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

Attila Pásztor,Gergely Markó,Zsolt Szép

doi:10.1103/physrevd.103.034511

Attila Pásztor, Gergely Markó + Show 1 more

Open Access

https://doi.org/10.1103/physrevd.103.034511

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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.

Highlights

Despite considerable effort invested so far, the phase diagram of QCD in the temperature(T)-baryon chemical potential(μB) plane still awaits determination from first principles
These results come either from the evaluation of Taylor coefficients with lattice simulations performed at μB 1⁄4 0 or via simulations performed at imaginary μB, where the sign problem is absent, with the Taylor coefficients obtained from a subsequent fit
We show that the Padeapproximant knows nothing about the location of the tricritical point (TCP), as this information is not encoded in TcðμBÞ

Summary

Introduction

Despite considerable effort invested so far, the phase diagram of QCD in the temperature(T)-baryon chemical potential(μB) plane still awaits determination from first principles. Whether the input data are the Taylor coefficients or the values of a function at several values of the imaginary chemical potential, fact is that the numerical analytic continuation needed to extrapolate the crossover to real μB is a mathematically ill-posed problem [4,5]. This means that the analytic continuation of a function

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Conclusion