Investigation of meson masses for real and imaginary chemical potential

Abstract

We investigate chemical-potential ($\mu$) and temperature ($T$) dependence of scalar and pseudo-scalar meson masses for both real and imaginary $\mu$, using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model with three-flavor quarks. A three-flavor phase diagram is drawn in ${\mu }^2$-$T$ plane where positive (negative) ${\mu }^2$ corresponds to positive (imaginary) $\mu$. A critical surface is plotted as a function of light- and strange-quark current mass and ${\mu }^2$. We show that $\mu$-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 ${\eta }^{\prime }$ meson mass around $\mu =0$ and $\mu =i\pi T/3$ with $T$ slightly above the critical temperature at $\mu =0$ where the chiral symmetry is restored at $\mu =0$ but broken at $\mu =i\pi T/3$, if it is measured in future.

Comments: 13 pages, 12 figures