Dynamical Density Fluctuations around QCD Critical Point Based on Dissipative Relativistic Fluid Dynamics-possible fate of Mach cone at the critical point-

TL;DR

This paper investigates the behavior of density fluctuations near the QCD critical point using dissipative relativistic fluid dynamics, revealing the softening of thermal modes and speculating on observable signals like Mach cones.

Contribution

It demonstrates the attenuation of sound modes and the emergence of thermal modes as soft modes at the QCD critical point, and discusses the applicability of relativistic fluid dynamic equations.

Findings

Thermal mode becomes the soft mode at the QCD critical point.

Sound mode is attenuated near the critical point.

First-order relativistic fluid equations are generally valid for long wavelengths.

Abstract

The purpose of this paper is twofold. Firstly, we study the dynamical density fluctuations around the critical point(CP) of Quantum Chromodynamics(QCD) using dissipative relativistic fluid dynamics in which the coupling of the density fluctuations to those of other conserved quantities is taken into account. We show that the sound mode which is directly coupled to the mechanical density fluctuation is attenuated and in turn the thermal mode becomes the genuine soft mode at the QCD CP. We give a speculation on the possible fate of a Mach cone in the vicinity of the QCD CP as a signal of the existence of the CP on the basis of the above findings. Secondly, we clarify that the so called first-order relativistic fluid dynamic equations have generically no problem to describe fluid dynamic phenomena with long wave lengths contrary to a naive suspect whereas even Israel-Stewart equation, a popular second-order equation, may not describe the hydrodynamic mode in general depending on the value of the relaxation time.