The relation between the NJL model and QCD with condensed gluons

TL;DR

This paper explores the connection between the NJL model and QCD by assuming gluon momenta are condensed around a specific scale, affecting the phase diagram and critical point location.

Contribution

It establishes a relation between the NJL model parameters and QCD based on gluon condensation, analyzing its impact on the chiral phase transition.

Findings

Effective interactions scale with the gluon energy scale _g.

The critical point location is highly sensitive to _g.

Phase diagram features depend on the gluon condensation scale.

Abstract

We try to find the relation between the three-flavor Nambu-Jona-Lasinio model and QCD based on the hypothesis that the gluon momenta are sharply condensed around the QCD scale, \mu_g. We find that the effective four- and six-fermion interactions, G_4 and G_6, should be scaled by G_4 proportional to \mu_g^(-2) and G_6 proportional to \mu_g^(-5) being consistent with the mass dimension counting in the obtained effective Lagrangian. We then study the \mu_g dependence on the phase diagram of the chiral phase transition at finite temperature and chemical potential and the location of the critical point. We find that the location of the critical point are sensitively affected by the value of the introduced gluon energy scale.