Shear viscosity eta to electric conductivity sigma(el) ratio for the quark-gluon plasma

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,eta/s, and the electric conductivity, sigma(el). Once the relaxation time is tuned to have a minimum value of eta/s = 1/4 pi near the critical temperature T-c, one simultaneously predicts sigma(el)/T very close to recent lQCD data. More generally, we discuss why the ratio of (eta/s)/(sigma(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 (eta/s)/(sigma el/T), independently on the running coupling as(T), should increase up to about similar to 20 for T -> T-c, while it goes down to a nearly flat behavior around similar or equal to 4 for T >= 4 T-c. Therefore we in general predict a stronger T dependence of sigma(el)/T with respect to eta/s that in a quasi-particleapproach is constrained by lQCD thermodynamics. A conformal theory, instead, predicts a similar T dependence of eta/s and sigma(el)/T. (C) 2015 The Authors. Published by Elsevier B.V.