Gauge dynamics in the PNJL model: Color neutrality and Casimir scaling

TL;DR

This paper introduces a gauge-invariant method for the PNJL model that ensures color neutrality and facilitates calculations involving the Polyakov loop, with applications to Casimir scaling.

Contribution

The paper presents a self-consistent, gauge-invariant prescription for mean-field approximation in the PNJL model, addressing color neutrality issues and enabling better computation of Polyakov loop functions.

Findings

The gauge-invariant prescription resolves non-zero color density artifacts.

The method ensures color neutrality in the model.

Application to Casimir scaling demonstrates the method's utility.

Abstract

We discuss a gauge-invariant prescription to take the mean-field approximation self-consistently in the PNJL model (Nambu--Jona-Lasinio model with the Polyakov loop). We first address the problem of non-vanishing color density in normal quark matter, which is an artifact arising from gauge-fixed treatment of the Polyakov loop mean-fields. We then confirm that the gauge average incorporated in our prescription resolves this problem and ensures color neutrality. We point out that the proposed method has an advantage in computing the expectation value of any function of the Polyakov loop matrix. We discuss the Casimir scaling as an immediate application of the method.