Shear viscosity to entropy density ratio of a relativistic Hagedorn resonance gas

The new state of matter produced at Relativistic Heavy Ion Collider reveals a strongly coupled quark–gluon plasma with an extremely small shear viscosity to entropy density ratio η/sη/s. We calculate the η/sη/s of an equilibrated hadron matter characterized by a relativistic hadron resonance gas with a Hagedorn mass spectrum that grows exponentially with the hadron mass. We find with increase in temperature of the system the η/sη/s value decreases due to rapid increase in the multiplicity of massive resonances. In the vicinity of the critical temperature for deconfinement transition, the minimum value of η/sη/s in the Hagedorn resonance gas is found to be consistent with the current estimates for a strongly coupled quark–gluon plasma.