QCD equation of state matched to lattice data and exhibiting a critical point singularity

TL;DR

This paper develops a family of QCD equations of state that match lattice data, include a critical point in the 3D Ising universality class, and can be used in hydrodynamic models to search for the QCD critical point in heavy ion collisions.

Contribution

It introduces a parametrized family of QCD equations of state with a critical point consistent with lattice results and applicable to RHIC energy ranges.

Findings

Equations of state match lattice QCD results up to d7^4

Critical point placed within RHIC scan range

Divergence of baryon number cumulant at critical point

Abstract

We construct a family of equations of state for QCD in the temperature range 30 MeV $\leq T\leq$ 800 MeV and in the chemical potential range $0\leq \mu_B \leq$ 450 MeV. These equations of state match available lattice QCD results up to $\mathcal{O}(\mu_B^4)$ and in each of them we place a critical point in the 3D Ising model universality class. The position of this critical point can be chosen in the range of chemical potentials covered by the second Beam Energy Scan at RHIC. We discuss possible choices for the free parameters, which arise from mapping the Ising model onto QCD. Our results for the pressure, entropy density, baryon density, energy density and speed of sound can be used as inputs in the hydrodynamical simulations of the fireball created in heavy ion collisions. We also show our result for the second cumulant of the baryon number in thermal equilibrium, displaying its divergence at the critical point. In the future, comparisons between RHIC data and the output of the hydrodynamic simulations, including calculations of fluctuation observables, built upon the model equations of state that we have constructed may be used to locate the critical point in the QCD phase diagram, if there is one to be found.