A Phenomenological Treatment of Chiral Symmetry Restoration and Deconfinement

TL;DR

This paper develops a phenomenological model combining the Polyakov loop and chiral condensate to describe deconfinement and chiral symmetry restoration in QCD, matching lattice simulation features.

Contribution

It introduces a combined thermodynamic potential model for gluons and quarks incorporating deconfinement and chiral symmetry restoration, with predictions aligning with lattice results.

Findings

Second order chiral transition for massless quarks

Confinement raises the transition temperature

Heavy quarks lead to a first order deconfinement transition

Abstract

A phenomenological expression for the thermodynamic potential of gluons and quarks is constructed which incorporates the features of deconfinement and chiral symmetry restoration known from lattice simulations. The thermodynamic potential is a function of the Polyakov loop and chiral condensate expectation values. The gluonic sector uses a successful model for pure (SU(N_c)) gauge theories in which the Polyakov loop eigenvalues are the fundamental order parameters for deconfinement. The quark sector is given by a Nambu-Jona-Lasinio model in which a constant background (A_0) field couples the chiral condensate to the Polyakov loop. We consider the case of (N_f = 2) in detail. For two massless quarks, we find a second order chiral phase transition. Confinement effects push the transition to higher temperatures, but the entropy associated with the gluonic sector acts in the opposite direction. For light mass quarks, only a rapid crossover occurs. For sufficiently heavy quarks, a first order deconfinement transition emerges. This simplest model has one adjustable parameter, which can be set from the chiral transition temperature for light quarks. It predicts all thermodynamic quantities as well as the behavior of the chiral condensate and the Polyakov loop over a wide range of temperatures.