Parton Distributions Functions of Pion, Kaon and Eta pseudoscalar mesons in the NJL model

Parton distributions of pseudoscalar pi,K and eta mesons obtained within the NJL model using the Pauli-Villars regularization method are analyzed in terms of LO and NLO evolution, and the valence sea quark and gluon parton distributions for the pion are obtained at Q^2 = 4 GeV^2 and compared to existing parametrizations at that scale. Surprisingly, the NLO order effects turn out to be small compared to the LO ones. The valence distributions are in good agreement with experimental analyses, but the gluon and sea distributions come out to be softer in the high-x region and harder in the low-x region than the experimental analyses suggest.Comment: (Latex, epsfig) 17 pages, 7 figure

Scalar-isoscalar states in the large-Nc Regge approach

Scalar-isoscalar states (0++) are investigated within the large-Nc Regge approach. We elaborate on the consequences of including the lightest f0(600) scalar-isoscalar state into such an analysis, where the position of f0(600) fits very well into the pattern of the radial Regge trajectory. Furthermore, we point out that the pion and nucleon spin-0 gravitational form factors, recently measured on the lattice, provide valuable information on the low-mass spectrum of the scalar-isoscalar states on the basis of the scalar-meson dominance in the spin-0 channel. Through the fits to these data we find m_sigma= 450-600 MeV. We compare the predictions of various fits and methods. An analysis of the QCD condensates in the two-point correlators provides further constraints on the parameters of the scalar-isoscalar sector. We find that a simple two-state model suggests a meson nature of f0(600), and a glueball nature of f0(980), which naturally explains the ratios of various coupling constants. Finally, we note that the fine-tuned condition of the vanishing dimension-2 condensate in the Regge approach with infinitely many scalar-isoscalar states yields a reasonable value for the mass of the lighest glueball state.Comment: 18 pages, 13 figures. Typos corrected. Remarks and references adde

Generalized parton distributions of the pion in chiral quark models and their QCD evolution

We evaluate Generalized Parton Distributions of the pion in two chiral quark models: the Spectral Quark Model and the Nambu-Jona-Lasinio model with a Pauli-Villars regularization. We proceed by the evaluation of double distributions through the use of a manifestly covariant calculation based on the alpha representation of propagators. As a result polynomiality is incorporated automatically and calculations become simple. In addition, positivity and normalization constraints, sum rules and soft pion theorems are fulfilled. We obtain explicit formulas, holding at the low-energy quark-model scale. The expressions exhibit no factorization in the t-dependence. The QCD evolution of those parton distributions is carried out to experimentally or lattice accessible scales. We argue for the need of evolution by comparing the Parton Distribution Function and the Parton Distribution Amplitude of the pion to the available experimental and lattice data, and confirm that the quark-model scale is low, about 320 MeV.Comment: 25 pages, 15 figures, added discussion of the end-point behavio

Gravitational and higher-order form factors of the pion in chiral quark models

The gravitational form factor of the pion is evaluated in two chiral quark models and confronted to the recent full-QCD lattice data. We find good agreement for the case of the Spectral Quark Model, which builds in the vector-meson dominance for the charge form factor. We derive a simple relation between the gravitational and electromagnetic form factors, holding in the considered quark models in the chiral limit. The relation implies that the gravitational mean squared radius is half the electromagnetic one. We also analyze higher-order quark generalized form factors of the pion, related to higher moments in the symmetric Bjorken X-variable of the generalized parton distribution functions, and discuss their perturbative QCD evolution, needed to relate the quark-model predictions to the lattice data. The values of the higher-order quark form factors at t=0, computed on the lattice, also agree with our quark model results within the statistical and method uncertainties.Comment: 12 pages, 4 figures, discussion and references adde

Generalized Quark Transversity Distribution of the Pion in Chiral Quark Models

The transversity generalized parton distributions (tGPDs) of the the pion, involving matrix elements of the tensor bilocal quark current, are analyzed in chiral quark models. We apply the nonlocal chiral models involving a momentum-dependent quark mass, as well as the local Nambu--Jona-Lasinio with the Pauli-Villars regularization to calculate the pion tGPDs, as well as related quantities following from restrained kinematics, evaluation of moments, or taking the Fourier-Bessel transforms to the impact-parameter space. The obtained distributions satisfy the formal requirements, such as proper support and polynomiality, following from Lorentz covariance. We carry out the leading-order QCD evolution from the low quark-model scale to higher lattice scales, applying the method of Kivel and Mankiewicz. We evaluate several lowest-order generalized transversity form factors, accessible from the recent lattice QCD calculations. These form factors, after evolution, agree properly with the lattice data, in support of the fact that the spontaneously broken chiral symmetry is the key element also in the evaluation of the transversity observables.Comment: 17 pages, 17 figures, regular pape