Thermodynamics and Phase Structure of the Two-Flavor Nambu--Jona-Lasinio Model Beyond Large-N_c

TL;DR

This paper applies the optimized perturbation theory to the two-flavor NJL model, going beyond the large-N_c approximation to analyze its thermodynamics and phase structure at finite temperature and density.

Contribution

It introduces a nonperturbative OPT approach to the NJL model that captures 1/N_c corrections and improves upon the mean-field approximation.

Findings

OPT results differ from large-N_c predictions for critical quantities

Phase diagram shows nonperturbative effects beyond mean-field

Deviations from Gell-Mann-Oakes-Renner relation are derived

Abstract

The optimized perturbation theory (OPT) method is applied to the $SU(2)$ version of the Nambu--Jona-Lasinio (NJL) model both at zero and at finite temperature and/or density. At the first nontrivial order the OPT exhibits a class of 1/N_c corrections which produce nonperturbative results that go beyond the standard large-N_c, or mean-field approximation. The consistency of the OPT method with the Goldstone theorem at this order is established, and appropriate OPT values of the basic NJL (vacuum) parameters are obtained by matching the pion mass and decay constant consistently. Deviations from standard large-N_c relations induced by OPT at this order are derived, for example, for the Gell--Mann-Oakes-Renner relation. Next, the results for the critical quantities and the phase diagram of the model, as well as a number of other thermodynamical quantities of interest, are obtained with OPT and then contrasted with the corresponding results at large N_c.