Transport coefficients for the hot quark-gluon plasma at finite chemical potential $\mu_B$

Abstract

We calculate transport coefficients of the quark-gluon plasma (QGP) within the dynamical quasiparticle model (DQPM) by explicitly computing the parton interaction rates as a function of temperature $T$ and baryon chemical potential $\mu_B$ on the basis of the DQPM couplings and partonic propagators. The latter are extracted from lattice QCD by matching the equation of state, entropy density and energy density at $\mu_B$= 0. For baryon chemical potentials $0 \leq \mu_B \leq 500 MeV$ we employ a scaling Ansatz for the effective coupling which was shown before to lead to thermodynamic consistent results in this range. We compute the ratio of the shear and bulk viscosities to the entropy density, i.e. $\eta/s$ and $\zeta/s$, the electric conductivity $\sigma_0/T$ as well as the baryon diffusion coefficient $\kappa_B$ and compare to related approaches from the literature. We find that the ratios $\eta/s$ and $\zeta/s$ as well as $\sigma_0/T$ are in accord with the results from lattice QCD at $\mu_B$=0 and only weakly depend on the ratio $T/T_c(\mu_B)$ where $T_c(\mu_B)$ denotes the critical temperature at finite baryon chemical potential.