Chiral symmetry in the low-energy limit of QCD at finite temperature

TL;DR

This paper derives a non-local Nambu-Jona-Lasinio model from QCD to analyze chiral symmetry restoration at finite temperature, providing exact critical temperature and supporting the instanton liquid vacuum picture.

Contribution

It introduces a form factor derived in the infrared limit to connect QCD with a non-local NJL model, enabling precise analysis of chiral phase transition at finite temperature.

Findings

Exact critical temperature for chiral symmetry restoration

Validation of the instanton liquid vacuum model

Derivation of a non-local NJL model from QCD

Abstract

We derive a non-local Nambu-Jona-Lasinio model from QCD with a form factor exactly obtained in the infrared limit. With this model, having all the parameters properly fixed through those of QCD, we consider the case of finite temperature and compute the solution of the gap equation at small temperature and small momenta and zero chemical potential. Taking the quark masses to be zero, it is proved that the theory undergoes a phase transition with a critical temperature exactly determined. These results prove unequivocally that the picture of the vacuum of QCD as a liquid of instantons is a very good approximation.