Equation of state for QCD with a critical point from the 3D Ising model

One of the major investigations in heavy ion physics concerns the search for the Quantum Chromodynamics (QCD) critical point, which has stimulated tremendous effort from both theory and experiment. A major role in the theoretical analysis of experimental results is played by hydrodynamical simulations of heavy ion collisions, which need as an input an equation of state (EoS) driving the evolution of the system.

Current knowledge of the finite-density QCD equation of state from first principles is limited to a Taylor expansion in the chemical potential. By means of a scaling form for the EoS in the vicinity of the critical point, and a non-universal map to QCD coordinates, we construct a family of equations of state matching state of the art first principle Lattice QCD calculations and including the correct critical behavior, which is the same as the 3D Ising model. This EoS can be readily employed in hydrodynamical simulations of heavy ion collisions at finite density, covering most of the Beam Energy Scan (BES) range at the Relativistic Heavy Ion Collider (RHIC). The impact on observable quantities related to critical behavior is studied.

This contribution reports on work done within the Fluctuations/Equation of State working group of the BEST Collaboration.