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

J Noronha-Hostler,J M Stafford,P Parotto,C Ratti

doi:10.1103/physrevc.100.064910

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 $N_t=12$. 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 $\mu_S=\mu_Q=0$. We also calculate the isentropic trajectories 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).

Highlights

Relativistic heavy-ion collisions have successfully recreated the quark gluon plasma (QGP) in the laboratory at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory and the Large Hadron Collider (LHC) at CERN
We constructed an equation of state for quantum chromodynamics (QCD) at finite temperature and B, Q, S chemical potentials, based on a Taylor series up to fourth power in the chemical potentials
Our methodology is based on a smooth merging between the HRG model and lattice QCD results for each one of the Taylor expansion coefficients; for all coefficients except χ2B, the parametrization function is a ratio of up-to-ninth-order polynomials

Summary

Introduction

Relativistic heavy-ion collisions have successfully recreated the quark gluon plasma (QGP) in the laboratory at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory and the Large Hadron Collider (LHC) at CERN. From these Taylor coefficients a variety of lattice QCD-based equations of state have been reconstructed [25,26,27] and later used within relativistic hydrodynamics [25,28,29,30,31].

Results

Conclusion