Langevin evolution of disoriented chiral condensate

As the matter produced in a relativistic heavy ion collision cools through the QCD phase transition, the dynamical evolution of the chiral condensate will be driven out of thermal equilibrium. As a prelude to analyzing this e volution, and in particular as a prelude to learning how rapid the cooling must be in order for significant deviations from equilibrium to develop, we present a detailed analysis of the time-evolution of an idealized region o f disoriented chiral condensate. We set up a Langevin field equation which can describe the evolution of these (or more realistic) linear sigma model configurations in contact with a heat bath representing the presence of oth er shorter wavelength degrees of freedom. We first analyze the model in equ ilibrium, paying particular attention to subtracting ultraviolet divergent classical terms and replacing them by their finite quantum counterparts. We use known results from lattice gauge theory and chiral perturbation theory to fix nonuniversal constants. The result is a theory which is ultraviolet cutoff independent and that reproduces quantitatively the expected equilib rium behavior of the quantum field theory of pions and or fields over a wid e range of temperatures. Finally, we estimate the viscosity eta (T), which controls the dynamical timescale in the Langevin equation, by requiring tha t the timescale for DCC decay agrees with previous calculations. The result ing eta (T) is larger than that found perturbatively. We also determine the temperature below which the classical field Langevin equation ceases to be a good model for the quantum field dynamics. (C) 2001 Elsevier Science B.V . All rights reserved.