Extrapolation for meson screening masses from imaginary to real chemical potential

TL;DR

This paper explores the use of imaginary chemical potential to extrapolate meson screening masses to real chemical potential, proposing a new method and validating its effectiveness within the EPNJL model.

Contribution

It extends meson screening mass calculations to finite chemical potential and introduces a novel extrapolation technique from imaginary to real chemical potential.

Findings

The imaginary-$mbda$ approach can reliably estimate screening masses at real chemical potential.

A new extrapolation method improves the accuracy of meson mass predictions.

The proposed method is validated within the EPNJL model for 2-flavor systems.

Abstract

We first extend our formulation for the calculation of $\pi$- and $\sigma$-meson screening masses to the case of finite chemical potential $\mu$. We then consider the imaginary-$\mu$ approach, which is an extrapolation method from imaginary chemical potential ($\mu=i \mu_{\rm I}$) to real one ($\mu=\mu_{\rm R}$). The feasibility of the method is discussed based on the entanglement Polyakov-loop extended Nambu--Jona-Lasinio (EPNJL) model in 2-flavor system. As an example, we investigate how reliable the imaginary-$\mu$ approach is for $\pi$- and $\sigma$-meson screening masses, comparing "screening masses at $\mu_{\rm R}$ in the method" with "those calculated directly at $\mu_{\rm R}$". We finally propose the new extrapolation method and confirm its efficiency.