Characteristic momentum of Hydro+ and a bound on the speed of sound near the QCD critical point

TL;DR

This paper analyzes the characteristic momentum scale in Hydro+ near the QCD critical point, establishing a bound on the speed of sound and elucidating the limitations of hydrodynamics in this regime.

Contribution

It introduces a spectral analysis of Hydro+ modes to identify the momentum scale where hydrodynamics breaks down near the QCD critical point.

Findings

Identification of a characteristic momentum set by spectral branch points

Derivation of an upper bound on the speed of sound near the critical point

Insight into the limitations of hydrodynamics at high momenta

Abstract

Near the critical point in the QCD phase diagram, hydrodynamics breaks down at a momentum where the frequency of the fastest hydrodynamic mode becomes comparable with the decay rate of the slowest non-hydrodynamic mode. Hydro+ was developed as a framework which extends the range of validity of hydrodynamics beyond that momentum value. This was achieved through coupling the hydrodynamic modes to the slowest non-hydrodynamic mode. In this work, analyzing the spectrum of linear perturbations in Hydro+, we find that a slow mode falls out of equilibrium if its momentum is greater than a characteristic momentum value. That characteristic momentum turns out to be set by the branch points of the dispersion relations. These branch points occur at the critical momenta of so-called spectral curves and are related to the radius of convergence of the derivative expansion. The existence of such a characteristic momentum scale suggests that a particular class of slow modes has no remarkable effect on the flow of the plasma. Based on these results and previously derived relations to the stiffness of the equation of state, we find a temperature-dependent upper bound for the speed of sound near the critical point in the QCD phase diagram.