Lattice-based equation of state at finite baryon number, electric charge, and strangeness chemical potentials

Abstract

We construct an equation of state for Quantum Chromodynamics (QCD) at finite temperature and chemical potentials for baryon number B, electric charge Q and strangeness S. We use the Taylor expansion method, up to the fourth power for the chemical potentials. This requires the knowledge of all diagonal and non-diagonal BQS correlators up to fourth order: these results recently became available from lattice QCD simulations, albeit only at a finite lattice spacing Nt = 12. We smoothly merge these results to the Hadron Resonance Gas (HRG) model, to be able to reach temperatures as low as 30 MeV; in the high temperature regime, we impose a smooth approach to the Stefan-Boltzmann limit. We provide a parameterization for each one of these BQS correlators as functions of the temperature. We then calculate pressure, energy density, entropy density, baryonic, strangeness, electric charge densities and compare the two cases of strangeness neutrality and µS = µQ = 0. Finally, we calculate the isentropic trajectories and the speed of sound, and compare them in the two cases. Our equation of state can be readily used as an input of hydrodynamical simulations of matter created at the Relativistic Heavy Ion Collider (RHIC).

Equation of state at finite densities for QCD matter in nuclear collisions

“…We construct the equation of state with net baryon (B), electric charge (Q) and strangeness (S ) using the pressure and susceptibilities of lattice QCD simulations and the hadron resonance gas model [2,3]. We then use it in hydrodynamic analyses to demonstrate its effects on the description of particle production.…”

Non-equilibrium cumulants within model A near the QCD critical point

“…In order to quantitatively describe the experimental observed cumulants of net proton multiplicities, more sophisticated and realistic dynamical modeling are required from the theoretical side [56,57]. Besides, a number of effects play their role, including the subject of the proper equation of state [58][59][60], of the unknown parameters of the Ising-to-QCD mapping [61], of the critical transport coefficients [62][63][64][65], of the finite size, finite size scaling and global charge conservation in the vicinity of a CP [66][67][68][69][70], of the non-critical baseline for the cumulants of net-proton number fluctuations [71], and of the nonuniform temperature/chemical potential effects [72]. In addition, further connections between the criticality and the experimental observables have been established through theoretical efforts [73][74][75][76][77][78].…”

Quartic cumulant of baryon number in the presence of QCD critical point

“…In our current study we focused on the equilibrium properties of the QCD equation of state that can lead to the potential discovery of the QCD critical point. However, because heavy-ion collisions are inherently dynamical systems, direct comparison with experimental data would require an event-by-event relativistic viscous hydrodynamics model with BSQ conserved charges [39,40] and critical fluctuations coupled to a hadronic transport code.…”