Susceptibilities and the critical band of crossover region in the QCD phase diagram

Abstract

The quark condensate and quark number density are commonly used to determine the QCD phase transition. However, the usually defined quark condensate is divergent in the case of non-chiral limit, and the quark number density suffers from the superficial divergence in numerical calculation. In order to address these issues, we redefine the quark condensate at finite temperature and density and propose a technique to deal with the divergence of the quark condensate and the superficial divergence of the quark number density in numerical calculations. Based on these improvements, we further discuss various susceptibilities as criteria to determine the critical points in the phase transition. It is found that different susceptibilities give different locations of the critical points in the crossover region, which suggests us to define a critical band, instead of some exclusive line in the phase diagram.