Shear viscosity of a hot pion gas

The shear viscosity of an interacting pion gas is studied using the Kubo formalism as a microscopic description of thermal systems close to global equilibrium. We implement the skeleton expansion in order to approximate the retarded correlator of the viscous part of the energy-momentum tensor. After exploring this in gφ⁴ theory we show how the skeleton expansion can be consistently applied to pions in chiral perturbation theory. The shear viscosity η is determined by the spectral width, or equivalently, the mean free path of pions in the heat bath. We derive a new analytical result for the mean free path which is well conditioned for numerical evaluation and discuss the temperature and pion-mass dependence of the mean free path and the shear viscosity. The ratio η/s of the interacting pion gas exceeds the lower bound 1/4π from AdS/CFT correspondence.