Chiral condensate and dressed Polyakov loop in the Nambu--Jona-Lasinio model

TL;DR

This paper studies the behavior of the chiral condensate and dressed Polyakov loop in the Nambu--Jona-Lasinio model at finite temperature and density, revealing their relationship and phase transition characteristics.

Contribution

It demonstrates that the dressed Polyakov loop can serve as an order parameter for deconfinement even without explicit confinement mechanisms in the NJL model.

Findings

In the chiral limit, critical temperatures for chiral transition and dressed Polyakov loop coincide.

For explicit chiral symmetry breaking, the transition temperatures differ in the crossover region.

The critical temperatures coincide at high baryon density where the transition is first order.

Abstract

We investigate the chiral condensate and the dressed Polyakov loop or dual chiral condensate at finite temperature and density in two-flavor Nambu--Jona-Lasinio model. The dressed Polyakov loop is regarded as an equivalent order parameter of deconfinement phase transition in a confining theory. We find the behavior of dressed Polyakov loop in absence of any confinement mechanism is quite interesting, with only quark degrees of freedom present, it still shows an order parameter like behavior. It is found that in the chiral limit, the critical temperature for chiral phase transition coincides with that of the dressed Polyakov loop in the whole $(T,\mu)$ plane. In the case of explicit chiral symmetry breaking, it is found that the transition temperature for chiral restoration $T_c^{\chi}$ is smaller than that of the dressed Polyakov loop $T_c^{{\cal D}}$ in the low baryon density region where the transition is a crossover. With the increase of current quark mass the difference between the two transition temperatures is found to be increasing. However, the two critical temperatures coincide in the high baryon density region where the phase transition is of first order. We give an explanation on the feature of $T_c^{\chi}=T_c^{\cal D}$ in the case of 1st and 2nd order phase transitions, and $T_c^{\chi}<T_c^{\cal D}$ in the case of crossover, and expect this feature is general and can be extended to full QCD theory. Our result might indicate that in the case of crossover, there exists a small region where chiral symmetry is restored but the color degrees of freedom are still confined.