Quark-Hadron Phase Transition in the PNJL model for interacting quarks

TL;DR

This paper investigates the quark-hadron phase transition at finite temperature using the PNJL model, highlighting the role of the Polyakov loop and mesonic excitations in different temperature regimes.

Contribution

It introduces a detailed description of the phase transition incorporating Polyakov loop effects and mesonic fluctuations within the PNJL model framework.

Findings

Low-temperature phase behaves as a free meson gas.

High-temperature phase features melted mesons into quark-antiquark continuum.

Polyakov loop effectively suppresses unphysical quark excitations at low T.

Abstract

We study quark-hadron phase transition at finite temperature with zero net baryon density by the Nambu-Jona-Lasinio model for interacting quarks in uniform background temporal color gauge fields. At low temperatures, unphysical thermal quark-antiquark excitations which would appear in the mean field approximation, are eliminated by en- forcing vanishing expectation value of the Polyakov-loop of the background gauge field, while at high temperatures this expectation value is taken as unity allowing thermal excitations of free quarks and antiquarks. Mesonic excitations in the low temperature phase appear in the correlation energy as contributions of collective excitations. We describe them in terms of thermal fluctuations of auxiliary fields in one-loop (Gaus- sian) approximation, where pions appear as Nambu-Goldstone modes associated with dynamical symmetry breaking of the chiral symmetry in the limit of vanishing bare quark masses. We show that at low temperatures the equations of state reduces to that of free meson gas with small corrections arising from the composite nature of mesons. At high temperatures, all these collective mesonic excitations melt into continuum of quark anti-quark excitations and mesonic correlations gives only small contributions the pressure of the system.