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

Abstract 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 μ 2 – T plane where positive (negative) μ 2 corresponds to positive (imaginary) μ. A critical surface is plotted as a function of light- and strange-quark current mass and μ 2 . We show that μ-dependence of the six-quark Kobayashi–Maskawa–'t Hooft (KMT) determinant interaction originated in U A ( 1 ) anomaly can be determined from lattice QCD data on η ′ meson mass around μ = 0 and μ = i π T / 3 with T slightly above the critical temperature at μ = 0 where the chiral symmetry is restored at μ = 0 but broken at μ = i π T / 3 , if it is measured in future.