SU(2) low energy quark effective couplings in weak external magnetic field

TL;DR

This paper calculates how a weak external magnetic field modifies the low-energy quark effective couplings in the SU(2) Nambu-Jona-Lasinio model, revealing new symmetry-breaking interactions.

Contribution

It introduces a method to compute magnetic field corrections to NJL couplings considering quark polarization and gluon exchange mechanisms.

Findings

Magnetic field induces isospin and chiral symmetry-breaking couplings.

Corrections to NJL and vector NJL couplings are quantified.

New B0-dependent effective interactions are derived.

Abstract

In this work corrections to the usual flavor SU(2) Nambu-Jona-Lasinio coupling due to a weak external magnetic field are calculated by considering quark polarization in a (dressed) gluon exchange mechanism for quark interactions. The quark field is splitted into two components, one that condenses and another one that is a background field for interacting quarks, being the former integrated out. The resulting determinant is expanded for relatively large quark mass and small magnetic field, $(eB_0/{M^*}^2)<1$ by resolving magnetic field dependent low energy quark effective interactions. Besides the corrections for the NJL and vector NJL effective couplings, different $B_0-$dependent effective couplings that break isospin and chiral symmetry emerge.