Pion constituent quarks couplings strong form factors: a dynamical approach

TL;DR

This paper investigates pion-constituent quark interaction form factors using a dynamical approach based on a one-loop background field method within a global color model, revealing their behavior up to 1.5 GeV and relating them to experimental data.

Contribution

It introduces a novel dynamical method to compute pion-quark form factors, expressing them with only two momentum-dependent functions and deriving a momentum-dependent Goldberger Treiman relation.

Findings

Form factors exhibit similar behavior to experimental nucleon data.

Pseudoscalar quadratic radii depend on sea quark effective mass.

A momentum-dependent Goldberger Treiman relation is established.

Abstract

Form factors for pions interactions with constituent quarks are investigated as the leading effective couplings obtained from a one loop background field method applied to a global color model. Two pion field definitions are considered and the resulting eleven form factors are expressed in terms of components of the quark and gluon propagators that compose only two momentum dependent functions. A momentum dependent Goldberger Treiman relation is also obtained as one of the ratios between the form factors. The resulting form factors with pion momenta up to 1.5 GeV are exhibited for different quark effective masses and two different non-perturbative gluon propagators and they present similar behavior to fittings of experimental data from nucleons form factors. The corresponding pseudoscalar averaged quadratic radii (a.q.r.) and correction to the axial a.q.r. are presented as functions of the sea quark effective mass, being equal respectively to the scalar and vector ones at the present level of calculation.