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 ${\ensuremath{\mu}}_{B}$ in finite density QCD. Taylor coefficients at ${\ensuremath{\mu}}_{B}=0$ and data at imaginary chemical potential ${\ensuremath{\mu}}_{B}^{I}$ are treated on equal footing. We consider two different constructions for the Pad\'e approximants, the classical multipoint Pad\'e approximation and a mixed approximation that is a slight generalization of a recent idea in Pad\'e 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 ${\ensuremath{\mu}}_{B}^{I}$ from the Wuppertal-Budapest Collaboration and Taylor coefficients ${\ensuremath{\kappa}}_{2}$ and ${\ensuremath{\kappa}}_{4}$ 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 ${\ensuremath{\mu}}_{B}\ensuremath{\approx}600\text{ }\text{ }\mathrm{MeV}$.