Shear Viscosity over Entropy Ratio of Hot Hadronic Matter

The ratio of shear viscosity to entropy density $\eta/s$ typically exhibits a minimum at phase transitions, which is prominent in the case of true phase transitions and is smooth if the transition is a crossover [1]. For quark gluon plasma both lattice QCD and extractions from data hint at a very small value of $\eta/s$, close to the conjectured lower bound $1/4\pi$, as the temperature approches $T_c$ from above. On the other hand, hadronic transport is predicting $\eta/s$ to be as large as $10/4\pi$ when the temperature approaches $T_c$ from below [2]. This discrepancy is uncomfortably large. In this talk we review the current results for $\eta/s$ from the literature and discuss the importance of a reliable estimate of $\eta/s$ for hot hadronic matter. We introduce the idea of extracting $\eta/s$ from data through an analysis of the freeze-out process using a Navier-Stokes approximation [3]. We quantify uncertainties from this extraction and correct for known biases. This method suggests a smooth minimum of $\eta/s$ at $T_c$ and a gradual rise below $T_c$. We discuss possible consequences of this scenario. [1] L.P. Csernai, J.I. Kapusta, L.D. McLerran, PRL 97, 152303 (2006) [2] J.-B. Rose et al., PRC97, 055204 (2018) [3] Z. Yang, R.J. Fries, arXiv:1807.03410