Chiral Symmetry transition in the Linear Sigma Model with quarks: Counting effective QCD degrees of freedom from low to high temperature

TL;DR

This paper uses the linear sigma model with quarks to analyze the chiral symmetry transition in QCD, linking changes in effective degrees of freedom to temperature-dependent coupling constants and comparing results with lattice QCD data.

Contribution

It introduces a method to connect low and high temperature regimes in the linear sigma model by adjusting couplings to match lattice data, providing insights into effective degrees of freedom in QCD.

Findings

The model reproduces lattice QCD pressure data across temperature ranges.

Coupling constants vary with temperature, reflecting changes in degrees of freedom.

The approach offers a unified description of chiral transition in QCD.

Abstract

We use the linear sigma model coupled to quarks, together with a plausible location of the critical end point (CEP), to study the chiral symmetry transition in the QCD phase diagram. We compute the effective potential at finite temperature and density up to the contribution of the ring diagrams, both in the low and high temperature limits, and use it to compute the pressure and the position of the CEP. In the high temperature regime, by comparing to results from extrapolated lattice data, we determine the model coupling constants. Demanding that the CEP remains in the same location when described in the high temperature limit, we determine again the couplings and the pressure for the low temperature regime. We show that this procedure gives an average description of the lattice QCD results for the pressure and that the change from the low to the high temperature domains in this quantity can be attributed to the change in the coupling constants which in turn we link to the change in the effective degrees of freedom.