Meson mass at real and imaginary chemical potentials

TL;DR

This paper investigates how pi and sigma meson masses depend on real and imaginary chemical potentials using the PNJL model, proposing a method to extract real chemical potential masses from imaginary ones, relevant for lattice QCD.

Contribution

The study analyzes meson mass dependence on chemical potentials with the PNJL model and introduces a new method to extract real chemical potential results from imaginary chemical potential data.

Findings

Meson masses exhibit Roberge-Weiss periodicity at imaginary chemical potential.

A proposed method allows reliable extraction of real chemical potential meson masses from imaginary data.

The approach facilitates future lattice QCD measurements of meson masses at finite chemical potential.

Abstract

The chemical-potential dependence of pi and sigma meson masses is analyzed at both real and imaginary chemical potentials, $\mu_\mathrm{R}$ and $\mu_\mathrm{I}$, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model that possesses both the extended ${\mathbb Z}_3$ symmetry and the chiral symmetry. In the $\mu_\mathrm{I}$ region, the meson masses have the Roberge-Weiss periodicity. Assuming that the meson masses will be measured at finite $\mu_\mathrm{I}$ by lattice QCD in future, we simulate how meson masses at finite $\mu_\mathrm{R}$ are extracted from those at finite $\mu_\mathrm{I}$, and propose a reliable extraction method.