Meson mass at real and imaginary chemical potentials

The chemical-potential dependence of pi and sigma meson masses is analyzed at both real and imaginary chemical potentials, $\mu_\mathrm{R}$ and $\mu_\mathrm{I}$, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model that possesses both the extended ${\mathbb Z}_3$ symmetry and the chiral symmetry. In the $\mu_\mathrm{I}$ region, the meson masses have the Roberge-Weiss periodicity. Assuming that the meson masses will be measured at finite $\mu_\mathrm{I}$ by lattice QCD in future, we simulate how meson masses at finite $\mu_\mathrm{R}$ are extracted from those at finite $\mu_\mathrm{I}$, and propose a reliable extraction method.