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

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 Padé 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.