Shear-Viscosity to Entropy Density Ratio of a Relativistic Hadron Gas

TL;DR

This paper calculates the shear viscosity to entropy density ratio of a hadron gas during heavy-ion collisions, highlighting its increase with temperature and the implications for the origin of low-viscosity quark-gluon plasma.

Contribution

It provides a detailed calculation of ta/s in the hadronic phase, showing it remains too high for hydrodynamic models, implying the low viscosity must originate in the partonic phase.

Findings

ta/s increases with temperature in the hadron gas phase.

Including non-unit fugacities reduces ta/s but not enough for hydrodynamics.

Low viscosity at RHIC likely originates in the partonic phase.

Abstract

Ultrarelativistic heavy-ion collisions at the 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-deSitter space/Conformal Field Theory (AdS/CFT) 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 and find that its value poses a challenge for viscous relativistic hydrodynamics, which requires small values of $\eta/s$ throughout the entire evolution of the reaction in order to successfully describe the collective flow observables at RHIC. We show that the inclusion of non-unit fugacities will reduce $\eta/s$ in the hadronic phase, yet not sufficiently to be compatible with viscous hydrodynamics. We therefore conclude that the origin of the low viscosity matter at RHIC must be in the partonic phase of the reaction.