Evolution of fluctuations near QCD critical point

TL;DR

This paper models the evolution of fluctuations near the QCD critical point using stochastic equations, reproduces known results, and explores how these fluctuations persist through heavy-ion collision stages.

Contribution

It introduces a stochastic Boltzmann-Langevin-Vlasov framework to analyze fluctuation dynamics near the QCD critical point, including during hadronic rescattering.

Findings

Reproduces equilibrium fluctuation results and critical scaling.

Shows conserved fluctuations can survive rescattering stages.

Provides an analytical formula for fluctuation 'memory' effects.

Abstract

We propose to describe the time evolution of quasi-stationary fluctuations near QCD critical point by a system of stochastic Boltzmann-Langevin-Vlasov-type equations. We derive the equations and study the system analytically in the linearized regime. Known results for equilibrium stationary fluctuations as well as the critical scaling of diffusion coefficient are reproduced. We apply the approach to the long-standing question of the fate of the critical point fluctuations during the hadronic rescattering stage of the heavy-ion collision after chemical freezeout. We find that if conserved particle number fluctuations survive the rescattering, so do, under a certain additional condition, the fluctuations of non-conserved quantities, such as mean transverse momentum. We derive a simple analytical formula for the magnitude of this "memory" effect.