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

Abstract

We study unpolarized cross sections for the endothermic nonresonant reactions: pion pion to rho rho for I=2, KK to K*K* for I=1, KK* to K*K* for I=1, pion K to rho K* for I=3/2, pion K* to rho K* for I=3/2, rho K to rho K* for I=3/2, and pion K* to rho K for I=3/2, which take place in hadronic matter. We provide a potential that is given by perturbative QCD with loop corrections at short distances, becomes a distance-independent and temperature-dependent value at long distances, and has a spin-spin interaction with relativistic modifications. The Schrodinger equation with the potential yields temperature-dependent meson masses and mesonic quark-antiquark relative-motion wave functions. In the first Born approximation with the quark-interchange mechanism, the temperature dependence of the potential, meson masses and wave functions brings about temperature dependence of unpolarized cross sections for the seven nonresonant reactions. Noticeably, rapid changes of pion and K radii cause an increase in peak cross sections while the temperature approaches the critical temperature. Parametrizations of the numerical cross sections are given for their future applications in heavy ion collisions.