Dynamics near QCD critical point by dynamic renormalization group

TL;DR

This paper analyzes the critical dynamics near the QCD critical point using dynamic renormalization group methods, revealing divergent transport coefficients and mode behaviors with specific critical exponents.

Contribution

It constructs a nonlinear Langevin equation based on relativistic hydrodynamics and applies dynamic RG to analyze critical behaviors near the QCD CP, showing similarities to liquid-gas CP dynamics.

Findings

Bulk viscosity and thermal conductivity diverge at QCD CP.

Thermal and viscous diffusion modes slow down (critical slowing down).

Sound mode speeds up (critical speeding up) with negative critical exponent.

Abstract

We work out the basic analysis of dynamics near QCD critical point (CP) by dynamic renormalization group (RG). In addition to the RG analysis by coarse graining, we construct the nonlinear Langevin equation as a basic equation for the critical dynamics. Our construction is based on the generalized Langevin theory and the relativistic hydrodynamics. Applying the dynamic RG to the constructed equation, we derive the RG equation for the transport coefficients and analyze their critical behaviors. We find that the resulting RG equation turns out to be the same as that for the liquid-gas CP except for an insignificant constant. Therefore, the bulk viscosity and the thermal conductivity strongly diverge at the QCD CP. We also show that the thermal and viscous diffusion modes exhibit critical slowing down with the dynamic critical exponents $z_{\rm thermal}\sim 3$ and $z_{\rm viscous}\sim 2$, respectively. In contrast, the sound propagating mode shows critical speeding up with the negative exponent $z_{\rm sound}\sim -0.8$.