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RHO M.­ New-York Univ., NY (USA). Dept. of Physics ; CEA Centre d'Etudes Nucléaires de Saclay, 91 - Gif-sur-Yvette (FR). Service de Physique Théorique

NUCLEON STRUCTURE AND THE CHIRAL FILTER

Communication présentée à : Conference on nuclear interactions and structures

Brighton (UK) 7-9 Sep 198/ 1

Nucléon structure and the chiral filter

Mannque RHO

Department of Physics, State University of New York, Stony Brook N.Y. 11794, U.S.A. and Service de Physique Théorique, CEN Saclay 91191 Gif-sur-Yvette - France*

ABSTRACT : I discuss the issues of quenched gA in nuclei, pionic enhancement of nuclear electromagnetic form factors, manifestation of the anomalous Wess-Zumino term in nuclear medium, all on the same footing, in terms of the nucléon structure as "derived" from a low-energy effective theory of QCD.

1 - INTRODUCTION

Denys Wilkinson asked, in early 1970's, whether one could not find out how a nucléon beta-decays inside nuclear medium, in particular whether one

could not understand how the axial-vector coupling constant gA gets modified inside nuclei (Wilkinson, 1973a,b). This question has since spurred a large number of experimental and theoretical papers on the subject, but no clear-cut answer has yet emerged. The main reason for this impasse is that QCD, presumed to be the correct theory of strong inter­ actions, is very little understood at low energies at which there are no controlled approximations to apply. In this talk, I would like to discuss the issue in light of what Gerry Brown and I have been finding on the structure of the nucléon in and outside of nuclear medium. I must confess that a systematic approach to putting our ideas into a more concrete form is still lacking, so ours cannot be considered a full story, but I personally believe that the basic idea has some merit and, even though rather vague, is sufficiently intriguing.

2 - TWO SIDES OF THE SAME COIN

There is evidence to indicate that when a nucléon makes ,- GamowTellcr transition in nuclei, the effective gA is quenched to a value close ici 1 (Wilkinson 1.978 : Buck and Perez, 1985). Is this fundament,!] or is it: a

Permanent address 2

trivial coincidence ? To answer this question, one would have to start with the notion of single-nucléon properties inside nuclear medium. At the moment, no satisfactory theory exists that starts from basic principles, i.e. QCD. It seems, however, reasonable to assume that one can talk about a "quasi-nucléon" whose properties such as mass, coupling constants, ^tc... are modified due to the background provided by other nucléons. I will thus take gjf* ~ 1 to mean that the nucléon response to the axial current inside nuclear matter is fundamentaIlv modified (there are some physicists in tne field who do not share this point of view).

The key theme in my argument is that the quenching phenomenon of gA is one of the many facets of the way chiral symmetry [SU(2) x SU(2)] manifests itself in nuclear matter (Rho and Brown, 1983). More precisely, I would argue that a proper understanding of this phenomenon requires understanding of where and when pion degrees of freedom show up explicitely (the pions being Goldstone bosons associated with the Nambu-Goldstone vacuum). Now the pions play a crucial role in the structure of the nucléon (Brown and Rho, 1987) and hence the issue boils down tc understanding the nucléon structure itself. My main conjecture here, which I have not yet been able to prove to my satisfaction but I believe to be quite likely true, is that the

quenching of gA is just the other face of a coin to the phenomena in which virtual pions "enhance" the transitions as seen in electrodisintegration of deuterons and magnetic form factors of H and 3He at l^rge momentum transfers. That chiral symmetry can manifest itself in nuclei in completely different fashions was referred to as "chiral filter hypothesis" (Rho and Brown, 1981; Rho, 1984).

3 - THE NUCLEON STRUCTURE

If a nucléon in nuclear matter is intrinsically modified, this must mean that the "vacuum" or the background in which the nucléon propagates is modified from that of a free nucléon. To understand what happens, we need to understand the structure of the nucléon. The key feature in QCP that is relevant to the problem is chiral symmetry associated with nearly massless up (u) and down (d) quarks (Brown and Rho, 1986).

Focusing on the nucléon, let us imagine that quarks are confined within a "bag" of radius R. By putting appropriate boundary conditions, one can indeed assure that they are confined at classical level. But it turns out that due to polarization of the Dirac vacuum, the quarks actually escape from the confining bag (Rho, Goldhabcr and Brown, 1983; Goldstone and Jaffe, 1983). The most concise way of seeing this phenomenon is through chira] anomaly. Suppose the quarks inside the bag satisfy the Dirar. equation :

i-Y.o" == 0 (r <• R) (1)

.subject to a boundary condition on (he .surface: 3

-in.-n|/ - U5* (r - R) (2)

with U5 some unitary operator U^ U5 - 1, and n^ outward normal unit four- vector. What can U5 be ? If one is confining oneself to the longest wave­ length oscillations which we will do in this discussion, IL must be of the form:

U5 * exp i-Y5 T.î/ftt (3)

where IT are the triplet Goldstone pion fields and fn the pion decay cons­ tant. If the pion field in Eq. (3) were of trivial configuration, say (IOQ - 0 , then the boundary condition (2) would confine the quarks even quantum mechanically. However suppose that the pion field posseses a non- trivial configuration, say, the hedgehog structure:

U0 - exp(iT.re(r)Tr5), (4)

u then while the "chiral rotation" ^ -» Ug>|/ renders the boundary condition trivial:

-in.-nj, = ,|/ (r = R) (5) the quark field sees an "induced" axial gauge field A^

i"Y.D»|/ = 0 (6) D^ - ^ + \ A^ where A^ - ir, U^d^A,. , with A. a surface 6-function. In the presence of an axial U(l) gauge field, the baryon current B^ is not conserved (or anomalous)

^ * 0 . (7)

Therefore the baryon charge leaks out. But the baryon number must be conserved in QCD. So what happens to the leaking baryon charge ? What hap­ pens to it was discovered by Skyrme more than two decades ago (Skyrme, 1961 ; Witten, 1983): the baryon charge is recovered in the soliton made up of the configuration (A). In (1 + 1) dimensions, this phenomenon can be understood in a precise way (Nielsen, 1987). Imagine a right-moving quark bounces off the "hag wall" and moves to the left as a left-moving quark. The left-moving quark cannot be found above the Dlrac sea ; it. can only move inside the Dime sea, i.e., it "drowns". As it plunger; into the nega­ tive energy sea at: the wall, it imparts its fermion charge to a kink which poves to the right with precisely the right shift in the meson field to accomodate the: transferred charge. How this happens is beautifully descri­ bed by Nielsen (1987). 4

In (1 + 1) dimensions, more things can be rigorously established. In particular, one can show that physics does not depend upon where one puts the tag wall. If one "shrinks" the bag away, leaving behind only the meson field, the resulting system describes the same physics as the original fermion system. Thus the bag is unphvsical. The fact that the physics is the same wherever the bag is put (whether in terms of fermion fields or in terms of boson fields) is known as "Cheshire Cat Phenomenon" (Nadkarni et al, 1985 ; Nielsen, 1987 ; Perry and Rho, 1986 ; Brown and Rho, 1986 ; Rho, 1986).

Although it cannot be rigorously proven in (3 + 1) dimensions, the Cheshire Cat Phenomenon is very plausible in QCD at low energies. It cannot be exact, since asymptotic freedom cannot be bosonized with a finite number of meson fields. But it can be approximately realized. In fact, recent works by Jackson and his co-workers have shown that static properties such as magnetic moments, charge radii etc.. . depend little on the precise value of bag radius in chiral bag models (Jackson et al., 1987 ; Wûst, Vepstas and Jackson, 1986 ; Jezabek et al., 1986).

As a first approximation, the Cheshire Cat can be assumed to be realizable as accurately as one wishes, at least at low energies (< 1 GeV), by introducing further meson fields as needed. [There is indication that low-energy QCD posseses this property. For instance, there is a natural way that the vector mesons p, 0), A^ , contribute, beyond the scales relevant to the pion, to the baryon structure. In fact, they are not arbitrary addi­ tions, but arise as hidden gauge bosons of low-energy effective QCD lagran- gians (Bando et al., 1985 ; Ball, 1987).) One notable consequence of the above observation is that the confinement size (sometimes loosely referred to as "bag size") cannot be measured. This result, crucially tied to chiral anomalies, is closely analogous to the similar properties of Callan-Rubakov effects in the monopole-fermion system (Rubakov, 1982 ; Callan, 1982) and of the cosmic strings (Witten, 1984): in these systems, the "intrinsic" size cannot be measured.

What this means is of course that it is not possible to see by low-energy experiments where quark degrees of freedom are delineated from hadron degrees of freedom. This may sound Lo mean that we will never "see" the quarks at low energies. This I will now argue is not true. In accordance with the "chiral filter idea", some, processes in nuclei can exhibit quark presence though in a very indirect way. This is discussed next.

4 - FROM QCD TO EFFECTIVE THEORIES

The Cheshire Cat Phenomenon described nbove suggests that at low energies we mipht as well work in the Skyrmion picture (for a review, see Zahed and Brown, 1987). But we do not know a systematic way to write down the effective QCI) lagranpian with which a Skyrmion theory can be constructed. 5

Ideally one should derive it from QCD, but this is asking for the very solution of QCD that we are trying to approximate. It is, however, possible •• derive it for very low-energy processes, say, for much less than 1 GeV and climb up to 1 fieV through symmetry arguments. For chiral

SU(Nf) x SU(Nf) (where Nf is the number of flavors) at long wavelength limit, two terras are definitely known:

SQCD ~ SCA + suz + -•• (8)

f f « VA + where SCA is the current algebra term I —Tr(ôpiU3 U ) where

U - exp iX.ir/f^ (with Tr X^Xp - 26ap) and Suz is the celebrated Wess-Zumino term (symbolically written here):

-iN, 5 Su, - C (ifdU) , C (9) J.; 5 240 T2 defined in five-dimensional manifold whose boundary is the physical space-

time (Witten, 1983). SCA describes normal parity processes at low energy and SU2 abnormal parity processes. S„z plays a key role in giving rise to some remarkable results I will discuss later. The terms denoted by... stand for the terras that are presumed to be negligible at low energy. Being an effective QCD lagrangian, (8) contains baryons through solitons, i.e., the Skyraions (Skyrme, 1962) (stability of the Skyrmions requires higher deri­ vative terms or other meson fields).

In a nut-shell, if color excitations are absent at low energies (confinement), then QCD (at low energies) can be described in terms of meson fields. Now how far in energy can one push this picture ? There is a good reason to believe that a natural mass scale to which the effective

theory can be applied with some confidence is the vector-meson (w, p, A1) mass ~ 1 GeV. One way of seeing this is to "derive" from QCD the leading corrections to the current algebra terms (Simic, 1985 ; Ball, 1987). Ano­ ther way is to exploit hidden symmetries of the current algebra lagrangian

(Bando et al., 1985). The result is that the vector mesons, w, p, A1 emerge as hidden local gauge particles whose masses are generated via a Higgs mechanism. Some well-known results such as vector dominance, universality and so on can be understood in a "natural way".

5 - CHIRAL FILTER PHENOMENA

With the baryons emerging as solitons, %QC0 is to describe all hadronic interactions, including inside nuclear matter, up to ~ 1 OeV. One obvious consequence of (8) is that the meson-theoretic approach used in nuclear physics is justified from the QCD point of view. More importantly, some recent "startling" results in nuclei can be understood in terms of (H), at leas t qua 11: i ta t i ve 1 y . 6

The current algebra part of the action (with the symmetry breaking term S,B to account for the non-vanishing quark masses) is well-established in the meson sector (Gasser and Leutwyler, 1984, 1985). The baryonic sector (the Skyrmion) is not yet fully understood, but SU(2) * SU(2) baryons do seem to be in a gcod shape i~ vectors mesons are properly taken into account (Meissner, 1987). In nuclei, as predicted some years ago (Kubodera, Delorme and Rho, 1978), it can be "seen" in isovector Ml transitions and axial charge transitions. The recent electron scattering experiments (Frois and Papanicolas, 1987), in particular electrodisintegration of the deuteron and magnetic form factors of 3He and H at momentum transfers up to q2 ~ 30-60 fm"2 , have firmly confirmed the role of pions and specifically

the role of SCA in nuclear (and nucléon) structure. Towner (1987) has recently reviewed a similar result in "axial charge" transitions (i.e. 0+ -* 0" , Ai - 1) in nuclei. What these results mean is that to a distance ^ — fm between two nucléons, the relevant degrees of freedom are (soft) pions when probed by, say, the isovector Ml current.

Now what about the Suz ? This term contains chiral anomalies ; namely, if electromagnetism is introduced, it describes T" -• 2"Y, ~Y -» 3T and other pro­ cesses of quantuum anomalies. It is more. It is in fact the "smile" of the Cheshire Cat, signalling underlying features of QCD. In the currently fa­ shionable terminology, it embodies a Berry's phase and contains low-energy signatures of QCD variables. Furthermore it mediates such vector meson transitions as 0) -» 3ir, 0) -• TT°"Y etc... (Fujiwara et al., 1985 ; Kramer et

al., 1984). Let me now claim that the Suz manifests itself in an elegant way in nuclei. To illustrate this point, consider the Adler-Bell-Jackiw anomaly for f* -• 2"f. In terms of QCD variables, it is given by the triangle diagram:

(10)

When Eq. (9) is suitably gauged for electromagnetism, it precisely reprodu­ ces this triangle diagram (Witten, 1983). Introduce now the vector mesons p and W as hidden gange particles as mentioned above. It is possible to rewrite the resulting action such that the process (10) is entirely given by (Ball, 1987):

(11) 7

A striking feature of the diagram (10) is that gluon radiative corrections (strong interactions) do not renormalize the triangle diagram, as proven by Adler and Bardeen (1969). Will the diagram (11) be protected by a similar non-renormalizability theorem ? Although there is no such proof at present, I find it appealing to assume that within the framework of Sj£p , the dia­ gram (11) - and in general Suz - is unrenormalized by radiative correc­ tions. If this is true, then the Ofcm vertex appearing in the exchange cur­ rent for isoscalar magnetic transitions

W (12) w fc N »W * \ » N ]P N • * •» N is expected to be entirely given by the Wess-Zumino action. We have some strong evidence that what I am "conjecturing" here comes true in Nature. Recently Nyman and Riska (1987) calculated deuteron magnetic form factors in the Skyrmion description. The predicted from factors are in good agree­ ment with experiments for momentum transfers up to q2 ~ 60 fm*2, confirming the crucial role of the Wess-Zumino term. What this implies is that the chiral anomaly faithfully translates quark degrees of freedom into meson degrees of freedom, extending the domain of validity of Sjjjp to a considerably shorter distance than one has the right to hope. I note that for the isoscalar current, the current algebras (e.g. soft-pion theorems) play no role. Nevertheless the two diverse responses seen here are clearly

"two sides of the same coin", to the extent that Sc, and Swz are related intimately.

Recent works in the Skyrmion picture by Nyman and Riska (1987b) and by Wa- kamatsu and Weise (1987) provide some support to the chiral filter notion.

6 - THE gA PROBLEM

Some people argue that gA ~ 1 in nuclei is coincidental and can be explained by trivial nuclear structure effects. They may he right

In my opinion, gA is an indicator of the vacuum structure inside dense hadronic matter and its behaviour in nuclear medium is an important quantity to study. Let me argue this point in terms of the effective action (8). Anomalies most probably play no role here. Therefore let me focus on

SCA . Consider a Skyrmion embedded in a dense nuclear matter (Rho, 1985). What happens to the Skyrmion when it is squeezed by the matter ? As Ions as the system is in Golristone mode, the Goldstone theorem should still be

applicable and hence there should be a Goldstone pole at <\ 0, qQ ~ 0 . (This implies that the Wigner-Seitz cell approximation uacd for 8 high-density Skyrmions cannot be a reliable one) . As in free space, the Skyrmion can then be characterized by two quantities f^ (the pion decay

constant in nuclear matter) and gA (the effective gA). The former characte­ rizes long-distance properties of the effective action (namely, current algebras) and the latter shorter-distance properties (e.g. the Skyrme quar- tic term or vector meson degrees of freedom). This way of classifying things may be a bit too simplistic, but I believe that it is qualitatively correct. If I denote by R the mean-square-radius of the baryon charge distribution

R2 - „„ „„ baryoK w n a simple scaling argument (Rho, 1985) leads to the relation

2 R « g;/f;2 (i3)

2 or gA « (f^R) . As density increases, f£ is expected to decrease (going to zero at the phase transition from Goldstone to wigner mode) and R to increase. However the increase in R will be slower than the decrease in f^.,

so the product (f^R) will be a net decrease. Thus the quenching of gA in nuclear matter is found to be an interplay of two opposing effects. There

is no obvious reason why gA cannot be less than 1 at some density, but we

expect gA to approach 1 asymptotically. There is a strong support for the above thesis from the QCD sum rule (Shifman et al. , 1979) applied to nuclear systems (Parthasarathy and Pasupathy, 1987). In the QCD sum rule approach (Ioffe, 1981), the nucléon mass is of the form:

1/3 ->.«[-0] where (qq>_ is the u- or d-quark condensate in the vacuum. Thus if the vacuum is modified, the condensate will be modified accordingly, as a con­ sequence of which in a dense medium, the nuclear mass will be modified : as

the density increases, nu. necessarily decreases. Now the gA, in the QCD sum

rule, depends crucially on mN or more specifically on (qq>0 and gA approa­ ching 1 in dense nuclear medium follows naturally.

What low-energy degrees of freedom are relevant for gA ? In the vector dominance picture currently revived, one can think of gA being dominated by an A1 exchange. A1 can be viewed as a vector boson of the hidden gauge symmetry whose mass sets the limit of the mass scale for chiral pertur­ bation theory. Thus we may consider it as a "short-distance" quantity, as opposed to fjt which is a "long-distance" quantity. It is perhaps of signi­ ficance that Eq. (13) connects the long- and short-distance properties in nuc. lear medium.

I am grateful to Prof. H. Umezawa for discussion.'; on this issue. 9

7 - CONCLUSION

I have discussed diverse facets of a common feature, spontaneously broken chiral symmetry, as manifested in nuclear physics. My key point has been that different probes "see" different facets of the same coin. I have sketched qualitatively how one can treat them, but a systematic treatment is still missing. Is there a way to do so ? I believe there is: chiral per­ turbation theory adapted to baryon-rich systems along the line that has been developed for "WW scattering, K -» 2""' decay and other "soft" strong interaction physics (Gasser and Leutwyler, 1985 ; Bardeen, Buras and Gerard, 1986). Exploiting the hidden gauge symmetry could lead to a consis­ tent calculation with (low-energy) unitarity.

8 - ACKNOWLEDGMENTS

This paper was written while I was visiting the Nuclear Theory Group of Stony Brook and was partially supported by USDOE Contract DE-AC02-76ER 13001.

REFERENCES

Adler S.L. and Bardeen W.A. 1969 Phys. Rev. 182. 1517. Ball R. 1987 in "Skyrmions and Anomalies" Krakow meeting (to be published). Bando M., Kugo T., Uehara S., Yamagida T. and Yamawaki K. 1985 Phys. Rev. Lett. 54 1215. Bardeen W.A., Buras A.J. and Gerard J.M. 1986 Max-Planck-Institute Preprint MPI-PAE/PTH 55/86. Brown G.E. and Rho M. 1986 Comm. Nucl. Part. Phys. 15 245. Brown G.E. and Rho M. 1987 Comm. Nucl. Part. Phys. (in press). Buck B. and Perez S.M. 1985 Phys. Rev. Lett. 54 767. Callan C.G. 1982 Phys. Rev. D25 2141 ; D26 2058. Frois B. and Papanicolas C.N. 1987 Ann. Rev. Nucl. Part. Sci. 32 (in press). Fujiwara T., Kugo T., Terao H., Uehara S. and Yamawaki K. 1985 Prog. Theor. Phys. 73 926. Gasser J. and Leutwyler H. 1984 Ann. Phys. 158. 142. Gasser J. and Leutwyler H. 1985 Nucl. Phys. B250 465. Goldstone J. and Jaffe R.L. 1983 Phys. Rev. Lett. 51 1518 Ioffe B.L. 1981 Nucl. Phys. R1R8 317. Jackson A..D. et al. 198' Nucl. Phys. A462 661. Jezabek M., Heller K.J. and Nowak M.A. 1986 Phys. Lett. 173B 221. Kramer G., Palmer W.F. and Pinsky S.S. 1984 Phys Rev. D30 89. Kubodera K., Delorme J. and Rho M. 1978 Phys. Rev. Lett. 40 755. Meissner U.C. 1987 Phys. Re|,r.-, (to he published). Nadkarni S., Nielsen U.K. and Zahed I. 1985. Nucl Phys. B253 308. Nielsen H.B. 198/ Lectures at. , ,• -; Houches (to be published^. Nyman E. and Riska 1). 0. 198/a Nu-1. Phys. A4 6 8 473. Nyman E. and Riska DO. 198/b Uni" of Helsinki preprint 10

Parthasarathy R. and Pasupathy J. 1987 Madras preprint. Perry R.J. and Rho M. 1986 Phys. Rev. D34 1169. Rho M. 1984 Ann. Rev. Nucl. Sci. 34 531. Rho M. 1985 Phys. Rev. Lett. 54 767. Rho M. 1986 Lecture Notes in Selected Topics in Theoretical Physics, ed. by H.S. Song (Kyohak Yunkusa, Seoul, Korea 1987) Rho M. and Brown G.E. 1981 Coram. Nucl. Part. Phys. 10, 201. Rho M., Goldhaber A.S. and Brown G.E. 1983 Phys. Rev. Lett. 51 747. Rubakov V.A. 1982 Nucl. Phys. B203 311. Shifman et al 1979 Nucj.. Phys. B147 385. Simic P. 1985 Phys. Rev. Lett. 55 40. Skyrme T.H.R. 1962 Nucl. Phys. 31 556. Towner I.S. 1986 Comm. Nucl. Part. Phys. 15 145. Wakamatsu M. and Weise W. 1987 Reggensburg preprint. Wilkinson D.H. 1973a Phys. Rev. Ç7 930. Wilkinson D.H. 1973b Nucl. Phys. A209 470. Wilkinson D.H. 1978 in Nucl. Phvs. with Heavy-Ions and Mesons, ed. R. Balian, M. Rho and Ripka (North-Holland, Amsterdam 1978). Witten E. 1983 Nucl. Phys. B223 422, 433. Witten E. 1985 Nucl. Phys. B249 557. Wust E., Vepstas L. and Jackson A.D. 1986 Phys. Lett. 173B 217. Zahed I. and Brown G.E. 1986 Phys. Rev. 14^ 1.