Spontaneous Breaking of Flavor Symmetry and Parity in the Nambu-Jona-Lasinio Model with Wilson Fermions

TL;DR

This paper investigates the spontaneous breaking of flavor symmetry and parity in a lattice Nambu-Jona-Lasinio model with Wilson fermions, revealing phase transitions and pion behavior consistent with lattice QCD expectations.

Contribution

It demonstrates the occurrence of spontaneous flavor and parity breaking in the NJL model with Wilson fermions and analyzes the pion spectrum near the phase boundary.

Findings

Three massless pions at the phase boundary

Only two massless pions inside the broken phase

Behavior aligns with lattice QCD results

Abstract

We study the lattice \njl~model with two flavors of Wilson fermions in the large $N$ limit, where $N$ is the number of `colors'. For large values of the four-fermion coupling we find a phase in which both, flavor symmetry and parity, are spontaneously broken. In accordance with general expectations there are three massless pions on the phase boundary, but only two of them remain massless inside the broken phase. This is analogous to earlier results obtained in lattice QCD, indicating that this behavior is a very general feature of the Wilson term.