Dynamical evolution of critical fluctuations with second-order baryon diffusion coupled to chiral condensate

TL;DR

This paper develops a dynamical model coupling baryon diffusion and chiral condensate fluctuations to better understand critical phenomena in heavy-ion collisions, emphasizing the importance of finite relaxation times for causality and signal persistence.

Contribution

It introduces a coupled dynamical framework incorporating second-order baryon diffusion and chiral condensate fluctuations with finite relaxation time, addressing scale separation and causality issues.

Findings

Finite relaxation time ensures causality in the model.

Propagating modes split into two at the critical temperature.

Critical fluctuation signals persist longer with finite relaxation time.

Abstract

We develop a dynamical model to describe critical fluctuations in heavy-ion collisions, incorporating the baryon diffusion current and chiral condensate as dynamical degrees of freedom, to address their nontrivial scale separation. The model couples fluctuations of the chiral condensate $\sigma$ with baryon density fluctuations $n$ and the diffusion current $\nu$ based on a second-order diffusion equation with a finite relaxation time of the baryon diffusion $\tau_\mathrm{R}$. We analyze the spacetime evolution and these correlation functions of the fluctuations in one-dimensionally expanding background. We confirm that an appropriate relaxation time $\tau_\mathrm{R}$ ensures causality. We show that propagating waves with finite $\tau_\mathrm{R}$ split into two modes at the critical temperature due to a rapid change of kinetic coefficients. In the correlation functions, we find that dynamical $\sigma$ blurs the structure and peak around the critical temperature. With finite $\tau_\mathrm{R}$, the effect of the critical fluctuations persists longer into the later stages of the evolution. These findings suggest importance of dynamical effects of the chiral condensate and baryon diffusion current in identifying critical-point signals in heavy-ion collisions, where the scale separation is nontrivial.