Properties of 2+1 -flavor QCD in the imaginary chemical potential region: A model approach

We study properties of 2+1-flavor QCD in the imaginary chemical potential region by using two approaches. One is a theoretical approach based on the QCD partition function, and the other is a qualitative one based on the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model. In the theoretical approach, we clarify conditions imposed on the imaginary chemical potentials μf=iθfT to realize the Roberge-Weiss (RW) periodicity. Here, T is the temperature, the index f denotes the flavor, and θf are dimensionless chemical potentials. We also show that the RW periodicity is broken if any one of θf is fixed to a constant value. In order to visualize the condition, we use the PNJL model as a model possessing the RW periodicity and draw the phase diagram as a function of θu=θd≡θl for two conditions of θs=θl and θs=0. We also consider two cases, (μu,μd,μs)=(iθuT,iC1T,0) and (μu,μd,μs)=(iC2T,iC2T,iθsT) here, C1 and C2 are dimensionless constants, whereas θu and θs are treated as variables. For some choice of C1 (C2), the number density of the up (strange) quark becomes smooth in the entire region of θu (θs) even in the high T region. This property may be important for lattice QCD simulations in the imaginary chemical potential region, since it makes the analytic continuation more feasible.