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

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 $\ensuremath{\sigma}$ with baryon density fluctuations $n$ and the diffusion current $\ensuremath{\nu}$ based on a second-order stochastic diffusion equation with a finite relaxation time of the baryon diffusion ${\ensuremath{\tau}}_{\mathrm{R}}$. We analyze the spacetime evolution and these correlation functions of the fluctuations in a one-dimensionally expanding background. We confirm that an appropriate relaxation time ${\ensuremath{\tau}}_{\mathrm{R}}$ ensures causality. We show that propagating waves with finite ${\ensuremath{\tau}}_{\mathrm{R}}$ split into two modes at the critical temperature due to a rapid change of kinetic coefficients. In the correlation functions, we find that dynamical $\ensuremath{\sigma}$ blurs the structure and peak around the critical temperature. With finite ${\ensuremath{\tau}}_{\mathrm{R}}$, the effect of the critical fluctuations persists longer into the later stages of the evolution. These findings suggest the 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.