Pion Generalized Distribution Amplitudes in the Nonlocal Chiral Quark Model

TL;DR

This paper employs a nonlocal chiral quark model to calculate pion GDAs, demonstrating consistency with soft pion theorems and comparing results with experimental data on form factors and quark distributions.

Contribution

It introduces a simple instanton-inspired nonlocal model for pion GDAs, allowing Minkowski space calculations and analysis of cutoff function sensitivity.

Findings

Model satisfies soft pion theorems for both chirally even and odd GDAs

Results are consistent with experimental data on pion form factors

The approach enables direct Minkowski space calculations

Abstract

We use a simple, instanton motivated, nonlocal chiral quark model to calculate pion Generalized Distribution Amplitudes (GDAs). The nonlocality appears due to the momentum dependence of the constituent quark mass, which we take in a form of a generalized dipole formula. With this choice all calculations can be performed directly in the Minkowski space and the sensitivity to the shape of the cutoff function can be studied. We demonstrate that the model fulfills soft pion theorems both for chirally even and chirally odd GDAs. The latter one cannot be derived by the methods of current algebra. Whenever possible we compare our results with the existing data. This can be done for the pion electromagnetic form factor and quark distributions as measured in the proton-pion scattering.