Shear viscosity and electric conductivity of a hot and dense QGP with a chiral phase transition

TL;DR

This study calculates shear viscosity and electric conductivity of hot, dense quark-gluon plasma near the chiral phase transition using the PNJL model, revealing their behavior across phase transitions and the critical endpoint.

Contribution

It introduces a detailed calculation of transport coefficients near the chiral transition and CEP within the extended PNJL model, comparing two methods for quark relaxation times.

Findings

Transport coefficients show similar behavior near the transition for both relaxation time methods.

Differences in transport coefficients increase with temperature.

First-order phase transition and CEP significantly affect transport properties.

Abstract

We calculate two transport coefficients -- the shear viscosity over entropy ratio $\eta/s$ and the ratio of the electric conductivity to the temperature $\sigma_0/T$ -- of strongly interacting quark matter within the extended $N_f=3$ Polyakov Nambu-Jona-Lasinio (PNJL) model along the crossover transition line for moderate values of baryon chemical potential $0 \leq \mu_B \leq 0.9$ GeV as well as in the vicinity of the critical endpoint (CEP) and at large baryon chemical potential $\mu_B=1.2$ GeV, where the first-order phase transition takes place. The evaluation of the transport coefficients is performed on the basis of the effective Boltzmann equation in the relaxation time approximation. We employ two different methods for the calculation of the quark relaxation times: i) using the averaged transition rate defined via thermal averaged quark-quark and quark-antiquark PNJL cross sections and ii) using the 'weighted' thermal averaged quark-quark and quark-antiquark PNJL cross sections. The $\eta/s$ and $\sigma_0/T$ transport coefficients have a similar temperature and chemical potential behavior when approaching the chiral phase transition for the both methods for the quark relaxation time, however, the differences grow with increasing temperature. We demonstrate the effect of the first-order phase transition and of the CEP on the transport coefficients in the deconfined QCD medium.