The Wigner solution of quark gap equation at nonzero current quark mass and partial restoration of chiral symmetry at finite chemical potential

TL;DR

This paper investigates the existence of Wigner solutions in the quark gap equation at nonzero current quark mass and finite chemical potential, proposing a new approach within a modified NJL model to explore chiral symmetry restoration.

Contribution

It introduces a novel method to find Wigner solutions with nonzero quark mass and extends the analysis to finite chemical potential, addressing a longstanding theoretical conflict.

Findings

Wigner solution can exist with nonzero current quark mass using the new approach

Partial chiral symmetry restoration occurs at finite chemical potential

Results differ from those in the normal NJL model

Abstract

According to the generally accepted phase diagram of QCD, at low temperature and high baryon number density the chiral phase transition of QCD is of first order and the co-existence of the Nambu-Goldstone phase and the Wigner phase should appear. This is in conflict with the usual claim that the quark gap equation has no Wigner solution in the case of nonzero current quark mass. In this paper we analyze the reason why the Wigner solution does not exist in the usual treatment and try to propose a new approach to discuss this question. As a first step, we adopt a modified Nambu-Jona-Lasinio (NJL) model to study the Wigner solution at finite current quark mass. We then generalize this approach to the case of finite chemical potential and discuss partial restoration of chiral symmetry at finite chemical potential and compare our results with those in the normal NJL model.