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.
Highlights
The search for a possible QCD critical point is receiving increasing attention, which will culminate in the second Beam Energy Scan (BES-II) at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory
The recipe to cure this problem is to make use of the fact that one can reasonably expect the system to find itself in a hadron gas state in that region of the phase diagram and find a way to smoothly merge the pressure coming from the procedure we developed so far with the one from the HRG model
We presented a procedure to construct a family of model equations of state for QCD, each of which features a critical point in the 3D Ising model universality class
Summary
The search for a possible QCD critical point is receiving increasing attention, which will culminate in the second Beam Energy Scan (BES-II) at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory. The main goal of the BES-II program is to discover a critical point, or constrain its location, on the phase diagram of strongly interacting matter. One of the central questions that these experiments aim to answer is whether the continuous crossover [1] between quark-gluon plasma and hadronic matter that occurs as a function of decreasing T at μB = 0 turns into a first-order phase transition above some critical point at a nonzero μB, corresponding to heavy ion collisions below some collision energy [2,3]
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