Thermodynamic potential with correct asymptotics for PNJL model

TL;DR

This paper proposes a method to derive the thermodynamic potential in PNJL models directly from gap equations, ensuring correct asymptotic behavior and finite regulators at finite temperature and chemical potential.

Contribution

It introduces a novel approach to obtain the thermodynamic potential from extremum conditions, fixing the integration constant via the Stefan-Boltzmann law, with improved regularization techniques.

Findings

Thermodynamic potential derived directly from gap equations.

Maintains finite regulators at finite temperature and chemical potential.

Ensures correct asymptotic behavior consistent with Stefan-Boltzmann law.

Abstract

An attempt is made to resolve certain incongruities within the Nambu - Jona-Lasinio (NJL) and Polyakov loop extended NJL models (PNJL) which currently are used to extract the thermodynamic characteristics of the quark-gluon system. It is argued that the most attractive resolution of these incongruities is the possibility to obtain the thermodynamic potential directly from the corresponding extremum conditions (gap equations) by integrating them, an integration constant being fixed in accordance with the Stefan-Boltzmann law. The advantage of the approach is that the regulator is kept finite both in divergent and finite valued integrals at finite temperature and chemical potential. The Pauli-Villars regularization is used, although a standard 3D sharp cutoff can be applied as well.