$\eta/s$ and Phase Transitions

TL;DR

This paper calculates the shear viscosity to entropy density ratio (eta/s) for meson gas and atomic Argon, showing its decrease near phase transitions and proposing its use to identify critical points in nuclear matter.

Contribution

It provides a unitarized NLO chiral perturbation theory calculation of eta/s for meson gas and explores its behavior across phase transitions, including atomic Argon.

Findings

eta/s decreases near the phase transition to quark-gluon plasma

eta/s is higher than previous LO estimates in chiral perturbation theory

eta/s can indicate phase transitions and critical points in nuclear matter

Abstract

We present a calculation of eta/s for the meson gas (zero baryon number), with the viscosity computed within unitarized NLO chiral perturbation theory, and confirm the observation that eta/s decreases towards the possible phase transition to a quark-gluon plasma/liquid. The value is somewhat higher than previously estimated in LO chi PT. We also examine the case of atomic Argon gas to check the discontinuity of eta/s across a first order phase transition. Our results suggest employing this dimensionless number, sometimes called KSS number (in analogy with other ratios in fluid mechanics such as Reynolds number or Prandtl number) to pin down the phase transition and critical end point to a cross-over in strongly interacting nuclear matter between the hadron gas and quark and gluon plasma/liquid.