Investigation of meson masses for real and imaginary chemical potential using the three-flavor PNJL model

We investigate chemical-potential (μ) and temperature (T) dependence of scalar and pseudo-scalar meson masses for both real and imaginary μ, using the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model with three-flavor quarks. A three-flavor phase diagram is drawn in μ2-T plane where positive (negative) μ2 corresponds to positive (imaginary) μ. A critical surface is plotted as a function of light- and strange-quark current mass and μ2. We show that μ-dependence of the six-quark Kobayashi-Maskawa-'t Hooft (KMT) determinant interaction originated in UA(1) anomaly can be determined from lattice QCD data on η′ meson mass around μ=0 and μ=iπT/3 with T slightly above the critical temperature at μ=0 where the chiral symmetry is restored at μ=0 but broken at μ=iπT/3, if it is measured in future.