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.