Shear-viscosity to entropy-density ratio of a relativistic hadron gas

Ultrarelativistic heavy-ion collisions at the Brookhaven National Laboratory Relativistic Heavy Ion Collider (RHIC) are thought to have produced a state of matter called the quark-gluon plasma, characterized by a very small shear-viscosity to entropy-density ratio eta/s, near the lower bound predicted for that quantity by anti-de Sitter space/conformal field theory methods. As the produced matter expands and cools, it evolves through a phase described by a hadron gas with rapidly increasing eta/s. We calculate eta/s as a function of temperature in this phase both in and out of chemical equilibrium and find that its value poses a challenge for viscous relativistic hydrodynamics, which requires small values of eta/s in order to successfully describe the collective flow observables at the RHIC. We therefore conclude that the origin of the low viscosity matter at the RHIC must be in the partonic phase of the reaction.