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

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 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 $mu_{f}=itheta_{f}T$ to realize the Roberge-Weiss (RW) periodicity. We also show that the RW periodicity is broken if anyone of $theta_{f}$ 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 $theta_{u}=theta_{d}equiv theta_{l}$ for two conditions of $theta_{s}=theta_{l}$ and $theta_{s}=0$. We also consider two cases, $(mu_{u},mu_{d},mu_{s}) =(itheta_{u}T,iC_{1}T,0)$ and $(mu_{u},mu_{d},mu_{s})=(iC_{2}T,iC_{2}T,itheta_{s}T)$; here $C_{1}$ and $C_{2}$ are dimensionless constants, whereas $theta_{u}$ and $theta_{s}$ are treated as variables. For some choice of $C_{1}$ ($C_{2}$), the number density of up (strange) quark becomes smooth in the entire region of $theta_{u}$ ($theta_{s}$) even in high $T$ region.