The Bulk Viscosity of a Pion Gas

We compute the bulk viscosity of a gas of pions at temperatures below the QCD crossover temperature, for the physical value of pion mass, to lowest order in chiral perturbation theory. Bulk viscosity is controlled by number-changing processes which become exponentially slow at low temperatures when the pions become exponentially dilute, leading to an exponentially large bulk viscosity zeta ~ (F_0^8/m_\pi^5) exp(2m_\pi/T), where F_0 = 93 MeV is the pion decay constant.