Stochastic treatment of Disoriented Chiral Condensates within a Langevin description

TL;DR

This paper models the stochastic evolution of disoriented chiral condensates using a Langevin approach, highlighting the effects of colored noise and memory, and suggests experimental signatures through higher order cumulants.

Contribution

It introduces a semi-classical Langevin framework with colored noise for DCC evolution, emphasizing non-Markovian effects and probabilistic event distributions.

Findings

DCC signals are most prominent near zero sigma field.

DCC formation is a rare, non-Poissonian event.

Higher order cumulants can help identify DCCs experimentally.

Abstract

Applying a microscopically motivated semi-classical Langevin description of the linear sigma model we investigate for various different scenarios the stochastic evolution of a disoriented chiral condensate (DCC) in a rapidly expanding system. Some particular emphasize is put on the numerical realisation of colored noise in order to treat the underlying dissipative and nonmarkovian stochastic equations of motion. A comparison with an approximate markovian (i.e. instantaneous) treatment of dissipation and noise will be made in order to identify the possible influence of memory effects in the evolution of the chiral order parameter. Assuming a standard Rayleigh cooling term to simulate a D-dimensional scaling expansion we present the probability distribution in the low momentum pion number stemming from the relaxing zero mode component of the chiral field. The best DCC signal is expected for initial conditions centered around $<\sigma > \approx 0 $ as would be the case of effective light `pions' close to the phase transition. By choosing appropriate idealized global parameters for the expansion our findings show that an experimentally feasible DCC, if it does exist in nature, has to be a rare event with some finite probability following a nontrivial and nonpoissonian distribution on an event by event basis. DCCs might then be identified experimentally by inspecting higher order factorial cumulants $\theta_m$ ($m\ge 3$) in the sampled distribution.