# The QCD Equation of state and critical end-point estimates at $\mathcal O(\mu_B^6)$

## TL;DR

This paper computes the QCD Equation of State at finite chemical potentials using a sixth-order Taylor expansion, providing insights into the critical end-point and freeze-out conditions relevant for heavy-ion collision modeling.

## Contribution

It introduces a sixth-order Taylor expansion approach with HISQ discretization to estimate the QCD phase diagram and critical end-point constraints.

## Key findings

- Calculated pressure along freeze-out lines at various chemical potentials.
- Estimated the radius of convergence of the Taylor series.
- Provided constraints on the critical end-point location.

## Abstract

We present results for the QCD Equation of State at non-zero chemical potentials corresponding to the conserved charges in QCD using Taylor expansion upto sixth order in the baryon number, electric charge and strangeness chemical potentials. The latter two are constrained by the strangeness neutrality and a fixed electric charge to baryon number ratio. In our calculations, we use the Highly Improved Staggered Quarks (HISQ) discretization scheme at physical quark masses and at different values of the lattice spacings to control lattice cut-off effects. Furthermore we calculate the pressure along lines of constant energy density, which serve as proxies for the freeze-out conditions and discuss their dependence on $\mu_B$ , which is necessary for hydrodynamic modelling near freezeout. We also provide an estimate of the radius of convergence of the Taylor series from the 6th order coefficients which provides a new constraint on the location of the critical end-point in the T-$\mu_B$ plane of the QCD phase diagram.