Searching for the QCD critical point along the pseudo-critical/freeze-out line using Pad\'e-resummed Taylor expansions of cumulants of conserved charge fluctuations

Abstract

Using high-statistics datasets generated in (2+1)-flavor QCD calculations at finite temperature we construct estimators for the radius of convergence from an eighth order series expansion of the pressure as well as the number density. We show that the estimator for pressure and number density will be identical in the asymptotic limit. In the vicinity of the pseudo-critical temperature, $T_{pc}\simeq 156.5$~MeV, we find the estimator of the radius of convergence to be $\mu_B/T \gtrsim\ 3$ for strangeness-neutral matter. We also present results for the pole structure of the Pad\'e approximants for the pressure at non-zero values of the baryon chemical potential and show that the pole structure of the [4,4] Pad\'e is consistent with not having a critical point at temperatures larger than $135~$MeV and a baryon chemical potential smaller than $\mu_B/T \sim \ 2.5$.