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

We calculate two transport coefficients—the shear viscosity over entropy ratio η/s and the ratio of the electric conductivity to the temperature, σ0/T—of strongly interacting quark matter within the extended Nf=3 Polyakov Nambu-Jona-Lasinio (PNJL) model along the crossover transition line for moderate values of baryon chemical potential 0≤μB≤0.9GeV as well as in the vicinity of the critical endpoint (CEP) and at large baryon chemical potential μB=1.2GeV, 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 η/s and σ0/T transport coefficients have similar temperature and chemical potential behaviors when approaching the chiral phase transition for 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.