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

摘要

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 T_c~χ of chiral crossover and the screening-mass difference between π and a_0 mesons in T > 1.1T_c~χ where only the U(1)_(A~-) symmetry breaking survives. The model well reproduces LQCD data on screening masses Ms_ξ~(scr)(T) for both pseudoscalar mesons (ξ = π,K,η,η′) and scalar ones (ξ = a_0,κ ,σ,f_0), particularly in T≥T_c~χ. Using this effective model, we predict meson pole masses M_ξ~(pole)(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 M_ξ~(scr()T) - M_ ξ~(pole)(T) ≈ M_ξ~(scr)(T) - M_ξ~(pole)(T) is pretty good when ξ and ξ′ are the scalar mesons, and show that the relation M_ξ~(scr)(T)/M_ξ~(scr)(T ≈ M_ξ~(pole)(T)/M_ξ~(pole)(T) is well satisfied within 20% error when ξ and ξ0 are the pseudoscalar mesons and also when ξ and ξ′ are the scalar mesons.