A model study of quark-number susceptibility at finite chemical potential and temperature

In this Letter, we try to give a direct method for calculating the quark-number susceptibility (QNS) at finite chemical potential and temperature. In our approach the QNS is given by a formula which solely involves G [ μ , T ] (p→ ,ω_n) (the dressed quark propagator at finite chemical potential μ and temperature T). From this the QNS at finite chemical potential and temperature is calculated in the framework of rainbow-ladder approximation of the Dyson-Schwinger approach using the meromorphic quark propagator proposed in [M.S. Bhagwat, M.A. Pichowsky, P.C. Tandy, Phys. Rev. D 67 (2003) 054019]. It is found that the QNS χ (μ , T) has a singularity when μ comes close to a critical value μ₀, and the susceptibility as a function of T becomes discontinuous at some values of T when μ is near μ₀. At high temperature the QNS approaches the ideal quark gas result, while at very small temperature (T < 40 MeV) the susceptibility equals zero. For all values of μ we studied, the susceptibility shows a rapid increase near T = 120- 140 MeV, which could be regarded as the signal of a crossover.