First, we recall that close to the chiral limit, and below the critical temperature, the long wavelength effective theory of QCD is not ordinary hydrodynamics, but SU(2)xSU(2) superfluid hydrodynamics (Son 2000). In this theory the usual hydrodynamic variables such as energy are momentum are augmented by long wavelength pions. When the pion is massive, the effective theory reduces to normal hydrodynamics at large distances, but is described by the superfluid theory at short distances. Using techniques developed by Akamatsu et al (Akamatsu 2017), we integrate out the superfluid modes to determine how the transport coefficients of QCD such as the bulk viscosity depend on the pion mass below the critical temperature. These expressions are given by the dissipative parameters in the superfluid theory. We show how to compute these parameters in chiral perturbation theory using the associated chiral kinetic theory.
D. Son, ``Hydrodynamics of nuclear matter in the chiral limit,'' Phys. Rev. Lett. 84, 3771 (2000).
Y. Akamatsu, A. Mazeliauskas and D. Teaney, ``A kinetic regime of hydrodynamic fluctuations and long time tails for a Bjorken expansion,'' Phys.\ Rev. C95, no. 1, 014909 (2017).