Analysis of meson screening mass at finite temperature and density in the effective model

Meson masses are not only fundamental quantities of hadrons but also a key to know the properties of QCD vacuum and the equation of state. At finite temperature ($T$), we can define two kinds of meson masses, which are so called pole mass ($M_{\rm pole}$) and screening mass ($M_{\rm scr}$). $M_{\rm pole}$ ($M_{\rm scr}$) is defined by the exponential decay of the meson propagator in the temporal (spatial) direction. At finite $T$, in lattice QCD (LQCD) simulation, the calculation of $M_{\rm pole}$ is more difficult than that of $M_{\rm scr}$ because the temporal direction is limited up to $1/T$. Moreover, it is possible to calculate the imaginary chemical potential ($\mu$) dependence of $M_{\rm scr}$ because LQCD simulation is feasible. Therefore, it is important to construct effective model which can describe the $T$ and $\mu$ dependence of $M_{\rm pole}$ and $M_{\rm scr}$ simultaneously. In this study, we calculate $M_{\rm scr}$ at imaginary $\mu$. Then, we discuss how to extrapolate $M_{\rm scr}$ from imaginary to real $\mu$ region. Finally, we predict the $\mu$ dependence of $M_{\rm pole}$ from that of $M_{\rm scr}$.