Meson mass at real and imaginary chemical potentials

Abstract

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.

Comments: 8 pages, 6 figures, typo corrected, some discussions clarified, version accepted for publication in Phys. Rev. D