Shear viscosity η to electric conductivity σ el ratio for the quark–gluon plasma

Abstract

The transport coefficients of strongly interacting matter are currently subject of intense theoretical and phenomenological studies due to their relevance for the characterization of the quark-gluon plasma produced in ultra-relativistic heavy-ion collisions (uRHIC). We discuss the connection between the shear viscosity to entropy density ratio, /s, and the electric conductivity, el . Once the relaxation time is tuned to have a minimum value of /s = 1/4 near the critical temperature T c , one simultaneously predicts el /T very close to recent lQCD data. More generally, we discuss why the ratio of (/s)/( el /T ) supplies a measure of the quark to gluon scattering rates whose knowledge would allow to significantly advance in the understanding of the QGP phase. We also predict that (/s)/( el /T ), independently on the running coupling s (T ), should increase up to about 20 for T T c , while it goes down to a nearly flat behavior around 4 for T 4 T c . Therefore we in general predict a stronger T dependence of el /T with respect to /s that in a quasi-particle approach is constrained by lQCD thermodynamics. A conformal theory, instead, predicts a similar T dependence of /s and el /T .