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 lattice QCD (LQCD) data on the renormalized chiral condensate around the pseudocritical temperature Tcχ of chiral crossover and the screening-mass difference between π and a0 mesons in T>1.1Tcχ where only the U(1)A-symmetry breaking survives. The model well reproduces LQCD data on screening masses Mξscr(T) for both pseudoscalar mesons (ξ=π,K,η,η′) and scalar ones (ξ=a0,κ,σ,f0), particularly in TTcχ. Using this effective model, we predict meson pole masses Mξpole(T) for scalar and pseudoscalar mesons. For η′ meson, the prediction is consistent with the experimental value at finite T measured in heavy-ion collisions. We point out that the relation Mξscr(T)-Mξpole(T)≈Mξ′scr(T)-Mξ′pole(T) is pretty good when ξ and ξ′ are the scalar mesons, and show that the relation Mξscr(T)/Mξ′scr(T)≈Mξpole(T)/Mξ′pole(T) is well satisfied within 20% error when ξ and ξ′ are the pseudoscalar mesons and also when ξ and ξ′ are the scalar mesons.