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 $\mu_{f}=i\theta_{f}T$ 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, $(\mu_{u},\mu_{d},\mu_{s}) =(i\theta_{u}T,iC_{1}T,0)$ and $(\mu_{u},\mu_{d},\mu_{s})=(iC_{2}T,iC_{2}T,i\theta_{s}T)$; 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.