Freezing Out Fluctuations in Hydro+ Near the QCD Critical Point

TL;DR

This paper develops a new freeze-out procedure linking critical fluctuations in quark-gluon plasma near the QCD critical point to measurable hadron multiplicity cumulants, incorporating out-of-equilibrium effects and conservation laws.

Contribution

It introduces a novel framework connecting Hydro+ critical fluctuations with hadron observables through an extended freeze-out process including a sigma field and baryon conservation.

Findings

Quantifies critical slowing down effects on fluctuations.

Demonstrates suppression of cumulants due to baryon conservation.

Provides a practical freeze-out procedure for Hydro+ simulations.

Abstract

We introduce a freeze-out procedure to convert the critical fluctuations in a droplet of quark-gluon plasma (QGP) that has, as it expanded and cooled, passed close to a posited critical point on the phase diagram into cumulants of hadron multiplicities that can subsequently be measured. The procedure connects the out-of-equilibrium critical fluctuations described in concert with the hydrodynamic evolution of the droplet of QGP by extended hydrodynamics, known as Hydro+, with the subsequent kinetic description in terms of observable hadrons. We introduce a critical scalar isoscalar field sigma whose fluctuations cause correlations between observed hadrons due to the couplings of the sigma field to the hadrons via their masses. We match the QGP fluctuations obtained by solving the Hydro+ equations describing the evolution of critical fluctuations before freeze-out to the correlations of the sigma field. In turn, these are imprinted onto correlations and fluctuations in the multiplicity of hadrons, most importantly protons, after freeze-out via the generalization of the familiar half-century-old Cooper-Frye freeze-out prescription which we introduce. The proposed framework allows us to study the effects of critical slowing down and the consequent deviation of the observable predictions from equilibrium expectations quantitatively. We also quantify the suppression of cumulants due to conservation of baryon number. We demonstrate the procedure in practice by freezing out a Hydro+ simulation in an azimuthally symmetric and boost invariant background that includes radial flow discussed in arXiv:1908.08539.