We construct a family of equations of state for QCD in the temperature range $30\mathrm{MeV}\le T\le 800\mathrm{MeV}$ and in the chemical potential range $0\le {\mu }_B\le 450\mathrm{MeV}$. These equations of state match available lattice QCD results up to $O\left({\mu }_B^4\right)$ and in each of them we place a critical point in the three-dimensional (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 the Relativistic Heavy Ion Collider. 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.

• Received 21 December 2018
• Revised 26 November 2019
• Accepted 7 February 2020

DOI:https://doi.org/10.1103/PhysRevC.101.034901

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Published by the American Physical Society