Dynamical Density Fluctuations around QCD Critical Point Based on Dissipative Relativistic Fluid Dynamics : Possible Fate of Mach Cone at the Critical Point(Nuclear Physics)

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 that 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 speculate on the possible fate of a Mach cone in the vicinity of the QCD CP as an indicator of the existence of the CP on the basis of the above findings. Secondly, we clarify that there are no problems in using the so-called first-order relativistic fluid dynamic equations to describe fluid dynamic phenomena with long wavelengths in general, contrary to the naive understanding, whereas even the Israel-Stewart equation, a popular second-order equation, may not describe the hydrodynamic modes in general depending on the value of relaxation time.