Interplay between chiral and axial symmetries in a SU(2) Nambu--Jona-Lasinio Model with the Polyakov loop

TL;DR

This paper investigates how chiral and axial symmetries are restored at finite temperature in a two-flavor PNJL model with explicit U_A(1) anomaly breaking, revealing that axial symmetry restoration requires additional mechanisms beyond chiral symmetry recovery.

Contribution

It introduces a temperature-dependent anomaly coefficient to simulate instanton suppression, showing that axial symmetry restoration is not automatic with chiral symmetry recovery in SU(2) models.

Findings

Axial symmetry restoration does not coincide with chiral symmetry restoration in SU(2).

A temperature-dependent anomaly coefficient is necessary to model instanton effects.

Different regularizations affect the symmetry restoration patterns.

Abstract

We consider a two flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model where the Lagrangian includes an interaction term that explicitly breaks the U$_A(1)$ anomaly. At finite temperature, the restoration of chiral and axial symmetries, signaled by the behavior of several observables, is investigated. We compare the effects of two regularizations at finite temperature, one of them, that allows high momentum quarks states, leading to the full recovery of chiral symmetry. From the analysis of the behavior of the topological susceptibility and of the mesonic masses of the axial partners, it is found in the SU(2) model that, unlike the SU(3) results, the recovery of the axial symmetry is not a consequence of the full recovery of the chiral symmetry. Thus, one needs to use an additional idea, by means of a temperature dependence of the anomaly coefficient, that simulates instanton suppression effects.