Freezing out critical fluctuations

Abstract

We introduce a novel freeze-out procedure connecting the hydrodynamic evolution of a droplet of quark-gluon plasma (QGP) that has, as it expanded and cooled, passed close to a posited critical point on the QCD phase diagram with the subsequent kinetic description in terms of observable hadrons. The procedure converts out-of-equilibrium critical fluctuations described by extended hydrodynamics, known as Hydro+, into cumulants of hadron multiplicities that can be subsequently measured. We introduce a critical sigma field whose fluctuations cause correlations between observed hadrons due to the couplings of the sigma field to the hadrons. We match the QGP fluctuations obtained via 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 fluctuations in the multiplicities of hadrons, most importantly protons, after freeze-out via a generalization of the familiar half-a-century-old Cooper-Frye freeze-out prescription [1] which we introduce [2]. This framework allows us to study the effects of critical slowing down and the consequent deviation of the observable predictions from equilibrium expectations quantitatively. We can also quantify the suppression of cumulants due to conservation of baryon number. We demonstrate the prescription in practice by freezing out the Hydro+ simulation in a simplified azimuthally symmetric and boost invariant background discussed in Ref. [3].

Off-equilibrium non-Gaussian fluctuations near the QCD critical point: an effective field theory perspective

“…For example, the interpretation of t in those equations should be elaborated [18] and might be related to the affine parameter parametrizing the streamline in the background hydrodynamic solution. To make contact with experimental observations, a freezeout prescription for W n s has to be formulated [44] (see also refs. [45,46]).…”

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

“…In this equation, c M is a constant and ξ denotes the equilibrium correlation length. The leading behavior of Q-dependent of Γ Q near the critical point is given by [29] Γ…”

Cumulants of conserved charges in hydrodynamic simulations

“…The fully-consistent way of studying fluctuations with hydrodynamics would be to include them in the hydrodynamic description itself [25][26][27][28]. Hydrodynamic fluctuations are large near a critical point [29][30][31], and have nontrivial effects even in the absence of a critical point [32][33][34][35]. Here, we postulate that fluctuations in heavy-ion collisions originate mostly from the initial state, and we simply neglect hydrodynamic fluctuations.…”