Determination of Lee-Yang edge singularities in QCD by rational approximations

TL;DR

This study investigates Lee-Yang edge singularities in QCD with physical quark masses using lattice simulations and rational approximations, revealing their scaling behavior and estimating the Roberge-Weiss temperature.

Contribution

The paper introduces a refined method to locate Lee-Yang edge singularities in QCD using Padé approximants on improved lattice data, advancing understanding of phase transition structures.

Findings

Singularities scale with the 3D Z(2) universality class near the RW transition.

Estimated the Roberge-Weiss temperature in the continuum limit.

Preliminary results suggest singularities near the chiral phase transition.

Abstract

We report updated results on the determination of Lee-Yang edge (LYE) singularities in $N_f = 2+1$ QCD using highly improved staggered quarks (HISQ) with physical masses on $N_\tau = 4, 6, 8$ lattices. The singularity structure of QCD in the complex $\mu_B$ plane is probed using conserved charges calculated at imaginary $\mu_B$. The location of the singularities is determined by studying the (uncancelled) poles of multi-point Pad\'e approximants. We show that close to the Roberge-Weiss (RW) transition, the location of the LYE singularities scales according to the $3$-$d$ $Z(2)$ universality class. By combining the new $N_\tau = 6$ data with the $N_\tau = 4$ data from our previous analysis we extract a rough estimate for the RW temperature in the continuum limit. We also discuss some preliminary results for the singularities close to the chiral phase transition obtained from simulations on $N_\tau = 6, 8$ lattices.