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Lattice calculations of the QCD trace anomaly at temperatures $T<160$ MeVhave been shown to match hadron resonance gas model calculations, which includean exponentially rising hadron mass spectrum. In this paper we perform a moredetailed comparison of the model calculations to lattice data that confirms theneed for an exponentially increasing density of hadronic states. Also, we findthat the lattice data is compatible with a hadron density of states that goesas $\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 ofstates, heavy resonances are most likely undergo 2-body decay (instead ofmulti-particle decay), which facilitates their inclusion into hadron transportcodes. Moreover, estimates for the shear viscosity and the shear relaxationtime coefficient of the hadron resonance model computed within the excludedvolume approximation suggest that these transport coefficients are sensitive tothe parameters that define the hadron mass spectrum.

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