A hadron resonance gas model including all known particles and resonances with masses $m<2\mathrm{GeV}$ and an exponentially rising density of Hagedorn states for $m>2\mathrm{GeV}$ is used to obtain an upper bound on the shear viscosity to entropy density ratio, $\eta /s\approx 1/(4\pi )$, of hadronic matter near $T_c$. We found a large trace anomaly and small speed of sound near $T_c$, which agree well with recent lattice calculations. We comment on the bulk viscosity to entropy density ratio close to $T_c$.

• Received 19 November 2008

DOI:https://doi.org/10.1103/PhysRevLett.103.172302