Hadron Mass Spectrum and the Shear Viscosity to Entropy Density Ratio of Hot Hadronic Matter

TL;DR

This paper compares lattice QCD data with hadron resonance gas models, confirming the need for an exponentially increasing hadron mass spectrum and analyzing its impact on shear viscosity and relaxation times in hot hadronic matter.

Contribution

It provides a detailed validation of the exponentially rising hadron mass spectrum and explores its implications for transport properties in hot hadronic matter.

Findings

Lattice data supports an exponential hadron mass spectrum with specific subleading terms.

Heavy resonances likely decay via 2-body processes, aiding transport simulations.

Transport coefficients are sensitive to the hadron mass spectrum parameters.

Abstract

Lattice calculations of the QCD trace anomaly at temperatures $T<160$ MeV have been shown to match hadron resonance gas model calculations, which include an exponentially rising hadron mass spectrum. In this paper we perform a more detailed comparison of the model calculations to lattice data that confirms the need for an exponentially increasing density of hadronic states. Also, we find that the lattice data is compatible with a hadron density of states that goes as $\rho(m) \sim m^{-a}\exp(m/T_H) $ at large $m$ with $a> 5/2$ (where $T_H \sim 167$ MeV). With this specific subleading contribution to the density of states, heavy resonances are most likely undergo 2-body decay (instead of multi-particle decay), which facilitates their inclusion into hadron transport codes. Moreover, estimates for the shear viscosity and the shear relaxation time coefficient of the hadron resonance model computed within the excluded volume approximation suggest that these transport coefficients are sensitive to the parameters that define the hadron mass spectrum.