A Comparative Analysis between Unbiased Exponential Resummation and Taylor Expansion in Finite-Density QCD with a new phasefactor for Isospin

Abstract: The recently introduced unbiased exponential resummation at finite chemical potential has become an important approach which promises to capture reliably the behaviour of higher order conserved charge cumulants appearing otherwise in the finite-density QCD Taylor series of thermodynamic observables. In this paper, we present a thorough analysis of the estimates of charge cumulants upto eighth order and have compared them using Taylor expansion method and unbiased exponential resummation approach for baryon and isospin chemical potentials. We also subsequently compare the different estimates of the radius of convergence obtained using these two methods and check if the zeros of phasefactor for baryochemical potential can indicate something about these estimated values. We propose a new method of finding a non-trivial phasefactor for isospin chemical potential and we attempt explaining the different estimates of radius of convergence from the zeroes of this newly constructed gauge-ensemble average phasefactor for isospin chemical potential. Lastly, we also illustrate kurtosis plots describing the behaviour of overlap problem in isospin chemical potential and check if it maintains consistency with the appearance of zeros of the newly proposed phasefactor.