Role of slow, out-of-equilibrium modes on the dynamic structure factor near the QCD critical point

TL;DR

This study investigates how slow out-of-equilibrium modes influence the dynamic structure factor near the QCD critical point, revealing asymmetric Lorentzian peaks and reduced peak widths, which relate to critical slowing down.

Contribution

It introduces a framework for including OEM in hydrodynamics near the QCD critical point and analyzes their effects on the dynamic structure factor.

Findings

Presence of OEM causes four asymmetric Lorentzian peaks in Snn.

OEM reduces the width of the peaks, indicating slower decay of fluctuations.

OEM effects are negligible in first-order relativistic hydrodynamics.

Abstract

The role of slow out of equilibrium modes (OEM), introduced to extend the validity of hydrodynamics near the QCD critical point on the power spectrum of dynamical density fluctuations has been studied. We have used the equation of motion of slow modes for the situation when the extensive nature of thermodynamics is not altered due to the introduction of OEM. We find that the extensivity condition puts an extra constraint on the coupling of OEM with the four divergence of velocity. The dynamic structure factor (Snn) in presence of the OEM shows four Lorentzian peaks asymmetrically positioned about $\omega (\text{frequency})=0$, whereas the dynamic structure factor without the presence of any OEM shows three well-known Lorentzian peaks. The width of the peaks are reduced in presence of OEM. We find that the asymmetric peaks originate due to the coupling of the out-of-equilibrium modes with the hydrodynamic modes. It is also shown that the OEM has negligible effects on Snn if first order hydrodynamics (relativistic Navier-Stokes) is used. The introduction of OEM reduces the width of the Rayleigh peak indicating the reduction in the decay rate of the fluctuation which leads to slowing down, a well-known characteristics of the critical end point (CEP).