Estimates of Lee-Yang zeros and a possible critical point on the pion condensate boundary in the QCD isospin phase diagram using an unbiased exponential resummation on the lattice

Abstract

Without invoking any cumulant determination at the input level, we present here the first calculations of direct estimates of the Lee-Yang zeros of QCD partition function in (2+1)-flavor QCD. These zeros are obtained in complex isospin chemical potential $\mu_I$ plane using the unbiased exponential resummation formalism on $N_\tau=8$ lattices and with physical quark masses. For different temperatures, we illustrate the stability of the zeros closest to the origin from which, we subsequently procure the radius of convergence estimates. From the temperature-dependence study of the real and imaginary parts of these zeros, we try estimating one of the possible critical points forming the second order pion condensate critical line in the isospin phase diagram. Further, we compare these resummed estimates with the corresponding Mercer-Roberts estimates of the subsequent Taylor series expansions of the first three partition function cumulants. We also outline comparisons between resummed and Taylor series results of these cumulants for real and imaginary values of $\mu_I$ and highlight the behavior of different expansion orders within and beyond the obtained resummed estimates of radius of convergence. We also re-establish that this resummed radius of convergence can efficiently capture the onset of overlap problem for finite real $\mu_I$ simulations.