Free Energy of a Large-$N$ Pion Gas and Chiral Symmetry Restoration

TL;DR

This paper investigates the thermodynamic properties of a large-N pion gas using a nonlinear sigma model, analyzing free energy, chiral symmetry restoration, and critical behavior with comparisons to lattice and scattering results.

Contribution

It introduces a diagrammatic calculation of the free energy to order TM^3 in a large-N pion gas within a nonlinear sigma model, including finite order parameters and critical exponents.

Findings

Agreement with lattice simulations on chiral transition

Consistent critical exponents with universality class

Effective vertex approach captures key thermodynamic features

Abstract

We study thermal properties of a large-N massless pion gas using a low-energy QCD approach given by an $O(N +1)/O(N)$ Nonlinear Sigma Model. We build diagrammatically the associated finite free energy to $O(TM^{3})$ in the pion mass expansion through an effective vertex that considers all the contributions coming from closed diagrams. Subsequently, we calculate finite order parameters such as the quark condensate and its respective derivative, i.e., the scalar susceptibility, in the chiral limit, along with their associated critical exponents. These results are compared with our previous unitarized scattering analyses for the chiral transition universality class, thus showing a reasonable agreement both with lattice simulations and these resonant studies.