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.

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

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• NNLO HTLpt predictions for the curvature of the QCD phase transition line
• New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential
• Overview of the QCD phase diagram -- Recent progress from the lattice
• Exploring Lee-Yang and Fisher Zeros in the 2D Ising model through multipoint Padé approximants
• Contribution to understanding the phase structure of strong interaction matter: Lee-Yang edge singularities from lattice QCD
• A new way of determining the Lattice QCD equation of state at a finite chemical potential
• Corrections to the hadron resonance gas from lattice QCD and their effect on fluctuation-ratios at finite density
• Resummed lattice QCD equation of state at finite baryon density: strangeness neutrality and beyond
• Lee-Yang edge singularities in lattice QCD : A systematic study of singularities in the complex ${\mu }_B$ plane using rational approximations