IC/IR/96/25 INTERNAL REPORT XA9743267 (Limited Distribution) United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS SU(3) SYMMETRY BREAKING CHIRAL QUARK MODEL AND THE SPIN STRUCTURE OF THE NUCLEON X. Song1 International Centre for Theoretical Physics, Trieste, Italy. ABSTRACT The chiral quark model, suggested by Eichten, Hinchliffe and Quigg, and extended by Cheng and Li, can explain many unexpected proton flavor and spin structures rea­ sonably well. The SU(3) values of /3//8 and A3/A8 given in Cheng and Li’s description are, however, inconsistent with the experimental data. Taking SU(3)-symmetry-breaking effect into account and extending the SU(3) calculation, we found that not only the above inconsistency can be removed but also better agreement obtained between many other theoretical predictions and experimental results. A consequence of this breaking is that the strange sea would be slightly negatively polarized, As —(0.05 — 0.06), and the total quark spin would contribute about one half of the proton spin, All = 0.45 — 0.47. MIRAMARE - TRIESTE August 1996 ‘Permanent address: Department of Physics, Hangzhou University, Hangzhou 310028, People’s Republic of China. I. INTRODUCTION One of the important goals in high energy physics is to reveal the internal structure of the nucleon. This includes to study the flavor and spin contents of the quark and gluon constituents in the nucleon and how these contents are related to the nucleon properties: spin, magnetic moment, elastic form factors and deep inelastic structure functions. In the late 1980’s, the polarized deep inelastic lepton nucleon scattering experiments [1] surpris­ ingly indicated that only a small portion of the proton spin is carried by the quark and antiquarks, and a significant negative strange quark polarization in the proton sea. Since then, a tremendous effort has been made for solving this puzzle both theoretically and ex­ perimentally (recent review see [2-4]). According to the most recent result [5,6], the quarks contribute about one third of proton’s spin, which is ony one half of the spin expected from the hyperon decay data (AE ~ 0.6) and the strange quark polarization is about —0.10, which deviates significantly from the naive quark model expectation. On the other hand, the baryon magnetic moments can be reasonably well described by the spin-flavor structure in the nonrelativistic constituent quark model. Most recently, the New Muon Collaboration (NMC) experiments [7] have shown that the Gottfried sum rule [8] is violated, which indicates that the d density is larger than the u density in the nucleon sea. This asymmetry has. been confirmed by the NA51 Collaboration experiment [9], which shows that u/d ~ 0.51 at x = 0.15. From the quark model of the nucleon, the density of u would be almost the same as that of d if the sea quark pairs are produced by the flavor-independent gluons (s could be different because of m, >> mUij). Many theoretical works, trying to solve these puzzles, have been published. Among these, the application of chiral quark model, suggested by Eichten, Hinchliffe and Quigg [10], and then extended by Cheng and Li [11], seems to be more promising. The chiral quark model was first originated by Weinberg [12] and then developed by Manohar and Georgi [13]. In this model, they introduced an effective Lagrangian for quarks, gluons and Goldstone bosons in the region between the chiral symmetry breaking scale (Axsb — 1 GeV) 2 and the confinement scale (Aqcd — 0.1 — 0.3 GeV). The great success of the constituent quark model in low energy hadron physics can be well understood in this framework. In the chiral quark model the effective strong coupling constant a, could be as small as 0.2-0.3, which implies that the hadrons can be treated as weakly bound states of effective constituent quarks. The model gave a correct value for (G/t/Gv)n-P = (5/3)= 1.25, with g* ~ 0.75, and a fairly good prediction for baryon magnetic moments. The extended description given by Cheng and Li [11] can solve many puzzles related to the proton flavor and spin structures: a significant strange quark presence in the nucleon indicated in the low energy pion nucleon sigma term <r„yv, the asymmetry between the u and d densities, the total net quark spin AS ~ 1/3 and nonzero negative strange polarization As ~ -0.10. However, Cheng and Li’s SU(3) symmetry description yields: and A3/Ag=5/3, which are inconsistent with the experimental values: fs/fs cz 0.23 and A;)/As — 2.1. In this note, we introduce an SU(3) symmetry breaking effect and extend their calculation. The result shows that not only the above inconsistency can be removed but also a better agreement between some other theoretical predictions and experimental results are obtained. II. SU(3) SYMMETRY BREAKING EFFECT. A. Cheng-Li’s description In the chiral quark model, in the scale range between Axsb and AqcDi the relevant de­ grees of freedom are the quasiparticles of quarks, gluons and the Goldstone bosons associated with the spontaneous breaking of the SU(3) x SU(3) chiral symmetry. In this quasiparticle description, the effective gluon coupling is small and the important interaction is the cou­ pling among quarks and Goldstone bosons, which may be treated as an excitation of qq pair produced in the interaction between the constituent quark and the quark condensate. Note that these Goldstone bosons can be identified, in quantum numbers, with usual pseudoscalar 3 mesons, but they propagated inside the nucleon. The sea quark-antiquark pairs could also be created by the gluons. Since the gluon is flavor independent, a valence quark cannot change its flavor by emitting a gluon. Also the spin cannot be changed due to the vector coupling nature between the quarks and gluons. On the, other hand, emitting a Goldstone boson a valence quark could change its flavor (for charge meson, but not for neutral meson) and certainly change its spin because of pseudoscalar coupling between the quarks and Goldstone bosons. The presence of Goldstone bosons in the nucleon cause quite a different sea quark flavor-spin content from that given by emitting gluons from the quarks. Hence the chiral quark model may provide a better understanding to the above puzzles. According to Ref.ll, the effective Lagrangian describing interaction between quarks and Goldstone bosons can be written ( u \ 2 _ , Li = ffs#.? + vfpoqv ? (2.1) where A+ \ 7T~ K° (2.2) K~ K° 'TV? I and A, (i=l,2,...8) are the Gell-Mann matrices. If the singlet Yukawa coupling is equal to zero g0 = 0, the quark sea created by emitting 0" meson octet would contain more d quarks than u quarks (and less a quarks). The resulting u-d asymmetry seems to be consistent with u-d < 0 indicated by the NMC data which show a significant violation of the Gottfried sum rule. However, according to the U(3) symmetry, the singlet is as important as the octet in the quark meson interactions and its Yukawa coupling is equal to the octet coupling go = g8. In this case, one surprisingly finds that the flavor asymmetry in the sea disappears and the numbers of uu, dd and as are equal. Cheng and Li suggested a reason to introduce an unequal singlet and octet coupling go/gs = ( ^ 1. This unequality may arise from the subleading contributions in the 1 /Nc expansion [14]. Having the parameter £ and another 4 parameter a ~ |g8|2, a straightforward calculation yields the following results: u = 2 + u; d = 1 + d; s = 0 + 5 (2.3) where 2,1, and 0 denote the numbers of valence u, d and s quarks in the proton, and « = |(C2 +2C + 6). d=^(C + S) (2.4) ■5 = ^(C2 -2( + 10) (2.5) For quark spin contents in the proton, similar calculation gives Au = ^ - ^(8(2 + 37 )o (2.6) Ad = -- + -(C2 - l)a (2.7) As = —a (2.8) One can see that the emission of the Goldstone boson leads to a reduced polarization to each flavor of up, down and strange quarks: less positive for Au, less negative for Ad, and a negative polarization for the strange quarks. This result can be very well understood in t he chiral quark model. Taking a = 0.1 and ( = —1.2, they obtained a/d = 0.53 (expt. : 0.51 ± 0.04 ± 0.05) (2.9) Ig = J dx 2V = 0.236 (expt. : 0.235 ± 0.026) (2.10) f- s iTWTJTT) = 019 :0.18±0.03) (2.11) Using the same parameters, the quark spin polarizations are also consistent with the data. However, the SU(3) symmetry description yields h/h = 1/3 (expt. : 0.23), A3/A„ = 5/3 (expt. : 2.1) (2.12) In Ref. 11, Cheng and Li guessed that this inconsistency between theoretical prediction and data could be attributed by some SU(3) breaking effects. In the next subsection, we in­ troduce an SU(3) breaking effect arising from the quark mass difference and extend their description. We find that the inconsistency can indeed be removed. B. SU(3) symmetry breaking description We assume that the breaking of SU(3)-flavor symmetry arises from a mass difference between strange and nonstrange quarks. Since the strange quark is heavier, this breaking would cause a smaller probability of strange meson emission from a u (or d) quarks to various quark-meson states. Defining $(u —» 7r +d) as the probability amplitude of a ir+ meson emission from a u quark etc., we have |tf(u —» 7r +d)|2 = |$(d —» 7T~u)| 2 = \g6\2 = a, etc.