Temperature dependence of the cross sections for Meson-Meson nonresonant reactions in hadronic matter

We study the unpolarized cross sections for the endothermic nonresonant reactions, ππ → ρρ for I = 2, KK → K*K* for I = 1, KK* → K*K* for I = 1, πK → ρK* for I = 3/2, πK* → ρK* for I = 3/2, ρK → ρK* for I = 3/2, and πK* → ρK for I = 3/2, which take place in hadronic matter. We obtain the temperature-dependent meson masses from the Schrodinger equation with the potential that is given by perturbative quantum chromodynamics (QCD) with loop corrections at short distances, that becomes a distance-independent and temperature-dependent potential at long distances, and that has a spin-spin interaction with relativistic modifications. In the first Born approximation with the quark-interchange mechanism, the temperature dependences of the potential, the meson masses, and the mesonic quark-antiquark wave functions bring about a temperature dependence of the unpolarized cross sections for the seven nonresonant reactions. Noticeably, rapid changes in the π and K radii cause a rapid increase in peak cross sections, except for the πK* → ρK cross section, as the temperature approaches a critical temperature. Compared to in-vacuum cross sections, the medium modifications of the cross sections are remarkable.