Universal dynamics near the O(4) critical point, and soft pion yields in heavy ion collisions.*

I present a stochastic hydrodynamic description of the O(4) phase transition, and present numerical work showing how the axial current-current correlator evolves near the psuedo-critical point. At high temperature the theory matches smoothly with ordinary hydrodynamics, while at low temperatures the theory matches smoothly with a non-abelian superfluid theory capturing broken chiral symmetry. This theory describes the dynamics of soft pions coupled to hydrodynamic modes.  We use this theory to present estimates for the yields of soft pions in heavy ion collisions, which are chronically underpredicted by traditional hydrodynamic simulations of heavy ion events.