ELSEVIER Nuclear Physics A721 (2003) 376c-379c www.elsevier.com/locate/npe

Quark-antiquark asymmetry of the nucleon strange sea

M. Wakamatsu”

“Department of Physics, Faculty of Science, Osaka University, Toyonaka, Osaka 560-0043

Theoretical predictions are given for the light-flavor sea-quark distributions in the nucleon including the strange quark ones on the basis of the flavor SU(3) version of the chiral quark soliton model. Careful account is taken of the SU(3) y s mmetry breaking effects due to the mass difference between the strange and nonstrange quarks, which is the only one parameter necessary for the flavor SU(3) generalization of the model. A particular emphasis of study is put on the Light-Favor sea-qua& asymmetry as well as the particle-antiparticle asymmetry of the strange quark distributions in the nucleon.

1. Introduction

We claim that the Chiral Quark Soliton Model (CQSM) is the simplest and most powerful effective model of QCD f or investigating sea-quark distributions in the nucleon. This t,otally owes to its field theoretical nature, i.e. the proper account of polarization of Dirac-sea quarks [l], [a]. W e h ave already shown that, without introducing any adjustable parameter, it reproduces almost all qualitatively noticeable features of the recent DIS observables including the NMC measurement as well as the famous EMC finding [3],[4],[5]. What was lacking for the flavor SU(2) CQSM was the neglect of hidden strange quark components in the nucleon. Here, we attack this problem by using the flavor SU(3) version of the CQSM, which is constructed on the basis of the SU(2) CQSM with some additional dynamical assumptions [6],[7].

2. Flavor SU(3) CQSM

The model lagrangian is a straightforward generalization of the SU(2) model with the flavor octet collective meson fields, except for one important new feature, i.e., the existence of the SU(3) symmetry breaking term due to the sizably large mass difference between the strange and nonstrange quarks. This mass difference Am, is the only one additional parameter of our model. The basic dynamical assumption of the flavor SU(3) CQSM is as follows. Firstly, the lowest energy classical solution is obtained by the embedding of the SU(2) self-consistent mean-field into the SU(3) matrix, analogous to the flavor SU(3) Skyrme model. The next is the collective quantization of the symmetry restoring rotational motion of the soliton in SU(3) collective coordinate space. Finally, we assume that the SU(3) symmetry breaking effects can be treated perturbatively. Actually, we have taken account of 3 possible SU(3) breaking corrections, which are all first order in Am,. The detail can be found in [7].

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M. Wakamatsu /Nuclear Physics A 721 (2003) 3 76c-3 79~ 3llc

3. Comparison with High Energy Data

First, after some trial, only one parameter of the SU(3) CQSM is fixed to be 100 MeV. Then, we use the predictions of the model as initial distributions given at the low energy model scale, simply assuming the smallness of the gluon distribution. Before making a comparison with the existing high-energy data, we briefly summarize the characteristic features of the model predictions. Concerning the unpolarized strange quark dist,ributions, we find that the asymmetry of s- and s-quark distributions certainly exists. The differ- ence function S(Z) - S(Z) has some oscillatory behavior with several zeros as a function of 5. This is of course due to the two general constraints of the PDF, i.e. the positivity constraint for the unpolarized distributions and the strangeness quantum number conser- vations. As expected, it turns out that the difference function S(Z) - S(Z) is extremely sensitive to the SU(3) breaking effects. Next we turn to the longitudinally polarized strange quark distributions. In the chiral limit case, the s and s are both negatively polarized. After introducing Am, correction, As(x) remains large and negative, while AS(X) becomes very small. As a consequence, the S-S asymmetry of the longitudinally polarized distributions is much more profound than that of the unpolarized distributions. This is reasonable because, for the spin-dependent distributions, there is no conservation laws, which prevents the development of asymmetry.

Now we compare in Fig.1 the theoretical strange-quark distributions evolved to Q2 = 4 GeV’ with the corresponding CCFR NLO fit of the neutrino-induced charm production, which was carried out with the constraint S(S) = s(z). 0 ne can say that, after inclusion of the SU(3) symmetry breaking corrections, the theory reproduces the qualitative feature of the CCFR fit.

without Am, correction with Am, correction 0.25 0.25

- x s (x) - x s (x) -. -. -. -. -. xi @)

0.05 0.05

0.0 * 0.0 lo-* 2 5 10-l 2 5 1 lo-* 2 5 10-l 2 5 1

X X

Figure 1. The theoretical unpolarized distribution functions S(Z) and S(Z) at Q2 = 4 GeV2 in comparison with the corresponding CCFR data obtained under the assumption S(X) = S(o) k31.

378c M. Wakamatsu /Nuclear Physics A721 (2003) 376c-3 79c

Recently, Barone et al. carried out quite elaborate global analysis of the DE data, especially by using all the available neutrino data [9]. This enables them to obtain some interesting information even for the asymmetry of the s and s distributions. The thick and thin shaded areas in Fig. 2 are the allowed regions for the ration s(s)/a(z) at Q2 = 20GeVa, respectively obtained by Barone et al. and by CCFR analysis. One clearly sees that the theory reproduces the qualitative tendency of the data only after including the SU(3) breaking effects.

s(x) I S(x) at Qz = 20 GeV’

5.0

---- 4.5 without Am, correction - with Am, correction

4.0 Barone et al. 3.5

3.0

2.5

0.5 ‘\ ‘i,

0.0 %___

0.0 0.1 0.2 0.3 0.4 0.5 0.6

x

xAs(x) and xAS(x) at Qz = 1 GeV*

oo’l

-0.05 I LSS fit

1

Figure 2. The ratio of S(Z) and S(Z) at Figure 3. The theoretical prediction of Q2 = 20GeV’ in comparison with the re- the SU(3) CQSM for the separate contri- sults of CCFR analysis [8] and of Barone et butions of s- and s-quarks to the longi- al’s global fit [9]. tudinally polarized distribution functions

z[As(e) + As(x)] in comparison with the LSS fit [lo].

Although we have no space to show them, we also find that the predictions of the SU(3) CQSM for the longitudinally polarized distributions including the strange quarks are qualitatively consistent with the recent elaborate analyses carried out by Leader, Sidorov and Stamenov [lo]. One interesting feature of the model prediction is that the polarization of strange-sea almost solely comes from s-quark and that the contribution of s-quark is tiny as illustrated in Fig.3.

Turning to the problem of isospin asymmetry of sea quark distribution, we recall that the SU(2) CQSM predicts that ~(2) - d(z) < 0, while AC(x) - A(i(z) > 0. Now the question is what the predictions of the SU(3) CQSM is like. We find that, for the isospin asymmetry of unpolarized sea, the answers of both models are nearly degenerate, which we already know is consistent with the NMC observation. On the other hand, the magnitude

M. Wahzmatsu /Nuclear Physics A 721 (2003) 3 76c-3 79c 379c

of A+)-A+) t urns out to be sizably reduced when going from the SU(3) model to the SU(2) one. Still, the positive polarization of AG and negative polarization of Ad in the proton is a definite prediction of both versions of the CQSM, which should be contrasted with the prediction of other models like the naive meson cloud convolution model.

4. Conclusion

To summarize, an incomparable feature of the CQSM as compared with many other effective models like the MIT bag model is that it can give reasonable predictions also for the antiquark distribution functions. We emphasize that this feature is essential for giving any reliable predictions for strange distributions in the nucleon, which totally have non-valence character.

With a single parameter, the SU(3) CQSM predicts that the s(x) - G(z) difference function has some oscillatory z-dependence, due to the positivity constraint for the spin- averaged distributions and the strangeness quantum number conservation. We have also shown that, after introducing the SU(3) breaking effects, the 5 dependence of S(X) - S(Z) and s(z)/s(z) are qualitatively consistent with the global analysis of Barone et al. The S-S asymmetry of longitudinally polarized sea is more profound than that of unpolarized sea. The model predicts that the polarization of s-quark is large and negative, while the polarization of s-quark is very small. The model also predicts quite large isospin asymmetry of the sea-quark distributions not only for the unpolarized distributions but also for the longitudinally polarized ones.

An important lesson learned from our investigation is that the nonperturbative QCD dynamics due to the spontaneous chiral-symmetry breaking manifest most clearly in the spin and isospin dependence of antiquark distributions in the nucleon. What is absolutely required for future experiments is therefore the flavor as well as the valence $ sea-quark decomposit ion of PDF.

REFERENCES

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