Phase structure of a generalized Nambu Jona-Lasinio model with Wilson fermions in the mean field or large $N$-expansion

TL;DR

This paper investigates the phase structure of a generalized lattice Nambu--Jona-Lasinio model with Wilson fermions, revealing new phases and challenging the completeness of Wilson Chiral Perturbation Theory in describing low-energy QCD.

Contribution

It introduces a generalized four-fermion lattice model with Wilson fermions, identifying novel phases beyond standard Aoki phases, and discusses implications for effective theories of low-energy QCD.

Findings

Discovery of new phases with non-zero <ar ext{ extbackslash}psi> in the model

Demonstration that Wilson Chiral Perturbation Theory does not fully capture the phase structure

Identification of phase structures analogous to recent lattice QCD results

Abstract

We analyze the vacuum structure of a generalized lattice Nambu--Jona-Lasinio model with two flavors of Wilson fermions, such that its continuum action is the most general four-fermion action with 'trivial' color interactions, and having a $SU(2)_V x SU(2)_A$ symmetry in the chiral limit. The phase structure of this model in the space of the two four-fermion couplings shows, in addition to the standard Aoki phases, new phases with $<\bar\psi \gamma_5\psi> != 0$, in close analogy to similar results recently suggested by some of us for lattice QCD with two degenerate Wilson fermions. This result shows how the phase structure of an effective model for low energy QCD cannot be entirely understood from Wilson Chiral Perturbation Theory, based on the standard QCD chiral effective Lagrangian approach.