Evolution of fluctuations near QCD critical point

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.