Pion Structure at High and Low Energies in Chiral Quark Models

Chiral perturbation theory, the low energy effective theory of the strong interactions for the light pseudoscalar degrees of freedom, is based on effective Lagrangian techniques and is an expansion in the powers of the external momenta and the powers of the quark masses, which correct the soft-pion theorems. Our primary emphasis will be on the problem of $\pi\pi$ scattering. After briefly reviewing these features and some results, we review some features of $\pi-N$ scattering...

Usual treatment of the Nambu--Jona-Lasinio (NJL) model using loop momentum cutoff suffers from ambiguities in choosing the loop momenta to be cut off and violation of (external) gauge invariance. We define the NJL model from the starting Lagrangian level by using a higher derivative fermion kinetic term with a cutoff parameter $\Lambda$. This definition is free from such ambiguities and manifestly keeps the chiral symmetry as well as the gauge invariance. Quantization of this...

We evaluate the valence double parton distribution (dPDF) of the pion in the Nambu--Jona-Lasinio model. At the low-energy quark-model scale and in the chiral limit a particularly simple factorized form $D(x_1,x_2, \vec{q}) = \delta(1-x_1-x_2) F(\vec{q})$ follows, where $x_{1,2}$ denote the longitudinal momentum fractions of the valence quark and antiquark, and $\vec{q}$ is their relative transverse momentum. For $\vec{q}=\vec{0}$ our result complies to the Gaunt-Sterling sum ...

The dependence of the nucleon mass on the mass of the pion is studied in the framework of the chiral quark-soliton model. A remarkable agreement is observed with lattice data from recent full dynamical simulations. The possibility and limitations to use the model results as a guideline for the chiral extrapolation of lattice data are discussed.

We analyze the equal-time Bethe-Salpeter quark wave function of the pion obtained from a quenched lattice QCD calculation with delocalized quark interpolators. We find that the result agrees remarkably well with the predictions of the Nambu--Jona-Lasinio model in all channels. We choose the quenched lattice QCD, since it is closer to the large-Nc limit of the Nambu--Jona-Lasinio model. We also show how transversity information, relevant for the light-cone physics, can be obta...

A status report is given for the current theoretical understanding of pion production close to threshold. In the first part of the talk predictions of a meson exchange model are compared to recent polarized data for the reactions $pp \to pp\pi^0$ as well as $pp\to pn\pi^+$ revealing, that the former reaction is badly described whereas the predictions for the latter turn out to be consistent with the data. Recent progress in the application of chiral perturbation theory allows...

We discuss the low energy effective action of QCD in the quark sector. When it is built at the CSB (chiral symmetry breaking) scale by means of perturbation theory it has the structure of a generalized Nambu-Jona-Lasinio (NJL) model with CSB due to attractive forces in the scalar channel. We show that if the lowest scalar meson state is sufficiently lighter than the heavy pseudoscalar $\pi'$ then QCD favors a low-energy effective theory in which higher dimensional operators (...

After a brief introduction to chiral perturbation theory, the effective field theory of the standard model at low energies, two recent applications are reviewed: elastic pion-pion scattering to two-loop accuracy and the complete renormalized pion-nucleon Lagrangian to $O(p^3)$ in the chiral expansion.

In this exploratory study, I present, for the first time, the implications of the charge symmetry breaking (CSB) that arise from the $u$ and $d$ quark mass differences on gluon and sea quark distribution functions of the pion and kaon in the framework of the Nambu--Jona-Lasino (NJL) model, which is a quark-level chiral effective theory of QCD, with the help of the proper-time regularization scheme to simulate color confinement of QCD. From the analysis, one finds that the cha...

The Nambu-Jona-Lasinio model is supplemented by the quark interaction generated by the one-gluon exchange. The employed gluon propagator exhibits the correct large momentum behavior of QCD, whereas the Landau-pole at low energies is screened. The emerging constituent quark model is one-loop renormalizable and interpolates between the phenomenologically successful Nambu-Jona-Lasinio model at low energies and perturbative QCD at high momenta. Consequently, the momentum dependen...