Using the Linear Sigma Model with quarks to describe the QCD phase diagram and to locate the critical end point

TL;DR

This paper employs the linear sigma model with quarks to analyze the QCD phase diagram, identifying the transition from crossover to first-order phase transition and locating the critical end point using effective potential calculations.

Contribution

It introduces a method to determine the QCD phase transition line and critical end point using the linear sigma model with finite temperature and chemical potential.

Findings

Pseudo-critical temperature $T_c = 155$ MeV used as a reference point.

Critical baryon chemical potential $c \u2248 1$ GeV identified.

Transition line changes from crossover to first order at specific parameters.

Abstract

We study the QCD phase diagram using the linear sigma model coupled to quarks. We compute the effective potential at finite temperature and quark chemical potential up to ring diagrams contribution. We show that, provided the values for the pseudo-critical temperature $T_c = 155$ MeV and critical baryon chemical potential $\mu_{Bc} \simeq 1$ GeV, together with the vacuum sigma and pion masses. The model couplings can be fixed and that these in turn help to locate the region where the crossover transition line becomes first order.