: The pion structure function is studied in the Nambu and Jona-Lasinio (NJL) model. We calculate the forward scattering amplitude of a virtual photon from a pion target in the Bjorken limit, and obtain valence quark distributions of the pion at the low energy hadronic scale, where the NJL model is supposed to work. The calculated distribution functions are evolved to the experimental momentum scale using the Altarelli-Parisi equation. The resulting distributions are in a reasonable agreement with experiment. We calculate also the kaon structure function and compare the ratio of kaon to pion valence u-quark distributions with experiment. * e-mail address : shige@atlas.phys.metro-u.ac.jp † Also at RIKEN, Wako, Saitama, 351, Japan Recently, the nucleon structure functions are discussed in terms of the MIT bag mode [4,5] as well as other models [6]. Those results are based on the assumption that the structure functions at low energy hadronic scale Q 2 = Q 2 0 (unknown) are obtained by calculating the twist 2 matrix elements within the effective models, since the twist 2 operators are dominant in the Bjorken limit and higher twist terms vanish at high enough. Once one obtains them at the hadronic scale, these parton distributions are evolved to the experimental scale by using the perturbative QCD, and the comparison with experiment can be made.In this letter, we concentrate on the pion structure function. The pion is believed to be the Goldstone boson due to the spontaneous breakdown of the chiral symmetry (SBχS).Thus, the information of the pion structure function gives us deeper understandings of SBχS. The experimental data of the pion structure function are extracted from πN scattering using the Drell-Yan process [7]. The valence, sea quark, and gluon distribution functions are obtained from a recent re-analysis of these data [8].We use the Nambu and Jona-Lasinio (NJL) model [9], where the chiral invariance is 2 the main ingredient. The NJL model describes the pion as a collective qq excitation of the non-perturbative QCD vacuum [10]. Recently, the generalized SU(3) f NJL model with the U(1) A anomalous term is demonstrated to reproduce the meson properties successfully, in spite of the lack of confinement [10,11,12]. This model is also applied to the chiral phase transition at finite temperature and density [13]. All these results indicate that the NJL model possesses the essential features of QCD dynamics.The SU(3) f NJL lagrangian is given by [10,11,12]where ψ denotes the quark field with current mass m, λ i are SU(3) flavor matrices, and [10,11,12]. Using this lagrangian, we will calculate the parton distribution of pion with no free parameter.Unfortunately, the NJL model is a non-renormalizable theory, and this model requires the finite momentum cutoff Λ ∼ 1 GeV, which is identified with a scale of SBχS. One may understand the physical meaning of the cutoff as an approximate realization of "asymptotic freedom" in the NJL model. This means that the interaction between two quarks with the relative mom...
We study the chiral-odd transversity spin-dependent quark distribution function h 1 (x) of the nucleon in a constituent quark model. The twist-2 structure functions, f 1 (x), g 1 (x) and h 1 (x) are calculated within the diquark spectator approximation.Whereas an inequality f 1 (x) > h 1 (x) > g 1 (x) holds with the interaction between quark and diquark being scalar, the axial-vector effective quark-diquark interaction, which contributes to the d-quark distribution, does not lead to such a simple relation.We find that h 1 (x) for the d-quark becomes somewhat smaller than g d 1 (x), when we fix the model parameter to reproduce known other structure functions. We also include corrections due to the non-trivial structure of the constituent quark, which is modeled by the Goldstone boson dressing. This improves agreements of f 1 (x) and g 1 (x) with experiments, and brings further reduction of h d 1 (x) distribution. Consequences for semi-inclusive experiments are also discussed.
We study the deep inelastic structure functions of mesons within the Nambu and JonaLasinio model. We calculate the valence quark distributions in π, K, and ρ mesons at the low energy model scale, which are evoluted to the experimental momentum scale in terms of the Altarelli-Parisi equation. The resulting distribution functions show reasonable agreements with experiment. We also discuss the semi-inclusive lepton nucleon scattering process with a slow nucleon in coincidence in the final state, which reveals the off-shell structure of the pion.
Nucleon structure functions, as measured in deep-inelastic lepton scattering, are studied within a covariant scalar diquark spectator model. Regarding the nucleon as an approximate two-body bound state of a quark and diquark, the Bethe–Salpeter equation (BSE) for the bound state vertex function is solved in the ladder approximation. The valence quark distribution is discussed in terms of the solutions of the BSE.
We study the structure functions of hadrons with the low energy effective theory of QCD. We try to clarify a link between the low energy effective theory, where non-perturbative dynamics is essential, and the high energy deep inelastic scattering experiment. We calculate the leading twist matrix elements of the structure function at the low energy model scale within the effective theory. Calculated structure functions are taken to the high momentum scale with the help of the perturbative QCD, and compared with the experimental data. Through a comparison of the model calculations with the experiment, we discuss how the non-perturbative dynamics of the effective theory is reflected in the deep inelastic phenomena. We first evaluate the structure functions of the pseudoscalar mesons using the NJL model. The resulting structure functions show reasonable agreement with experiments. We then study the quark distribution functions of the nucleon using a covariant quark–diquark model. We calculate three leading twist distribution functions, the spin-independent f1(x), the longitudinal spin distribution g1(x), and the chiral-odd transversity spin distribution h1(x). The results for f1(x) and g1(x) turn out to be consistent with available experiments because of the strong spin-0 diquark correlation.
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