Searching for the QCD critical endpoint using multi-point Pad\'e approximations

TL;DR

This paper employs multi-point Padé approximations to locate the QCD critical endpoint by analyzing Lee-Yang edge singularities in lattice QCD data, providing estimates for its temperature and chemical potential.

Contribution

It introduces a novel application of multi-point Padé approximations to locate the QCD critical endpoint from lattice QCD data at imaginary chemical potential.

Findings

Estimated critical endpoint at T=105 MeV and μ_B=422 MeV

Identified Lee-Yang edge singularities in lattice QCD data

Provided a slope of the transition line at the critical point

Abstract

Using the multi-point Pad\'e approach, we locate Lee-Yang edge singularities of the QCD pressure in the complex baryon chemical potential plane. These singularities are extracted from singularities in the net baryon-number density calculated in $N_f=2+1$ lattice QCD at physical quark mass and purely imaginary chemical potential. Taking an appropriate scaling ansatz in the vicinity of the conjectured QCD critical endpoint, we extrapolate the singularities on $N_\tau=6$ lattices to pure real baryon chemical potential to estimate the position of the critical endpoint (CEP). We find $T^{\rm CEP}=105^{+8}_{-18}$~ MeV and $\mu_B^{\rm CEP} = 422^{+80}_{-35}$~ MeV, which compares well with recent estimates in the literature. For the slope of the transition line at the critical point we find $-0.16(24)$.