R. Bijker, E. Santopinto
We present an unquenched quark model for baryons in which the effects of quark-antiquark pairs (light flavors, u, d and s) are taken into account in an explicit form. The method is illustrated with an application to the flavor asymmetry of the nucleon sea.
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Implication of the modified Gottfried sum rule is discussed by focusing its theoretical bases, the range of validity, and physical interpretation.
We report on recent work concerning the effect which the change in vacuum structure (negative energy Dirac sea), in the presence of a confining scalar field, has on the nucleon structure functions and parton distributions. Using the Dirac equation in 1+1 dimensions, we show that distortions in the Dirac sea are responsible for part of the violation of the Gottfried sum rule -- i.e., part of the flavor asymmetry in the proton sea. Our basic argument is that, even if isospin is an exact symmetry, the presence of a confining potential changes the vacuum structure, and inevitably leads to a violat…
1) Spin and flavor sum rules based on a parton model, 2) SU(2) flavor breaking in antiquark distributions
1)在讨论Gottfried求和规则的基础上，讨论了自旋为1的强子的张量结构函数$b_1(x)$的求和规则。这两个求和规则在某种意义上是相似的，它们都是基于朴素部分子模型的唯象规则。由于Gottfried求和规则在研究反夸克分布的SU（2）$_{flavor}$破缺中变得有用，因此$b_1$求和规则可以提供海夸克张量极化的重要信息。2)讨论了π介子对反夸克分布$\bar u-\bar d$的贡献以及对戈特弗里德和规则的违反。我们发现，贡献约占一半的差异发现的新μ子合作的结果和求和规则。为了区分不同的理论解释，我们需要独立的实验测试，例如使用Drell-Yan过程。作为介子计算的一个应用，简要讨论了核子中奇异夸克和反奇异夸克分布的差别。
1. Introduction 2. Possible violation of the Gottfried sum rule 2.1 Gottfried sum rule 2.2 Early experimental results 2.3 NMC finding and recent progress 2.4 Small $x$ contribution 2.5 Nuclear correction: shadowing in the deuteron 2.6 Parametrization of antiquark distributions 3 Expectations in perturbative QCD 3.1 Operator product expansion 3.2 Perturbative correction to the Gottfried sum 4 Theoretical ideas for the sum-rule violation 4.1 Lattice QCD 4.2 Pauli exclusion principle 4.3 Mesonic models 4.3.1 Meson-cloud contribution 4.3.2 Chiral models 4.3.3 Anomalous $Q^2$ evolution 4.4 Diquark …
A brief summary on the Wigner rotation effect in the understanding of the proton spin ``crisis" related with the Ellis-Jaffe sum rule violation, and on the proton-neutron isospin symmetry breaking explanation of the Gottfried sum rule violation. The proton spin could be fully provided by the spin sum of quarks if one considers the Wigner rotation effect in the measured quark helicity distributions.
The modified Gottfried sum rule multiplied by 3/2 can be interpreted as the one to measure the mean $I_3$ of the [(quark) - (antiquark)] in the proton . Based on this interpretation we find the sum rule which can be understood as the one to measure the mean charge of the light sea quarks (u,d,s) in the proton, and show that it takes the value 0.23 for the proton and 0.34 for the neutron .
The mean charge sum rule for the light sea quarks in the nucleon which holds under the same theoretical footing as the modified Gottfried sum rule shows that a usual parameterization of the strange sea quark distribution underestimate its contribution in the small $x$ region. We give a discussion of the soft pion contribution at high energy as a possible explanation of the saturation of the sum rule and show that it naturally explains why the strange sea quark is suppressed in the region above $x \sim 0.01$ while it becomes abundant below it.
Baryon magnetic moments and beta decay ratios ($G_A/G_V$) are calculated in a phenomenological quark model. Non-static effects of pion exchange and orbital excitation are included. Good agreement with experiment is found for a combined fit to all measured baryon magnetic moments and beta decay ratios. The model predicts an antiquark content for the proton that is consistent with the Gottfried sum rule.
The modified Gottfried sum rule makes clear importance of the high energy region not only in the theoretical meaning but also in the numerical analysis. In this talk, it is shown that the soft pion theorem in the inclusive reaction at high energy can explain the magnitude about $0.02 \sim 0.04$ in the NMC deficit. The main contribution comes from the small $x$ region. We also estimate the soft pion contribution to the Ellis-Jaffe sum rule and show it to be negligible. However we find that the contribution to $g_1^{ep}$ becomes positive below $x = 0.002$.
Quark light cone momentum distributions in the nucleon are calculated in a relativistic 3-body approach to the NJL model by using a simple 'static approximation' for the Faddeev kernel. A method is presented which automatically satisfies the number and momentum sum rules, even in the regularized theory. In order to assess the sensitivity to the regularization scheme, two schemes which can be formulated in terms of light cone variables are discussed. The effects of the (composite) pion cloud are taken into account in a convolution approach, and the violation of the Gottfried sum rule is discuss…
It is shown that the proton spin problem raised by the Ellis-Jaffe sum rule violation does not in conflict with the SU(6) quark model, provided that the relativistic effect from the quark transversal motions, the flavor asymmetry between the $u$ and $d$ valence quarks, and the intrinsic quark-antiquark pairs generated by the non-perturbative meson-baryon fluctuations of the nucleon sea are taken into account. The meson-baryon fluctuations of the nucleon sea provide a consistent picture for connecting the proton spin structure with a number of other anomalies observed in the proton's structure,…
The response of a relativistic particle bound in a linear confining well is calculated as a function of the momentum and energy transfer, q, ν. At large values of |q| the response exhibits scaling in the variable y=ν-|q|, which is proportional to the Nachtmann variable, ξ. The approach to scaling is studied at smaller values of |q|. Scaling occurs at ν~|q| at relatively small |q|, and its validity extends over the entire ξrange as |q| increases; this behavior is observed in electron-proton scattering. About 10% of the response at large |q| is in the timelike region where ν>|q|, and it is neces…
We present the first direct lattice calculation of the isovector sea-quark parton distributions using the formalism developed recently by one of the authors. We use $N_f=2+1+1$ HISQ lattice gauge ensembles (generated by MILC Collaboration) and clover valence fermions with pion mass 310 MeV. We are able to obtain the qualitative features of the nucleon sea flavor structure even at this large pion mass: We observe violation of the Gottfried sum rule, indicating $\overline{d}(x) > \overline{u}(x)$; the helicity distribution obeys $Δ\overline{u}(x) > Δ\overline{d}(x)$, which is consistent with the…
Recent calculations of charge symmetry violation(CSV) in the valence quark distributions of the nucleon have revealed that the dominant symmetry breaking contribution comes from the mass associated with the spectator quark system.Assuming that the change in the spectator mass can be treated perturbatively, we derive a model independent expression for the shift in the parton distributions of the nucleon. This result is used to derive a relation between the charge and flavor asymmetric contributions to the valence quark distributions in the proton, and to calculate CSV contributions to the nucle…
We discuss the dressing of constituent quarks with a pseudoscalar meson cloud within the effective chiral quark model. SU(3) flavor symmetry breaking effects are included explicitly. Our results are compared with those of the traditional meson cloud approach in which pions are coupled to the nucleon. The pionic dressing of the constituent quarks explains the experimentally observed violation of the Gottfried Sum Rule and leads to an enhanced nonperturbative sea of quark-antiquark pairs in the constituent quark and consequently in the nucleon. We find 2.5 times more pions and 10-15 times more k…
We show that the model which naturally explains the $\bar u \ne \bar d$ asymmetry in the nucleon and is in quantitative agreement with the Gottfried sum rule data, also predicts that in the proton $Δ\bar u > 0 > Δ\bar s > Δ\bar d$ and $Δ\bar u - Δ\bar d > \bar d - \bar u > 0$. At the input scale, these results can be derived even analytically. Thus the violation of the flavor symmetry is more serious in the polarized case than in the unpolarized case. In contrast, many recent analyses of the polarized data have made a simplifying assumption that all the three $Δ\bar q$'s have the same sign and…
Although the distributions of sea quarks and antiquarks generated by leading-twist QCD evolution through gluon splitting $g \rightarrow \bar q q$ are necessarily CP symmetric, the distributions of nonvalence quarks and antiquarks which are intrinsic to the nucleon's bound state wavefunction need not be identical. In this paper we investigate the sea quark/antiquark asymmetries in the nucleon wavefunction which are generated by a light-cone model of energetically-favored meson-baryon fluctuations. The model predicts striking quark/antiquark asymmetries in the momentum and helicity distributions…
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