Viscosity in the excluded volume hadron gas model

TL;DR

This paper investigates the shear viscosity to entropy density ratio in an excluded volume hadron gas model, considering relativistic effects and particle mixture, revealing a minimum near 0.3 at certain hard-core radii and its variation along collision energies.

Contribution

It extends the non-relativistic hard-core particle gas model to include mixtures and relativistic corrections, analyzing viscosity behavior in high-energy nuclear collisions.

Findings

The ratio η/s decreases monotonically with increasing collision energy.

A broad minimum of η/s ≈ 0.3 occurs near r ≈ 0.5 fm at high energies.

Minimum η/s ≈ 0.24 is found at T=180 MeV for r ≈ 0.53 fm.

Abstract

The shear viscosity $\eta$ in the van der Waals excluded volume hadron-resonance gas model is considered. For the shear viscosity the result of the non-relativistic gas of hard-core particles is extended to the mixture of particles with different masses, but equal values of hard-core radius r. The relativistic corrections to hadron average momenta in thermal equilibrium are also taken into account. The ratio of the viscosity $\eta$ to the entropy density s is studied. It monotonously decreases along the chemical freeze-out line in nucleus-nucleus collisions with increasing collision energy. As a function of hard-core radius r, a broad minimum of the ratio $\eta/s\approx 0.3$ near $r \approx 0.5$ fm is found at high collision energies. For the charge-neutral system at $T=T_c=180$ MeV, a minimum of the ratio $\eta/s\cong 0.24$ is reached for $r\cong 0.53$ fm. To justify a hydrodynamic approach to nucleus-nucleus collisions within the hadron phase the restriction from below, $r~ \ge ~0.2$ fm, on the hard-core hadron radius should be fulfilled in the excluded volume hadron-resonance gas.