An innovative approach for sketching the QCD phase diagram within the NJL model using Lagrange Multipliers

TL;DR

This paper introduces a novel method using Lagrange multipliers within the NJL model to map the QCD phase diagram, effectively identifying phase transition types and the critical end point without relying on traditional observables.

Contribution

The paper presents a new approach that allows sketching the QCD phase diagram and locating the critical end point directly from thermodynamic parameters in the NJL model.

Findings

Successfully distinguishes continuous and discontinuous phase transitions.

Locates the critical end point using thermodynamic parameters alone.

Applicable to effective chiral quark models with momentum-independent masses.

Abstract

We develop a new approach for sketching the quantum chromodynamics phase-diagram within the Nambu--Jona-Lasinio model for arbitrarily large values of the coupling constant, temperature and chemical potential based upon the strategy of Lagrange multipliers that constrains the corresponding gap equation and its mass gradient. Our approach distinguishes continuous from discountinuous phase transitions and thus is capable of locating the position of the Critical End Point from the thermodynamical parameters of the model alone, without direct reference to the chiral susceptibility or any other observable. The approach can be straightforwardly extended to those effective chiral quark models with a momentum independent constituent quark mass.