The Wigner solution and QCD phase transitions in a modified PNJL model

Zhu-Fang Cui,Hong-Shi Zong,Chao Shi,Yong-Long Wang,Wei-Min Sun

doi:10.1140/epjc/s10052-014-2782-x

Abstract

By employing some modification to the widely used two-flavor Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model, we discuss the Wigner solution of the quark gap equation at finite temperature and zero quark chemical potential beyond the chiral limit, and then try to explore its influences on the chiral and deconfinement phase transitions of QCD at finite temperature and zero chemical potential. The discovery of the coexistence of the Nambu and the Wigner solutions of the quark gap equation with nonzero current quark mass at zero temperature and zero chemical potential, as well as their evolutions with temperature is very interesting for the studies of the phase transitions of QCD. According to our results, the chiral phase transition might be of first order (while the deconfinement phase transition is still a crossover, as in the normal PNJL model), and the corresponding phase transition temperature is lower than that of the deconfinement phase transition, instead of coinciding with each other, which are not the same as the conclusions obtained from the normal PNJL model. In addition, we also discuss the sensibility of our final results on the choice of model parameters.

Highlights

Nambu and Wigner phases are described, respectively, by two different solutions of the quark gap equation. The existence of those two solutions is generally accepted in the chiral limit, it is generally believed that the quark gap equation only has the Nambu–Goldstone solution beyond the chiral limit, whereas the Wigner solution disappears
It should be noted that, since G is taken to be a constant in the normal (P)NJL model, it is the same in different phases, and it does not change when the temperature and/or quark chemical potential vary
We find that thanks to the introduction of quarks coupled to both ψψ and fields, the first-order deconfinement phase transition seen in pure-gauge lattice Quantum Chromodynamics (QCD) is a continuous crossover2, as found in Refs. [31,32]

Summary

Introduction

As will be discussed later, the discovery of the coexistence of the Nambu and the Wigner solutions of the quark gap equation beyond the chiral limit when temperature and chemical potential are both zero, along with their evolutions with temperature is very interesting for the studies of the phase transitions of QCD. We display the calculated result of the chiral and deconfinement phase transitions in the case of zero chemical potential and finite temperature, and we make some discussions on the effects of varying the weight factor of the influence of the quark propagator to the gluon propagator.

Objectives

Results

Conclusion