Stochastic field evolution of disoriented chiral condensates

TL;DR

This paper models the time evolution of disoriented chiral condensates using Langevin equations, ensuring a finite quantum theory that matches equilibrium behavior and estimates viscosity for dynamical response.

Contribution

It introduces a UV cutoff independent Langevin field theory for chiral condensates, integrating lattice and chiral perturbation theory results for accurate equilibrium and dynamical modeling.

Findings

Quantitative reproduction of pion and sigma field equilibrium behavior.

Estimation of viscosity ta(T) for dynamical response.

UV divergence subtraction leading to finite quantum results.

Abstract

I present a summary of recent work \cite{BRS} where we describe the time-evolution of a region of disoriented chiral condensate via Langevin field equations for the linear $\sigma$ model. We analyze the model in equilibrium, paying attention to subtracting ultraviolet divergent classical terms and replacing them by their finite quantum counterparts. We use results from lattice gauge theory and chiral perturbation theory to fix nonuniversal constants. The result is a ultraviolet cutoff independent theory that reproduces quantitatively the expected equilibrium behavior of pion and $\sigma$ quantum fields. We also estimate the viscosity $\eta(T)$, which controls the dynamical timescale in the Langevin equation, so that the near equilibrium dynamical response agrees with theoretical expectations.