575

BEYOND QCD: WHY AND HOW

Giuliano PREPARATA Istituto di Fisica,Universita di Bari and Istituto Nazionale di Fisica Nucleare Sezione di Bari,

Abstract: Arguments based on recent experi­ mental information are presented to stress the necessity of going aeyond the present formu lation of Quantum Chrome Dynamics (QCD) . A new theory,Anisotropic Chromo-Dynamics (ACD) , based on the hadrodynamical pillars : ,co­ lour and local symmetry, is discussed and its fi rst successful steps in describing are outlined. 576

The aim of this talk is two-fold: first to argue in favour of going beyond the theoretical paradigm of the day: QCD, and then to present a concrete propo­ sal of how can one proceed to go beyond QCD . In order to clear the way from any ambiguity and misunderstanding, I would like to reiterate with all clarity that I believe that the basic theoretical no­ tions that underly QCD: (i) Quarks, (ii) Colour, (iii) a gauge-principle; are destined to remain with us . They do in fact represent an important step for­ ward in our understanding of subnuclear phys ics . Such notions have been legated to us by two decades of immense efforts both experimen tal and theoretical, and • have shown their validity in a countless number of physical situations . Thus my criticism of QCD will not question the above mentioned pillars ,upon which rests all our understanding of subnuclear phenorr.ena , but rather the natu­ ral-but logically unwarranted-step that has led almost everybody to conclude that gen must be the theory of hadrons . For if the latter dictum is accepted, then experimental difficulties with the present understanding of QCD would imply that there is something wrong with our basic hadrodynamical notions , and this would certainly leave us in a hopeless mire . In the following I shall give arguments, based on the presently available experimental information, that we should abandon the generally accepted notion of QCD, based both on perturbative calculations (Perturbative QCD) and on latti­ ce calculations , whose physical meaning and relevance, least at the present stage , are far from being well established . This shall atcons titute the "pars de­ struens" of my discourse. The "pars construens" shall be focussed on the description of a new theory of hadrons which, making use of the three basic pillars of hadrodynamics, not only shall avo id but will also explain away the difficulties encountered by the "accepted" QCD framework .

BEYOND QCD: WHY? 1. In this section I shall produce arguments, based on present experimental knowledge, >Illich strongly suggest that we should try to go beyond the generally accepted QCD paradigm. I shall concentrate on two points : (A) Gluons; (B) Asymptotic Freedom.

lA. Gluons

One of the qualifying features of QCD is the existence of 8 coloured gluons . 577

These gluons have in QCD a dual role: to provide for the colour-confining force (scalar and longitudinal gluons) and to give rise to new, independent de­ grees of freedom of hadronic matter (transverse gluons) . Thus if we are to make any sense of QCD as a physically relevant theory, the transverse degrees of free­ dom of the colour-fields should give rise to a number of characteristic physical effects that , I believe, could not have escaped our observation. Let 's briefly review them:

(i) Glueballs While we have good and unequivocal experimental evidence for several hun­ dred states of the q , qqq-type. Clear evidence for glueball states has so far eluded the most sophisticated experimental attempts to observe them. Several rea­ sons have been advocated for the elusiveness of glueballs, mo st notably lack of a q clear signature, mixing to the qq states , etc. But it should be recalled that sirn ple MIT-bag calculations (which yield acceptable spectra for qq and qqq ground ++ ++ states) make us expect 0 ,2 gluon-gluon states with ma sses smaller or equal to 1 GeV. Now it would not appear entirely reasonable that such states had esca­ ped the experimental search, being located in a well studied region of the hadro­ nic spectrum . The recently reported states 1(1440) and 8(1640) by the Crystal (2) Ball group at SPEAR, (l) have been convincingly argued not to be glueball states . In any event it is certainly fair to say that we have come to a point where the elusiveness of glueball states begins to appear as a serious embarassment for the generally accepted form of QCD-theory .

(ii) "Hermaphrodite states"

Such are the states of the type qqg,qqqg, •••. where g has the charac­ teristics of a transverse gluon. The existence of such states would considerably enrich the particle spectrum even in the mass range below 2 GeV . Again this is what one would expect from simple MIT-bag calculations . But from experimental knowledge, which in the case of baryon resonances with rn 2 GeV is remarkably (3) detailed , no room seems available for hermaphrodite states � . Furthermore predictions for narrow states of the bbg-type have been contradicted by recent (4) experiments at CESR . The outlook for gluonic states either pure ( glueballs) or accompanied by quarks (hermaphrodite states) seems at present particularly dim.

(iii) "Glue jets" + ­ The change in the pattern of hadronic final states in high energy e e (S) collisions , first observed at PETRA about three years ago , has been universal­ ly taken as strong evidence for the active presence of the (transverse) gluon de­ gree of freedom. Even though the hint for the radiation of a hard gluon appears at first rather strong, a detailed comparison of the experimental information 578

with theoretical expectations reveals grave difficulties , In fact, were we al­ lowed to consider "partons" only, the situation would appear quite confortable for the hard gluon interpretation. However , when we give a closer look the to fragmentation properties of the "three-j et events" observed in sucb expe­ riments we find the strange result that all jets look alike . This cannot be easi ly understood. For, when we try to form a picture of the gluon fragmentation properties along the lines , embodied in the Field-Feynman model, that have been rather successful for quar ks , we fall immediately in the difficulty that

(a) in its colour field the gluon prefers (9 : 4) to create a gluon-pair rather than a pair:

(b) the gluon pair gives rise to "glueballs" . (See FIG. l)

transverse gluon longitudinal gluon

FIG. I. The main fr agmentation process for the gluon.

As glueballs (if they exist at all) must be quite heavier than low-lying qq­ states (pseudoscalar and vector mesons), secondary hadrons ...) would be (n,K, produced much more copiously in gluon than in quark-fragmentation. Thus it ap­ pears inevitable to expect gluon jets to have a considerably softer energy distri_ bution and higher multiplicity than quark-j ets . As we have recalled, experimen­ tally this is not borne out. No believable way out has so far been proposed from what appears as a very serious , possibly fatal , difficulty . Should we fail within the QCD framework to gain any understanding on this puzzling behaviour of gluon­ j ets, we would be faced with the somewhat ironical situation that a strong eviden ce for ,on closer look becomes strong evidence againsl0 the (transverse) gluonic degrees of freedom of hadronic matter. Admittedly the status of gluons is still unclear , but it seems to me that in the few points discussed above the QCD enthusiasts may find more than one rea­ son to worry .

lB. Asymptotic Freedom 579

As is well known the first indication (judged very strong by many people) that QCD might be the theory of strong interactions has come from the discovery that in perturbation theory a non-abelian gauge theory, such as QCD, is asympto­ ( O) tically free � For this would then imply that the remarkable scaling properties observed in deep inelastic phenomena could thus find an elegant theoretical ex­ planation. Furthermore, if one gives for granted the highly non-trivial circums tance that the properties of a perturbative theory go over to the (unproved) confined situation without any change , Asymptotic Freedom (AF) predicts a characteristic pattern of scaling violations which in the last few years has been claimed to be shown by the data. However the size of such violations is controlled (modulo unimportant theoretical subtleties) by the all-important A -parameter which de- termines the "running coupling constant"

(2.1)

And over the years success has been claimed with values of A which have shown an ominous trend to decrease . FIG.2 gives a rough description of how the general- ly accepted A-values have changed

BEBC 1978

1979 CDHS .9 A 1980 CDHS

1981 EMC .7

.5

.3

.1

78 79 80 81

T

2 A rough sketch of the "generally accepted" FIG . values of A [See Eq . (2. 1) ] as a function of time. as a function of time, A being now 1 • a most consistent with zero (no asymptotic 580

scaling violations) . The interpretation of FIG.2 might become easier if we re­ call that the maximum values of. Q2 (current 's momentum transfer) have consisten­ tly increased over the last few years . The aspect which I find most striking in ' 2 the high Q2 experiments now completed,is that for Q t 10 GeV Bj erken scaling is exhibited almost unadulterated by the dat:a. In order to fit the experimental

points with AF one must consider a value of so low " 100 MeV) that elabora­ te analysis of non-leading effects (the so callef\ d "higher(/\ twists") is necessary before one can disentangle the minute AF-corrections . Be as it may , it has also been shown that all of scaling violations in deep­ inelastic scattering can be very economically described by subasymptotic contri­ butions of 0 which within the MQM-framework were predicted long before Q2 t h eir. o b servat1on(�, ). (l) , Suppose, however, that AF holds and is as low as 100 MeV, then the possi­ bly naive question that one might ask is: whof\ keeps the quarks inside the bag? For with such a low value of we find that the colour forces become non pertur­ bative at distances of the orderf\ of 2 Fermis! Well beyond the radius of a reaso­ nable bag . Again, the situation is far from clear , but here are a few more subj ects for meditation offered to the QCD enthusiasts:

(i) The "explanation" of the I =j rule in non-leptonic decays offered by AF (8) f\ (9) at short distance with. 100 MeV completely evaporates . f\oe (10) (ii) There occurs in deep-inelastic muon-nucleon scattering the bizarre f act

that in order to describe the structure functions one needs " 100 MeV, f\ while the p -distribution of planar events requires " 500 MeV . Note T that the data used in the two analyses are the same . f\

(iii) The "big successes" of perturbative QCD are only qualitative . However would like to ask a few questions : I ll) (a) onia: where is the Coulomb potential expected at short distancesf (l2) (b) high p -physics: where are jets? T (c) -pair hadro-production: what happened to the K-factor? (d) exclusive physics, form factors etc: how can we make it to agree with experiments, especially when spin is involved?

Let me end this Section with one question (Q) and one remark (R) .

Q: Aren't we being too wishful thinking in claiming that the data strongly suggest that QCD is the theory of hadrons?

R: Perturbative QCD cannot provide a basis for "explaining" the phenomena to which it is currently applied , because it lacks in a most serious fashion 581

any provision for confinement. Only after the confinement phenomenon has been correctly and realistically taken into account can we assess the mea ning and the limits of applicability of perturbative QCD .

2. BEYOND QCD: HOW?

It is a remarkable fact that a number of puzzling aspects of hadrodynamics, which QCD finds so difficult to account for, are natural and well understood in two-dimensional (one space - one time) gauge theories . For instance

(i) Confinement is a natural property of one-dimensional space due to the natu re of the Coulornbpotential which in one-space dimension at large distances e2 behaves as Y+i

(iii) The gauge fields in two-dimensions do not carry any independent dynamical degree of freedom; transverse dimensions in fact do not exist. Thus "physi­ cal" gluons disappear from the theory .

Should we take up this clue? And if so, how? Anisotropic Chroma-Dynamics (ACD) has been proposed in the attempt to conjuga­ te the basic pillars of hadrodynamics: quarks , colour and local SU(3) symmetry, c with the peculiar characteristics of two-dimensional gauge dynamics, just mentio­ ned . In the rest of the talk I shall be concerned with a brief discussion of its ideas and its present achievements . The interested reader is invited to consult . ' (13-14) the existing. literature .

2A. The theory(l3)

The basic idea of ACD is to construct a gauge dynamics for the colour field which is isomorphic to a two-dimensional gauge-theory . In order to achieve this one enlarges the base-space of the theory from the Minkowskian manifold M to a 4 S is a 3-dimensional pseudosphere] seven-dimensional spece-time structure [ 3

M x 4 s3 , to be called Anisotropic Space-Time (AST) . The points of AST are the elementary physical events E, which are represented by a pair of 4-vectors : E= (x,n) , where and n S with n n\1 = -1. The principle of relativity is schematically X EM 3 µ 4 µ E µ represented by the following diagram: 582

(x,n) ... (x'=Ax, n'=An)

Rot) i0 JO' (S, that indicates that if the inertial observer 0 gives the events E the coordina­ tes (x,n) , the inertial observer O' assigns the same event E the coordinates (x' ,n'), with both vectors x' and n' obtained from x and n by the � homoge­ neous Lorentz-transformaion , connecting 0 and O'. J\ The theory is then defined by the action:

(2.1) where [dµ (n) is the invariant measure of s; 4 S = d d x q(x,n ) (2. 2) F J dµ(n) J µ (n') J (x,n) [il-mJ ' is the quark-Dirac type action; � (2.3)

is the gauge-field action (AYM stands for Anisotropic Yang-Mills) , whose Lagran­ gian density is a f (x,n) Fµv(x,n) (a'"l, ...,8 ), (2 .4) µv a

with the usual field "intensity"-tensor a a a abc b c F (x,n) = A (x,n) A (x,n) +g f A (x,n)A (x,n) , (2.5) µv a µ -av µ µ v and the field "magnitude" -tensorv given by a a f (x,n) = (n) F (x,n) , (2.6) µv EaSµv the "anisotropy"-tensor being given bya s

B (n) = - n + (2 . 7) µv µ v v µ EaS 2 [oan o sn na ] Finally the interaction term S has the form: INT .a - a q(x,n) (x,n) q(x,n) . \ (2. 7) J,. �2 (l3) It is straightforward to check that at the classical level S [Eq. (2.1) ] describes a confined theory of quarks , whose dynamical structure is isomorphic 583 to that of a two dimensional theory. This is made possible by the "anisotropy di­ us rection" nµ , which allows to construct a theory whose spatial dynamics evolves along the space-direction of n only. FIG.3 attempts to give an intuitive pictu­ µ re of the dynamical possibilities afforded by our extension of the usual Minkows­ kian space-time to AST.

G �.iii

� q(y.n'J AAE,

q(x, �) creates a colour charge at (x, �J ,while FIG. 3 q(y,»1J creates a charge at (y, �9 .The colour electric fi eld configurations produced by the charges according to the action(2. 1) are described by their lines of force. Ee We see that creating for instance a charge at produces a colour electric field whose lines of force are completely focussed along the direction n. This + is characteristic of two-dimensional gauge dynamics, where the electric lines of (�,ti) force have no other direction to follow but the only spatial direction. As a re­ sult the work to be done to displace a charge to infinity along the direction of the electric flux is infinite, due to the constancy of the intensity of the elec tric field. Cl3) 2B . The Quantum Structure

As remarked above any gauge theory constructed according to (2.1) is confined at the classical level . The crucial question to ask now is whether this is also true when quantum fluctuations are properly taken into account . By analysing this 584

(lJ ) problem we find the remarkable result that a bifurcation accurs between vec­ tor (parity-conserving) and chiral theories (maximally parity-violating) : the foE_ mer preserving the classical confining structure, the latter losing confinement and becoming usual , isotropic Yang-Mills gauge theories. Thus it is possible to describe in a unified way both confined ,coloured quarks and liberated interacting via a GSW parity-vio lating electroweak interac­ tion of the standard type . As a further bonus sin2 e b•,comes calculable and , to w lowest order in electroweak interactions , turns out to be equal to 0.25. Reverting now to the hadronic theory, quark confinement implies : (i) only colour singlets can have finite energies and therefore be physically realizable; (ii) the classical trajectories of zero triality states must have the follo­ wing structure [p=l, ...,N]

(2.9)

wh ere x (t) .u(t) 0. In FIG.4 we report two configurations for a baryo- +� + = nic system, of which one is forbidden. Thus in this theory hadrons form

QE (wh F:(B) jj YES ®- ®-- ---@

NO

FIG. 4 Two configurations of a qum•k system, of which only one (YES) carries3 fi nite energy . linear structures . (iii) The number of indeependent degrees of freedom(excluding C.M. motion) for a N-quark system is instead of 3(N- l) ,

n = N+l (2 . 10) DF

For a Meson system (qq) there is no difference with the quark-model , but for ba­ ryons (2. 10) gives 4 degrees of freedom, wh ile the naive quark model has 6. This prediction of our approach can be tested by determining whether the bayon spec­ trum has fewer states than expected on the basis of the quark model . 585

(l4) 2C . The Perturbative Structure

Another very interesting feature of ACD is that it leads naturally to a loJ:ll sought property of hadronic interactions; its perturbative structure . Several theoretical notions have in the past been tried out to account for the surprisiJ:ll validity of the quark model, the Zweig rule, the (relative) smallness of hadronic 1 widths etc., mo st notably:planarity in the dual model , and expansions in QCD. This is how ACD brings out such a structure: N (i) we write the Hamiltonian as:

(2 .11) where the kinetic part of the hamiltonian is the usual Dirac hamiltonian and the (l3) field part H is given by (o, the current-current expression f nµ'= [

3 -a ..,.x ..,. H = dµ( ) d x tl(x,..,.u) ..,. J ( ,u) , ..,.u) (2 .12) f f f ;:)]µ 2 + a 2 (ii) we quantize the quark fields canonically on a surface t"Const and decompose J)J(- � + it in creation and;: annihilation operators for quarks (b ,b) and antiquarks + (d ,d) . a (iii) we decompo se the colour-currents J ( , ) appearing in (2.12) in their + + np + + P no-pair creation part (b b,d d) J , and pair)J creation part (bd,b d ) J and µ µ ' write i � H H + H (2 . 13) np p f = np where H cointains J only and H the rest. \J p (iv) we �further decompose the Hamiltonian (2. 11) as

H H + H' , (2.14) = 0 where H (2.15) 0 and H' H (2.16) p = (v) we treat H' as a perturbation.

Why are the steps that bring us from (2. 11) to (2. 16)meaningful? The reason is that when we compute the Hamiltonian H , it is only the H piece that exhibits f np the behaviour �\J2r, where r is the relative distance between colour charges . H p is perfectly well behaved when r and is explicitly proportional to the "string tension" µ2 • Suppose now +that � µ2 is very small, then we can treat H as p 586

a perturbation while H can never be so treated. It is sufficient to take r lar np ge enough. Thus in the limit of small µ2 a perturbative structure is seen to ari ­ (l3) se naturally. An analysis of the spectrum yields 2 � . 3 GeV2 , which on the µ hadronic standard is a fairly small number· Thus we obtain a perturbative structure in the number of quark pairs, which is readily seen to be strongly related to the experimentally observed features of hadrons .

Cl ) 2D. The qq-spectrum 4

I will not elaborate on this first step toward calculating strong interac­ (lS) tions which shall be treated in J.L.Basdevant contribution. It suffices to say that with 5 parameters; the string tension and the 4 quark masses m =m , 2 u d m ,m µ s c and we calculate the Meson spectrum and get agreement with experiments within 100 MeV, perfectly consistent with the size of the corrections that we (l4) expect from the neglected part of the Hamiltonian, H' . � (l6) 2E. PCAC and Chirality

In solving H in the qq-sector, for the lowest-lying states S=O and S=l we 0 can calculate their Masses Mas a function of the quark masses m .The result of q

such calculations is reported in FIG.5 •

µ, 2. .M

1.

o.r------'---r----'------'----

.2 .3 m IT

-1.

The lowest lying sttttes of a qq-system -2. FIG. 5 [S=0, 1] as a function of the qua:l'k mass,

in units of , the string tension. µ

We obtain the remarkable fact that for .16 th,� pseudoscalar meson (S=O) � acquires a negative mass, while the vectorµ state (S=l) mass remains positive. .;', 587

The occurrence of a negative mass triggers an instability,q -pairs condense and we obtain a new ground state, through a mechani sm akin to BCS superconductivity. Such a peculiar phenomenon appears as a consequence of our "two-dimensio­ genuine q nal" dynamics coupled to a "four-dimensional" spin, that engenders a magnetic interaction which is singular when m +O. Thus, when m + 0 we have q q (i) a BCS condensation;

(ii) a "constituent" quark mass m· c ' (iii) the pseudoscalar meson becomes the Nambu-Goldstone boson of chiral symmetry. (rr) (l6) and we find the value It turns out that we can calculate mq

17 MeV, (2 .17) mq = well below the critical value 110 MeV, at which BCS condensation occurs . Thus ACD gives an explicit realization of the long sought mechanism that would give the the dual role of a q -bound state and of the (almost) Nambu-Goldstone rr boson of chiral symmetry.

q 3. CONCLUSION

I would like to conclude this talk by leaving the possibility open that QCD may be, in the end, the theory of the hadronic world, with the nagging feeling, however, that it may take a very long time before we know. For it appears quite clear that its present status is, to say the least, not very healthy . In the meantime what should we do , besides seeking for the real QCD? I hope I convinced you that there is a definite advantage in keeping physics open, and in trying out new realizations of the fundamental pillars upon which rests all our understanding of hadronic interactions . In this direction, ACD does seem to be able to conquer the hadronic world with surprising ease and at an intel- lectual level which is not obviously inferior to QCD. 588

REFERENCES

See Aschman 's contribution at this Wo rkshop. 1.2. Carlson 's report at the "Orbis Scientiae " Conference in Coral Gab les (January 1982) contains the most articulate discussion of the subject that I know of. 3. Consult fo r instance F. Close 's report at the EPS Lisbon Conference (1981) . (to be published) 4. See J.Lee Franzini ' s Contribution at this Workshop. 5. 1.'he first reports of the PETRA discovery were given on the occasion of the 19 ?9 Fermi lab Conference [see the Contributions by H. Newman, Ch. Berger, G. Wo lf, and S. Orito, in Proceedings of the In ter�1tional Symposium on Lepton and Photon In teractions at High Energies, 1.'.B. W. Kirk and H.D.I. Abarbane l ed, Batavia (1979) and were hai led as the discovery of the "g luon ". 6. H.D. Politzer, J Phys .Rev .Letters 26, 1346 (19?3) . D.J. Gross and F. Wi lczek, Phys . Rev-:Le tters 26, 1343 (1981) . ?. P. Castorina, G. Nardu Ui and G.Preparata, Pliys . Rw. Letters 4?, 468 (1981) 8. M. K. GaiUard and E. W. Lee , Phys .Rev.Letters 33, 108 (19 ?4} . G.AltareUi and L.Ma iani, Phys .Letters 52B, 351 (1974) . 9. G. NarduUi and G. Preparata, Phys . Letters-104B, 3.99 (1981) . 10. See P.Renton 's report at the EPS Lisbon Conference (1981), to be pub lished. 11. See in this context BuchmUUer 's contribution at this Wo rkshop . 12. I referring to the interesting results reported by the NA 5 Col laboration at theam CERN -SPS . See C. de Marzo et al. , A study of deep inelastic hadron-hadron collisions with a large acceptance colorimeter tr��gger, (submi tted to Phys. Let­ ters) . 13. G. Preparata, Phys . Lett. 102B, 32? (1981); ibid 108B, 18? (1982) �� G.Preparata, Nuovo Cimento A, 66, 205 (1981) . 14. J. L.Basdevant and G. Preparata,The Structure of S:�rong Interactions in Aniso­ tropic Chromody�ics I, Nuovo Cimento A, 67, 19, '1982) J.L.Basdevant, P. Colangelo and G. Preparata,The St1oUcture of Strong Interac­ tions in ACD 1.'he Me son Spectrum. Preprint BA·-GJ.'-81/23. 15. Cfr J. L. BasdevantII: 's contribution to this Workshop . 16. P. Castorina, P. Cea, P. Colangelo, G. Nardu Ui and G.Preparata, Chirality and its breaking in a new theory of hadrons, Preprint BA-GT-81/22.