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

## TL;DR

This paper develops a comprehensive equation of state for QCD at finite temperature and chemical potentials for baryon number, electric charge, and strangeness, using lattice QCD data and the HRG model, suitable for heavy-ion collision simulations.

## Contribution

It introduces a new parameterization of BQS correlators and merges lattice QCD results with the HRG model to cover a wide temperature range for QCD matter.

## Key findings

- Provides parameterized BQS correlators as functions of temperature.
- Calculates thermodynamic quantities and compares strangeness neutrality and zero strangeness cases.
- Offers equations of state for use in hydrodynamical simulations at RHIC.

## 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).