Meson mass at real and imaginary chemical potentials

Abstract

Chemical-potential dependence of pi and sigma meson masses is analyzed at both real and imaginary chemical potentials, ${\ensuremath{\mu}}_{\mathrm{R}}$ and ${\ensuremath{\mu}}_{\mathrm{I}}$, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model that possesses both the extended ${\mathbb{Z}}_{3}$ symmetry and chiral symmetry. In the ${\ensuremath{\mu}}_{\mathrm{I}}$ region, the meson masses have the Roberge-Weiss periodicity. The ${\ensuremath{\mu}}_{\mathrm{I}}$ dependence of the meson masses becomes stronger as temperature increases. We argue that meson masses and physical quantities in the ${\ensuremath{\mu}}_{\mathrm{R}}$ region will be determined from lattice QCD data on meson masses in the ${\ensuremath{\mu}}_{\mathrm{I}}$ region by using the PNJL model, if the data are measured in the future.