Chiral symmetry restoration and properties of Goldstone bosons at finite temperature

TL;DR

This paper investigates how chiral symmetry is restored at finite temperature by analyzing meson properties using Dyson-Schwinger and Bethe-Salpeter equations, revealing pion dissociation at the critical temperature and potential survival of heavy mesons above it.

Contribution

It provides a detailed analysis of meson spectral functions at finite temperature using a symmetry-preserving approach, connecting chiral symmetry restoration with meson dissociation and deconfinement.

Findings

Pion degenerates with sigma at the critical temperature.

Pion rapidly dissociates above the critical temperature.

Heavy mesons may survive beyond the chiral transition temperature.

Abstract

We study chiral symmetry restoration by analyzing thermal properties of QCD's (pseudo-)Goldstone bosons, especially the pion. The meson properties are obtained from the spectral densities of mesonic imaginary-time correlation functions. To obtain the correlation functions, we solve the Dyson-Schwinger equations and the inhomogeneous Bethe-Salpeter equations in the leading symmetry-preserving rainbow-ladder approximation. In the chiral limit, the pion and its partner sigma degenerate at the critical temperature $T_c$. At $T \gtrsim T_c$, it is found that the pion rapidly dissociates, which signals deconfinement phase transition. Beyond the chiral limit, the pion dissociation temperature can be used to define the pseudo-critical temperature of chiral phase crossover, which is consistent with that obtained by the maximum point of the chiral susceptibility. The parallel analysis for kaon and pseudoscalar $s\bar{s}$ suggests that heavy mesons may survive above $T_c$.