et a l., Lawrence Berkeley Report LBL 6770 (1977). 30. I. Otterlund and Bstenlund, Lund University Report LUIP 7806 (1978). 31. M. Bogdanski et a l., Helv. Phys. Acta 42 (1969) 485. 32. K.K. Gudima and V.D. Toneev, Tad. Fyz. 2? (1978) 658, Phys. Lett. B73 (1977) 297. (Ref. from Rev. l) . 33. J.R. Hiz, contribution to Darmstadt Symp. March (1978), Los Almos Report LA-UR 78-571. 34. J. HUfner and J. Knoll, Hucl. Phys. A 290 (1977) 460. 35.. A. Bar, Proc. Darmstavdt Symp., March (1978). 36. H.C. Bradt and B. Peters, Phys. Rev. 77 (1950) 54. 37. O.D. Westfall et a l., Lawrence Berkeley Report LBL-7162 (1978). - 23 6 - FIGURE CAPTIONS Fig. l. A Schematic outline of pseudo-rapidity distribution in high energy heavy ion reactions for peripheral, quasi central and central cases. Fig. 2(a) A peripheral interaction of 1.8 Gev/n 40 Ar in nuclear emulsions. 2(b) A central reaction of 1.8 Gev/n 40Ar with a heavy emulsion nucleus. This reaction has the highest number of fragments (63) in the expt. of H.H. Heckman et a l ^ . Fig. 3(a) Nuclear Fireball model^, fireball (A) target (B) spectator, projectile spectator (c). 3(b) The numoer of nucleons in the fireball and the spectators for different impact parameters in (4) Fe + CNO and Fe + AgBr reactions . Fig. 4(a) Angular distributions in low multiplicity events (Nfa = 0 , Np 0 NQ < 10) in Fe reactions^13^. 4(b) Angular distributions in high multiplicity events (Nfa v< 5, Ns > 26) in Fe reactions^13^. The dotted curves show the distribution expected from a pure ( 1 3 ) fragmentation process' '• Fig. 5 An example of central reactions of Fe with C, N, 0 nuclei. Fig. 6(a and b) Examples of Fe central reactions with number of o particles. 237 P ig . 7„. u = log tan 6/2 distribution of shown particles (a) in central Fe + AgBr reactions, (b) in central Pe + CNO reactions. The curves show predictions from the fireball model + spectator evaporation (dotted) and spectator fragmentation (solid). Pig. 8. Diagrams of the locations of the 80 plastic scintillators looking down the beam line. These three events (4000 Mev/A *®Ar on Ca) the shading indicates which plastic scintillators fired in concidence with the telescope, which is at 90° to the beam on the right-hand side of the figure, (a) peripheral collision,(b) central collisioiy :• < and (c) asymmetric event. Pig. 9(a) Angular distribution of S' particles. S* particles are shower-particles without non-interacting singlly charged fragments. 9(b) Mean multiplicities per interacting nucleon as a function of the number of interacting nucleons. Pig. 10. A sketch of pseudo-rapidity distributions in high energy nucleon-nucleon (N-N), nucleon-nucleue (N- a ) and nucleus-nucleus (A-A) reactions, predicted from the independent particle model. Pig. U. Pseudorapidity distribution of s-particles in a central Ca Pb reactfon at 300 Gev/n. The dotted - 238 - curve shows the distribution expected for the projectile nucleus fragmentation protons. The dashed curves show the distributions predicted from the independent particle model discussed. Schematic illu stration o f the dependence of the ground state energy per nucleon Iy(n) upon nucleon number density n, illustrating these possible phase transitions. Note the discontinuity in the energy scale above 200 Mev. (Rev. 4). A te /vs. i >'r 100 yun w jm b si o f rixifO N S 'He . t ly mt A ; li miyk*y werti t r e w y * k ity im Hl#i ;; A ts wm clty JtW .. ■fl §■ fl)£ < > ■ vl. k $ s ML* *>»? uo- log ton 0/2 Fiji tlbj (*6iej|M 50 2.1 A GeV 30 20 Ca) 10 0 coaegl *1 5 w r IA» I 15 & = SCATTERED NUCLEONS 0>) 5 O 2 6 10 FLg. 10 Ca*Pb 1300 ~ 300 QeV/N- Possible phoses of nuclear matter n,= 518 Quark m atter??? 150 Nh- 10'. Nf= CO <200 Nt= 81-9C ■ PROJECTRE NUCLEUS FRAGMENTATION PROTONS »r 100 1 Density isomer ?? too CO 50 Pion condensate? It Normal nuclear matter V /ZX %-^4- .6 8 10 12 Nucleon Number Density n (Units of n0 ). •In tan 6/2 Rj 12- Fig. 1.1 - 245 PISCOSSIOH S.P. Mlara : In one place, yon mentioned that b = 0 for some small nuclei Is less central than b = 7 fm for some heavy nuclei. In what sense do you use the te rm 'central'? Is It regarding establishing thermal equilibrium with multi ple scattering? . K.B. Bhalla : B Jakobsson^ev* ^ has calculated overlap density (I)from the relation l(Sx.Sy) - / e’[fA 1 (S,Z) + ? A 2 (S-S,Z)] dz where f A Is the nucleon density distribution (Woods - Saxon) for nucleus with mass number A; and S = (Sx,Sy) Is the position vector In the plane transverse to the beam direction Z. He shows that T is peaking In the overlap region also when b ” 7 fin. for Ar + Pb and so if we look for f > > ? 0 signals in the experiments on central reactions we could expect a b = 7fln Ar + Pb reaction to be more 1 centred1 than a b = 0 £tn reactions. IBSTANTONS, CP-VIOIATION AND AXIONS S.R. Choudhury Physics Department, University of Delhi The remarkable paper of Belavin, Polyakov,- Schwarz and Tyupkin1 (BPS!) on Pseudoparticle solutions of Gauge theories about three years ago has sparked off some very Interesting developments subsequently. The scope o f th is talk Is to discuss some specific aspects of these developments without any pretensions of presenting a complete review of the subject. Theoretical develop ments and also a variety of experimental data have encouraged 2 ------theorists during the la st six years or so, to consider non- , abelian color gauge theories as a framework for the-description of hadronic Interactions. The most favoured candidate for the underlying group in these models is a direct product of an SU(3) ‘Color1 group and a flavour group SU(N) with N at the moment un specified beyond the restriction N > 5. The quark fields, which form the fundamental representation o f this group thus form a 3xN matrix. (In literature, the three colored states are sometimes referred to as the red, white and blue whereas the various flavour indices are referred to as up, down, strange, charm, beauty etc.) The symmetry is realized locally, so that, we have In the theory, In addition to the quark fields, a set of massless vector meson fields Ap, which again carry both color and favour. The lagrangian density is thus proposed to have the form F,*... (1) where % is the quark field, X ^ 'b are the analogs of the X -matri ces for the present gauge group, M is a diagonal mass matrix of the quarks and la the covariant field derivative of the gauge fie ld s. Three observations concerning (1) are relevant to our dis cussion. - 246 - - 2 47 - Although the quarica are ‘colored*, all physical states are supp osed to color singlets. This Is proposed to he achieved by making the color group a perfect symmetry, so that Its associated gauge bosons have zero mass. The exclusion of the colored states from the physical spectrum is presumed to be achieved through a ‘confinement1 potential between colored particles created by the Infrared diver gences associated with the massless vector particles. Colored sin glet states, which do not couple directly to the colored gauge bosons on the other hand are not affected by the Infrared singularity. This 3 picture which is present In some two dimensional models is far from being established In the realistic case but In tills lecture the possible role of ‘lnstantons1 in the confinement mechanism will be discussed a little while later. The second feature concerning the Lagrangian (1) Is the obser vation that in the limit M •-» o , the flavour symmetry group (tak ing H c 3 for simplicity) becomes the full chiral group SV(3) @ So(3) In the limit of exact symmetry all the sixteen associated currents are conserved but the conservation Is presented to occur according to the Haiabu-Goldstone mechanism. This Implies Immediately an octet of massless Pb- Goldsone bosons. In the real physical world, the quark masses break the symmetry dynamically so that the mesons acq uire masses and current algebra calculations have been performed to obtains agreement with the ratio of the masses of the h, k , ‘j mesons with the rather obvious Input information vu^x << ius . There Is a third feature about (1) w. lch is rather discomfort ing. In the limit M — > o , the full symmetry group is actually * So Cl) X u( V X l/a ( U rhere U A ( 0 is the axial dialog of u( i) , its associated current being the ninth axial eurr- - 248 - ento ^ i a rather embarasslng conservation of nine rather than eight currenta Implies that when the symmetry la realisiei In the Nambu- Goiistone sense, there will be nine rather than eight Paeudosoalar mesonsc t:hen one considers explicit aymmetry breaking, ene would have. In addition to the octet ef psuedosoalar mesons, a ninth lae* scalar pseudescalar meson. ^'elnbertf * has nroved the Inequality i < j 'T1 ^rom current algebra and hence In view of the very low masa of this hypothetical meaon, one oan safely conclude that It la not experimentally seen. One rather seemingly possible way to get out of thla dilemma la to observe that the ninth current la well known to have an ane- c maloua .divergence J 1 r ! s' « p p 1 / i;, v< N,,V hA.oV Hovever the anomalous term la a divergence of another local operater 1 A "'V ‘ A / w - ",v- [ * ' r V * > > s'A*c C~^.^:aav A5x4Cvr] . ... u ) The usual proof ef the ®el dart one theorem ® la unaltered even with thla anomalous term, '"'e will very aoon See hev the presence *r lnatan- tons provide a solution to this difficulty as pointed out first by t*Hooft and by Cali an, Baahen and Gross II. Pseudopartlole Saintlnns (Inatantona). In dealing with strong Interaction Lagrahglan theories, of which (l) la an example, aemlolassloal approximation methods have been used lately aa a means of extracting dynamical results out of the theory®, Polyakov ® In 1975 pointed out the Importance In this context of cla- - 249 - aaloal finite act Ion aolutlena of the fleli equations In an Ifciolidean apace after continuation te purely Imaginary time. Simultaneously, BPST were able te work out an explicit sel.utlen ef finite action In a self-ofcupled Yang-Mllle theory where the underlying symmetry la an SU(2 ) greup. The Euclidean action In auoh a case la where we are using a matrix notation and similarly for the field tenaor pr . The vaeuum-to-vacuum amp litude In such a case la given by ( o U V j • ■= | [ e * „ ']• . g .< p [ - j x . l l * t ....,. >! , ’ where the Integration la to be done over all field oonflguaratlena which approach F^v - c at Infinity and obviously which have finite action. Unlike non-gauge theories, thla condition however doea not topi y that 4 ^ -* o at Infinity but that A ; 0 - 7 ° i '(>-) V ,v --4 O .) where 1 (7 4 la a STT(2 ) matrix. N0 w, If we oonelder a large feur- dlmenslonal sphere S^ ; a" r -■ ,the boxmdary configuration la speci fied by spec 1 'ying at each point on the surface a unitary matrix. But the manifold of 2 x 2 unitary matrices la also S 3 , ao that the vari ous configurations are simply a Question of mapping a sphere onto a sphere continuously' to ensure that derivatives and hence action Int egral remain finite. The situation becomes absolutely O ear In the (1 ♦ 1 ) dimensions where the group is U(1 ). Clearly, the various oontrlbutlone to (5) fall Into various homo- - 2 5 0 - topy classes yanking free -o> to unless we are able to prove that only the honotopy el&aa zero (corresponding to.4»-c) haa fin ite action X most important ste p In this direction waa taken by BPS! who prove! the inequality betxeen the topological quantum number V an! the pseuie* action 5^ 5 L' £ — ^ I V ) - - - (S ) 9* &p it is clear that the equality‘ w in ($) will be achieve! , for ' jr - * p zC« >/ (instantone) a n ! for fA* V- »c /V. v , (anti-lnatantona). Furthermore, in view of the inequality these configurations are extremum of action an! hence solutions of the classical equations of motion. , What la the interpretation of V . M s is male_very easy in the a -x c, gauge where one can write •V - n — -r\ ( (r- - <» ) - - - ■ ("lo ) where >i i t ) = ■ eVj-* . j " . tw • - - m O M e is the se-oall el wlniing number in the mapping A (*) - 9 T(>/> ^ 3- (*) V V « (11$) is easily recognized as the wlniing number. We can always oheae ri(i - o * so that integral V implies - integer. We stiU have to convince ourselves that oonflguratiena with V t- a but finite action lo actually exist. Per v = I , a simple an! hbvioua ansatz gives us the required solution. “Qie crucial clue was that the solution would behave like a tensor under combine! rote® - 251 tioa la space and i,no«pn.cfl, However, leoopoco rotation fuxn an SU(2) group wheraa spacetime rotations form an 0(4) group. This how- aver present* no problem because 0(4) Is homomorphic to SU(2) x SU(2)» so that we can extend our Internal symmetry group to 0(4) obtain a solution which Is a tensor under combined 0 (4 ) rotation and then reduce the Internal symmetry part according to one of ■“ * the SU(2) subgroups, The resultant solution was given by M S as _ 11' CO = V C x ^ t 7 0 ' ^ J n v The solution becomes even more clear In the - o gauge, we can arrange to hare A ^ c at L-= - o by a global gauge transformation, whence at t = + , thla solution reads A c. ■=■ c * <' ^ X — '* t ~~? A (> ) - I ~ ± ) 2.V A x.cr V X ' X * " ^ X L. x - x — ; • 1 a, X -constants. ■■■(u) t This- path in function space thus connects two zero field tensor configurations which would have been impossible in Minkowski space time along any extremum path, IH The -vacua.’ - . We are thus forced to admit in addition to the A - o con figuration which v» denote by | o >• , other configurations labelled by positive and negative lntergers ^ which we denote by jv> ,rem embering that only configurations belonging to the ho m o topy class - 252 - % can connect configuration with W- M ^ rV i t h ’ finite weight T « If this were not so, our vacuum state would have been around | a} with its zero point fluetuationa. Bet now it is clear that the vacuum state will be a superposition ef all these configurations and that in calculating any path integral, t a configurations contribute te with a relative weight of F (-Hl | I 9 >. - k f v* 6-) I r.} such that / T ! 6 ) Cy-h (-C6-) ) &> . ’-- (IS'. Stability of the vacuum therefore Implies the existence of an inf inity of vacua | , o < d In a given f 0 > - vacuum, the computation of the vacuum-to-vaeuum amp litude once again should involve summation over all homotopy class paths. If we denote by ["BA U]V , the paths belonging to olase v , then ( 0 ) c- > -5L < > j? f" i " fr - f r>' tr 3 . ( VI ’ | n ^ .1 M t _ 2" ~ c- ] s I I r ( 1 ig.p .f -253- where we have used the relationship between *J and F s • The third term in (15) is of the form £. ~h and explicitly violates f and f • If we had fermlons in the theory also, them one can make the foll owing observation* ,A chiral transformation on the fermi fields changee the action integral by & $ e-lf. — & ] a ‘f A • 1 e i f • ~ S i m ) . = - i ( A t x ■ ( ^ T j ) . cr r - ' V ' ‘ ’ ' t n }> i.e., effectively & - » e - -ir • Thus in a theory with mass- less fermlons, 6- can sfcxe always be readjusted to the P and $ conserving value fr- =o by suitably redefining the fermi fields. Also, in a theory with massless fermi fields we will have no tunn elling because, one will have a conserved axial charge .£^v> [ T, £f5J ^ o • . ■■ ( r V However, even in this case, one if forced to accept only the \ i>_> vacua because of another requirement in field theory! cluster dec omposition property. Consider an operator of some chirality,whence < n-■ | f> J > = 0 - 254 Cluster decomposition would imply, However, we will have a state I of suitable chirality for which. A large number of the results above are of the type of ( If 1) Schwinger model and in fact were motivated by it,, One would like also to see whether the phenomena of confinement is also related to 10 the existence of instanton configurations , One of course does not have a definite angwer in this case but the followingresult of Calien,I)ashen and Gross i:> very Instructive, we consider the Abelian Higgs model in two dimension which exhibits the instanton 11 configurations also. One uses the Wilson criterion for conflniment namely the vacuum expectation values of c 7- < **!-• f l-t/L . f23y> where L is a Euclidean loop of spatial extent R and temporal extent T « We know that a A - 1,T/ e or zero dep ending upon whether the loop encloses an instanton or not. Hence our vacuum expectation value is proportional to e * l ^ ^ j M+ n * . " 1 V 0 L = i ^ C i p ] ...... nh) - 255 - where the superscript L stands for inside the loop* As one can see for ^/e. integral there is no volume dependence* For ^/ e. not integral, the summation can easily be carried out leading to , £(*) T x e* |» (~£c ty) .(\- ("2-r ) The expression (15) clearly indicates a confinement potential for fractionally charged particles* Generalisation of tills line of reasoning to the realistic case is not straightforward hut Call an 10 et. al,, were able to identify a certain type of configurations (necessarily implying the neglect of an infinity of other, possible paths) that could lead to a similar phenomenon* y* CP non-conservation. We shall finally touch upon the implication of instantons on the problem of strong Ci non-conservation* We had seen that the structure of the vacua forces us to have a term in the Lagrangian which violate both f and I except for the choice 9- - • Even if \ we" set 0- equal to zero, we might be required to perform.a phase rotation in the quark mass matrix, which again is tantamount to in troducing strong CP-violation, which is totally unacceptable exp erimentally. She effective lagrangian in a &- -vacua gets modified from its original value in equation (1 ) to £ 6 3-r,.T'te-*-£vj • --•(«> However, for gauge fields coupled to massless fermionafc as re have seen, chiral invariance allows one to redefine the1 fermlflelda to - 256 - to change the parameter effectiv ely into 9- - o *i.e., one obtains a situation of no strong CB-violation in sueh a theory, Por massive 12 quake this simple reasoning no longer holds, but Pecoai and cuinn have pointed out all alternate possiblity of avoiding atrong 01- violation in suoh a case, Their ideas are best illu strated in terms 13 of the 4-quark model of Weinberg , which has enough richness to accomodate 0P-coneervation, The weak group here la 5" u / v * u ( O and the model involves four quarks • ( > !l ' . ( idoubletse iP n (P n IR } 2 R > z r : singlets, There are also two scalar doublets (under weak St(2jj <^,^1 and I $ i tC/ I and the Yukawa coupling le i 1 = 1 C' . niR ( r t-'-'j i . ) L', .)' 1 . » ■ + X p v ; GYu- - - < 2 . v whioh conserves the flavour ouantum numbers, strangeness and charm ( S.L.Glashow and S.i-einberg* Ihys. Rev, .015,1958(1977) 1 The weak g oup is to be broken spontaneously and hence one introduces the self coupling of the doublets i ?(*; - i n,l f Kt*) «r r >„ ( ( tit*) ’ r i ■ ‘ t £ l>r« C t v ) ( -h £ .'< “« ( t r t s ) ■■ - L ~%J y > ^ 4 257 - where hermiticity demand ■ that C-rs - f s -> end ti<, a , 't> are real* As written, the theory has an U(l) symmetry —? € < h ( i'X « Jr5 ') '•'i <2 X t= ( i c< T 5- * s ( 04« ro< ^ e / ' t ' 0 , ° , < —J c w ^ T t —y f x [ - r + 4 c ’ e * L> - l , with f -k „ r -v f.) ^ o .How there is a formal cyimetxy of the lag- ranglan under this* In general, under a chiral traneformation the action integral will change hy ticjf - J a'f X C fD • = - C . ( 9 Z/3XTi^) f -A** . fr , which effectively oeane 6- t> - Lo- . Hence, under Winters* e U(l) group e- — » & i t « j, - e- and hence redefinition of fields serves no purpose la achieving CB-conservation, Peecei and ouizm however demand invariance under the transformations ( H ) hut without the condition 1 = %, ( 11 ) L $ , * R "f" % t U ^ L A * g + U ' . with two Higgs doublet , , * V is assumed not sensitive to separate phase rotations of and , we assume <^,6> = i?, and ( C) - "to 1)6 b°th real. Then this lagrangiafc possesses the «lR , ? x - > e ! a f 2_ - • - - ( t o These two separate phase rotations here give us two Rambu-Goldeione bosons if the vacuum is not Invariant under them. One of these, the one coupling to Hypercharge is absorbed in generating mass for the vector boson but the other orthogonal component *°( — ~ n > S-vvx f- x . .Lv* tL dVvv ^ 'V i_z ) is physio ally present and physical base mass eoual to aero as can be eeen by n*l$lag the / s M the eon ef the 133 vacuum expe ctation YaluBB and, a quantum field and substituting ta tho Log* rangian ( 3 | )« Such a particle will however acquire a non-zero physical Qas8 generated by vertices violating the phase inva riance, I.e., Instanton effects. Illustrated In the accompanying figure* Prom an estimate of .the visible coupling constants and a scale of hadron physios ( say the mass of the pion we get the order of magnitude estimate for the mass of the particle as: ,M a1- ^ p ' ,M it ~ Ido . 'kd V- - • • ( Shis hypothetical particle, called the Axion was psoposed indep- 14 15 endently by Wilczek and by weiriberg • we will not discuss In de tail the experimental Implications of the axion (k :) beyond men tioning that if it exists It is expected to be seen in processes like (e) radiative decay of vector bdsons v' -r -J r 1 (b)fligh energy bremdstrahlung processes (0 ) decay of the charged K r fi rr y ® Also if ./ > i>'v. , such a particle will be seen to decay into electron-positron pairs. So this date, experimental evidence is against the existence of the axion . and if that is really so, the only other possibility of avoiding strong CI^ vlolat-on is to have one of the quarks massless. Although this apparently leads to immediate difficulties in K r- k ^ mass difference eaal eulatlona, this line of thought has nevertheless been considered 16,17 by several authors > • . - 2 60 AiSFBRBSCBS . 1. A. A. BtlftYlu ot> tl* Phyi> fiBB j 85 (1976}r . 2. S.Weinberg, toys.' Rev. Lett., 31, 494 (1973). H. Frltaeh^M. Cell-Matin and H. Leutvylar, Phys. Lett. 48B, 366 (1973). 3. Se# J. Lovenateln and A. Swleca, Ann. Phya. 68 (.1971), 172 and references therein. 4. 3. Weinberg, toys. Rev. Oil, 3583 (1976). 5. J.S. Bell and A. Jacklw, Nuovo Clmento 60A, 47 (1969)$ 3. U Adler toys. Bar. 177, 2426 (1969). 6. J. Goldstone et. al., Phys. Hev. 127, 965 (1962). 7. a. 0. CAllan et. al., Phys. Lett, 638, 334 (1976) 0. t ’Rooft, toys. Rev. Lett., 37 , 8 (1976). 8. See R. Rajaraman, toys. Reports 21C (1976) 277 and Proceedings of the HSP Symposium, Bhubaneswar (1976) The Instanton Solutions are also briefly discussed In the second reference.. 9. A.M. Polyakov, Phys. Lett. 59B, 82 (1976). 10. C. Q. Callan et. al. Phys. Lett. 663, 376 (1977). 11. X.Wilson, Phys. Rev. 179, 1499 (1969). - 261 - 12. S. P. Peace* 4 H. H. Quinn, Phys. Hev. D16, 1791 (1977). 13. S. Weinberg, Phys. Hev. Lett., 37, 657 (1976). 14. P. Wtlogek, Phye. Hev. Lett. 40, 299 (SB ) .15. S. Wllnter, Phys. Hev. Lett. 40, 223 (1978). 1 6 . N. G. Peshpande D. B. Soper, toys. Rev. Lett. 41 (1978) 17. A. B. Zeplda, Phys. Hev. Lett. 47 (1978) 139. 0 NEW RESULTS FROM COSMIC RATS S.C. Tonwar Tata Institute ef Fundamental Research Hoasi BhaSsha RoasS, Bombay-400 005 I wish to discerns here some of the interesting results that have become available In last few years f r o m experiments carried out using cosmic ray beam. These results provide information about particle physics at energies well above these available at particle accelerators. I have also included in this discussion some experimental results which were obtained many years back but have been reinterpreted recently in the light of our present knowledge of high energy processes v . , and cosmic ray composition. I must emphasize right in the beginning that most of the interesting results obtained in cosmic ray experiments suffer from poor statistics due to very low luminosity of the cosmic ray beam at high energies. Further the interpretations of observed phenomena, in some cases, are not unique due to our lack of precise knowledge of the composition of primary cosmic rays at these'energies. Therefore, the cosmic ray experiments, by their very nature, can provide in some cases only a glimpse of the interesting phenomenon which may be occurring at very high energies. An idea of the statistical problems faced by a cosmic ^ray^physicist may be given by a comparison of the cosmic ray particle flux with the beam luminosity obtained, say, at ISR machine. For - 262 - - 2 6 3 - energies above 2000 GeV (2 TeV) the proton flux at the top of atmosphere is about 70 m"^sr"*hr“l and only about 0.5 m '^sr^day*1 at mountain altitude (730 g. cm*^). On the other hand one can observe about 10® interactions per second at any of the ISR intersections. Of course these difficulties do not really discourage a cosmic ray physicist because they are more than compensated by the excitement due to the possibility of observing completely new phenomenon at very high energies. The new results discussed here, can be conveniently grouped into three categories : (i) Results on hadron-nuclei and hadron-hadron interaction cross-sections, (ii) Results concerning possible violation of scaling behaviour at high energies, and (iii) Results on New Particles and New Phenomenon. Though most of the results discussed here belong to hadron physics, interesting phenomenon observed recently in underground experiments at Kolar Gold Fields has also been included in the discussions on new phenomenon. Finally I plan to mention briefly some of the new experiments being planned which would provide certainly new and possibly • exciting information about high energy processes at super high energies. , - 264 INTERACTION CROSS-SECTIONS AT HIGH ENERGIES Most cosmic ray experiments measure hadron-nude us Inel inelastic cross-sections O^-A corresponding value for taadron- T proton total cross-section is then deduced using Glauber theory of multiple scattering. There are basically two methods which have been Inel used for determination of Around 1975 there were basically two viewpoints regarding the T energy dependence of CTp.p which suggested very different behaviour T of (Tp.p at very high energies. The first viewpoint was represented by the -results obtained by Yodh, Pal and Trefil* in 1972 indicating that T 1 2 CTp-p is increasing with energy as In s, s being the c*.m. energy.* - 265 - This result was obtained by comparing the expected attenuation of primary proton flux through the atmosphere and the measured flux at Mt. Chacattaya (550 g. cm ) as given by Kaneko et al (1971) of . unaccompanied charged hadrons. The second viewpoint was later given by Ganguli and Subramanian^ in 1975 who reanalysed the same data using a different primary energy spectrum and also added information obtained from N jjl, -Ne measurements at air shower energies. They concluded T that CTp_p is increasing slowly with energy as Ins and might become constant at high energies. The basic difference between these two view points, obtained using essentially the same experimental data in the 2-20 TeV energy range, was due to the assumption of different shapes for the primary proton energy, spectrum at energies above 2 TeV, apart from small corrections. The primary proton.energy spectrum Np (E,0) enters in the calculation of O'pi air through the expression: „ . 2.4 xlO4 11161 (E) = —— — - • In„ | r--- ”------j j mbarns °p -a ir x L n ? ( E .,) J where Np(E,s x) is the surviving proton flux at depth x g. cm- in 2 the atmosphere. Since - 2 6 6 - Inel = Total _ Elastic Op-air ~ Op-air " ®"p-air _ Total Elastic ' T and ^ ^ .a ir (o. r, fpp) 0-p.TC =* j 1 d5d2 ' ' lFP-air<^.r,I fpp) Here Fp.gir is the elastic scattering amplitude which is related to the proton-proton scattering amplitude fpp, nuclear radius r and momentum transfer A and Can be computed using reasonable assumptions about nuclear parameters and the formalism developed by Glauber for multiple scattering. The proton-proton scattering amplitude fpp is given by here oC is the ratio of real to imaginary part of the scattering amplitude, b is the diffaractive width, k is the proton momentum and t is the momentum transfer. The energy dependence of o( and b is assumed as given by the experiments at machine energies. V - 2 6 7 - Inel Apart from the crucial dependence of f T p .^ and hence of T the deduced 0~pp on 016 assumed shape of the primary proton energy spectrum, corrections are also necessary for the fact that experiments measure the unaccompanied charged hadron flux which include secondary hadrons (p, ic , K etc.) produced by higher energy primary cosmic rays higher up in the atmosphere. Thus Np " Nch - NP ' % " N * However Np and Nr are negligible in proportion to among secondary hadrons and correction needs to be applied only for the pion content of the unaccompanied charged hadron flux. Note that the error Inel in determination of CTp-air is quite small for even a large error in measured flux due to the logarithmic factor. The measured value of 0*ptair using the flux (NCh - ) also needs to be corrected for quasi elastic scattering, diffaractive excitation and inelastic screening processes 4 as discussed in detail by Gaisser et al . There have been only two direct measurements of primary proton energy spectrum. The measurement using balloon borne calorimeter by 5 Ryan et al (1972) gave the integral energy spectrum as Np(E.O) = 1.14E‘1,75cm-2sec-1 for 20 < E< 2000 GeV . The measurements by Grigorov and his colleagues®*7 gave the energy 1 - 268 - spectrum for primary protons as Np(E, O) = 3 x 10’4 (-™ -)1' 62 • Q + (--y0-)2j cm-2sec-1 for 20< E< 20,000. These measurements have been made in a series of experiments using satellite borne calorimeters. Surprisingly the measurements of Akimov et al 7 show the proton energy spectrum to be steepening for energies greater than 1500 GeV. This particular feature has invited lot of attention and criticism to these measurements since such a bend in the proton energy spectrum has not revealed itself in any of the measurements at higher energies of various cosmic ray components at mountain or airplane altitudes or muon energy spectrum at sea level. Yodh et al* have therefore used an extrapolation of the spectrum 5 given by Ryan et al in their analysis for obtaining energy dependence of ^ "^ a ir °* G"pp' ®n 016 other hand Ganguli and Subramanian^ P 7 have used the proton energy spectrum as given by Akimov et al . They Inel have also included in their analysis the results on deduced from - Ne data obtained at air shower energies. The air shower date" shows the O '^ ^ ir t0 near*y independent of energy and therefore a slow increase as Ins of a-*116* is suggested by Ganguli and p-air Subramanian from their analysis shown in figure 1. - 269 This picture has gone considerable change in last 3 years due to a series of new measurements with much improved detector systems. These measurements have come mainly from two groups: Yodh and colleagues from University of Maryland at College Park. (USA) and Nikolsky and co-workers from Lebedev Institute in Moscow (USSR). 8 The Maryland group (Siohan et al , 1978) has measured the unaccompanied charged hadron energy spectrum in the 100-10,000 GeV range at mountain altitude of 730 g. cm 2 (Sunspot, New Mexico). They have used a 4 m 2 area 8 m. f. p. deep iron calorimeter having wide gap spark chambers 9 inside as well as above. Similarly the Lebedev Institute group (Nam et al , 1977) measured the unaccompanied charged hadron energy spectrum in O the energy range 2000-50,000 GeV at 700 g. cm" (Tien-Shan) using a 2 36 m area, 4. 5 m. f. p. deep lead calorimeter. Nikolsky and his co- workers^® have also determined C pltdr *or hadrons energy 15,000 GeV by studying the zenith angle distribution of these hadrons. Inel This method of determining • ^ is independent of the shape of the primary proton energy spectrum and depends only weakly on the composi tion of charged hadrons at the observational level. A further refinement of the experimental results for the purpose of determining tT ^ ^ ir ^ also 1,6611 achieved by Maryland group8 through a direct, measurement of the proton content of the charged.hadron - 2 7 0 flax. Since this is a new and interesting development it is appropriate to describe this measurement in seme detail. As is well-known the conventional methods like magnetic bending, ionisation measurements etc. for measuring the particle mass have severe practical limitations for hadrons of energies greater than about 300 GeV. The phenomenon of transition radiation, on the other hand, starts becoming interesting for this purpose at only these energies. The transition radiation is emitted when a charged particle traverses an interface between two media of different dielectric properties. The intensity and the energy spectrum of the emitted radiation depends on the Lorentz factor Y (= E/m) of the particle. For a single interface between vacuum and dielectric medium the intensity is proportional to Y and is equal to | • t\u*p • Y where e( is the fine structure constant, «p is the plasma frequency of the medium and "ft is the Plaint's constant. For vacuum-mylar interface this intensity is only 0.178 keV for Y = 3000 400 GeV) and hardly detectable in any detector in presence of the ionisation by the particle itself. The TR intensity can be Increased by using a large . number of interfaces, for example, by using large stack of stretched mylar foils. But in such a stack, due to interference between radiation emitted at different interfaces and due to absorption of the radiation in the medium itself, the TR yield is no longer proportional to Y and increases only slowly with Y . However the fact that for same total 271 energy ia seven times Yp helps in distingoishing pions from protons. The Maryland group^, *^ constructed a transition radiation detector consisting of a sandwich of 24 layers of styrofoam radiator and multiwire proportional chambers. The TR emissivity for this particular type of foam was measured by Fabjans (1975) at ISR. Also a small area but otherwise identical 3 layer detector was calibrated 15 directly at BNL using electrons. The complete experimental system including TR detector, calorimeter, spark chambers etc. as used at Sunspot to measure the unaccompanied charged hadron flux and the pion to proton ratio is shown in figure 2. A typical hadron interaction and cascade development in the calorimeter as shown by spark chamber picture is shewn in figure 3. Using this system the pion to proton ratio has been measured*6 to be 0.96 + 0.14 for hadrons of energy 400-800 GeV and 0.45 + 0.25 for hadrons of energy > 800 GeV. Another interesting result obtained by the Maryland group from the same experiment concerns the measurement of instrumental effects 17 which could have led to wrong identification of protons as o( -particles and heavier nuclei by Grigorov and his colleagues, in their satellite experiment. Ellsworth et al*? have reported that due to back scattered particles (particularly neutrons) from interactions inside the calorimeter the electronic detectors like scintillation detectors and multiwire - 2 7 2 proportional chambers located above the calorimeter give pulses of amplitude much larger than expected for singly charged particles. Thus it has been shown that the identification of protons by proportional chambers alone is' highly suspect and that this error increases with increasing energy. Though an exact quantitative correction to the results of Akimov-et al cannot be deduced from the studies made by Ellsworth et al 17 due to different geometrical arrangement of detectors, it is quite ’ clear (fig. 4) that the steepening in the proton energy spectrum is partly, if hot fully, due to instrumental effects. With these new measurements of unaccompanied charged hadron 8 flux in the energy range t 7 200-50,000 GeV by Siohan et al and Nam et al® a consistent picture of the energy dependence of O ^ a d r T of Q"pp can be obtained using for primary proton spectrum an extrapolation of the measurements of Ryan et al® to energies of about 4 g 10 GeV. In figure 5 are shown the results obtained by Siohan et al on Inel G“ air usin8 the experimentally measured "*t>/p ratio. As seen in Inel fig. 5 the 0*p-air ^lu es obtained by the Maryland group are in good agreement with Ln^s extrapolation of ISR measurements of C pp Inel Inel and converted to (J'p -air. Also shown in this figure is the CS"p a with proper corrections* are shown in figure 7 along with recent results obtained by Amaldi et al*® (1977) at ISR. Also shown in the figure is the curve fitted by Amaldi et al*® to their measurements which is represented by the expression V - EJ)-,,t» 0S - (24.2. 1.1) E-0 55! 0 02] p p U , 2. 10+ 0.10 + (27.0+ 1.0)+(0.17 + 0.08) • 018 18 It should be noted that Amaldi. et al have also measured the energy dependence of 0( , the ratio of real to imaginary part of the scattering amplitude, and the best fit represented by the expression given above has been obtained through a simultaneous fit procedure for both Qt T T "9 and - The It is quite clear that the N^. - Ne data does net agree with T this result and requires (T*pp to be almost independent of energy in 5 8 the 10 -10 GeV energy range. Apart from some systematic uncertain* ties in measuring for air showers with small number of }Judetectors, / - 274 - Inel the Nikolsky and his colleagues*® have also measured hadron-lead nuclei inelastic cross-sections and deduced proton-lead cross-section at energies of 5 and 15 TeV. Compared to a value of 1780 + 18 mb for Inel 10 Inel It is of interest to compare the cross-section values predicted by Glauber theory for interactions with various nuclei using the observed T Cj h_p values at machine energies and the experimentally measured G'tf-A * This comParison' ahown 18 Fig. 9, reveals clearly the success ^.Inel T of Glauber formalism for converting 0* h-A 8140 ®*h-p since ratio of expected to measured value.is close to unity (+10%) for all the measurements. It is appropriate to remark here that the sensitivity of Inel t T Crp_A for changes in 0 ”pp reduces with increasing 0~pp 88 shown by Barger et al^1 (1974). Their result (^.1 0 ) indicates that measurements Inel of. tr*p_A have to achieve higher and higher accuracy with increasing . T energy to obtain tT pp with given accuracy. - 2 7 6 - SCALING VIOLATION AT HIGH ENERGIES There are many experimental results obtained from air shower studies which have been interpreted as indicating a violation of scaling characteristics at air shower energies (10®- 10® GeV). Some of these observations have been interpreted in terms of a rather rapid increase 1. ( ~ E 2) of particle multiplicity with increasing energy. However these interpretations are not unique since they depend on the assumed composi tion of primary cosmic rays at very high energies. I would discuss briefly three of these observations. The first observation concerns the longitudinal development of air showers. Suga and colleagues (LaPointe et al'22 ) measured the .epth of shower maximum for various primary energies using constant intensity method (fig. 11). They concluded from these observations that showers develop much faster than expected from calculations based on the scaling model. Similarly Kalmykov and Khristiansen®® have observed the variation of N ^ ( > 10 GeV) with shower size Ne and have found Nj*. to be much larger than expected (fig. 12). Vatcha and Sreekantan®* have studied high energy hadrons in , air showers and find too few hadrons (fig. 13) compared to the predictions using scaling-model. All these three observations require violation of scaling characteristics to varying extent. However recently it has been shown 25 that the first two observations can be interpreted in terms of a .*%«.»•.» i » i. V. i/rnil • I* i : it «>*.. ’ .a.*, utjx. .* scaling model if the primary composition at energies of 10®-10® GeV is assumed to be purely iron group nuclei. The hadron observations ' 24 also would require much less drastic changes in interaction characteristics if the primaries are all iron group nuclei. The possibility that iron group nuclei may dominate at energies above 10 GeV5 was first suggested experimentally by the measurements on primary composition by the Goddard group^6 in early 70’s, They had found that while the energy spectra of protons, oL -particles, CNO group nuclei etc. had an energy exponent of about -2.75, the iron group nuclei had a much flatter spectrum with an exponent of about -2.2 in the energy range of 5-100 GeV/n" Recently the Maryland group 27 (Goodman et al 1978) have presented evidence on the basis of arrival time distribution of hadrons in air showers for enrichment of primary cosmic rays with iron group nuclei with increasing energy'.1 They find that the observed hadron flux accompanied with small showers and the proportion of delayed hadrons require that the exponents for the energy spectrum of protons and iron group nuclei in the 1-100 TeV/n energy range be -2.71+ 0.06 and - 2l. 36 + 0.06 respectively. These results suggest that Iron group nuclei Would be the dominant component 6 of primary cosmic rays at energies 10 GeV. These results also support the interpretations of the longitudinal development of air showers , 22 Njju’ - Ne variation 23 • , and hadron component studies 24 in terms of iron group nuclei thus weakening the evidence for large scale violation of scaling characteristics at air shower energies. - 278 - ’ There are of course some problems about this interpretation S * e I since the observations of Srinivasa Rao and his colleagues on high £ { energy muons ( > 220 GeV) in small sise air showers do not seem to i • • I agree with Iren nuclei dominated composition (fig. 4). However the fact that at about 10** eV the Iron nuclei may constitute less than 40% of primaries and that there are relatively large statistical errors in | the high energy muon data 28 suggest that these observations may be | consistent with the primary composition indicated by the measurements of Goodman et al*7. HEW PARTICLES OR PHENOMENA (I) Long flying component: \ _ Nikolsky and his colleagues** (Aaeikin et al 1975) have studied the absorption of high energy cascades in their large area lead calorimeter. They determine the absorption length of the cascade after it has reached ' the maximum by fitting an exponential decay curve to the cascade from 300 to 1400 g. cm'* (Fig. 15a). Surprisingly they find that Aabs changes from a value of 685 + 85 g. cm for hadron energies of le ss than 40 TeV to a value Of 1100 + 100 g. cm** for hadrons of energy above 40 TeV (fig. 15b). This change in is seen for single hadrons incident on the calorimeter as well as for air shower cores.~~ Aseikhret al*® interpret - 279 - these observations as due to the production of some new particles at energies > 40 TeV which have different interaction characteristics (either small interaction cross-section or small inelasticity or both). No other cosmic ray group has such a large area calorimeter to observe a significant number of very high hadrons in reasonable amount of time. Also most other calorimeters use iron as absorber where dependence on energy may be different since equilibrium between electro magnetic and hadronie component is reached faster in lead calorimeters compared with iron calorimeters. These results on are very interesting indeed and need to be studied in detail with different experimental techniques. > • (ii) Centauro_events: . The Broxlt-Japan Emulsion Chamber collaboration group^® has reported observation of 5 events which show very unusual characteristics. All 5 events have very large multiplicities, about 70 to 90, and have 6 primary energies > 10 GeV. The details about these events are given in the table below. The almost complete absence of V-rays from the main interaction is a peculiar feature of these events. These 5 events are out of a total of 44 events having > 200 TeV. Figures 16a and 16b show schematic - 2 8 0 - TABLE : Interesting features of Centauro Events Event Number I II in IV V Chamber Number CH-15 CH-17 CH-17 CH-17 CH-16 Height of main Intn (m) 50 80 230 500 - Observed Multiplicity Pb jets 20 23 29 25 19 C jets 29 9 8 13 8 Total 49 32 37 38 27 Calculated total Multiplicity 74 - 71 76 90 - Multiplicity Y -rays arriving,the chamber 0 0 17 51 34 Produced in A-jets - - 17 47 - Multiplicity of V - rays produced in main inttf 0 0 0 4 illustrations of Centauro I and IV events. It has been suggested that only baryons may have been produced in these ultra high energy interactions. While no satisfactory and detailed explanation has been offered so far for these events it is clear that very interesting phenomenon is taking place at energies /v* 10® GeV. (iii) Delayed particles: * In 1971 the Ooty group of31 Tata Institute had reported observation - of some very energetic hadronic type of events in their calorimeter which were delayed relative to shower particles incident above the calorimeter by more than 25 nanoseconds. In a preliminary experiment using cloud chamber Tonwar et al 32 also reported observation of 2 such events with measurable cascades seen in the chamber. In a recent experiment using 2 the large area (4 m ) calorimeter having wide gap spark chambers, the Maryland group 33 has studied the arrival time distribution of hadrons associated with small air showers. They have also observed three interesting events whose energies can be estimated to be more than about 50 GeV which are.delayed by 30 nanoseconds or more. Figure 17 shows the observations of Goodman et al 33 as a diplot of pulse height in terms of equivalent particles from a scintillation detector located inside the calorimeter and time delay of this signal relative to the signal from the shower particle detectors located above the calorimeter. No such event is expected from known particles or processes including fluctuations as shown by detailed Monte Carlo simulations of air showers in the atmosphere. However such events could be interpreted as due to production of some 2 new type of massive particles with mass in the range of 5-20 GeV/c . Since the observed flux of such particles is about (4.3 + 1. 3) x 10"** cm -2 sec 1 sr 1 , the production cross-section required to explain the observations is about 10-100 yu-b depending on the assumed energy dependence of the cross-section above threshold. - 282 - These observations of delayed energetic events by Goodman et al 3 3 and by Tonwar et al 31 ’ 3 2 earlier imply the existence of new massive relatively long lived ( ^ 10 -7 sec.) particles which are produced only at very high energies ( > 10 eV).14 Detailed information about the production and interaction characteristics of such particles can be obtained through air shower studies using visual detectors. Such a study is now being carried out by the Ooty group using34 the large multiple cloud chamber with two scintillation detectors placed inside the chamber (fig. 18). The arrival time of the particle producing the cascade is measured by these two detectors relative to shower particles detected by two similar detectors located above the lead layer shielding the chamber. The energy of the partible is estimated from the observed cascade by track counting method. (iv) High energy cascades in underground experiment: Recently Krishnaswamy "et al 35 (1977) have reported observation of 4 high energy ( > 1000 GeV) cascades in their experiments being carried out deep underground in Kolar Geld Mines. The detectors used were large area vertical and horizontal telescopes and magnet spectrographs having scintillation detectors and neon llash tubes with a variety of absorbers. In addition to detection of single and multiple muons of very high energies, the telescopes record showers of different sizes generated either in the - 283 - rock enveloping the detectors or the absorbers Inside the telescopes. Most of these showers are due to normal electromagnetic interactions of atmospheric muons near the detector. Of the high energy showers observed 2 have been seen in the detector located at a depth of 3375 hg cm -2 and two have been seen at 7000 hg cm‘‘ level, suggesting depth independence of the phenomenon responsible for these events. No event of such high ■ energy is expected in the given exposure area factor from any known process. The observed features suggest that they are produced by a highly penetrating and isotropic component such as the cosmic ray neutrinos. However it is difficult to account for the observed frequency of these events unless the neutrino interaction cross-section for such processes is much higher than the extrapolated values from lower energies. Observations at various depths underground with improved detection system are continuing and further detailed observations are awaited with great interest. (v) Charm hadron production in hadron collisions: i ■ : ; : ' Charm particle production was probably first seen in cosmic ray experiment in 1952 by Kaplon et al36 but was obviously not recognised. Niu. et al3^ (1971) and Sugimoto et al3® (1975) reported observations of very interesting events in cosmic ray interactions at high energies ( > 10 TeV) which can now be easily explained as due to production of a pair of charm hadrons. Figure 19 and 20 show, schematically the events seen by Niu et al 37 1 and Sugimoto et al 38 respectively. Recent searches 39 for charm hadrons in accelerator experiments at 200-400 GeV have given the production cross-section of about 100 job. The cross-section is estimated to be about 1 mb at energy of about 10 TeV. It is interesting to note the continuing rise in charm production cross-section from 400 GeV to 10 TeV... If the cross-sections continue to. rise with increasing energy by an order of magnitude, charm production may be playing a dominant role for some of the observed features like muon component in air showers. Therefore a determination of charm production cross-section at energies of ~ 100 TeV will be,of considerable significance for cosmic ray experiments. NEW EXPERIMENTS Cosmic ray experiments continue to provide interesting information about high energy physics since the present generation of accelerators have highest equivalent laboratory energy of only about 2 TeV (ISR).' However, in next,3 to 4 years,this situation would be changing with CERN/SPS and FLAB/MR facilities providing ]p-p interactions of as high an energy as 10*4 eV and interaction rates of about 10® per second. Therefore many of the experimental techniques presently being used by cosmic ray experimen ters would require considerable improvement to enable them to explore - 2 8 5 - successfully the very high energy region above 10 eV.1 5 The experiments would necessarily have to be large scale since the flux of cosmic ray particles above energies of 3 x 10 15 eV (projected energy of FLAB/ED) is only about 0.2 m • 2 day-1. 1 Some experiments being planned or being started now are indeed looking forward to study high energy physics at energies > 10*6 eV. Two of these promising efforts are worth mention 40 here. One is the Akeno air shower project near Tokyo being implemented by a group whose members belong to various Universities in Japan. The main aim of this project is to study in detail all the components of air showers for primary energies of 10*® -10*® eV. Electron component, shower arrival direction, and shower front curvature would be measured using an EAS array of a large number ( ~ 500) of detectors spread over few square kilometers. The muon component would be sampled for each 2 shower by detectors of nearly 500 m area spread around with muon energy thresholds of 0.5 and 1 GeV. This would enable the muon density to be measured accurately for distances of 50-500 meters from shower axis and would yield an accurate value.of Nj*. ( > 0.5 GeV) and Np. (> 1.0 GeV) for the shower.. The energy flow in the shower core would also be measured by a large area system of shielded detectors. A 90 m area2 8 m.f. p. deep calorimeter using concrete as absorber would measure the energy in the hadron component. For obtaining an accurate estimate of the energy loss in - 2 8 6 - the atmosphere which is a good measure of the primary energy/'Cerenkev light produced by the shower particles in the atmosphere would be measured by a complex set of Cerenkov detectors (2m diameter mirrors viewed by 19 photomultipliers each). The Akeno experiment should yield good data IE ifl on high energy physics in the 10 - 10* eV energy region. The other promising project is the Fly's Eye experiment of the group** at University of Utah. The experiment aims to detect and measure the air fluorescence light generated by air shower particles passing through the atmosphere. The detector system will consist of an array of specially fabricated UV sensitive photomultiplier tubes clustered in the focal plane of a large number of 1. 5 meter diameter parabolic mirrors. The mirrors with their photomultiplier arrays, mounted on a geodesic-like structure will be exposed to the night sky on clear moonless nights. This design enables measurements on a shower at different stages of development through the atmosphere. The timing system measures the shower trajectory. The effective selection area of the detector system increases with .increasing energy of the shower ■ since higher energy showers being brighter in terms of air fluorescence can be detected at larger distances. The estimates of Bergeson et al 41 on indicate that showers of energy 5 x 10 eV striking as far away as 50 Km from the Fly's Eye system could be detected.' A prototype consisting of 3 mirrors with 12 photomultipliers each was operated by Elbert et 43 in association with the large Volcano Ranch array of John Linsley The results of the measurements with this prototype system have been very encouraging. The complete Fly's Eye system holds great promise for giving new information on high energy physics in 1017 - 10^® eV energy range. Another very interesting and rather large scale experiment 1 being planned for by an International collaboration group44 is the „ DUMAND (Deep Underwater Muon and Neutrino Detector)Project. Basically the experimental system would consist of a very large array of detectors immersed 5.5 Km under water in Pacific Ocean. In its Gigaton (1 Km3) version the experimental plan envisages a detector array of about 1200 strings, each 630 meters long with 18 sensors equally spaced vertically. Many experimental and theoretical studies are being conducted to optimise the detection system. One possible system can be optical detection by photomultipliers of Cerenkov light produced by relativistic charged particles'in water. Sonic detectors are also being considered for detection of high energy particles and cas cades though early tests indicate energy threshold for such detectors to be rather high ( > 10 15 eV). The potential of an experimental system like DUMAND for high energy physics and astrophysics is tremendous. For example, it can yield very valuable information on intermediate - 2 8 8 - vector boson and other new particles, neutrino oscillations, muon interactions at very high energies, cosmic ray composition at high energies, neutrino bursts etc. As expected the financial requirements for this experiment are rather large. Therefore it could be some time before the whole system gets assembled and starts giving new and exciting physics. In the discussion above I have attempted to give a flavour of some of the new interesting results that have been obtained in last few years in cosmic ray experiments and of some of the new experiments which may add valuable knowledge and.help in improving our under standing of high energy phenomenon. It is clear that information about high energy processes for energies above 10 eV15 can be obtained only from experimental studies using cosmic rays since machines of energies 10*** eV are unlikely to be built in next two decades. New and bold ideas about possible experiments at these superhigh energies are being actively discussed by various cosmic ray research groups. - 2 8 9 - REFERENCES 1. G.B. YODH, YASH PAL, and J.S. TREFIL, Phys. Rev. Lett. 28 (1972) 1005. 2. T. KANEKO et al. Conference Papers, 12th Int. Conf. Cosmic Rays, Hobart, Australia, 7 (1971) 2759. 3. S.N. GANGULI and A. SUB RAMAN IAN, Conference Papers, 14th k Int. Conf. Cosmic Rays, Miinchen, Germany, 7 (1975) 2235 ; S.N. GANGULI, R. RAGHAVAN, and A. SUB RAMAN IAN, Pramana 2 (1974 ) 348 ; S.N. GANGULI, Invited Talk, 2nd High Energy Physics Symposium, Santiniketan, India;(1974) 63. 4. T.K. GAISSER, G.B. YODH, V. BARGER and F. HALZEN, Conf. Papers, 14th Int. Conf. Cosmic Rays, Miinchen, Germany, 7 (1975) 2161. 5. M.J. RYAN, J.F . ORMES, and V.K. BALASUBRAMANYAN, Phys. Rev. L ett., 28 (1972) 985. 6. N, L. GRIGOROV et al, Conference Papers, 12th Int. Conf. Cosmic Rays, Hobart, Australia, 5 (1971) 1746.. 7. V. V. AKIMOV et al, Acta Physica Acad. Sci. Hungaricae, 29. Suppl. 1 (1970) 517. 8. F. SIOHAN et al, J. Phys. G: Nucl. Phys. 4J1978) 1169. 9. R. A. NAM et al. Conference Papers, 15th Int. Conf. Cosmic Rays, Hovdiv, Bulgaria, 7 (1977) 104. - 290 - 10. R.A. NAM et al. Conference Papers, 14th Int. Conf. Cosmic Rays, Munchen, Germany, 7 (1975) 2258. 11. V.L. GINZBURG and I.M. FRANK, Zh. Eksp. Teor.Fiz., 1£ (1946) 15 ; G. M. GARIBIAN, Zh. Eksp. Teor.Fiz. 37 (1959) 527 ; G. M. GARIBIAN, Proc. Int. Conf. on Instrumentation for High Energy Physics, Frascati, Italy (1973) ; X. ARTRU, G.B. YODH, andG. MENNESSIER, Phys. Rev. D12 (1975) 1289 ; L. DURAND, Phys. Rey. D ll (1975) 89 and references contained therein. 12. R.W. ELLSWORTH et al, Conference Papers, 14th Int. Conf. Cosmic Rays, Munchen, Germany, 9 (1975) 3284. 13. J.R. MACFALL, Ph.D. Thesis, Univ. of Maryland (1976) Unpublished. 14. C. FAB JANS, Private Communication. 15. R.E. STREITMATTER et al, Preprint (1976) Unpublished. 16. J.R . MACFALL et al, Conf. Papers, 15th Int. Conf.Cosmic Rays, Plovdiv, Bulgaria, Late Papers Volume (1977). 17. R.W. ELLSWORTH et al, Astr. Sp.Scl., 52, (1977) 415. 18. U. AMALDI et al, Phys. Lett. 66B (1977) 390. 19. J.R. MACFALL et al, Preprint (1978) To be published. 20. G.B. YODH, Invited talk, VUth Int. Colloquium mi Multiparticle Reactions, TUTZING, Germany (1976). 21. V. BARGER, F. HAL ZEN, T.K. GAISSER, CiJ. NOBLE and G.B. YODH, Phys. Rev. Lett. 33 (1974) 1051. - 291 22. M. LAPOINTE et al, Can. J. Phys. 46 (1968) S68. 23. N.N. KALMYKOV and G.B. KHRISTIANSEN, Conf. P liers 14th Int. Conf. Cosmic Rays, Munchen, Germany, 8 (1975) 2861. 24. R.H. VATCHA and B. V. SREEKANTAN, J. Phys. A: Math., Nucl. Gen., 6 (1973) 1078, ibid, J. Phys. A. Math., Nucl. Gen. (1973) 1050 ; ibid, J. Phys.A: Math. , Nucl. Gen. 6 (1973) 1067. 25. T.K. GAISSER, R.J. PROTHEROE, K.E. TURVER, and T. J. L. McCOMB, Rev. Mod. Phys., 50 (1978) 859. 26. V.K. BALASUBRAHMANYAN and J.F . ORMES, A p.J., 186 (1973) 109. 27. J. A. GOODMAN et al, Preprint (1978) To be published ; J.A. GOODMAN, Ph.D. Thesis, Univ. of Maryland (1978) Unpublished. 28. B. S. ACHARYA et al, Conference Papers, 15th Int. Conf. Cosmic Rays, Plovdiv, Bulgaria (1977). 29. V.S. ASEDCIN, G. Ya. GORYACHEVA, S. L NIKOLSKY, and V.I. YAKOVLEV, Conference Papers, 14th Int. Conf. Cosmic Rays, Munchen, Germany, 7 (1975) 2462. 30. M. TAMADA et al, Nuovo Cimento, 41B (1977) 245 ; J.A. CHINELLATO et al-, Preprint (1978). 31. S.C. TONWAR, S. NARANAN and B. V. SREEKANTAN, J. Phys. A. Gen. Phys. JS_(1972) 569. 32. S. C. TONWAR, B. V. SREEKANTAN and R. H. VATCHA, Pramana, _8_(1977) 50. 33. J.A. GOODMAN et al, Preprint (1978) to be published. - 2 9 2 34. S. C. TONWAR, Invited talk on 'Delayed Particles in Air Showers', Workshop on Charm Production and Lifetimes, Univ. of Delaware, Newark, USA (1978) ; S. C. TONWAR et al, Paper presented at 4th High Energy Physics Symposium, Jaipur (1978). 35. &LR. KRISHNASWAMY et al, Conf. Papers, 15th Int. Conf. Cosmic Rays, Plovdiv, Bulgaria, 6 (1977) 137. 36. M. KAPLON et al, Phys. Rev. 85 (1952) 900. 37. K. NIU et al, Prog. Theor. Phys. 46 (1971) 1644. 38. H. SUGIMOTO et al, Prog. Theor. Phys. 53 (1975) 1541 ; 39. C. RUBBIA, Summary Talk, Topical Conf. on Cosmic Rays and Particle Physics above 10 TeV, Univ. of Delaware, Newark, USA (1978). 40. K. KAMATA, Invite ' Talk, Topical Conf. on Cosmic Rays and Particle Physics above 10 TeV, Univ. of Delaware, Newark, USA (1978). 41. H.E. BERGESON, J.C. BOONE, and G. L. CASSIDAY, Conf. Papers, 14th Int. Conf. Cosmic Rays, Munchen, Germany, 8 (1975) 3059 ; G. L. CASSIDAY et al, Conf. Papers, 15th Int. Conf. Cosmic Rays, Plovdiv, Bulgaria, 8 (1977) 270. . 42. J.W, ELBERT et al, Conf. Papers, 15th Int. Conf. Cosmic Rays, Plovdiv, Bulgaria, 8 (1977) 264. 43. J. LINSLEY, Conf. Papers, 15th Int. Conf. Cosmic Rays, Plovdiv, Bulgaria, 8 (1977 ) 206. • ■ x 44. A. ROBERTS, Invited Talk, Topical Conf. on Cosmic Rays and Particle Physics above 10 TeV, Univ. of Delaware, Newark, USA (1978).' 45. S. P. DENISOV etal, Phys. Lett. 36B (1971) 528 ; S. P. DENISOV etal, Nucl. Phys. B61 (1973) 62. 46. W. BUSZA et al, Phys. Rev. Lett. 34 (1975) 836. - 293 - Captions for the Figures Variation of q -1*161 with energy deduced by Ganguli Fig. 1 p-air Subramanian (1975). Points shown for energies below 10® GeV are based on measurements of unaccompanied charged hadron flux and have been obtained using the primary proton energy spectrum as given by,Ryan et al ( if ) or as given by Akimov et al ( 4 ). Points shown for energies above 10® GeV are obtained from Nj*. -Ne data. Fig; 2 : The experimental arrangement at. Sacramento Ridge Cosmic Ray Laboratory, Sunspot (Siohan et al, 1978). Fig. 3 : - Photograph of spark chamber system used by Yodh and Colleagues showing a typical unaccompanied charged hadron cascade. Fig. 4 Integral energy spectrum for primary protons reported by Akimov et al, with and without correction for back- scattered particles Fig. 5 : Lower bounds to the proton-air inelastic cross-section. Shaded areas reflect statistical uncertainties in experi mental data. Points if are based on composition corrected charged hadron flux. Point $ is based on zenith angle distribution (Nam et al. 1975). Solid curve is the expected variation of cr1” , with energy based w p-air on ISR measurements. Broken curve is a straight line eye fit to the 3 points. Fig. 6 : Variation of q*|f a*r with energy based on measurements of unaccompanied charged hadron flux at Tien-Shah (Nam et al, 1977). Points if are obtained using an extrapolation of primary proton energy spectrum given by Ryan et al (1972). Points ^ are obtained using an extrapolation of primary proton energy spectrum given by Ryan et al (1972). Point if are obtained using the energy spectrum given by Akimov et al (1970). _ . 294 T Fig. 7 Variation of with energy. The ISR measurements PP and the fitted curve are as given by Amaldi et al, (1977). Points ^ are C'pp values by Nam et al (1977) from their measurements of charged hadron flux.. Point $ at 16 TeV is the computed q -T value obtained using the PP zenith angle distribution of hadrons measured by Nam et al (1975). Fig. 8 Variation of with energy (MacFall et al, 1978). For comparison, a c c e p to r datS*Denisov et al4** (1971) and Busza et al4 (1975) are also shown in the figure. Fig. 9 A comparison of the computed inelastic hadron nuclei cross-section rr using z-rT as measured at h-A PP ISR energies and Glauber formalism for multiple scattering inside a nucleus (A) with the experimentally measured ^ "h A a* var^ous energies. The ratio ^.Theory j ^-Expt is close to unity (within about 10%) for energies upto about 104 GeV (Yodh 1976). Fig. 10 Variation of the sensitivity of hadron-nuclei absorption cross-section rr-31)8 to change in as a function X ~ h-A 6 ° P P of z r-1 . U PP Fig. 11 Variation of the depth of shower maximum with primary energy. Cbmputed curves using (A = 56) nuclei as primaries are seen to give better agreement with experimental data. Fig. 12 Variation of the number Nj* of muons of energy > 10 GeV per shower with shower size Ne. Computed curves with iron nuclei as primaries seem to give better fit to the experimental data. Fig. 13 Integral energy spectrum of hadrons in air showers. Scaling model calculations do not agree with data. Fig. 14 Lateral distribution of high energy ( > 220 GeV) muons in air showers of size (1-4) x 104. The curves labelled 1 to 5 show the expected lateral distribution for various assumptions about primary composition. 1 I - 2 9 5 - Fig. 15a Typical cascade curve observed by Aseikin et al (1975) for single hadrons inTien-Shan lead calorimeter. Fig. 15b : Variation of the absorption length with energy for single hadrons and air shower cores. Fig: 16a - : Schematic illustration of Centauro event I. " Fig. 16b : Schematic illustration of Centauro event IV. Fig. 17 : A diplot of pulse height in terms of equivalent number of particles from a scintillation detector located inside the calorimeter and the arrival time delay of this signal relative to arrival time of shower particles (Goodman ’ et al, 1978). i Fig. 18 Schematic drawing of particle detectors located inside the large multiplate cloud chamber operating at Ooty (Tonwar 1978). Fig. 19 Schematic illustration of the new particle event seen by Niu et al (1971). Fig. 20 Schematic illustration of the new particle event seen, by Sugimoto et al (1975). **** 296 - Enar^ <«• GoV FIS-1 TOO SENSITIVE VOLUME S * C * L COSMIC m v FLUI OETECTO* SCINT 0■ < I 2i S« «I » I FEET FIG. 2 . Integral Proton Intensity (particles/cm2, sr, sec) sn Ti (pe limit) (upper i, T using limit) (lower PCI, using Hi spectrum rtn *- exps. 1*2-3 proton pcrm fe correction after Spectrum correction after Spectrum observed toFit / . FIS. 4- FIS. 97 - 7 29 - I nry (GeV) Energy / I ./ l » I / I . ~ - 29a - 2 6 0 W* E C^»v) FIG. 5 a .eecA. ^ -smiftt ^ - (MaiitflA. uaveg B jefttttals ^ednim , 1 5 ^ - cMbiiraA. u»w^ A k u w n a t a l l s ^ ^ ti s It to* Enarg^ tew GeV F1G .G - 2 9 9 - 60 5Sl 60 40 So 100 3 0 0 VI GeV F16.7 ° w . vs- Energv 700 ■ „ ^ 600 ■ .1 t= x Denisov ▲ Buszo • This Expt 500 - 10* 10 Energy (GeV) F IS .8 300 - L l 0 8 *V7 ENEMY, w 6eV f i g .9 <3 F IS . 10, t - 301 - 800 Protons 11) Protons, present ,'e . work, a increasing » 600 ; -t E IGoisser E r 1974) 1 e 400 2 0 0 - FI6.11 Fe. . GG P. KK P.GG p. CM - 302 - 1 *5 IDFB sI Hodron energy (£*)(5eV) F I G .13 » COW MfMU (• m.). FIG. 14- Absorption Length (g/cm2) NO.Of PARTICLES 10 10 1200 1600 800 400 4 5 • 0 400 200 ISE RNS DRON A H SINSLE lS.tSb P E (TeV) 0 - 303 - FIS. 154. FIS. ET 9/cm DEPTH HetE e lH S - i HADRONS* £ _ ftA S CORE CORE S ftA _ £ 0 . 2 . 600 •400m - 305 - 100.00 | *0.00^ 2 8 0 .0 0 ^ ui 1 7 0 .0 0 d 6 0 .0 0 < 50.00 O * 0 .0 0 (£ Mi:::::!?)) 3$ 3 0 .0 0 Z 2 0 .0 0 _- D6LAT FIS. 17 LEAD N CLOUD CHAMBER Fe PLATES 14 g. cm "* each FIG. IB EVENT «B-a 1 frrnr|iunniiiinmni imijection. - 3 0 7 - DISCUSSION T. Das : Among the various total cross-section data that you have presented, some (like the Echo Lake data) do not seem to extrapolate smoothly to the ISR energies. Do you think this difference is serious ? Or in other words, is anything drastic expected between the accelerator and the cosmic ray energies ? S. C. Tonwar : Inel / The differences seen between the c rp-air data as obtained from Echo Lake experiment and the expectation from ISR measurements are mainly due to non-inclusion of the correctum for the composition of the hadron beam. Some systematic effects also are present due to different criteria used by various groups for selecting unaccompanied events. The experimental data corrected for these effects agree well with extrapolation from ISR energies. D.S. Narayan : The scaling violation you reported, I want to know whether the violation takes place in the central region or in the fragmentation region. S. C. Tonwar : The rapid longitudinal development of air showers and also the observed variation of N^. ( > 10 GeV) with shower size Ne have been interpreted as due to scaling violation in central region assuming primaries to be protons. K. V.L. Sarma: i) How direct is the evidence for the absence of charged pitins in the Centauro events ? ii) Could the large angle cascades observed deep underground in the Indo-Japanese Collaboration experiment be some kind of Centauro events initiated by Neutrinos ? - 3 0 8 - S.C. Tonwar: i) There is really no direct evidence for the absence of charged pions in the Centauro events. However this absence is indicated by the fact that very few high energy gamma-rays are observed in these events suggesting the absence of neutral pions. ii) Regarding possible similarity of high energy cascades seen by Krishnaswamy et al with Centauro events, may be Dr Ito would like to comment ? N. Ito : The anomalous cascades observed at KGF do not have any penetrating particles among them. Hence it is difficult to understand them as due to Centauro type of events in neutrino interactions. M. V. S. Rao : By Monte Carlo simulation of air shower cores we find that some 'Centauro' events in which considerable number of gamma- rays are observed can be understood as due to fluctuated air shower cores. Thus the fraction of Centauro events is perhaps smaller by a factor of about 2. S.C. Tonwar : It is very interesting to know that Dr Rao and his colleagues have been able to generate two events out of a total of about 140 simulated air shower cores which have great similarity to Centauro event IV. If their interpretation is right, there should be some more particles around the main event with decreasing lateral density away from the core. This can be experimentally checked by Prof. Fujimoto and colleagues. However it may be mentioned that Centauro event IV is really the least striking event as compared to the first three events since for about same total energy the observed number of Y -rays striking the upper emul sion chamber is 51 for event IV compared to 0, 0, and 17 for first three events respectively. Also the observed 5 events are out of a total of 44 high energy events suggesting rather frequent occurrence of this type of phenomenon at very high energies. OS SUPERS Y1METRY M.S. Hari Saas Raman Research Institute, Bangalore-06 In the quantum world we have rather two diatinct, or ao it appears to us now, species of particles namely Fermion s and Bosons. The Bosons obey Boae-Einetein statistics according to which any number of thaee particles can occupy a given quantum state. This aleo implies that Boson fields can have classical limits a familiar example being the elsetromag-netic field. In matter under unuaual conditions it is not unreasonable for other Boson fields e.g. the coalar pion field to have "classical" limits. In quite contrast' to the Bosons stand the Feroione, no two of which, obeying the pauli Exclusion principle, occupy the same quantum state. This remarkable property among other things is responsible for the stability of matter ate. Aleo, one cannot have classical Fermion fields. Despite these striking differences, Bosons and Fermiona have many formal similarities too. Both the fields and their dynamics may be incorporated into a single action principle, both are bound by the ,CPT theorem etc. In a more phenomenological sense thair differencae far outweigh their similarities. The Boson and Fermion spectra look completely different with degeneracy occuriing only for the photon and the neutrino. The differences not withstanding, can one put the Fermiona and Bosona on the "same footing" - whatever that means? Asking in a group theoretical context, can we envisage a structure where Fermi and Boas fields would - 3 0 9 - - 310 - be Included In, the ease multiple t? Then, can one have Feral on gauge fields and poealbly Goldete no-Fermi one*. If b o , ia the neutrino one such? These questions in a nutshell pose the basic motivations for what is now popularly called "Superaymmetry" or Fermi-Bose ayomatry. Either in operate*, quantum field theory where the Fermion propagatora emerge as functional derivatives of the generating functional with respect to anticommuting Graesmenn elements (possibly space-time dependent) or in the equally successful source theory approach, which dispenses with the operator nature of quantum fields as an unwarranted and cumbersome mathematical requ ire men t» where the sources of Fermion fields are the space-time dependent Grasemann elements one ia stuck with these G-numbers wherever Fermiona are concerned. We shall later come back to these two diverse approaches to the physice of. the microjtorld to once again demonstrate two different approaches to aupersyametry# For the moment we digress from the world of elementary particles and discuss briefly some remarkable properties of the anticommuting G-numbers in Mechanics. Mechanics ia characterised by conserved quantities like Energy-momentum, angular momentum etc. When a rotating object is considered whose dimensions are much smaller than that of the region of motion, one may think of this as an "intrinsic" angular momentum though there are obvious differences from the quantum mechanical intrinsic spin. The usual equations of motion are o f '' the type (1) - 311 - : © r i» the proper tine. Now introduce e S-no^eueh that ^©,e} = o / ©1=< (2 ) further X^t)^ -t l »> The euper "gauge" tranaforwations axe« ■C-^-C-vV'j© © ^ 's (4) Defining = 3 X X ' - ' 3 X " end the coweriant de- ’ a© • . rivotives (5 ) Dx- xV'-Qx, V x * x'- L Ox , loo. cU-niv<. following traneforBatione ■ ' X = ^ ^ X- Hence the definition of covariant bX- f ^ X "derivative". ^ S x'=- “j x‘ \ J- x ^G>x) =■ £■ TH'D*) 161 The eupex— Lagrangian and action are *e$l ^ o a Ia'cIa ) c£> = - V i X ^ X wJ = (7 ) For a free particle ■ (ease leaa) V - V^Ctc2 -«-v i>S ) with the condition a S = 0 We introduce a 'super potential1 ^ ^ which has the expansion + t©S A (8) there are no quadratic and higher terms in @ because Q 1 =• O Then we have 312 - = l5^ Ltvu - A ^ ,v Z>X v r = 1 > x P ,A p \ p V&1VJL = XP <9 Under the supergauge transformation a (4) one has *b-JV ' t ’&'&*■ (10) which leads to The coupling to the supee-particle is provided by the minimal . coupling ? X. x t- e A *(1 21 The interaction Lagrangian then become a ■-fy-V'X*' . ««> Superaymmetry and elactromagnetic gauge iiw variance are joined in the single invariance of the action under vjAp. A v ^ \ M (14 ) The equations of motion turn out to be X)X|j. - G-j ^ A v, p S * “ 5 A~ p ) V) A-p (15) In terms of real space-time variables one gets - ^ p v ^ v ^>p “ P p v S V (16) The gyromagnatic ratio emerges to be 1 characteristic of classical distributions. Thus we see that the introduction of the k-nutaber into mechanics neatly unifies the spin and mo man turn degrees of freedom. Thera may be conceptual problems in interpreting the "eupergauge" transformations (4). When a similar procedure is adopted for the gravitational field wa see the geodesic and Fermi transport equations emerging ee e single equation viz. UfT, V"KX) rr q.v'l *-V. <9 S* ^ (17) which in terms of reel variables raede ■ t l * = - ^ S ’* ■= ♦ **P S3" (18) Incidentally the spin equation of nation in (18) holds irrespective of whether one is deeling with elementary particles or classical rotating objacta. After..these brief remarks oh the "super mechanics", we peas on to a proper discussion of suparfialda. SuGarfisldsi Thera are two distinct approaches to euperfielde one of which employe the concept of auper space while the other still retains the usual notions of apace time. Even in the second category where is a further division into an approach which a priori specifies the group structure of the auper symmetry transformations while a second more phenomenologically oriented approach (source theory) ragarde the group structure as some thing to be derived and in the process admits partial invariance. Me shall diacuaa thsss three approaches in detail now. Suoar apace t The idea hare ia to enlarge the apace time to include G-number coordinates the extra dimensionality depending on the problem of interest but v"> 4-. The @ S satisfy ' 1 - 3H - Now we consider fields in thie super epeee of the type V- (**1 ©*), ® ^ ■ ( 20) where A collectively stands for the indices ^ Al, • The super coordinate is dasicpiated by •? ^ ^ X^, ^ . The supersygroetry transformations are produced by v K® x -^ x' © -^ st- y v ■ (21 ) •Now the Sraesmann elements have been generalised to Majorana spinore. The super space is characterised by a super metric a ^ a s l = (2 2 ) The super metric transforms according to a t 1' ■ . We will discuss the general properties of the aupa rao trie later on. Let ua go back to our auper scalar field "2^ (4 J : ^ C.a j®.) = $(J*-«6 ) (24) Let us expand in terms of 0 remambaring 0* = O 5* («•»©) = ftix) -v-"© wa have Q )$ Q "= O ', © QT^v ® - ° • Thua w 880 tltit the single auper field ^ ie equivalent to a variety of tensor fields in ordinary apace. In this particular example, the scalar - 315 - auperfield contains threo ecalar fields A,F,D one paeudoscalar field G, an axial vector field end two Majorana apinor fields r and X . We note however that the number of Fermionic and Bose components are the aaae viz. B. This equality is a featuzs of all superfields. Now consider the super .coordinate transformation © -=* O * £ (26 ) From (24 ) we conclude , . > A = 1 S vV = - 6 + i + _L (, + i t I K K A*'- a 3 s (27) We eee in (27) a transformation that connects Fermi and Bose fields and is an example of "aupersymmatry11 transformation. We shall reserve comments on the group structure of these trans formation to a later stage. So far we heva not 'imposed any conditions on the various fields in ^ . It is possible, for example, to reduce the number of fields by imposing subsidiary conditions on in a super symmetric invariant manner of the form " w $ = 0 (2a) Aleo in (27) it ie to be noted that the variation of D ia e total derivative. Thus if we consider two super fields ^ and 5i^it ie suggestive to treat 80 **'B Lagtengian density for tha interaction of the various fields contained in $ and 3) • Need— less to say the . action derived from such e Lagne’ngian density is • invariant under supersymmetry transformation*. - 316 An example of such a euparaymmatric interaction is provided by "&> = -t- — V>)a L"i;g_YV>)'~V - A. yyn - A ~ Interesting features of this theory are that fermiona and Bosons have the same mass and the coupling constants of the various interactions ere all related, for this reason, tha degree of renormelisability is improved over the conventional Yukawa interactions. But the relevance of the modal to an actual physical situation is still remote though the possibility of rendering an a prioni non-renorraaUsable theory renormalisable by imposing supersyir-.etry is of interest if renormalleability is an important criterion in one's view point. Super gravity It We go back to the supermetric 9^ ) introduced in (22 ), This - metric has three sectors - V U ) ; i -‘P U ; = (30) In the flat space limit ^ ' ° ’> 9 ^ = - ic '1) ^ (31) Each sector has a super coordinate expansion (V )U)= 3 ^ ^ ) + o© C2; = ©J.<5>^(.r) v - % / i U) = p.+ ©^vVp * • - - - ' (32J - 317 - consider the super coordinete transformations ■ ■=-'= x ■ © ' = V7"l x ) Q (33) Then we find F t.x) = ACx)^tx) •, vy’c*) = A W vVC*-) which ere the appropriete scale transformations for Fermion and Boson fields. In addition, (33) inducee an abelian gauge transformation on (5m.Cx ) = (5)ml(-x) -*• (34 ) One can generalise (33) in an appropriate way to generate the electromagnetic gouge transformation. . For this introduce © uulkA c^ = »,x •, Th,n- * > • < » = t>- ACX) e ^ , 135' O/ndL a _ _ ^ *V = V* VNv One can generalise’'to the genera tion of non—abelian gauge transformations e.g. SU(n) as follows! introduce with a. - ■ then, •x'.x ©'*«= [t-t.E ^*) X**lw transformations into a single supercoordinate transformation. - 318 Choosing an action of ths type ^ R. it is easy to recover the Fermion and Boson field equations. In a compatified fore st read# ^ Alb ” ° (31 Uhlika - O which inplias source free Einatoin *s equations, (38) has all the source terms and includes the stress tensors of various Fereion and Boson fields. Spontaneous symmetry breaking may be introduced through G* - where ^ — \oW CneV. (also the scale introduced in Duel models) Though there are a number of interesting features in this approach to gravitation, the conceptual problems of interpreting the superspace remain. 6— uo Structure t The algebraic structure of supersymmetry transformations is described by graded" Li e Algebra's! “If we consider elements lying in vector spaces L^, then L ~ is a graded vector space. L is a graded Lie algebra if there exists a bilinear map c/^ L x L L such that £• L v* t (39) Further if xfcV* ^ cvwJL 3. £ * -(-•)** (40) A graded derivation of degree M. is defined by (41 ) Mtjl) I -t- y DZ Thus ws see that the bracket between even elements is a commutator, brackets between even and odd is also a commutator, - 319 - whi-la the bracket between odd elements ie en anticommutator. Several simple examples of 6LA may be givent e = ! ^ = ^ 'c ^ < r 8 ) c M.e. e l0> x e l, , -36 i—« (42) Likewise tx, -Ix*'- X, A j ~ 'tf, £<~ I w h o r e d is an annihilation operator for a fermion also obey GLA. Once the even element elgebre ie given it ia possible to fill the rest of GLA though not in a unique manner. Without going into the motivations that led to it we simply state the result of filling in the GLA with PoinCaxe. algebra ae [{) expanded to include conformal tr. and dilatations; L»; \>MV,fv> - V xvV tj,xv>K £PM,Pvl = o. I T 1" , - - i. 3 mXk V l-$vX 1 * “ . KV1 > 0 [K h,V v 1 = -2.1-3 " v T ) - 2 L 7 - uv £t>,PMl - i-PK / £ .D , . - i. £ X>, T|JV3 = o (43) For closing the GLA, one has to introduce sn additional element acting trivially on the even generators C fc.^ ’ IE , PU3 = LE1 KU1 = LEl»3= 6 14,1 - 3 20 - The full GLA is now given by the additional relationei y HV, R p l - L < h i r * 1 = P R p L ^ M, ^ l"3 - ~ Q p L ? > ^ = - 1 - H z <3* " " U V * * ! - - 1J a fc* L £ ) ^ oL ^ - (7^ (45) ( v ^ i > - M * „ c , U p “ j ?d, - -_2- (jS^C K ^ The adjoint operators s q ^ »ay also be included such that H,"M - *ft v y " V v \ OL.OnS -- ' iS*..s^T <47) In an approach baeed on the group structure, eupereymmetric theories are constructed by looking at the irreducible representations of the GLA and constructing the appropriate action. We give an example of this in an §lternative approach to supergravity. Super oravitv II t This approach ie based on the observation that e representation of GLA contains a neutral boson and a Majorana - 321 - Feroion, of-adjacent-spins- 'J'+ 1/ (both masslsaa ). The multiplet consisting of helicity-2 and hslicity 3/2 fields ia taken to be the gravitational eupermultiplet. The action at first ia taken to be a sum of Rarita-Schwinger and Vierbian actiona and an invari ance under vc -'D k ^ x ) w p = i VC ~ lvC "ttX) ^ (48) It is found that with an additional term signifying "interaction* the action can be made super symmetric invariant. The "attra ctive" features of thia approach■ are that few more one loop graphs become amenable to investigation. Hultlspinor basis of auDBravmmatrv i (Source Theory) Schwinger has recently proposed an alternative approach to Fermi-Bose symmetry based on the so called multispinor formulation. This approach rejects the idea of a super apace, but unlike tha second approach which also rejects the super space.idea does not presuppose a definite group structure. The group structure emerges from the particular examples considered. The starting point of this approach is the observation that any spin value can be constructed out of basic spin /2 objects provided attention is given to the appropriate symmetry operations. The. basic object in source theory is the vacuum persistence amplitude denoted by \ VJC S ) e (49) where | * refer to the vacuum states in asymptotic future and past and S is the source. 3 2 2 - Under conditions of no interaction, W (a) has the form K in momentum space ) vj (s) = a s(.-n"W tC V " -* )* .’ s i p ) + (50) selects = 1 for every spinor index in the particle rest frame* The real multi spin dr source S has the structure S"v .... y (J?) - S (,-f) and corresponds to spin value if total . Jy» i r " ' T v » a. symmetry among the indices is used* latrix transposition of the kernel combined with “I? /p -9 - Is in (50) produces an overall" factor end to match thia the algebraic property of the source must be one of total commutativity for even Y\ and anticommutativity for odd rt. Thia is the statement of the spin-statistics connection* The fieldaX. ore defined by hvJu; = {k W - v y ir xr xv*) JiaR)* * x X(.V) = ^ (^YVA- S(^>) (51 ) As an exapple of how supersymmetry arises in this frame work consider two particles with spins , Xli.' with non zero 2 2 masses. An infinitesimal change in the source - is a i Jvn*i characterised by ^ S I, ^ |VXy, - -LVX S, .... .vx (.V) (52) where (jf) ia a apin-X2 source (hence totally anticoamuting) and complete symmetrisation of products is implicit in (52). Tha response of (50) to this variation is ^ i n . , ’ " s, which can be lads to counter by choosing (54) with appropriate symmetry.(52 and (54) dearly connect Fermi and Bose fields. It i e also clear that invariance of Vx)"-* VxJ ia poaaible only if 'Vv\Vv + \= fV1vx^VY' . If the two fields of oppoeite intrinsic parities, appropriate 'Sj* have to be introduced into (53), (54). This exercise can be carried out for various multipleta e . g . Spin 0 , sp in y 2 ,/s p in 3 /2 e t c . The whole p ro gramme may be /s p in 1, enlarged by admitting representations other than the spinorial ones e.g. Vectorial etc. A possibility not so far entertained in conventional approaches to supersymmetry viz. unit epin transfor mations may be produced just es easily in the..source approach. The invariance of the graviton and photon actions under such transformations hee also been established. Once the invariance of the action has beensestabliahed the group structure can be established by considering the totality of. such transformations. Thia way Schwingar has demonstrated the structure.that was here before assumed a* Priori £.forW 8^o3 Extensione to interacting systems can be carried out in a straightforward and systematic manner. Partial in variance, broken only by the mass difference in the multiplet may also be achieved. In conclusion the personal opinion of the author ie that the multispinor approach ia the best suited for future studies * of supersymmetry by virtue of ita broad frame work and conceptual difficulties inherent in the other approechee. Ultimately the concept of eupersymmetry w ill be vindicated only if i t proves useful in correlating the phenomenological aspects of the behaviouf of Fermions and Bosons. References i P. Nath and-R. Amowitt Phya.Latt 56B 177 (1975) L. Coreein, Y. Neeman, S. Sternberg Rav. Mod. Phye. 47 (1975) Sv Deser, B. Zumino, Phys. Lett. 62B 335 (1976) D.Z. Freedman, P.Van Nieuwsnhuizen and S. Ferraro Phye. Rav D1 3214 (1976) J. Sehwingar, UCLA preprint no. ULLA/7B/TEP/11 May 1978 - 325 - DISCUSSIONS T. Das: I have a general question. Is it clear that the source - theory approach will always give the results obtained by either of the other two approaches you talked about? N.D. Hari-Dass: Source theory provides a much larger frame work and to that extent possibilities considered in other approaches are already contained in the source approach as special c a s e s . . M. Seetharaman: ( 1) Since fermions bosons are in the same M u ltip let, how does one assign fermion number to ferm ions only? ( 2) I am surprised that in a 60 minute talk on supersymnetry, Salam's name has not been mentioned even oncel N.D. Hari Daaa: Super symmetry s till maintains statistics and hence there is no problem with Fermion numbers. Regarding your comment I just wish to say that I have only tried to give an account of the conceptual features of supersymmetry without going to historic detail s. The references I have given at the end are by no means complete but hopefully they contain reference to all previous work. ProbJLr Boy: What is the present status of renormalizability " ( a l a Freedman et a l) upto two loop s and three loops? N.D. Hari Dass: The status is vague. . V - 326 - H.S. Sharatchandra: 1) In the supersymmetric extension of non-A 6 gauge theories can you have the fermions in any representation? Does this model have Goldstone fermions left over? 2 ) Are th e problems one encounters with" higher spin theories both at the classical and quantum le v e ls evaded in supersymmetric, models? N.D. Hari Dass:. 1) In the superspace approach it appears to me that one has freedom regarding the represen tation to which the Fermions belong. The question of Goldstone Fermions depends on the details of spontaneous symmetry breaking. Phenomenoiogleally the Goldstone - neutrino concept does not seem to work too w ell (De Wit and Freedman, 1976) 2) The d if f i c u l t i e s seem to haive been mitigated only partially (spin 3/2 case) but no general proof of this phenomena for other spin value is available. M.S. Sri Ram: Are th ere any attem pts to break th e symmetry systematically, (to correspond to the real world) as there is too much symmetry in these th e o r ie s. N.D. Hari Dass: The problem is to break supersymmetry in such a way that the nice properties of super- symmetric theories (renormalisability) are not destroyed. A.K. Kapoor: Are there any problems in principle with supersymmetric model with explicitly broken supersymmetry? N.D. Hari Dass: Inqproved r e n o rm a lisa b ility may be l o s t in such models. ASYMPTOTIC BEHAVIOUR IS FIELD THEORY "* H. BAHERJEE Saha Institute of Unclear Physics, Calcutt&-700C09 1. Introduction: We have been studying asymptotic behaviour in field theory for several years now. one important lesson that has emerged from these studies is that some approximation schemes quite popular in this area of research are not always reliable. I shall start my talk by illustrating this piece of wisdom with the help of two examples. In the first I shall consider infrared and fixed angle high energy behaviour in the simplest non-trivial case of the ’box* amplitude in a scalar- scalar theory (i.e., scalar particles of mass m exchanging scalar 'photons* of mass X. ). The second example relates to the high energy behaviour of a sixth-order Yang-Mills diagram. The final diagnosis in the Yang-Mills example is not yet complete though, we believe, we are very close to it. as for the first example the clue is presented in Sec.3 in terms of a set of rules for writing down the precise leading infra red behaviour of an arbitrary generalised ladder diagram (GLD) in QED. These rules, are the final result of a detailed analysis of the relevant amplitudes in the Feynman parameter space. The connection between the infrared and the fixed angle high energy limits of generalised ladder -diagrams (without vertex and self - 327 - - 328 - energy Insertions) is explained in Sec.4 and it is argued that the same set of rules yield the fixed angle high energy lim it. 2. The Anomalies: (a) The Example of the Box Diagram; C onsider the box diagram w ith momenta as la b e l led in Fig.1. The leading infrared ( ?i-> 0) and high energy fixed-angle behaviour of the amplitude Cl) is contained in the formula F* K f^ -r M -t) <2) .where "t and f 1 i t °< {*) — J -rrV"-y5 o(. (t-ot) - i ° (3) is the Regge-trajectory function. As a tool for analysis of infrared structure the eikonal approximation |[l} has been and is still very popular, in this approximation one ignores in the ‘particle* propagators the quadratic terms in loop momenta p-erW_ {<^4 f ______„ —_— . 1 = T w V J I'*-'?) ( ' 2h (4) This gives a leading infrared behaviour F ^ a J— In.(*/»*) * (■») z ‘S32.7V 0 -TV1 t (5) which is smaller by a factor of two than the correct expression in Eq.( 2). The ‘hard scattering * approximation popular [23 in the fixed-angle domain p Won-J _ i ‘| ‘4 1 , j o l4 k "" v J f6 ) i s again d e f ic ie n t by the same fa c to r two compared with correct formula (2). (b) The Yang-M ills Example: Several authors ^3,4^ have obtained the high energy behaviour of sixth order graphs for fermion- - 330 - fermion scattering in Yang-Mills theory with SO(2) gauge symmetry. Unfortunately, their results for individual diagrams disagree and it is necessary to clarify the s prevailing confusion, we have only recently started working to this end. The Yang-Mills diagram in Fig.2 together with its - U, crossed partner plays a very important role in the high energy domain. It has, as we shall see, pieces behaving asymptotically as } /6 I£ 3 and whereas the full amplitude of all the sixth order diagrams has the leading behaviour [_3,43 . The d if f ic u lt y stems e s s e n t ia lly from the m ultiplicity of terms in the numerator of the Feynman amplitude contributed by the two Yang-Mills vertices. Considerable simplification follows from the analysis of Nieh and Yao [4] who show that the asymptotically important (up to term of terms are contained in the p iece N t = ( k-i) 5 - where k-i, k*, are the two loop-momenta labelled in F ig .2. The crucial point now is to identify the* terms responsible for the ^ and /5 •tw3/6 asymptotic beha viour. we observe that if we write - 'SSI - , (8 ) the first term k ills the gauge-boson propagator carrying momentum (see*Flg.2) and the result is* the. quendied * diagram in. Pig.3. Its contri bution quadratic in is completely cancelled by the Yang-Mills diagramwith four-boson vertex which looks .exactly similar to that in Fig.3. The second and the third terms in Bq. quench the boson lines carry in g momenta k, and k* respectively and give rise to the quendied diagrams in Fig A . The /& I * A behaviour arises from these quendied diagrams. This follows directly from scaling arguments. Thus for the diagram in Fig .4 (a) there are three scalings of unit length £5 } corresponding to th e l i n e s la b e lle d by Feynman parameters c / S 3 . In addition to these there is also a singular scaling of effective length unity corresponding to the loop (o< > / 6 , > (S3J. Finally» the last term ln Bq.(8) gives rise to the leading behaviour /& . . 1 . Thus even if we ignore the /» . terms contri buted by the quenched diagram in Fig.3 the leading beha viour is actually A> ^vv/6 a r isin g from th e two - 332 - quenched diagrams in Fig.4. It is, therefore, puzzling th a t McCoy and Wu £ 3 ] obtained a leading behaviour A> A for 016 Yang-Mills diagram in Flg.2. in our opinion the question to be settled is how the authors missed in their approach (integration in infinite- momentum variable space) the crucial /t>in/6 terms which really follows from straightforward scaling arguments. It should be pointed out that the /S L-l/6 terms ' do not survive in the full amplitude. For example, the contribution (Fig .4a) from the second term in Bq.(8) to the isospin-flip amplitude, is completely cancelled by sim ilar quenched diagrams arising from the two Yang-Mllls graphs in Fig.5. 3. The Infrared Rulesi The InfSared rules tell us how to obtain the precise form of the leading infrared divergence, if any, of a generalised ladder diagram (OLD) of arbitrary order in QED. For details of derivation I refer to our pzper in reference |j>] - . Here I shall try to explain what these rules are. We first observe that the infrared divergence of a GLD with YL 'photon* (infrared regulator mass A,) exchanges can at most be of order 'K . A particular - 333 - GLD may or may not exhibit this leading behaviour, the question,therefore, arises when can a GLD exhibit lea ding infrared divergence* The answer is given by the •external line rule*I A GLD exhibits leading infrared divergence if at least one of its photon lines is leading. In a GLD a photon line labelled ' V is leading if starting from the 'tree* diagram with only the i-th photon line exchanged between the two fermions one can reconstruct the entire diagram by attaching the remaining photon lines successively such that at each stage the ends of these photon lines are fixed to the external fermion legs and not an internal propagator. The external line rule is wellknown in lite rature £l] . What is new in reference [<>J is that1’it gives a derivation based entirely on Feynman parameter space analysis• . A leading line in a GLD mpy admit of different sequences of attachment of the remaining photon lin es. The total number of distinct admissible sequences asso ciated with the i-th line gives its weight tOf . I may illustrate these definitions with the help of the eighth order diagrams in Fig.6. In diagram 6(a) all the photon lines are leading.lines labelled /3« > are each of weight 1 whereas those labelled , (Si are o f - 334 - weight 3. in 6(b) only /St and fix lines are leading with weight 1 whereas in 6(c) none of the lines is le a d in g . Another im portant parameter i s the number ^ of lines crossing a leading line, in it has been proved that the number of lines crossing a leading line i s the saine fo r a l l lea d in g lin e s in a p a r tic u la r diagram. Thus is a parameter characteristic of the diagram. Referring again to the diagrams in pig.6 we have - 0 for 6(a) and i for 6(b). Having defined all the parameters necessary for our purpose we now state; The infrared Rule; The .leading infrared beha viour of a diagram is the sum of contributions - from all of its leading lines. The contribution of the i-th leading line depends on its weight and on Tg. » the number of lines crossing the leading line, in terms of these parameters the leading infrared behaviour of a GLD with Yl-photon lines is given by "(S) where It has also been shown In £sj that this leading behaviour exponentiates when summed over all v diagrams of a given order and then over all orders TV . But this Is as far as we can go. we cannot, for example, prove with the present method exponentiation of all In frared divergences, leading and non-leading, as Is . believed to be the case jji] . We can now try to understand why the elkonal approximation (4) falls to give the correct Infrared behaviour for the box diagram In Fig. 1. For this dia gram both the meson lines are leading with weight 1. When, however, one makes the propagator elkonal approxi mation only the line through which the momentum transfer q Is routed continues to be leading whereas the other line cases to be so. This explains the discrepancy of factor 2 In the elkonal formula (5). 4 . Fixed Angle High Energy Behaviour• The Infrared and the fixed angle high energy lim its o f GLD's are intimately related and, indeed, as I shall argue, are contained in the same formula (9). In both these cases the dominant flow of external momenta is along the elkonal path i.e ., the momentum transfer flows along one of the leading photon lines while the large Incident momenta are routed along the respective - 336 - spinor lines. Let us examine how this identity of flow pattern comes about, the infrared domain is fay 11 \, "w1" z’^ and hence, in Che Feynman parametric approach, the zeros of the coefficients S,T,U, and M in the denominator fu n ction D (10) are of interest in this domain. Here are the parame ters associated with the photon lines and C the usual dicriminant [.sj . in the fixed angle high energy lim it | t | y y 'm?', X1- we look for zeros of only S,T, and U. I f there is no enhancement from, pinch e f f e c t s then in spinor electrodynamics the dominant scaling set for S and U coincide with the elkonal set [_sj (i.e., the set of Feynman parameters associated with the spinor lines). Thus for the leading behaviour in both infrared and fixed angle high energy lim its it is enough to consider [ 7 ] 1 . ..t ik D ■= ,.sS€l-t- t /Sf--r^ + ulJ + ™ ^ - > C d ! ) instead of (10). Recall [6J that the popular propagator elkonal approximation as in (4) is incapable of reprodu cing the form (11). As a result, whether for individual diagrams or their sum, propagator approximation leads to incorrect answer both in the infrared and in the fixed - 337 angle high energy lim its. Insplte of this Identity of the flow pattern of external momenta a search of the infrared lim it does not necessarily yield the fixed angle high energy lim it or vice versa. This w ill be apparent from the vertex Insertion diagrams In pig.7 both of which are leading in the large t lim it. But in the Infrared lim it only diagram 7a is leading. The GLD’s without the vertex or self-energy insertions, however, have the special feature that here the scale of 't' is essen- tialfydetermined by X and that of and U. by Yri. This can be easily verified from the approximate form (]£)) of D £.6] . Thus the infrared rules and hence formula (9) also yield the leading fixed angle high energy lim it.of GLD's. It is interesting to note that for planar ladders f T„ =. o ) formula (9) coincides with the Regge for- 3 - * ■ i v mula valid for t eventhough in the derivation of (9) no assumption regarding the relative magnitude of /& and "t was made. This, indeed, is an evidence that to the leading order "t is scaled by X*" , the infrared regulator mass. - 338 - Acknowledgment It is a pleasure to acknowledge the contributions of Dr. s. Mallik, Dr. s'. K. Sharma, and Mr. M. Sengupta who, at various stages, participated in this research project. R eferences 1. F. Bloch and A. Nordsieck, Phys.Rev. 52(1937),54; D. R. YennJ.e, S. Frautschi and H. Suura, Ann.Phys. (N.Y.) 13(1961)379; S.Weinberg. Phys.Rev. 140(1965).B516. 2. See for example J . L. Cardy, Nucl.Phys.Bl7(1970).493. 3. B. McCoy and T.T.Vu, Phys.Rev. 012(1975),3257. 4. H.T.Nieh and Y.Yao, Phys.Rev.Dl3(1976),1082; L.Tyburski,Phyf.Rev,D13_(1976),1107. 5. See for example RJ.Sden e t.a l., The Analytic S-Matrix (Cambridge U n iv ersity P r e ss, 1966). 6. H.Banerjee and S.K.Sharma, Ann.Phys. (N.Y.) (to appear in March, 1979); H. Banerjee, S.K.Sharma and S.Mallik, Phys.Letters 66b a 976)239. - 339 - 7. I. G. HaUiday et. a l., Nucl. Phys. B83 (1974), 189. 8. G. Tiktopoulos and S. B. T reloan, Phys. Rev. D3 (1971), 1037. - 340 - Figure Captions 1« The box diagram. 20 The Yang-Mills graph having pieces behaving as and a sym p totically. 3. The only Yang-Mills graph with^four bosom vertex *Mch cancels the contribution of the quenched diagram resulting from the first term of eq. (8). 4. The two quenched diagrams resulting from the second (Fig. .4 (a))and the third terms (Fig.4(b)) of eq. (8) behaving asymptotically as • 5. The -Yang-Mills graphs wleh cancel the contributions of the diagram in Fig. 4(a). 6. Bxamples of leading lines. in (a)each line is leading. Lines labelled ,8,, ^are each of weight 1 and ^ i;^'are of weight 3. in (b) only |S, and ^8^ are leading with weight 1. In (c) none of the lines is leading. 7. Sixth-order vertex insertion graphs asymptotically leading in the fixed angle high energy lim it. Only the diagram in Fig. 7 (a) has leading infrared diver gence. * 1-6 ■ w w w v A A Z V W X A / 6 K £19- 2 ►* ' w v v w w w i IS % 4 (< 0 fig -4 to . - 342 - <■ V > — t> ■ Pl 1 ►i r c q <13. $ ( » K K * K * 0 _ <\ ■N/V'gVNZ' z v z v z x ^ f K yXZ%^v~V ^ b e C / '/ zxyN^zxzv < H K ti 9. 6 fc> ii3.6fc> UHBBBSTABDIHG 0? QCD THROUGH SOEVABIB MODEIS gatjtam bhaitachabya Department of Physics Indian Institute of Technology, Bombay-400 076. I . HJTRQDUCTIOH In spite of remarkable progress in the field of strong interaction physics from the time of Yukawa to the end of last decade, no fundamental consistent dynamics, i.e . a Hamiltonian theory, could be conceived which would explain everything about hadrons, at least in principle. On the other hand the tremendous, success of QBD was tempting the physicists to find a similar renormalisable field theory (in the language of formal perturbation analysis) which wauiA quantitatively describe strong-interaction. However unlike electrodynamics, the strong interaction does not have any direct macroscopic realisation. Therefore any interaction theory first has to be made theoretically self-consistent and has no to exp lain th e e x is tin g phenomq^-ogies before any attempt to make predictions. The observed BJorken scaling of the structure functions of the hadrons in deep-inelastic lepto-production considerably narrowed down the choice of the underlying .field theory that would describe strong interaction. One is now hopeful that the basic structure of the Iagrangian is known - commonly known as Quantum chromodynamics (qCD). Unfortunately, one does not know, as*yet, how to extract physical information in different kinematical domains, since like, any other realistic dynamical problem it cannot be solved exactly. - 343 - - 344 - One has to use different approximation methods, with the phenomenology and physical analogies justifying it. It is well-known that the scaling reflects a peculiar behavior of the matrix-element of the product of hadronic currents at short-distances^. If one assumes that the constituent fields from which these hadronic currents are constructed, are behaving like free-fields in this kinematic domain (large momentum transfer), one finds scaling. Whether a Lagrangian field theory in a formal perturbative frame-work w ill exhibit such asymptotic freedom.can be seen by the use of renormalisation group equation^. Such technique enables one to relate one physical matrix element as function of the kinematic variables and the dimensionless physical coupling constant with another where the. kinematic variables have been scaled. *( [xp±j , g) = Xd(s) . g’(g.X)) (1.1) g'(g«X) is called the ’effective coupling constant’ and is obtained (3) from the renormalisation group equation which is basically obtained ffcm the fact that physically observed quantities are invariant under a continuous scale-shift of the renormalisation point. If g' - 0 as X - oo and also d approaches the canonical free-field dimension (no anomolous dimension), the theory is called asym p totically fr e e . The la rg e momenta (unphysical as in th e case of deep-inelastic phenomena) behavior is equivalent to scaled free field matrix elements. Perturbation theory^ inv terms of the small effective coupling constant makes sense even though the actual - 345 - Physical coupling constant may be large, and one gets quantitative results in the asymptotic region. (4) Coleman and Gross made a system atic a n a ly sis o f renorm ali- sable field theories in (3*1) dimensions and showed that a ll of them except one kind are not asymptotically free. The analysis was based on a formal perturbative power-series expansion of the renormalisation group functions. A self-consistent argument was obtained^ - that the power series is valid only when the effective coupling constant decreases in the asymptotic region and it would decrease provided the leading term in the power series behaves in a particular way (p-fn must have a zero with negative slooe at g = 0). The only asymptotically free renormalisable field theories having classical energy bounded from below are the nonabalian gauge theories having no abelian invariant subgroup^. Deoending oh th e typb o f gauge-group a c e rta in number o f fermions coupled minimally to these gauge fields w ill s till keep the theory asymptotically free. . Gellmann used quarks as mathematical objects* a convenient choice of fundamental multiplet to show the hadrons belonging to certain representation of the flavour symmetry group. He himself came across d ifficu lties^ at the time of interpreting these quarks as spin- 1/2 objects obeying Fermi statistics. The larger group SU(6) where the basic multiplet involves all the degrees of freedom of quarks gave a 56-plet low lying qqq baryon multiolet having mass formula consistent with experiment. But the wave- functions were not antisymmetric in the quark-exchange, violating - 3 4 6 the Fermi statistics. Such anomaly could he explained in two ways : i) the quarks obey parafermi statistics of rank 3, or 11) they have some hidden degrees of freedom which w ill not show uo in the (8 ) hadron spectroscopy. They are actually equivalent statements . These hidden degrees of freedom Eire popularly known as colour. If each quark is given three extra degrees of freedom, the 56-plet w ill have the required consistency. These extra degrees of freedom showing So(3) or SU(3) symmetry would not enhance the hadronic spectra since only the singlet combination is observable. All h igh er m u ltip le ts w i l l be somehow nonobservable. The th ree colou r theory was further justified by the observed x° — 2 / decay rate . The basic Hamiltonian of strong interaction in terms of quarks must have a colour So(3) or SU(3) symmetry. If we choose Su(3) it means that un*ar the transformation of quark fields - exp ( ie a — ) _ (2) < 2 *Cr P • («,p = 1,2,3 the colour index, 6* = arbitrary real parameters, = generators of SU(3) group in defining representation, 8 in ^ number), the Lagrangian must be invariant. One. can now demand this . symmetry in the local sense, i.e. _ model fo r small pT and the quark-parton model fo r large p$ . The difference with angle of the proton-antiproton ratio is pre sumably due to the leading particle effect for the proton near 9 cm I I I . THE QUARK RECOMBINATION MODEL The model in i t s present form i s about two years old though some of its ideas have been expressed earlier?"®- ^®) Very high energy, non-diffractive, low pT collisions are pic tured as follows?) the valence quarks of the incident hadrons tend to fly through giving rise to the leading hadrons, while the excitation of the gluonic content gives rise to the central dus ters (glue balls?) resulting in the hadrons in the central region. The fast valence quarks form hadrons by recombining with each other and with slow (small x) constituents from the parton sea (q, q emd gluons). These hadrons appear in the fragmentation region which is characterized by medium to high values of 1 x 1 . In the recom b in ation mechanism envisaged here there i s no large momentum transfer probe to Interact instantaneously with the constituents of.the energetic.hadron.”, /Presumably- the quark"recombination pro- - • cess is characterized by a longer time scale though one has no , 374 - real understanding of how It "occurs. A. Recombinations of the valence quarks. The recombination model describes the production of the hadrons in the fragmentation region only. Consider specifically the inclusive reaction p + Nucleus —> h + ...... (1) where the hadron h is produced in the fragmentation region of the in cid en t proton. The hadron h can be a meson M or a baryon B depending on how the valence quarks (uud) of the proton reconu- b in e » ) ■ (i) Recombination of a single valence quark. Two possibilities arise: (a) the valence quark q (with fraction xq of the proton momentum) recombines with a single sea antiquark q (with fraction x - ) to give a meson M w ith a x-value XM - Xq * Xq ~ Xq ' (2) since the valence quark is assumed to retain its large momentum in the recombination and since the q andq in the sea have small momentum. Thus the x-distribution of the valence quark and the meson get related . For. q = u(d) and q = d(u)the meson M w ill be x+ («“ ) , while K+ w ill r e su lt fo r q = u and q = 5 ; (b) Instead of forming a meson, the valence quark could also re combine with two sea quarks'to give a baryon in reaction (1) with a x-value os.x_ . . (ii) Recombination of two valence quarks. Here two basic types of recombinations can take place: (a) The two valence quarks of the proton together pick up a sea quark to give a baryon in reaction (1)> - 375 - (b) The two valence quarks recombine separately with the sea q and q to give two hadrons h^ and hg thus contributing to the inclusive process p + Hucleus —> h^ + h ^ + ...... (3) in the proton fragmentation region. Depending bn how each valence quark recombines with the sea the two hadrons can either be two mesons or two baryons or a meson and a baryon. ( i l l ) , Recombination of all three valence quarks. In this case three basic type of processes can take place: (a) All the three valence quarks recombine to give the leading proton i.e . h = p in reaction (1); (b) Two valence quarks together recombine with a sea quark to give a baryon while the third recombines with a sea antiquark to give a meson. This w ill contribute to reaction (2); (c) All three recombine separately with the sea to contribute to • the three particle inclusive process in the fragmentation region of the proton. Of the various recombination possibilities enumerated above clearly some are more likely than others and a detailed analysis vis-a-vis the data is needed to work out the probability for a particle process. Intuitively one would expect the recombinations involving more sea quarks to be less probable. The analysis of q) K alinowski, Pokorski and Van Hove ' shows that the dominant proces ses are indeed (i)(a), (ii)(a) and (ill)(a) involving one and no sea quark, with probability for a meson(through (i)(a)) ~ 0.3 and that for a.baryon 0.7 through (ii) (a) and (ill) (a) with / both contributing comparably. - 37 6 - B. Formulae for Inclusive spectra. Consider the fragmentation of an incoming hadron A into a meson H which is formed out of a valence quark q and an antiquark q carrying fractions x and y res p e c tiv e ly of .the, momentum of A. The meson M i s assumed to g.dme out with fraction xM = x+y of the momentum of A. The inclusive cross-section integrated over transverse momenta in the fragments- 7 ) tion region of A, in QRM, is written ' as (oT = total inelastic . cross-section) h UM) = — — = I dx dy U.y)9MU»y)6(xifX-y) (4) °T dxM o o whex'e the sum runs over the permutations of qq with the quantum numbers of the meson M. 9^(x,y) is the probability for the two- A body recombination of qq to form the meson M. Fq-(x,y) is the joint probability to find a valence quark q at x and a sea anti quark at y in hadron A. The single valence quark distribution is q ) given byJ/ .y)dy r qq(*»y)dx dy (5) o where n^ is number of valence quarks of type q in hadron A. Thus, if A is a proton then for q = u, ^ = 2, and 0^(x) = u(x), w hile fo r q = d, nd * 1 and G^(x) = d (x). Using (1=1,2..,.) for valence quarks and yd for the sea quarks and aniiquarks the expression for the fragmentation of A into a baryon B (recombination (ii)(a) ) is - 377 - A-> B v I _A H (*b> - Z J Pqq<1XIl ' x2'yl ),PB(xl ' ;r2'yl )6(xB-:,l- Z2-yl )dxl ( 6 ) Similarly the generalization Bq.(4) for fragmentation of a baryon . A into two mesons and Mg is A^M1H2 . J*1«2 ' ! -(VV ’ 5iliiil4% = ^ | Fqqqq{Xl ,yl'x2,y2*<,lH1 (^ l^l^ N g^a'3^ x 6(xH^-x1-y1)6(xM^-x2-y2)dx1 The new functions introduced in Bq.(6) and Bq.(7) have an inter pretation analogous to those in Bq.(4). The inclusion of the delta-functions in the above formulae implies that other (multibody) recombinations for the quarks involved have been neglected. To proceed further one should know their forms and for that one has to be guided by intuition and experiment. In case of Bq.(4) one can proceed farther by doing the delta-function giving A-> M f . H (xM) - 2. ) dy ^q(xM-y,y)9M(xtr7.y) (3) One now assumes factorization . F ^ ( x ,y ) - 6A (x ) G|(y) ^>(x,y) (9) as one expects q and q to be uncorrelated for x y apart from kinematic constraints (x+y ^ 1) expressed by the phase space fa c to r ^(x,y). Now since the sea quark distributions are concen trated at * small y , and valence quark distribution is more important - 378 - for large x , Bqs.(8) and (9) yield A-*M _ r^H A A H (x„) = dy (^(x^-y) G| (y) ^(xg-y.yl^Cx^y.y) o ci oj^) j dy o|(y) ^(^-y.y) ^(x^y.y) (IQ) o Thus one expects the inclusive Spectrum of M to be approximately proportional to the distribution of the valence quark which It shares with A, the fragmenting hadron. For quantitative work explicit expressions used by Das and Hwa 7) ' are ^>(x,y) = Const.(1-x-y) and 9M(x,y) = Const, xyXjj . The expressions for ^ and + X - HP (x) = (Constant)^ t1"*) | u(x-y)d(y)(l - |) ydy (11) o P-**~ _ p-*K+ _ For H replace u->d, d->u, while for H replace d-*i in B q .(11). What happens (in QBM) in the case of mesons which do not share a valence quark with the fragmenting hadron? Das and Hwa7) suggest that these result from the recombination of a sea qq-pair; for example they use Bq.(11), for p-?K* with u-»s and d-»u , that i s with two sea d istr ib u tio n s. However, Van Hove^) f e e ls that the sea gluons must play an important part and that QBM has no speci fic prediction in such situations. - 379 - As can be seen from the foregoing that the choice ^ = 1 In E q.(9) to s a tis fy Bq.(5) s t i l l leaves the two body recombination probability to be specified. This is the real unknown in the model. IV., COMPARISON VITH DATA AND DISCUSSION The quark recombination model has been mainly applied to pp- collieions where the most extensive data are available. To some extent, these data (eee section II) have guided the formulation of the model, so that, its qualitative predictions for particle ratios and single inclusive spectra are in accord with them. For example the increase of K+/K~ ratio as x-> 1 is expected as K~ 's 'cannot come out with large x because they do not share a valence quark with the proton. Similarly for the reaction (3), one would expect the particle ratio n+ n~/ x- iT to increase as x—* 1■ because the proton has only one valence d quark which can form one fa s t n~ but not two. Such qualitative predictions are borne 2 0 ) out by the data. A more detailed but approximate expectation, f r o m Eq.(lO) that the particle ratio x, - «v«* ~ ,12) is in agreement with ISR data except for x } 0.7. This is because d(x) does not agree with the it- spectrum beyond 0.7 (see Fig.4). In fact, in the limit x 1, the use of the u(x) and d(x) deduced from ep-scattering would make Rn->co since •VV|^(x)/uV|n(x) —> 4 experimentally. In contrast the pp-data 7 (see Fig.l) requires 5 for low pT implying a value j for the ratio of the structure functions. v.- •- - 380 - Duke and Taylor‘S ^ have used the Das and Hwa m odel^ to make 2 i) a quantitative fit to the Fermilab data ' for the inclusive ± ± spectra for it and K as well as for the corresponding particle ratios. For the quark distributions, u(x) and d(x), they use 2 2 ) Feynman and F ield ' parametrization for the valence part but different distributions for the sea (u(x) etc.). Their^^ sea distributions (see Table 1) give an enhanced sea of qq pairs by a factor of ten over those determined from lepton-hadron processes'. 11) — X. They ' interpret this as the contribution of the gluons to' the recombination process. Presumably this contribution is absent .in the deep-inelastic processes, although the gluons account for 50 % of the proton momentum. The reason for this may possibly be that in the lepton-hadron processes the gluons cannot directly interact with the leptons. ' 23) - Comparison of t..e QRM has been made in it p -c o llis io n s at 200 GeV/c for the fragmentation of the incident x~ as well as the target proton. The results for the latter agree with the QRM. 23) From the pion fragmentation, the authors determine the quark distributions' in the pion using QRM. Of the various parametriza- tions of the quark distributions the Feynman-Field parametrization agrees best with their data?^ If correct the QRM offers the exciting possibility of determining the quark distributions of hadrons (available as beams) other than the nucleons. Lehman et.al.^ ^ have tested the QRM t o t two p a r tic le in clu sive spectra using Bq.(7) in *“p collisions, at 360 GeV/c, for proton fragmentation and find results in agreement with the model. As can be'seen the naive use.of the quark-parton model in.^. . the recombination model seems to be working fairly Well. However, - 381 - at this level effects of multibody recombination, resonance formation ( £ ,K*etc.), colour and spin have-not been considered2^) The model does not say fo r example why the u and d preferen tially form the spin zero s+ rather than a spin one -which could decay to give the n+. Even though these contributions may turn out to small10), the problem of a large sea required for the quantitative fits remains. Phenomenologically, this arises due to thjB choice of the two-body recombination function Acknowledgements: I am grateful to F. Roy for discussions on the quark-parton model. - 382 - References X) R.P. Feynman, Phys. Rev. L etts. 22, 1415(1969); R.P.Feynman, •Photon hadron interactions', Benjamin, New Yor^ (1972). 2) JVC: Bjorken and E.A. Paschos, Phys.Rev. 185. 1975 (1969) J. Kuti and V.F. Weisskopf, Phys. Rev. D£, 3418 (1971). 3) J.J.J. Kokkedee, The Quark Model, Benjamin, New York,(1969). 4) For application to other deep-inelastic processes see S.M. Berman,. J.D. Bjorken and J.B. Kogut, Phys. Rev. D ,4, 3388 (1971). 5) R. Blankenbecler and S.J. Brodsky, Phys.Rev.10, 2973 (1974; B. Andersson et.a l., Physics Letts. 69B. 221 (1977) and 'Dynamical Valence Quark Models', preprint no. LU TP 77-19, Lund University, (1977); S. Nandi e t . a l . , Bonn preprint HB-77-16 (1977) ;• S .J. Brodsky a i * J. Ounion, preprint no.SLAC-PUB-1939 (1977) 6) W. Ochs, Nucl. Phys. 118. 397 (1977) and V.Ochs, Contribution to the XII Recontre de Moriond, Flalne, (1977)- 7) K.P. Das and R.C. Hwa, Phys. Letts. 68, 459 (1977) 8) L. Van Hove and S. Pokorski, Nucl. Phys. B86. 243 (1975). 9) L. Van Hove, Invited Talk at the International Meeting on Frontier of Physics, Singapore, 14-18 August (1978) (CBRN preprint TH-2580). 10) M.J. Teper, 'Applying the Parton Model to the Fast Hadrons at low pT ', Rutherford Lab. preprint RL-78-022/A (1978) and references-therein. A critique of the models in Ref.5 is given here. 11) D.tf. Duke and F.B. Taylor, Phys. Rev. D1J, 1788 (1978). - 38 3 - 12) The number of u(d) quarks with fraction of momentum between x and x+dx within the proton are given by u(x) (d(x)). 13) J. Singh e t.a l., 'Production of High Momentum Mesons at small angles at centre-of-mass Energy of 45 Ge7 at the CERN IRS', preprint, (1978); to be published in Nucl. Phys. B. 14) G. Miller e t.a l., Phys. Rev. DJ, 528 (1972). 15) A. Bodek e t.a l., Phys. Rev. Lett. J O , 1087 (1973); Phys. Lett.~51B, 419 (1974). 16) H. Goldberg, Nucl. Phys. B44, 149 (1972). 17) V.V. Anisovich and V.M. Shekhter, Nucl. Phys. B55. 455 (1973) 18) J.D. Bjorken and G. Fa;rrar, Phys. Rev. Dg, 1449 (1974). 19) The p ossib ilities for the fragmentation of a meson can be similarly worked out. 20) R. Diebold, Plenary Talk,XIX International Conference on High Energy Physics, Tokyo (1978). 21) J.R. Johnson e t.a l., Phys. Rev. D17. 1292 (1978). 22) R.D. Field and R.P. Feynman, Phys. Rev. D15. 2590 (1977). 23) N.N. Biswas e t.a l., 'Valence- and Sea Quark Distributions in the Pion1, Notre Dame-Durham-Toronto-Montreal Collaboration preprint, (1978). 24) E. Lehman e t .a l ., 1 Tests of the Quark-Parton Model in Soft Hadronic Processes’ , preprint no. MSU-HEP-78/1 (1978). 25) See reference 10 for a discussion of these. 26) T.A. De Grand and H.I. Miettinen, Phys. Rev.Letts..40. 612 (1978). - 384 - Momentum Parametrization - fraction Field and Duke and Feynman(Ref.22) Taylor (Ref.11) 1 x u(x) dx 0.285 0.403 r1 1 x d(x) dx 0.145 0.257 •1 - | x u(x) dx 0.015 0.133 0 1 ^ x d(x) dx 0 .0 2 1 0.133 0 1 1 ^ x s(x)dx=|x s(x)dx 0.011 0.020 0 0 Table I . Comparison of the momentum carried by the various partons . Total momentum carried by quarks and antiquarks is 49 % and 96.6 % in columns 1 and 2. - 385 - Figure CaptIona Fig.. 1. Comparison of particle ratios at small and large centre- 2 PL of-mass scattering angle 8-„ versus i,. = ------■ and 2 p „ U ' & x. = ----- respectively. The straight lines correspond.to V® the power law (l-x)n indicated next to them. Quark count ing rules; predict n = 0, 4, 12 at 0° for K+/K~ and p/p ratios. (Figure is taken from Ocha®^ where references to data used are given). F ig . 2 Inclusive production, cross-section for Vs = 45 GeV (from, reference 13 ). F ig . 3 Inclusive K+ production cross-section for V® = 45 OeV (from reference 13 ). . . . F ig . 4 inclusive; x“ production cross-section for V® = 45 OeV (from reference; 13 ). - 386 - 100 - 5 0 - 10 - 5 - 0 .8 0 .6 0 a 0.0 0.0 O.A 0.6 0.8 0.9 FIG. I - 387 - pT =0 55 GeV p «• p —* TC* ♦ X u(x) (see text) 0-75 GeV 0 95 GeV 115 GeV 10" FIG. 2 .GeV" 0-4 075GeV 5 v 7 '0 05 06 FIG.3 - 8 8 3 - 0-7 se text) (see u u (x) 08 09 10 - 389 - = 0 55 GeV p ♦ p — 10" FIG. 4 THIS PAGE WAS INTENTIONALLY LEFT BLANK - 3 9 1 - LIST OP CONTRIBUTED PAPERS (A) THEORY PAPERS: 1. Should DlBaryon Resonances Exist? G. Bhamathi, Madras 2. Can we observe the charmed baryons C^, C®, C ❖ P. Mukhopadhyay, Calcutta 3. On the suppressions of the P-meson productions: Sankari Saha and P. Mukhopadhyay, Calcutta. 4. Possible Existence of a Hew Particle with Mass in ^the Neighbourhood of the Pion: S. Banerjee and A. Subramanian, Bombay 5. Quark model and off-shell effects in nuclei J. Thakur, Patna University 6* Quark fragmentation function in e+e“ annihilation and nature df quark jets: S.P.Misra, L. Maharana and A.R. Panda, Bhubaneswar 7. Production of heavy pseudo scalar mesons in eV annihilation: . » S.P. Mlsra, K. Biswal andfeB.K. Parlda, Bhubaneswar 8. Diffractive photoproduction of vector mesons and vector dominance model: S.P. Misra, L. Maharana and A.R. Panda, Bhubaneswar 9. Angular distribution of muons pair-produced in pp collisions M. Homan and Saurabh D. Rindani, Kanpur - 3»Z> 10. Aaymietry parameter in the fireU-Tan production of dlleptons with polarised beam ind target! M. Be— and H.8, Meal, la q a t 11. Ooleer effects la teeU-yae process* P«B. P a a d lte and Soffixtr Ysran^ape, Bootay 12. Study «f tbe pettere of sea lini deviation to m aaa ly tlo model: B.P. aebapetra, BudUt. 1$. H>4el tear elastic and inelastic torn factors of tbe plena 8. P. B&apstra, to lt 14. GIM Obama aa4 0bar«e Sy aetry flotation to neutrino scatterings ?•». Fasdita and S.V.L.Seme 15. Eeotral Current Oroee Seetlcme fer Seetrlnea on Protons: 6. Baj&oekaraa, Kadras and K.V.L, Sanaa, Eatibaor 16. Sautral Current Cross-aaotion® tor Double Pion Fneduotion by Beutrieos: S. S. Biewas, S.B. Choudbury, A.K. Goyal and J .l. Pass! 17. Seats of Second-Class Currents: S.I.* Biswas, S.B. Cbeudbaxp, tohek Oeydl tftt J.B. Passl, Delbl 18. Becoll deuteron polarisation in el turtle electron deateron scattering* S.K. Singh, Gwalior, and M.V.H. Ihrtby and G. Baoachandran, Bfyaore - 393 - 19« A four quark-parton model analysis of recent high energy y N scattering data from CERN:, S. Hashim Rizvi and Shoeb Abdullah, Aligarh 20. Neutral-Current Interactions in Single-Boson and Two-Boson Models: M.K. P arida, Burla and 0 . Rajasekaran, Madras 21. Testing Locality of Weak Neutral Currents in e+e“ ~ u+u“: G.V. Bass and P. Ram Babu, Bombay • 22. Parity, violating effects in dilepton production using ■ . " polarized targets: H. S. Man! and S.D. Rindani, Kanpur . x 23. Can SU(2)l SD(2) r U(1) gauge models be ruled out by neutral current experiments? Jatlndier K. Bajaj and G. Rajasekaran, Madras 24. Renormalization of models with broken gauge symmetry: A.K. Kapoor, Allahabad 25. Chiral Models as Gauge Theories: R. Ramachandran, Kanpur, A.P. Balachandran, U.S.A. » H. Rupertsberger, Austria and B.S. Skagerstrom, Sweden 26. Radiative decays of vector-mesons in broken SU(3): I . Jatinder K. Bajaj, Madras 27. Two-body radiative processes in a vector dominance model with off-shell corrections: B. Bagchi, V.P. Gautam and A. Nandy, C alcu tta - 3 9 4 - 28. Leptonic decays of s in covariant harmonic oscillator model with tensor mixing: Iriptesh De and A. Nandy, Calcutta 29. Quetifching of cahibbo angle and, total muon capture rates: R. Parthasarathy and V.N. Sridhar, Madras 30. Second class currents in muon capture and neutrino inter actions the structure of elementary particles: R. Parthasarathy, Madras .31. On the simplification of the coupled-ehannel analysis for non-zero spin bosons: - ; P. Mukhopadhyay, Calcutta 32.. Weak Honleptonic Decays in SU( 3) Dynamical .Considerations: Ramesh C. Verna and .M.P. Khanna, Chandigarh 33. Parity Violating Hadronic Decays of Baryons and Right-handed current in SU(8) symmetry: Satish Kanwar, P.E. Pandit and R.C. Verma, Chandigarh 34. A study of the energy dependence of charge multiplicity distributions: Parthojyoti Datta and D. Bondyopadhyay, Delhi 35. Inclusive processes in hadron-hadron collisions in neutral vector gluon theory: / Probhas Raychaudhuri, Agartala 36. Scattering of hadrons at high energies: S.P. Misra, Bhubaneswar t 3 9 5 - 37. Field theoretic model for diffraction scattering of hadrons: 5.P. Misra and I. Maharana, Bhubaneswar 3 8 . Classical Solutions of a Model of Quark Confinement: 6. Rajasekaran and V. Srinivaaan, Madras 39. Consistency of the electromagnetic Interaction of arbitrary spin particles: P.M. Mathews, M. Seetharaman, I.R. Govindarajan et al., Madras and J. Prabhakaran, Madras 40. Quantum field theories with attractive feroion-feraion interactions: P. Mitra and H.S. Sharatchandra, Bombay 41. Metamorphosis of colour into mass in two dimensions: P. Mitra and Probir Roy, Bombay 42. The gauge fixing problem in SD< 2) gauge theory: M.S. Narasimban and T.R. Ramadas, Bombay 43. Spin-Gauge Theory: P.C. Balk and T. Pradhan, Bhubaneswar 44. Scattering of high energy photons by atoms: B.C. Mishra and T. Pradhan, Bhubaneswar 45. Gravitational self-energy of electron: Radhey Syam, Kanpur - " 46. Should nature possess a genuine scalon? A. Das, Calcutta / - 396 - . 47. Convergent and Semioonvergent Polynomial Expansion, for Elastic and Inelastio Diffractive Processes: M.K, Parida, Orissa 48. A 64-plet superquark model of the hadrons: S. Navare, Kolhapur 49. Proton-proton Scattering at High Energy: R.C. Badatya and P.K. Patrtaik, Sambalpur 50. Analytic Parametrlzation of Deuteron Form Factor: Asymptotic Behaviour and Bxtraporation into the Timelike Region: M.K; Parida, Orissa 51. High Energy behaviour of fermion-fermion scattering in non-abelian gauge theory: M. Sengupta and H. Banerjee, Calcutta 52. Multiple direct exchange processes in the Young-MilIs theory at high energy: Triptesh De and H. Banerjee, Calcutta .5-3. On the validity of elkonal approximation for relativistic scattering: S.K. Sharma and H. Banerjee, Calcutta 54. An inequality on Functions of positive type on the three dimensional rotation group: S.M. Roy, Bombay - 3 9 7 55. Renormalisation problems In unified theories of weak and electromagnetic interactions: N. D. Hari Dass, Bangalore 56. Parity violations in deep inelastic electron^scattering: A source theory view point: N.D. Hari Dass, Bangalore 57. Alternative searches for parity violation in atomic physics N.D. Eauri Dass, Bangalore 58. lepton polarization experiments to probe parity violating VINC: N.D. Hari Dass, Bangalore 59. The neutron may be split: - A. Subramanian 60. Composite structure of leptons - A naive model: S.C. Tiwal, Rajasthan 61. Spontaneous creation of electron-pisitron pairs in lnhoniogeneous magnetic fields: P. Achuthan, T. Chandramohan and K. Venkatesan, Madras 62. lime scales in hadronic collisions, 'disturbed hadrons' and structure functions of the nucleon: S.P. Misra, Bhubaneswar 63. Quantization of Electric Dipole n»ment: 1. Pradhan, Bhubaneswar- - 3 9 8 - 64. Fabrication of magnetic charge from excited H-atom: * T. Pradhan, Bhubaneswar 65. Completeness of Tests of Local Hidden variable theories: S.M. Roy and V. Singh, Bombay (B.) experimental papers 1. Inclusive Production of K® and A in pp interactions at 3.6 GeV/c: S. Baner jee, S.N. Ganguli, P.K. Malhotra et al., Bombay 2. Inclusive production of K (890) and T (1385) in pp interactions at 3.6 GeV/c: S, Banerjee, S.N. Ganguli, P.K. Malhotra et al., Bombay 3. Principal axis study of pp interactions at 0.76 and 3.6 GeY/c S. Banerjee, S.N. Ganguli, P.K. Malhotra et al., Bombay 4. Observation of Mass Enhancements in ~ -p and E**p Invariant Mass Spectrum: i).P. Goyal, A. 7. Sodhi and J.H. Mi era, Delhi 5. Characteristics of Leading Protons in 67 GeV/c p-p Interactions: U.S. Arya, D.P. Goyal, P.K. Sengupta et al., Delhi 6. Some Aspects of Rapidity Gaps in High Energy Hadron-Hadron Interactions: U.S. Arya, D.P. Goyal, P.K. Sengupta et al., Delhi - 3 9 9 - 7. Azimuthal Asymmetry and Fireball Models U.S. Arya, D.P. Goyal, P.K. Sengupta et al#, Delhi 8. Production and decay of"the D(1285) meson In 4.2 GeV/c K“p Interactions: A. Gurtu, Bombay 9. Search for charmed particles In 400 GeV/c proton-nucleue Interaction In emulsion: S.K. Badyal, I.K. Daftarl, V.K. Gupta et a l., Jammu 10. A search for direct electron production In pp Interactions at 2.0 GeV/e: T.B. Rangaswaay et a l., Boeibay 11. Seeling of M ultiplicity Distribution In High-Energy Hadronle Collisions: ' I.Aslsam d *. Zafar, Aligarh 12. Some Characteristics of 24 GeV/o Proton Interactions with Light Bhelel of HUelear Emulsion: 1. Ahmad, M. Zafar.M. Irfan et al., Aligarh. 13. H uelear In te ra c tio n s o f 50 GeV/c Plona :ln B ralslon: 2. Asia, A.R. Khan, A. Ahmad et a l., Aligarh 14. Some Aspects of Transverse, and Longitudinal Momenta of P a rtic le s Produced la 50 GeV/e *”-Huoleue C o llisio n s: S. Ahmad, A. Ahmad, T. Aziz e t a l . , A ligarh 15. Some experimental results on ***” — n°n°: S.K. Tull - 4 00 -r 16* Samoa production la s*p interactions at 4*0 GeV/c: Indrani Dhar and 3*K. Tull, Varanasi 1?. Study of angular distributions of secondaries in proton- nucleus Interactions at 400 GeV: M.M. Aggarwal, I*S,. Mlttra, J.B. Singh et al*, Chandigarh 18. Some characteristics of deuterons produced from Ag and Br nuclei by protons at 400 GeV/c: M.M. Aggarwal, I*S, Mlttra, J.B. Singh et al., Chandigarh 19. Angular distribution of the shower particles and production of the clusters/fireballs in 50 GeV/c «~-Em. nuclei Interactions: S,C. Verma, V. Kumar, U.S. Vermaet al., Kurukshetra 20. Preliminary results of momenta (p, pt, ), charge and rapidity of shower particles produced in 50 GeV/e n~-Ekn. collision: V. ..Kumdr, N.S. Verraa and A.P. Sharma, Kurukshetra 21. An experimental investigation of collision at 50 GeV/c: V, Kumar and A, P. Sharma, Kurukshetra 22. Intranuclear Cascading in Nuclei at Accelerator and Cosmic-Ray Energies: "Mohammad Tantawy, Jaipur 2 3 . Study of particle production through clusters in proton- nucleus interactions at 200 GeV/c: S.K. Badyal, I.K. Daftari, V.K. Gupta et al., Jammu - 4 01 - 24. Rapidity correlation In proton-nuclena Interactions at 70 OeV/c In Emulsion; D.K. Bhattacharya et al., Calcutta. .25. ibltiple Parallel Hhions In Cosmic Rays and Their Relevance to Ultra High Energy Hadron Collisions; M.R. Krlshnaswamy, M.G.K. Menon, N.K. Mondal et al., Bombay and Y. Hayashi, S. Ito, S. Kawakami et al., Japan 26. Large cascades observed in deep underground neutrino experiments In Kolar Gold Mines: M.R. Krlshnaswamy et al., Bombay '27. P^ - distribution at 10^eV from a study of high energy muons in Extensive Air Showers: B.3. Acharya, S. Haranan, M.7.S. Rao et al., Bombay 28. Is 'Centauro* Really a New Type of Interaction? B.S. Acharya, M.V.3. Rao, K. Sivaprasad et al., Bombay 29. Search for Massive Particles In Extensive Air Showers: S. C. Ton war, P.N. Bhat, S.K. Gupta et al., Bombay 30. Search for Tacbyons In Extensive Air Showers: P.H. Bhat, N.V. Gopalakrlshnan, S.K. Gupta, et al., Bombay 31. Relation between the primary proton energy and secondary pion energy In proton-proton collisions from hydrodynamical model: R.K. Roychoudhury, D.P. Bhattacharya and D. Basu, Calcutta - 4 0 2 - 32. Derivation of sea level muon spectrum from the primary cosmic ray nucleon spectrum and vice versa using the GKP model: A.K. Chakrabarti, A.K. Das and A.K. De, Calcutta 33. Parent nucleon energy distribution for muons observed at sea level and underground: A.K. Das, Calcutta and A.K. De, Hooghly 34. Primary cosmic ray nucleon spectrum from the sea level muon spectrum using the scaling model: A.K. Daa Calcutta and A.K. De, Hooghly - 4 0 3 - LIST OF PARTICIPABTS A ligarh Physics Department Afzal Ahmad Allgarb University Shafiq Ahmad Aligarh Z. Ahmad Usman A ll Tariq Aziz U. Irfan A, S. Khan A.H. Kaqvl Mohd. S hall M. Zafar Z.K. College o f Bng. and Shoeb Abdullah Technology S, Hashim Rlzvl A ligarh Muslim U niversity A ligarh All ababad Physics Department T.M. Gupta Allahabad university ... A.K. Kapoor Allahabad Bangalore Raman Research Institute H.D. H ari Dass Hebbal Post Bangalore-560006 Benaraa Physics Department Indran! Dhar BenaTas Hindu U niversity Go pal OJha Varanas1-5 S .£. Tull Bhubaneswar Institute of Physics A.V. Khare A/105 Saheed Bagae L, Haharana Bhubaneswar-751007 S.P. Mlera O rissa B.C. Mlshra P.C. Halk A.R. Panda T. Pradhan Bombay Indian Institute of P. Ram Babe Technology G. Bhattacharya Powal, Bombay-400076 Tata Institute ef Fundamental B.S. Acharya R esearch, S. Baner jee Homi Bhabha Road, P.K. Bhat T. Das Bombay 400005. S.K. Ganguli A.D. Gangal R. V. Gaval - 4 0 4 - Bombay lata Institute of Fundamental S.K. Gupta Research (Contd. ) A. Gurtu N. Ito P.K, Malhotra P. M itra U.K. Mon dal A. Mukher jee D.S. Narayan L.K. Pandit S.K. Pandit P.K. Pandlta S. Paranjape R. Raghavan T.R. Ramdas M.V. S rin iv a sa Bao Srikantha Rao S.M. Roy Probir Roy D.P. Roy K.V.L. Sarma H.S. Saratchandra A. Subramanian K. Sudhakar S.C. Tonwar C a lcu tta P h y sics Department H. Banerjee Saha Institute of Nuclear I. Dey Physics M. Sengupta 92 Acharya P r a fu ll a Chandra S.K. Sharma Road C alcu tta-9 Physics Department D.K, Bhattacharya Jadavpur University P. Mukhopadhyay Calcutta-32 R.K. Roychoudhury Shankari Saha , Indian Association' for the B. Bagchi Cultivation of Science D.P. Bhattacharya Jadavpur, Calcutta-32 Department of Physios A. Das KCC C ollege Calcutta-35 Physics Department A.K. Dm University College of Science C alcu tta-9 - 4 0 5 - Chandigarh Physics Department M. M. Agarwal Panjab University S a tish Kanwar Chandigarh-160014 J.M. K ohli I.S. Mlttra Jasbir Singh R.C. Verma Coimbat&re N.G.M., C o lleg e 0 . Alagar Ramanujam P o lla c h l Coimbatore Tamil Nadu 642001 D elh i Physics Department J . Anand University of Delhi N .S. Arya D elh i-7 D. Bandopadhya S.N. Biswas S.R. Chaudhary K. D utta V.K. Gupta A tish Majumdar J.N. Mishra R.P. Saxena R.K. Shivpurl S. Singh T. Singh Department of Physics A. Goyal Hans Raj C o lleg e J.N . P a ss! D e lh i-1 1 Hooghly Bejoy Barayan Mahavidyalaya A.K. De P.O. Itachuna Hooghly, W. Bengal Jaip u r Physics Department A.K. Arora University of Rajasthan K.B. Bhalla Jaipur-4 M. Choudbury , J.M. Gandhi R.K. J o sh i L.K. Malhotra R.S. Purohit G. Shankar N.K. Sharma M. T ant away Jammu Physics Department S.K. Badyal Jammu U n iv ersity I.K. Daftari Canal Road, Jammu Tawi V.K. Gupta Vinay Joshi B alvinder Kaur Jammu(Contd.) G.L. Kaul L.K, Mangotra Yog Prakash U.K. Rao S.K. Sharma Gian Singh M.L. Sharma T.R. Verma Kanpur Indian Institute of Technology K. Homan Kanpur R. Ramacbandran Kharagpur I.I.T. V.Y. Rajopadhye Kharagpur-2 Kolhapur Department of Physics S. Navare Shivajl University Vldyanagar Kolhapur-416004 Kurukshetra Physics Department V. Kumar Kurukshetra University A. P. Sharma Kurukshetra, Haryana N .S. Verma Madras Maths. Department P. Achutan IIT, Madras-600036 Theoretical Physics Dept. J.K . B ajaj University of Madras G, Bhamati A.C. College Bldgs. V,- '£&irugan Madras-600025 S. Raghavan S.D. Rindani M. Seetharaaan M. 5. Sriram MATSCIENCE . R. Parthasarathy The Institute of Mathematical S cien ces Madras-600020 Mysore PhysiCs Department M.V.N. Murthy University of Mysore. Mysore-570006 Patna Physics Department Jagannath Thakur Science College Patna University Patna-800005 - 4 0 7 - * Sambalpur Post-graduate Dept, of Pbys. R.C. Badatya Sambalpur University B.P. Mohapatra Burla 768017 M.K. P arida Sambalpur, Orissa ; P.K.. Patnaik Santiniketan Vi ava-Bharat i A.K. Ray Santiniketan Tripura Department of Mathematics P. Raychaudburi Calcutta University Post Graduate Centre Agartala-799004 Tripura - 408 - LIST OF PREVIOUS SYMPOSIA 1. Delhi 1955 2. Ahmedabad 1956 3. Bombay 1957 4. Bombay 1953 5. Bombay 1959 6. Ahmedabad , 1960 7. Chandigarh 1961 (February) 8. Madras 1961 (December) 9. Bombay 1965 10. Aligarh 1967 11. Delhi 1969 12. Bombay 1972 13. Santiniketan 1974 14. Bhubaneswar 1976 and <1-T> distribution.‘One see that a lim ited pj Monte Carlo cannot describe the data. Fig.4.8(c) shows the thrust distribution for W > 6 GeV. Again, th e .d a ta d if f e r from th e LPS m odel. The.QCD curve with correction for the hadronization of the gluon agrees remarkably well with the experimental data.#, 1 <-T> and distributions for the fragmented-hadrons