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

A thermal QCD Finite Energy Sum Rule (FESR) is used to obtain the temperature dependence of the axial-vector coupling of the nucleon, gA(T). We find that gA(T) is essentially independent of T, in the very wide range 0≤T≤0.9 Tc, where Tc is the critical temperature. While gA at T=0 is q2-independent, it develops a q2 dependence at finite temperature. We then obtain the mean square radius associated with gA and find that it diverges at T=Tc, thus signalling quark deconfinement. As a byproduct, we study the temperature dependence of the Goldberger-Treiman relation.