Critical point in finite density lattice QCD by canonical approach

We propose a method to find the QCD critical point at finite density calculating the canonical partition function ZC(T, N) by Monte-Carlo simulations of lattice QCD, and analyze data obtained by a simulation with two-flavor p4-improved staggered quarks with pion mass mπ ≈ 770MeV. It is found that the shape of an effective potential changes gradually as the temperature decreases and a first order phase transition appears in the low temperature and high density region. This result strongly suggests the existence of the critical point in the (T, μq) phase diagram. 1. First order phase transition and canonical partition function The critical point terminating a first order phase transition line in the phase diagram of QCD at high temperature and density is one of the most characteristic features that may be discovered in heavy-ion collision experiments. To understand the phase structure, first principle calculations of QCD by numerical simulations are very important. One of the interesting approaches to find a first order phase transition is to construct the canonical partition function ZC(T, N) by fixing the total quark number (N) or quark number density (ρ). From the canonical partition function, one can estimate the quark number giving the largest contribution to the grand partition function ZGC(T, μq). Because two different states coexist at a first order transition point, two different quark numbers give equally large contributions simultaneously if the transition is of first order. The canonical partition function is defined by a fugacity expansion of ZGC(T, μq), ZGC(T, μq) = ∫