Investigation of meson masses for real and imaginary chemical potential

TL;DR

This paper explores how scalar and pseudo-scalar meson masses depend on real and imaginary chemical potentials using the PNJL model, providing insights into phase diagrams and anomaly effects relevant for lattice QCD.

Contribution

It introduces a detailed phase diagram in the $\mu^2$-$T$ plane and links meson mass behavior to lattice QCD data on the $\eta'$ meson, highlighting the $\mu$-dependence of the KMT interaction.

Findings

Phase diagram in $\mu^2$-$T$ plane with positive and negative $\mu^2$ regions.

$\mu$-dependence of the KMT interaction can be inferred from lattice QCD data.

Chiral symmetry restoration at $\mu=0$ and breaking at imaginary $\mu$ near the critical temperature.

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 $\eta'$ 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.