Pion Generalized Parton Distributions within a fully covariant constituent quark model

TL;DR

This paper extends a covariant constituent quark model to include tensor distributions and evolution effects, enabling meaningful comparisons with experimental and lattice data on pion generalized parton distributions.

Contribution

It introduces a covariant quark model with a 4D Bethe-Salpeter amplitude and minimal parameters, incorporating tensor distributions and evolution for pion GPD analysis.

Findings

Calculated tensor distribution for the pion.

Included evolution for meaningful data comparison.

Model uses only two parameters, quark mass and decay constant.

Abstract

We extend the investigation of the Generalized Parton Distribution for a charged pion within a fully covariant constituent quark model, in two respects: (i) calculating the tensor distribution and (ii) adding the treatment of the evolution, needed for achieving a meaningful comparison with both the experimental parton distribution and the lattice evaluation of the so-called generalized form factors. Distinct features of our phenomenological covariant quark model are: (i) a 4D Ansatz for the pion Bethe-Salpeter amplitude, to be used in the Mandelstam formula for matrix elements of the relevant current operators, and (ii) only two parameters, namely a quark mass assumed to hold $m_q=~220$ MeV and a free parameter fixed through the value of the pion decay constant. The possibility of increasing the dynamical content of our covariant constituent quark model is briefly discussed in the context of the Nakanishi integral representation of the Bethe-Salpeter amplitude.