Shear viscosity of a hadron gas and influence of resonance lifetimes on relaxation time

TL;DR

This paper investigates the shear viscosity to entropy density ratio in a hadron gas, highlighting how resonance lifetimes significantly influence relaxation times and cause discrepancies between different computational approaches.

Contribution

It provides an independent calculation of /s using the SMASH transport code and clarifies the impact of resonance lifetimes on transport properties.

Findings

Resonance lifetimes strongly affect /s in hadron gases.

Shortening resonance lifetimes interpolates between different computational results.

Resonance formation and decay dominate the relaxation process.

Abstract

We address a discrepancy between different computations of $\eta/s$ (shear viscosity over entropy density) of hadronic matter. Substantial deviations of this coefficient are found between transport approaches mainly based on resonance propagation with finite lifetime and other (semi-analytical) approaches with energy-dependent cross-sections, where interactions do not introduce a timescale. We provide an independent extraction of this coefficient by using the newly-developed SMASH (Simulating Many Accelerated Strongly interacting Hadrons) transport code, which is an example of a mainly resonance-based approach. We compare the results from SMASH with numerical solutions of the Boltzmann equation for simple systems using the Chapman-Enskog expansion, as well as previous results in the literature. Our conclusion is that the hadron interaction via resonance formation/decay strongly affects the transport properties of the system, resulting in significant differences in $\eta/s$ with respect to other approaches where binary collisions dominate. We argue that the relaxation time of the system ---which characterizes the shear viscosity--- is determined by the interplay between the mean-free time and the lifetime of resonances. We show how an artificial shortening of the resonance lifetimes, or the addition of a background elastic cross section nicely interpolate between the two discrepant results.