Model prediction for temperature dependence of meson pole masses from lattice QCD results on meson screening masses

We propose a practical effective model by introducing temperature ($T$) dependence to the coupling strengths of four-quark and six-quark Kobayashi-Maskawa-'t Hooft interactions in the 2+1 flavor Polyakov-loop extended Nambu-Jona-Lasinio model. The $T$ dependence is determined from LQCD data on the renormalized chiral condensate around the pseudocritical temperature $T_c^{\chi}$ of chiral crossover and the screening-mass difference between $\pi$ and $a_0$ mesons in $T > 1.1T_c^\chi$ where only the $U(1)_{\rm A}$-symmetry breaking survives. The model well reproduces LQCD data on screening masses $M_{\xi}^{\rm scr}(T)$ for both scalar and pseudoscalar mesons, particularly in $T \ge T_c^{\chi}$. Using this effective model, we predict meson pole masses $M_{\xi}^{\rm pole}(T)$ for scalar and pseudoscalar mesons. For $\eta'$ meson, the prediction is consistent with the experimental value at finite $T$ measured in heavy-ion collisions. We point out that the relation $M_{\xi}^{\rm scr}(T)-M_{\xi}^{\rm pole}(T) \approx M_{\xi'}^{\rm scr}(T)-M_{\xi'}^{\rm pole}(T)$ is pretty good when $\xi$ and $\xi'$ are scalar mesons, and show that the relation $M_{\xi}^{\rm scr}(T)/M_{\xi'}^{\rm scr}(T) \approx M_{\xi}^{\rm pole}(T)/M_{\xi'}^{\rm pole}(T)$ is well satisfied within 20% error when $\xi$ and $\xi'$ are pseudoscalar mesons and also when $\xi$ and $\xi'$ are scalar mesons.