The isentropic equation of state of (2+1)-flavor QCD: An update based on high precision Taylor expansion and Pad\'e-resummed expansion at finite chemical potentials

Abstract

The HotQCD Collaboration performed Taylor expansion calculations in 2017 for the pressure, energy density, and entropy density at non-zero chemical potentials up to the $6^{th}$ order. Since then, they have significantly improved the statistics for lattices with temporal extents of $N_\tau=8$ and $12$, and have also included results for $N_\tau=16$ that were not previously available. They have also calculated the $8^{th}$-order expansion coefficients for $N_\tau=8$. These calculations showed that the Taylor series expansion for the pressure is accurate up to $\mu_B / T \leq 2.5$. In this study, we use the high-statistics results on Taylor expansion coefficients, calculated with HISQ fermions and extrapolated to the continuum limit, to determine the QCD equation of state under conditions relevant for hot and dense matter produced in heavy ion collisions. We also calculate the energy density and pressure along lines of constant entropy per net baryon number.