QCD determination of the axial-vector coupling of the nucleon at finite temperature

TL;DR

This study uses thermal QCD Finite Energy Sum Rules to analyze how the nucleon's axial-vector coupling varies with temperature, revealing its stability up to near the critical temperature and indicating quark deconfinement.

Contribution

It provides the first detailed analysis of the temperature dependence of the nucleon axial-vector coupling using QCD sum rules, including the divergence of the associated radius at deconfinement.

Findings

$g_A(T)$ remains nearly constant up to 0.9 $T_c$

The mean square radius diverges at $T_c$

Finite temperature affects the $q^2$ dependence of $g_A$

Abstract

A thermal QCD Finite Energy Sum Rule (FESR) is used to obtain the temperature dependence of the axial-vector coupling of the nucleon, $g_{A}(T)$. We find that $g_{A}(T)$ is essentially independent of $T$, in the very wide range $0 \leq T \leq 0.9 T_{c}$, where $T_{c}$ is the critical temperature. While $g_{A}$ at T=0 is $q^{2}$-independent, it develops a $q^{2}$ dependence at finite temperature. We then obtain the mean square radius associated with $g_{A}$ and find that it diverges at $T=T_{c}$, thus signalling quark deconfinement. As a byproduct, we study the temperature dependence of the Goldberger-Treiman relation.