Effective Model Approach to the Dense State of QCD Matter

TL;DR

This paper introduces a new method to constrain effective QCD models by matching them with the Statistical Model, improving understanding of the phase transition in dense QCD matter.

Contribution

It proposes a novel prescription to fix model parameters using a matching condition with the Statistical Model, enhancing the effective model's reliability at finite baryon density.

Findings

The matching condition is successfully implemented in the PNJL model.

Results suggest the chiral transition occurs at slightly higher temperature than deconfinement.

The phase diagram aligns with chemical freeze-out points.

Abstract

The first-principle approach to the dense state of QCD matter, i.e. the lattice-QCD simulation at finite baryon density, is not under theoretical control for the moment. The effective model study based on QCD symmetries is a practical alternative. However the model parameters that are fixed by hadronic properties in the vacuum may have unknown dependence on the baryon chemical potential. We propose a new prescription to constrain the effective model parameters by the matching condition with the thermal Statistical Model. In the transitional region where thermal quantities blow up in the Statistical Model, deconfined quarks and gluons should smoothly take over the relevant degrees of freedom from hadrons and resonances. We use the Polyakov-loop coupled Nambu--Jona-Lasinio (PNJL) model as an effective description in the quark side and show how the matching condition is satisfied by a simple ansatz on the Polyakov loop potential. Our results favor a phase diagram with the chiral phase transition located at slightly higher temperature than deconfinement which stays close to the chemical freeze-out points.