Nonlocal quark model beyond mean field and QCD phase transition

TL;DR

This paper extends a nonlocal chiral quark model beyond mean field using a 1/Nc expansion, analyzing mesonic corrections and their impact on the QCD phase transition temperature.

Contribution

It introduces a consistent 1/Nc expansion scheme for the nonlocal quark model and refits parameters to physical pion properties.

Findings

1/Nc corrections can change sign of the quark condensate correction.

Corrections lower the chiral phase transition temperature.

Near the transition, the expansion breaks down, requiring non-perturbative methods.

Abstract

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/Nc expansion scheme. The parameters of the nonlocal model are refitted to the physical values of the pion mass and the weak pion decay constant. The size of the 1/Nc correction to the quark condensate is carefully studied in the nonlocal and the usual local Nambu-Jona-Lasinio models. It is found that even the sign of the corrections can be different. This can be attributed to the mesonic cut-off of the local model. It is also found that the 1/Nc corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/Nc expansion breaks down and a non-perturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition point.