The universality of the QCD equation of state near the critical point is expressed by mapping pressure as a function of temperature T and baryon chemical potential µ in QCD to Gibbs free energy as a function of reduced temperature r and magnetic field h in the Ising model. The mapping parameters are, in general, not universal, i.e., determined by details of the microscopic dynamics, rather than by symmetries and long-distance dynamics. In this paper we point out that in the limit of small quark masses, when the critical point is close to the tricritical point, the mapping parameters show universal dependence on the quark mass mq. In particular, the angle between the r = 0 and h = 0 lines in the (µ, T ) plane vanishes as m 2/5 q . We discuss possible phenomenological consequences of these findings.1 These considerations would also apply, mutatis mutandis, to the tricritical point separating the second and first-order transitions as a function of the strange quark mass [5,6], instead of the baryon chemical potential.
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].
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