Critical Line Back-Bending Induced either by Finite <i>N_c</i> Corrections or by a Repulsive Vector Channel

Abstract

We analyze the two flavor version of the Nambu - Jona-Lasinio model with a repulsive vector coupling ( G V ) , at finite temperature and quark chemical potential, in the strong scalar coupling ( G s ) regime. Considering G V = 0 , we review how finite N c effects are introduced by means of the Optimized Perturbation Theory (OPT) which adds a term to the thermodynamical potential. This 1/ N c suppressed term is similar to the contribution obtained at the large- N c limit when G V ≠ 0. Then, scanning over the quark current mass values, we compare these two different model approximations showing that both predict the appearance of two critical points when chiral symmetry is weakly broken. By mapping the first order transition region in the chemical potential-current mass plane , we show that, for low chemical potential values, the first order region shrinks as μ increases but the behavior gets reversed at higher values leading to the back-bending of the critical line. This result, which could help to conciliate some lattice results with model predictions, shows the important role played by finite N c corrections which are neglected in the majority of the works devoted to the determination of the QCD phase diagram. Recently the OPT, with G V = 0, and the large- N c approximation, with G V ≠ 0, were compared at zero temperature and finite density for one quark flavor only. The present work extends this comparison to finite temperatures, and two quark flavors, supporting the result that the OPT finite N