What is a realistic picture of hadrons?

Nuclear PhysicsA478 (1988) 79c-93c North-Holland, Amsterdam

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WHAT IS A REALISTIC PICTURE ® r' HADRONS?* G.E . BROWN Department of Physics, State University of New York at Stony Brook, Stony Brook NY 11194, USA Abstract : Chiral invariance hasbeen astrong guide in constructing themeson presence in nuclei. Whereas low-energy theorems have pinned down isovector exchange currents, by gauging thebaryon density anomaly, a good description at both low and high momenta of the deuteron (isoscalar) magnetic form factor has been achieved. At low energies, both the nucleon and piun can be divided intc an interiur quark care and exterior meson cloud. At high energies one sees the quarks in both regions. The quark core in strange baryons tends to be somewhat larger than in the nucleon because thereis little pion coud to compress it. From the anomalously large tensor coupling of the p-meson to the nucleon, the nucleon quark core is found to have a radius R--0.5 fm. A case is made that nonperturbativeQCD should be used for low-energy descriptions, although perturbative QCD may be applicable to systems with strangeness. It is argued t:iat the exclusion principle operating at the quark level does not have very large effects in low-energy nuclear physics. Two-phase models, with a Wigner (perturbative) phase at short distances should be used to properly incorporate theasymptotic freedom property of QCD. Through nonperturbative QCD, elegant and deep connections can be made between nuclear physics phenomena and theQCDanomalies. 1. Introduction in trying to understand strong interaction physics, it has always seemed to me that nature shows her hand in auant4!'.cz ikat are e, ~eptional in some way or other. One of the earliest such quantities that I encountered was the S-wave isospin-even scattering length ation") giving

ao+,

the value of which was very small, the most recent evaluaâ+ =(-0.0097t0.0017)m_t ,

(1 .1)

two orders of magnitudeless than wouldfollow from thestandard processes available in the 1950's for the scattering of pseudoscalar pions by nucleons (see fig . la).

(a) (b) Fig. 1. (a) Scattering of pions by nucleons through virtual pair production. (b) Scattering through exchange of thescalar o meson. ' Work supported by USDOE underContract DE-AC02-76ER13001 . 0375-9474/881'$03.50 © Elsevier Science Publishers B.Y. (North-Holland Physics Publishing Division)

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G.E Brown / Realistic picture of hadrons?

In contorted ways, people triedfruitlessly to damp out the virtual pair terms, but by beginning with something so large, ^-m-.', it proved impossible to make them nearly zero. When the o-model of Gellman and Levy 4) [and, not remarked by me at the time, the nonlinear or model of Skyrme 5)] came along, it provided a very natural explanation forthe near vanishing of aou+; namely, the 0--exchange of fig. lb almost exactly cancelled the virtual pair terms. Indeed, at a slightly off-shell point, the so-called Adler point"), the cancellation was exact. These developments, as well as those by Schwinger, led to the concept of chiral invariance, in thich the pion and tr are united into a 4-vector (ar, or), out which the small aoo+ arises as a simple and natural consequence, provided that the or-particle is heavy, mQ - m , where m is the nucleon mass . From chiral invariance, one had a unique prescription in terms of low-energy theorems') for constructing isovector exchange currents in nuclei . These soft pion expressions worked extremely well in predicting the electro-disintegration of the deuteror_') up to momentum transfers g, I GeV/c. Since the relevant figures have been shown many times, I will not repeat them here, but shall show how well they work') in explaining the isovector exchange currents in thethree-body system, fig. 2. As with the electrodisintegration of the deuteron, the soft-pion calculation fits experiment up to a high momentum. In detailed calculations in the deuteron

N

Cr

q2 (im2) Fig. 2. Magnetic form factor of 'He. Thecalculated curve is impulse approximation plus pion exchange current corrections °) . A similarly good fit is obtained for thetriton 9).

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electrodisintegration it was found that the charged p-meson did, in fact, enter into individual processes. Enhancements came from couplings of the y-ray to the p-meson, but exchange currents were cut down by form factors which, in vector dominance models, could be thought of coming from the y-ray coupling to avirtual p. The various p-effects cancelled with each other to a fairly good approximption. It was noted some time ago') that the soft pion results seemed to extend to high momentum transfers q--1 GeV. These exchange currentcalculations and agreement with experiment show unambiguously that mesons and nucleons are the appropriate variables to use up to momenta ;~, q =1 GeV/ cin nuclearphysics, or down to distances R --0.5 fm. (There is a factor of -,/6 that generally comes in relating r.m.s . distances to inverse momenta.) At thesemomenta, or inside. these distances, we have always needed phenomenological cut offs in boson exchange models of the nucleon-nucleon force. The exciting developments have been in developing the structure of the nucleon so that we now have models in terms of underlying structure forthese cut offs . 2. Low energy phenomenology Chiral invariance is, to the extent bare quark masses are zero, a property of the underlying Yang-Mills theory. Consequently, when quarks andgluons areintegrated out in lieu of effective variables, mesons and nucleons, it is clearly good to keep this invariance in the effective theory,and we now understand why Chral invariance gave such strong guidelines . Possibly even more intereRing is that new quantum numbers arise in the effective theory, mirroring topology in theunderlying Yang-Mills theory . One such quantum number is thebaryon number proposed first by Skyrme 5). In SU(3) x SU(3)theories the relevant information is summarized in effective theories through the WessZumino term. This is an imaginary term in the action which contains all pertinent results of the infinite quark sums, and is to be used in calculation of physical quantities as a pseudopotential . E.g., in calculating the iro --2y decay, used in first order the relevant piece of the: Wess-Zumino term gives the correct result to all orders (whatever this latter statement means, because we definitely are not using perturbative theory). In an extremely elegant paper, Witten showed '°) that the Wess-Zumino term is quantized in termsof thenumbe.: of colors n,;. In the integrand of theWess-Zumino term, if onefactors out atwo-dimensional disc containing thetime and an additional coordinate,onefinds Skyrme's baryon density. Thus, the quantization of the baryon number follows from that of the Wess-Zumino term . Should nuclearphysicists view these elegant developments as irrelevant high-brow mathematics and continue uninfluenced by them in model-making and calculating? I think not. And I shall outline why not, using some examples. I shall skip over

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G.E. Brown/ Realistic picture of hadrons 7

formalities, such as the fact that SU(2)xSU(2) does not have the Wess-Zumino term that I'm discussing, assuming that the anomaly, Skyrme's baryon density, remains One of the most exciting recent developments has been the discovery by Nyman and Riska t') that the isovector magnetic form factor of the deuteron follows from Skyrme's baryon density. Gauging this anomaly gives the relevant current. It is, however, not a usual current, but orc given by the anomalies and constrained by topology . Thus, in the same sense as the vro ->2y reaction expresses results from (regularized) infinite sums over negative-energy states, this current of topological origin unites low- andhigh-energy features. Although much of its origin mayinvolve high intermediate momenta, it should give the correct low-energy behavior. But it should not be restricted in validity to low momenta, as the soft-pion theorems in the isovector form factor; (at least formally) were. This unification of low- and high-energy properties was completely unexpected. Of course, the fit shown in fig. 3 is not completely model independent. Nyman and Riska choose a chiral angle 8(r) which will reproduce the dipole form factor

20

ao so g2(fm2) Fig. 3. The magnetic form factor of the deuteron for momentum transfers up to 70 fm-2. The curve labelled impulse approximation includes correction from the velocity-dependent interaction using the Gar)-Kriimpelmann fit 12) to the nucleon form factors . The curve labelled Wess-Zumino term . . . uses a chiral angle 0 fit to reproduce thedipole form factor forasingle nucleon. Thedeuteron wave function is calculated with the Paris potential . Experimental data are from Arnold et al. ") .

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for a single nucleon, but the exchange current effects then follow. This is much more satisfactory than throwing in these exchange current effects, such as y-ray coupling to a p-w vertex, piecemeal and the adjusting coupling constants and form factors to reproduce the data . 3. Sizes Acommon misconceptionis that since the electromagnetic rms radii (electricand magnetic) proton are ^-0.86 fm, and the radius of an average sphere containing a nucleon in nuclei is ro --1 .25 fm, nucleons often overlap in nuclei. Most of the electromagnetic radius comes front the meson cloud. It is true that clouds often overlap. The interference of one cloud with another is just what we have always called meson exchange. A small, linear interference, is just one-pion exchange. The real question in the nucleon is to draw the line between the quark/gluon core and the meson cloud. In terms of bag models, this line is a sharp one, but that is, of course, an oversimplification . In some sense this line is like an R-matrix radius. One could draw it in a wide range, provided one were prepared and able to calculate all higher-order effects, and the answers should come out the same . This idea is embodied in the Cheshire cat picture, first suggestedby KenJohnsonandthen developed by Nadkarni, Nielsen and Zahed 14) and others ' s) . On the other hand, the exchange-current calculations involving IF-nucleon coupling and boson exchange models, such as the Bonn potential, definitely require cut offs at q -1 GeV/ c in momentum space, or distances R s0.5 fm. The bosonexchange expressions simply have to work down to such distances. An important ingredient of the Cheshire cat model is thequantization of baryon number . Topology unifies the internal quark region and the external soliton cloud, so that, whatever the dividing radius R, the total baryon number must add up to be unity. This indicates that these regions must be strongly interconnected, in practice through the continuity of the axial-vector current (as one would suspect from the underlying chiral invariance). For chiral angle O(R) =Zar, half the baryon number is in the quark sector, half in the cloud. This is a particularly convenient chiral angle to work with, because there is a complete symmetry between positive- and negative-energy quark states at this chiral angle (as there is for ®(R)=0 or ar.) Within the framework of the topological chiral bag, a straightforward argument* which starts from the fact that the tensor coupling of the p-meson to the nucleon is about twice the value it would have in the vector dominance model indicates that the bag radius must be near chiral angle O(R) =Zar, or R--0 .5fm . On general grounds, it is clear that the tensor coupling of the p-meson is a good place to look because : * This argument was developed more rigorously in the YKIS'87 seminar last week, to be published as a Supplement of the Progress of Theoretical Physics.

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G.E Brown / Realistic picture of hadrons 7

(i) Since it is nonminimal, it must come from loop corrections in thequarksector, and these should be small. Indeed, for 6(R) = Zar one cansee that they are small -in

the chiral bag model. (ii) In the nonperturbative hedgehog solutions, quantities involving onr survive in projection by rotation, whereas those involving %r or r alone average out. This gives an explanation of why the tensor coupling of the p-meson is large, whereas that ofthe w-meson, which involves only o, is small. On theother hand,even though the vector coupling of the p-meson to the nucleon is small, involving only T, none the less it can be pinned down by the known electric form factor of the nucleon. Let us define the nucleon electromagnetic current J,_el~FN

I

2T3y,WN_

+ .,N 2ET3 W m +KS~ o-,,,k,*N} . n

The coupling of the p-meson to the nucleon looks like the isovector piece of this ll ~~~ .I' Kv 82p =fpNN1 9'N im 4 ' Pw4GN+WN (3 .2) ?F~~kvT ' Pla`YN ( .

I l

21>1

Jn

Empirically one has ' 6) KP =6.6t0.6 K v =3 .7,

(3 .3)

whereas they should be equal in the vector dominance model, because once the -/-ray couples to the vector meson, then there is no more freedom in the VDM. In fact, however, Kv°=2Kv . Let us see how this comes about. One knew already from the work of Iachello, Jackson and Lande ") that the vector part of theelectromagnetic form factor comespartly through coupling through vector mesons, partly through coupling directly to the internal structure of the nucleon, which we now identify with the quark core . See fig.4. The tensor coupling can, however, come only (at least chiefly) through coupling through vector mesons. These couple only to the meson cloud; the p-meson cannot "holdtogether" in theinternal quark region, because with asymptotic freedom there the forces between quark and antiquark are weak. The tensor coupling lacks the

Fig. 4. Following thepicture of Iachello, Jacksonand Lande 17), the nucleon vector form factor comes partly from coupling of the y-ray directly to thequarks, partly from coupling throughthe vector mesons. Thetensorpiece oftheform factor canonly come from thelatter. Theweight factor Icorrespondsto 0=1a:

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coupling directly to the quarks that the vector coupling has. To compensate for only half the baryon number being in the cloud, the tc' must then be twice the tcv , since one has to end up with the latter in the electromagnetic current J, Thus, the topological chiral bag model gives a simple explanation for the large deviation from the VDM in the tensor coupling of the p-meson provided the bag radius R is ^-0.5 fm. This radius agrees well with theother sensitive determinations outlined earlier. Why does the -/-ray couple only ^-3 of the time throeôh the p-meson for small spacelike momenta, essentially t= 0? I believe that the answer lies in the finite size of the p-meson. Because of this, there is a form factor in the coupling f,, of the p-meson to the y-ray. We can model this by the simple form with

fp,(t)=f,Y(t = .P)r(t)

(3.4)

f(t)= AL- mp . A -t

(3 .5)

AZ=2 mp

(3 .6)

With the choice the factor of two drop between. the on-shell kinematics t = mP and t =0 will be realized. Naively, the A in (3 .6) would indicate an rms radius of the p-meson of ^-V96/A=0.43 fm . Following the empirics of Povh and Hiifner r$) one might expect the p-meson radius to be slightly greater than that of the ca, which they give as (r2)'/Z =0.4210.03 fm. If the p were much larger than this, one would expect a greater change in the extrapolation with t. We have argued '9) that the 0, although in the nonperturbative treatment it is projected out of the same hedgehog solution as the nucleon, has a somewhat larger quarkcore than the nucleon . Ourtheoretical arguments in ref. '9) arenotcompelling, but theempirical situation dictates that the p-meson couple only weakly in thepNA vertex, suggesting that there is rather little baryon number in the A-cloud for the p-meson to couple to. The baryon number in the cloud goes down rapidly as the radius increases and 9(R) drops. The empirical evidence is that low energy, ^-40 to 50 MeV, pion scattering off nuclei exhibits very little multiple scattering. The multiple scattering is virtually eliminated s° ) with the Ericson-Ericson LorentzLorenz correction of g'=3 which follows from the effect of short-range correlations on pion exchange . Were the p-meson to couple appreciably, as in the case of the nucleon, g' wouldbe -2-3 times this andthis wouldstrongly reinstitute the multiple scattering . The A seems to be a halfway house to the strange baryons. These have very little pior. cloud, so that their properties should follow chiefly from those of the quarks andphenomenology, such as the magnetic moments, require R , I fm. Formassless

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quarks, the confinement requires the magnetic moment (the Bohr magneton is essentially a length) to scale linearly with bag radius R, so in the absence of large meson cloud contributions we would expect the magnetic moments to be good indicators of R The introduction of masses for the strange quarks does not change this qualitatively. We show in table 1 fits to experiment . In fact, aside from the inclusion of one-gluon-exchange corrections, which are appreciable, these are substantially the same as those following from the cloudy bag Zs). One might be apprehensive of using the one-gluon-exchange corrections calculated to only first order in a, with a as large as a,=2.2. However, Ushio 2') *has shown that these corrections minorthe SU(3) symmetry in the problem, so that really only ar. Overall factor, the reduced matrix element, could be changed. Inclusion of the one-gluonexchange corrections improves the agreement between theory and experiment substantially. We have not included corrections for removal of spurious center-of-mass motion . There is considerable controversy about these, effects from this removal going in both directions. TABLE 1

Contributions to hyperon magnetic moments from quarks, pion cloud 2'), kaon cloud 22 ) and one-gluon exchange corrections 22) Hyperon A E8°

-r

Quark contributions s u d -0.66 0.22 0.22 -0 .88 -0 .88

1 .90 -0.48

-0.95 0.24

Pion cloud 0.24 -0.24 0 .02 -0,02

Kaon cloud

One-gluon exchange

Totel

Exp.

0.03 -0.01 -0.01 0.03

0.05 0.02 -0.11 -0.10 -0.08

-0.61 2.41 -1.09 -l.25 --0 .71

-0.613 :0.004 2 .38 :0.02 -1 .10 :0.05 -1.250 :0.014 -0.69 :04

The strange quark contribution (including kaon cloud self-energy) is chosen to reproduce the A magnetic moment. The up and. down quirk magnetic moments and all other corrections except the kaon cloud are evaluated for R =1 .1 fm. The kaon cloud values quoted are for R =1 fm; for 1.1 fm, they are expected to be somewhat smaller. The experimental data are taken from ref. "). (All numbers are in units of nuclear magnetons e/2M.)

We close this section by discussing thepion, one of the most complicated objects. In the 1960's the pion form factor was fit reasonably well** (the largest error was ^-20%, in thetimelike region) by the vector dominancemodel (VDM). In this model the y-ray always coupled through the p-meson, theelectromagnetic structure of the pion resulting from its "p-meson cloud" . The intrinsic quark core of the pion was essentially assumed to have zero radius in this model. Once bag models were introduced for pions, it was not immediately realized that this was an essentially opposite picture. The description of the point pion with p-meson cloud fits in well

* Introduction of one-gluon-exchange corrections seems also to clear up some problems in non-leptonic weak decays. ** It is well known that the monopole form factor which follows from this model works well up to momentum transfers of g-1 GeV.

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with the attractive scheme of vector mesons arising from gauging hidden symmetries 26) For the low-energy region, resolution of the problem of small size and of the problem of double counting came from the realization 27,28) that the piota is, like theAnderson mode in superconductors, or like a low-lying collective state in nuclei, a collective excitation. The particle and hole making up these collective modes correspond to the quark and antiquark in the pion. The attractive interaction which brings the state very low in energy correlates the particle and hole, or quark and antiquark, so that they are physically close together. Indeed, for a short-range interaction to bring the collecive state low in energy, the particle and hole must be correlated very close to each other. Thus, the resulting quark core of the pion is small in extent, estimated to be --0.35 fm [ref. 29 )] . With a little core of this extent, thesmall discrepancy betweenthe vector dominance fit andthe empirical pion form factor can be removed. 4. Sizes are energy dependent At low energies it makes sense to divide hadrons up into core and cloud, if they have a cloud. These two components behave vastly differently in nuclei . Clouds brush by each other, interpenetrating relatively freely, the interference between clouds, when they overlap, being expressed through boson exchange. Cores don't really collide in the case of low-energy nucleons, because the strong short-range repulsions from .w-meson exchange keep them apart. Since the cores occupy only -(0.5 fm/1.25fm)3 = 0.064 of the volume, one can understand whythe shell model works well . At high energies in, for example, deep inelastic scattering, the probe sees the quark content of cloud or core more or less equally, a single amalgam of quarks and gluons. I imagine that this is roughly so in thescattering of any very high-energy particles. In an interesting preprint whichcollects a low of data in the hundred GeVV range, Povh aad Hiifner "s) find : (a) '1rhe values for proton and pion hadronic r.m .s. radii agree with the electromagnedc ones, a rather surprising observation." (b) A, E and d.' r.m .s. radii are found to be 0.77 t0.01 fm, 0.77:h 0.01 fm and 0.72±0.01 fm, respectively. The K* and K-arefound to be 0.57 t 0.01 and 0.60 t 0.01 fm, respectively, slightly less than the pionic 0.64 or 0.65±0.01 fm, which agrees with the known electromagnetic form factor . It is amusing that point (a), at least in my interpretation, requires that the high-energy probes see both the quark core and p-meson cloud of the pian. Regarding the strange-baryon radii, these baryons have very little pion cloud, and the kaon cloud is relatively unimportant, so one would roughly expect these

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radii to be given by those of the valence quarks. A uniform distribution of quarks in a bag of radius 1 fm will give an r.m .s. radius of 0.77fm l Viewed with high-energy probes, one can say that the nucleon is larger in extent than the strange baryons. But this does not preclude the confinement region in the nucleon, the quarkcore, being substantiallysmallerthan that of the strangebaryons as regards low-energy behavior. In a rough picture, the small quark core in the nucleon, of radius -0.5 fm (when viewed by low-energy probes) results from the pressure from the meson cloud, whichcouples strongly to the quarks,compressing the core . In arather sophisticated calculation 3°), Nadeau et al. find that "the strangeness flavor induces the baryon `size' (and bag radius) to be larger in hyperons than in nonstrange baryons". They also discuss the implications on the Sî3(3) chiral bag. Again, roughly, the quark cores in strange baryons are little compressed, because the coupling to the cloud is weak . S. Nouperturbatïve versus perturbative ; vector mesons Many remarkable developments have taken place with skyrmions . Ismail Zahed and I summarized these recently in an -100 page Physics Report 3') . The skyrmion is reached in the limit as the radius It of the topological chiral bag goes to zero (actually to an infinitesimal e) . Not only has the study of skyrmions uncovered a richness of connections, through topology, with the QCD anomalies, but for many purposes the skyrmions have given us deeper understanding of nature . E.g ., in the nonperturbative hedgehog solution which contains both nucleon and isobar, upon projection only the invariants 1 and a, " a2T, " i2 survive for interactions. Indeed, these are the known strong pieces of the interaction. (The T, " T2 symmetry energy arises chiefly from second-order terms, each involvinga, " a2 T, - 12 interactions 32).) We saw earlierthat isoscalar exchange currents dould be obtained from the WessZumino term ") . In a practical sense, introduction of vector mesons through gauging the WessZumino term gives an excellent description of phenomena involving vector meson decay or short-range interactions . In straightforward gauging 33) some freedom remains, which is removed by imposition of the assumption of vector dominance. More closely associated with the vector dominance concept is the introduction of vector mesons as gaugeparticles of hidden symmetry 25). Building the vector mesons in this waygives a very successful 3°) (except that it does not explain the largetensor coupling of the p-meson) description of the nucleon, especially its electromagnetic and axial properties. The net result is essentially that of introduction of vector mesons through gauging the baryon density anomaly and imposing vector dominance. In practice, this is aresuscitation of the physicsof the 1960's, butwith amuch deeper understanding of the conceptual grounds and of many elegant interconnections.

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To be blunt, in plain English this means that short-range repulsions between nucleons arise from vector meson exchange; the spin-orbit interactions aris:s from vector meson exchange in relativistic equations. To considerable extent, -/-rays couple to nucleons or pions through vector mesons. This is the conventional picture of boson exchange, with form factors introduced to cut interactions off at distances r,0.5fin . Conventional or not, it now is a physics that is justified in the region where perturbative methods are not. In my opinion, the introduction of quarks into low-energy nuclear physics has not lei to a new or deeper understanding or any phenomenon (with the oxceptior of the p-meson coupling mentioned earlier) that could not be better understood within the framework of boson exchange. Of course, no one doubts that nucleons are made up out of quarks,andthe spectrum of excitedstates ofnucleons, especially the odd-parity states, exhibit the quark structure clearly. But quarks do not show up explicitly in low-energy nuclear phenomena. As noted earlier, we believestrange baryons have substantiallylarger confinement regions than nucleons, in line with the MITor cloudy bagmodels. Maybethe quark picture is dominant here ; Rubinstein and Snellman 35 ) suggested that perturbation theory is more applicable in the strange sector. Earlyattempts to extend theskyrmion to SU(3) x SU(3), treating thecurrentquark masses as perturbations, ran into difficulties 3e-3s) . This ledCallan and Iüebanov 39 ) to a strong coupling scheme, in which strangeness is achieved by binding a kaon to the SU(2) xSU(2) soliton. The work of Nadeau et al. 3°) I quoted earlier, was an attempt to extend this work to thechiral bag. It now appears from a very interesting work by Yabu and Ando °°) that the perturbative and strong-coupling models were two extremes of an intermediate-coupling model, and that thelatter does quite well in incorporating baryons into the Skyrme treatment extended to SU(3) x SU(3). It remains to be seen whether phenomenology, such as magnetic moments, can be reproduced as well as those in table 1. Because the meson cloud couples so much less strongly in the case of strange baryons, I have the feeling that the large bag model may have advantages in the phenomenology of strange baryons . 6. Do quarks get in the way of each other is nuclei? There have been a lot of discussions about whether the quarks don't manifest themselves in the substructure of nucleons through the exclusion principle, i .e ., through their fermion nature. Perhaps the clearest suggestion has been made by Toshimitsu Yamazaki °') (see fig. 5) . If we are right that the radius of the quark core in the nucleon is -0.5 fm and the radii of the quark wave functions in the strange baryons are -1 fm, then there should be very little overlap, -10-15%, between a is,/2 wave function in one bag with that in the other, even when the bag centers are right on top of each other. The effect after averaging over positions of bag centers will be substantially smaller

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u- quark

p

O d -quark

p

® s -quark

n

n

Fig . 5. It may be difficult to add the A to the Is,i2 orbit in He, because in terms of quark variables, the up and down orbitals are already occupied.

than this. There may, however, be phenomena which are particularly sensitive to a few percent overlap. I have on my desk an entire folder of preprints which purport to explain various effects such as the "dip" in the charge distribution of 'He, properties of electron scattering, etc. in terms of the exclusion principle applied to quarks . If one used, however, the relatively large sizes for quark cores in the nucleon used by these authors, one would be unable to reconstruct boson-exchange models which explain nucleon-nucleon scattering. I would rather stick with the latter, and then with radii ^-0.5 fm for quark distributions, the effects of antisymmetrization between quarks in different nucleons is small.

7 . Why two-phase models? I have focused in this talk on the topological chiral bag, a two-phase model with asymptotic freedom, the Wigner phase in the interior. Certainly this emphasis does not minor the proportion of papers in the literature devoted to skyrmions and to solutions of the o--model, with quarks and mesons coexisting . My fixing t fthe bag radius through the anomalously large tensor coupling of the p-meson specifically depended on having asymptotic freedom in the interior, the quark and antiquark being unable to form a bound state there. To the extent that one looks at long-range behavior r - 1 fm, it should be all right to use the a-model, a one-phase model. However, neither it nor the Skyrme model have the correct behavior in going to short distances ; they are not asymptotically free. There is a lot of theoretical activity these days with the trace anomaly:

2g

2 0'= ß ) (Fw~) .

(7.1)

(Weneglect here currentquark masses.) Classically, where there is no scale, 0,1,' =0 . Through quantum effects, a scale AQc p is picked up, resulting in the appearance

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of the QCD ß(g)- the 91 going, for small g, as gz. Asymptotic freedom is here mirrored in the ß-function . Neither the Skyrme theory nor the ir-model have the correct trace anomaly. Peter Simic °z), who made an attempt to include effects from gluons in his derivation of effective lagrangians for low-energy physics, found his lagrangian shutting off at small distances, indicating the onset of asymptotic freedom. Progress in finding the vector mesons in hidden symmetry in the gluon sector has been made by Richard Ball °'). In another work °°), ascalar glueball has been added to an effective chiral lagrangian of pions and vector mesons to account for thaanomalous scale behavior of QCD. In this model bags are formed with typical confinement scales of 2fm. Simply said, if one wants to obtain low-energy effective theories from QCD, one should put in the known property of asymptotic freedom at short distances. In theories which do not have this, there is no reason to believe in their short-range properties . The extent to which the vacuum is "cleansed" (i .e., the condensate cleared out) by the presence of the bag, or bubble `"), is an interesting one, connected with the proposed kaon condensation °'). The little bag seems ") to be a good "vacuum cleaner". The large MIT bag may leave some condensate in the vacuum. The view taken in the Russian sumrules°8) is that the presence of valencequarkfields doesn't influence the vacuum condensate . There are unresolved questions, very much in the forefront, here. 8. Concluding discussion Over the past decade many nuclearphysicists, including myself in the beginning, rushed about to see specific quark signatures in nuclei . Nobody ever doubted that quarks were there, because they had been seen in high-energy deep inelastic scattering and quarks as constituents were needed to understand simply the excited states of the nucleon, especially the odd-parity ones. We have not seen specific quarksignatures, certainly notones like thediscrepRncy between theory and experiment in the reaction n+p->d+y (8.1) which led to pinning down the meson presence in nuclei through exchange currents . Should we be disappointed? I think not. Instead of slavishly translating concepts already established in the high-energy regime (perturbative QCD), we have been understanding deep connections between physical processes and the QC.D anomalies, the role of topology, etc. Nucleons and nuclei simply are not perturbative systems. What we have discovered is elegant and beautiful. More important, it works! Furthermore, as an intellectual discipline nonperturbative QCD connects intimately with so many other fields of physics, that never have I had more interaction with nonnuclear physicists, and never have students found it more interesting to step into nuclear physics.

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G.E Brown / Realistic picture ofhadrons7

As we move upwards in energy, it is clear that matters will change . Strangeness is bringing intricate and unexpected conceptual problems and I am sure that there will be new interesting phenomena. Relativistic heavy ion collisions will bring us to a field of new concepts and phenomena. So we have a rich conceptual future! I acknowledge my debt to Mannque Rho, who has been my close collaborator for many years and from whom I have learned much (hopefully correctly) of what I have written here . References 1) G. Hdhter, in Landolt-BÜmstein: Numerical data and functional relationships in science and technology, ed.by H. Schopper (Springer, Berlin, 1983), Group 1, Vol. 9, Part . 6 2) R. Koch, Z. Phys. CIS (1982) 161 3) R. Koch and E. Pietarinen, Nuch Phys . A336 (1980) 331 4) M. Gellmann and M. Lévy, Nuovo Cim, 16 (1960) 705 5) T.H.R. Skyrme, Proc. Roy. Soc. A260 (1961) 127; Nucl. Phys. 31 (1962) 556 6) S.L. Adler, Phys . Rev. 137 (1965) B1022 7) M. Rho and G.E. Brown, Comments Nucl. Part . Phys . 10 (1981) 201 8) M. Bornholm,E. Jans,J. Mougey, D. Royer, D. Tarnowski, S. Turck-Chieze, I. Sick, C.P. Capitani, E. De Sanctisand S. Frullani, Phys. Rev. Lett. 46 (1981) 402 9) P. Sauer, private communication 10) E. Witten, Nucl . Phys . B223 (1983) 422 11) E.M. Nyman andD.O. Riska, Nucl . Phys. A469 (1987) 473 12) M. Gari and W. Krümpelmann, Phys . Lett . 173B (1986) 10 13) R.G. Arnold et aL, SLAC-PUB-4145 (1986) . 14) S. Nadkarni, H.B. Nielsen and I . Zahed, Nucl. Phys . B253 (1985) 308 15) G.E. Brown and M. Rho, Comm . Nucl. Part. Phys. 15 (1986) 245, general discussion 16) G. Witter and E. Pietarinen, Nucl . Phys . B95 (1976) 1 17) F. lachello, A.D. Jackson an(" A. Lande, Phys. Lett. 43B (1973) 191 18) B. Povh and J. Hiifner, 1987 University of Heidelberg preprint 19) G.E. Bmwn, M. Rho and W. Weise, 1986 Stony Brook preprint 20) M. Thies, Phys. Lett . 63B (1976) 43 ; G.E. Brown, B.K . Jennings andV.I. Rostokin, Phys. Reports 50 (1979) 227 21) F. Myhrer, Phys . Lett . 125B (1983) 359 22) P. Gonzalez, V.Ventoand M. Rho, Nucl. Phys. A395 (1983) 446 23) K. Ushio, Phys. Lett. 158B (1985) 71; K. Ushio, Z. Phys . C30 (1986) 115; K. Ushio and H. Konashi, Phys. Lett. 135B (1984) 468. 24) L.G. Pondrom, Phys . Reports 122 (1985) 57 25) S. Théberge and A.W. Thomas, Nucl . Phys . A393 (1983) 252 26) M. Banao, T. Kugo, S. Uehara, K. Yamawaki andT. Yanagida, _ ' .ys . Rev. Lett. 54 (1985) 1215 ; K. Yamawaki, Nucl. Phys. B259 (1985) 493 27) G.E. Brown, Nucl . Phys. A358 (1981) 39c 28) V. Bernard, R. Brockmann, M. Schaden, W. Weise and E. Werner, Nucl . Phys . A412 (1984) 349; W. Weise, Nucl. Phys . A434 (1985) 685c; V. Bernard, R. Brockmann and W. Weise, Nucl. Phys. A440 (1985) 605 29) G.E. Brown, M. Rho and W. Weise, Nucl. Phys. A545 (1986) 669 30) H. Nadeau, M.A. Nowak, M. Rho and V. Vento, Phys . Rev. Lett . 57 (1986) 2127 31) 1. Zahedand G.E. Brown, Phys. Reports 142 (1986) 1 32) G.E. Brown, J. Speth and J. Wambach, Phys. R, Left. 46 (1981) 1057

GE Brotm I Realistic picture of hadrons? 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48)

Ô. Kaymakcalan, S . Rajeev and J. Schechxi, Phys. Rev. D30 (1984) 594 U.G. Meissner, N. Kaiser and W. Weise, Nucl. Phys . A466 (1987) 685 H .R. Rubinstein and H . Snellman, Phys. Lett. 165B (i985) 187 A. Monobar, Nucl. Phys. B248 (1984) 19 A.P. Balachandran, F. Lizzi, V.G.J . Rogers and A.Stua, Nucl. Phys. B256 (1985) 525 S .A . Yost and C.R. Nappi, Phys. Rev. D32 (1985) 8_5 C.G. Callan and 1. Klebanov, Nucl. Phys . B262 (19f_) 365 H . Yabu and K . Ando, 1987 University of Kyoto prcorint T. Yamazaki, Nucl. Phys. A446 (1985) 467c P. Simi6, Phys . Rev . D34 (1986) 1903 R . Ball, private communication Ulf-G. Meissner and N. Kaiser, Phys . Rev. D35 (198') 2859 J.F. Donoghue and C .R. Nappi, Phys . Lett . 168B (1Ç -6) 105 G.E. Brown, K . Kubodera and M . Rho, Phys. Lett . .:92 (1987) 273 D.B. Kaplan and A.E. Nelson, Phys. Lett. 175B (19<~) 57 For a review, see L .J. Reinders, H. Rubinstein and S Yazaki, Phys . Reports 137 (1985) 1

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