Langevin Evolution of Disoriented Chiral Condensate

Abstract

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 evolution, 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 of 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 other shorter wavelength degrees of freedom. We first analyze the model in equilibrium, 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 equilibrium behavior of the quantum field theory of pions and sigma fields over a wide range of temperatures. Finally, we estimate the viscosity $\eta (T)$, which controls the dynamical timescale in the Langevin equation, by requiring that the timescale for DCC decay agrees with previous calculations. The resulting $\eta (T)$ 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.

19 pages, 7 figures, uses RevTex; v2 very small change to the caption of Fig.7. Version to appear in Nucl. phys. A

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• Disoriented Chiral Condensate: Theory and Experiment
• Evolution of fluctuations near QCD critical point
• Can dissipation prevent explosive decomposition in high-energy heavy ion collisions?
• From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group
• Hadronization geometry from net-charge angular correlations on momentum subspace ($\eta ,\varphi$) in Au-Au collisions at $\sqrt{s_{NN}}=130$ GeV
• Langevin Simulation of Scalar Fields: Additive and Multiplicative Noises and Lattice Renormalization
• Langevin dynamics of the pure SU(2) deconfining transition
• Dissipation at Two-Loop Level: Undressing the Chiral Condensate
• The Chiral Phase Transition in Dissipative Dynamics
• The role of noise and dissipation in the hadronization of the quark-gluon plasma
• Dissipation near the QCD phase transition
• Stochastic field evolution of disoriented chiral condensates