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

Abstract

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, $({\mu }_u,{\mu }_d,{\mu }_s)=(i{\theta }_{u}T,i{C}_{1}T,0)$ and $({\mu }_u,{\mu }_d,{\mu }_s)=(i{C}_{2}T,i{C}_{2}T,i{\theta }_{s}T)$; 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.

Comments: 9 pages, 8 figures