Apparent convergence of Padé approximants for the crossover line in finite density QCD

Abstract

We propose a novel Bayesian method to analytically continue observables to real baryochemical potential ${\mu }_B$ in finite density QCD. Taylor coefficients at ${\mu }_B=0$ and data at imaginary chemical potential ${\mu }_B^I$ are treated on equal footing. We consider two different constructions for the Padé approximants, the classical multipoint Padé approximation and a mixed approximation that is a slight generalization of a recent idea in Padé approximation theory. Approximants with spurious poles are excluded from the analysis. As an application, we perform a joint analysis of the available continuum extrapolated lattice data for both pseudocritical temperature $T_c$ at ${\mu }_B^I$ from the Wuppertal-Budapest Collaboration and Taylor coefficients ${\kappa }_2$ and ${\kappa }_4$ from the HotQCD Collaboration. An apparent convergence of $[p/p]$ and $[p/p+1]$ sequences of rational functions is observed with increasing $p.$ We present our extrapolation up to ${\mu }_B\approx 600$ MeV.

Comments: 10 pages, 4 figures, clarifications and references added, published version