Apparent convergence of Pad\'e approximants for the crossover line in finite density QCD

TL;DR

This paper introduces a Bayesian approach using Padé approximants to analytically continue finite density QCD observables from imaginary to real chemical potential, showing convergence and providing extrapolations up to 600 MeV.

Contribution

The paper develops a novel Bayesian method combining different Padé approximants for analytic continuation in finite density QCD, excluding spurious poles, and demonstrates convergence with lattice data.

Findings

Observed convergence of Padé sequences with increasing order.

Performed extrapolation of QCD observables up to 600 MeV.

Joint analysis of lattice data from different collaborations.

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 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 $\mu_B^I$ 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.