Low energy constituent quark and pion effective couplings to external electromagnetic field and a weak magnetic field

TL;DR

This paper compiles and refines effective electromagnetic couplings to pions and constituent quarks, including corrections for weak magnetic fields, enhancing understanding of symmetry-breaking effects in effective models.

Contribution

It provides a comprehensive compilation and correction of electromagnetic couplings in effective quark and pion models, including weak magnetic field effects.

Findings

Redefinition of coupling constants to include weak magnetic field dependence.

Corrections to NJL and vector NJL effective couplings.

Analysis of isospin and chiral symmetry breaking effects.

Abstract

In this work, a compilation of effective electromagnetic field couplings to pions and constituent quarks and their effective interactions derived previously, including corrections to the NJL model, is presented. The particular case of a weak external magnetic field along the $\hat{z}$ direction is considered shortly and effective coupling constants are redefined to incorporate the weak-$B_0$ dependence. They correspond to corrections to well known pion-constituent quark couplings and to the NJL and vector NJL effective couplings that break isospin and chiral symmetries.