  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.

High Energy Physics - Phenomenology;High Energy Physics - Lattice;High Energy Physics - Theory;Nuclear Theory