Chiral Symmetry Restoration for the large-$N$ pion gas

TL;DR

This paper investigates chiral symmetry restoration in a large-$N$ pion gas using an effective field theory, deriving thermodynamic quantities and critical behavior consistent with lattice results and previous studies.

Contribution

It provides a diagrammatic analysis of chiral restoration in the large-$N$ limit without renormalization complexities, extending understanding of low-energy QCD at finite temperature.

Findings

Critical behavior aligns with lattice analysis.

Susceptibility dominated by thermal $f_0(500)$ pole.

No renormalization needed at the considered order.

Abstract

We analyze chiral restoration within the $O(N+1)/O(N)$ Non-Linear Sigma Model for large $N$ as an effective theory for low-energy QCD at finite temperature $T$. The free energy is constructed diagramatically to ${\cal O}(TM^3)$ in the pion mass expansion, which allows to derive the quark condensate and the scalar susceptibility in the chiral limit. At this order, we do not have to deal with renormalization, neither from divergences from mass tadpoles nor from those of higher order loop contributions. Our results for the critical behaviour are consistent with expectations from lattice analysis and with previous works where the susceptibility is saturated by the thermal $f_0(500)$ pole.