Pion Structure at High and Low Energies in Chiral Quark Models

We present a brief review of results of chiral quark models for soft matrix elements in the pion state, appearing in high-energy processes as well as accessible in present and future lattice studies. A particular attention is paid to the recently explored double parton distribution functions of the pion.

We discuss the predictions of chiral quark models for basic pion properties entering high-energy processes: generalized parton distributions (GPD's) and unintegrated parton distributions (UPD's). We stress the role of the QCD evolution, necessary to compare the predictions to data.

The evaluation of partonic distributions presents a challenge for QCD, and in particular for its Euclidean lattice realization. Recently, objects called quasi-distributions (which become standard distributions in a limit of the longitudinal momentum of the target hadron going to infinity) have been proposed. We present a non-perturbative, dynamical evaluation of the quark quasi-distribution amplitude (QDA) of the pion in the framework of chiral quark models (the Nambu--Jona-L...

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, ...

Results of the chiral quark models for the soft matrix elements involving pions and photons, relevant for high-energy processes, are reviewed. We discuss quantities related to the generalized parton distributions of the pion: the parton distribution functions, the parton distribution amplitudes, and the generalized form factors. The model predictions are compared to the data or lattice simulations, with good agreement. The QCD evolution from the low quark model scale up to th...

We describe the present status of the pion distribution amplitude as it originated from two sources: (i) a nonperturbative approach, based on QCD sum rules with nonlocal condensates and (ii) a NLO QCD analysis of the CLEO data on F^{\gamma\gamma^*\pi}(Q^2), supplemented by the recent high-precision lattice calculations of the second moment of the pion distribution amplitude.

We evaluate nonperturbatively the quark quasidistribution amplitude and the valence quark quasidistribution function of the pion in the framework of chiral quark models, namely the Nambu--Jona-Lasinio model and the Spectral Quark Model. We arrive at simple analytic expressions, where the nonperturbative dependence on the longitudinal momentum of the pion can be explicitly assessed. The model results for the quark quasidistribution amplitude of the pion compare favorably to th...

We show the results of low-energy chiral quark models for soft matrix elements involving pions and photons. Such soft elements, upon convolution with the hard matrix elements, are relevant in various high-energy processes. We focus on quantities related to the generalized parton distributions of the pion: the parton distribution functions, the parton distribution amplitudes, and the generalized form factors. Wherever possible, the model predictions are confronted with the dat...

This talk presents issues pertaining to the quark structure of the pion within QCD, both from the theoretical and from the experimental point of view. We review and discuss the pion-photon transition form factor and the pion's electromagnetic form factor vs. corresponding experimental data from the CLEO Collaboration and the JLab. We also examine the extent to which recent high-precision lattice computations of the second moment of the pion's distribution amplitude conform wi...

Based on the self-consistent scheme beyond mean-field approximation in the large $N_c$ expansion, including current quark mass explicitly, a general scheme of SU(2) NJL model is developed. To ensure the quark self-energy expanded in the proper order of $N_c$, an approximate internal meson propagator is deduced, which is in order of $O(1/N_c)$. In our scheme, adopting the method of external momentum expansion, all the Feynman diagrams are calculated in a unified way by only ex...