QCD phase diagram from chiral symmetry restoration: analytic approach at high and low temperature using the Linear Sigma Model with Quarks

TL;DR

This paper investigates the QCD phase diagram using the linear sigma model with quarks, analyzing chiral symmetry restoration at high and low temperatures with finite chemical potential, and locating the critical end point.

Contribution

It provides an analytic approach to the QCD phase diagram employing the linear sigma model, including plasma screening effects and fixed physical parameters.

Findings

Critical end point located at low T and high μ

Effective potential computed at leading order with ring diagrams

CEP position estimated between 315-349 MeV in chemical potential

Abstract

We use the linear sigma model with quarks to study the QCD phase diagram from the point of view of chiral symmetry restoration. We compute the leading order effective potential for high and low temperatures and finite quark chemical potential, up to the contribution of the ring diagrams to account for the plasma screening effects. We fix the values of the model couplings using physical values for the input parameters such as the vacuum pion and sigma masses, the critical temperature at vanishing quark chemical potential and the conjectured end point value of the baryon chemical potential of the transition line at vanishing temperature. We also make the analysis for the same input parameters but with vanishing pion mass. We find that the critical end point (CEP) is located at low temperatures and high quark chemical potentials $(315<\mu^{\text{CEP}}<349\ MeV,18< T^{\text{CEP}}<45\ MeV)$.