Abstract
We analyze the two flavor version of the Nambu-Jona-Lasinio model with a repulsive vector coupling (GV), at finite temperature and quark chemical potential, in the strong scalar coupling (Gs) regime. Considering GV = 0, we review how finite Nc effects are introduced by means of the Optimized Perturbation Theory (OPT) which adds a term to the thermodynamical potential. This 1/ Nc suppressed term is similar to the contribution obtained at the large-Nc limit when GV ≠ 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 Nc corrections which are neglected in the majority of the works devoted to the determination of the QCD phase diagram. Recently the OPT, with GV = 0, and the large-Nc approximation, with GV ≠ 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
Highlights
Most of the results obtained up to now seem to support the quantum chromodynamics (QCD) critical point (CP), an interesting observation against its existence comes from the numerical simulations of QCD at imaginary chemical potential by de Forcrand and Philipsen [1,2,3] which shows that the region of quark masses where the transition is presumably of the first order, tends to shrink for small positive values of the chemical potential as shown in the upper panel of Figure 1
We extend the comparison between the Optimized Perturbation Theory (OPT) and the large-Nc approximation to the non abelian Nambu-Jona-Lasinio model (NJL) model at finite temperature and density in the strong coupling and small quark mass regime showing that, as expected, both methods agree from the qualitative point of view leading to a back-bending which would be completely missed by a standard large-Nc evaluation
We have considered the two flavor NJL model in the strong scalar coupling regime (GSΛ2 4) in order to compare two distinct model approximations
Summary
Most of the results obtained up to now seem to support the quantum chromodynamics (QCD) critical point (CP), an interesting observation against its existence comes from the numerical simulations of QCD at imaginary chemical potential by de Forcrand and Philipsen [1,2,3] which shows that the region of quark masses (mc) where the transition is presumably of the first order (for quark masses smaller than the physical ones), tends to shrink for small positive values of the chemical potential as shown in the upper panel of Figure 1. The value of the coexistence chemical potential for a given temperature occurs at a higher value when GV ≠ 0 and, as a consequence, the critical end point happens at smaller temperatures to be higher chemical potentials than in the case of vanishing GV Such a vector term is known to be important at high densities in theories such as the Walecka model for nuclear matter, its consideration is more delicate within a non renormalizable model such as the NJL where usually the integrals are regulated by a momentum cut-off, Λ. We extend the comparison between the OPT (at GV = 0) and the large-Nc approximation (at GV ≠ 0) to the non abelian NJL model at finite temperature and density in the strong coupling and small quark mass regime showing that, as expected, both methods agree from the qualitative point of view leading to a back-bending which would be completely missed by a standard large-Nc evaluation.
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