Extrapolation for meson screening masses from imaginary to real chemical potential

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 ($\mu =i{\mu }_{\mathrm{I}}$) to real one ($\mu ={\mu }_{\mathrm{R}}$). 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 ${\mu }_{\mathrm{R}}$ in the method" with "those calculated directly at ${\mu }_{\mathrm{R}}$". We finally propose the new extrapolation method and confirm its efficiency.

Comments: 9 pages, 11 figures