Nonlocal Nambu-Jona-Lasinio model and chiral chemical potential

TL;DR

This paper derives the critical temperature in a nonlocal Nambu-Jona-Lasinio model with a chiral chemical potential, showing it increases with the square of the chemical potential, based on a form factor consistent with Yang-Mills theory and lattice results.

Contribution

It introduces a nonlocal NJL model derived from QCD with a form factor aligned with Yang-Mills and instanton models, providing an analytical expression for the critical temperature with no free parameters.

Findings

Critical temperature always exists in the model.

Critical temperature increases quadratically with chiral chemical potential.

Model aligns with lattice computations and Yang-Mills theory.

Abstract

We derive the critical temperature in a nonlocal Nambu-Jona-Lasinio model with the presence of a chiral chemical potential. The model we consider uses a form factor derived from recent studies of the gluon propagator in Yang-Mills theory and has the property to fit in excellent way the form factor arising from the instanton liquid picture for the vacuum of the theory. Nambu-Jona-Lasinio model is derived form quantum chromodynamics providing all the constants of the theory without any need for fits. We show that the critical temperature in this case always exists and increases as the square of the chiral chemical potential. The expression we obtain for the critical temperature depends on the mass gap that naturally arises from Yang-Mills theory at low-energy as also confirmed by lattice computations.