Shear viscosity η to electric conductivity σel 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, η/sη/s, and the electric conductivity, σelσel. Once the relaxation time is tuned to have a minimum value of η/s=1/4πη/s=1/4π near the critical temperature TcTc, one simultaneously predicts σel/Tσel/T very close to recent lQCD data. More generally, we discuss why the ratio of (η/s)/(σel/T)(η/s)/(σel/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 (η/s)/(σel/T)(η/s)/(σel/T), independently on the running coupling αs(T)αs(T), should increase up to about ∼20 for T→TcT→Tc, while it goes down to a nearly flat behavior around ≃4 for T≥4Tc. Therefore we in general predict a stronger T dependence of σel/Tσel/T with respect to η/sη/s that in a quasi-particle approach is constrained by lQCD thermodynamics. A conformal theory, instead, predicts a similar T dependence of η/sη/s and σel/Tσel/T.