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Investigation of meson masses for real and imaginary chemical potential

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 $U_\mathrm{A}(1)$ anomaly can be determined from lattice QCD data on $η'$ meson mass around $μ=0$ and $μ= i πT/3$ with $T$ slightly above the critical temperature at $μ=0$ where the chiral symmetry is restored at $μ=0$ but broken at $μ=i πT/3$, if it is measured in future.