  We study inelastic meson-meson scattering that is governed by quark-antiquark
annihilation and creation involving a quark and an antiquark annihilating into
a gluon, and subsequently the gluon creating another quark-antiquark pair. The
resultant hadronic reactions include for I=1: pion + pion to rho + rho, kaon +
antikaon to kaon* + antikaon*, kaon + antikaon* to kaon* + antikaon*, kaon* +
antikaon to kaon* + antikaon*, as well as pion + pion to kaon + antikaon, pion
+ rho to kaon + antikaon*, pion + rho to kaon* + antikaon, and kaon + antikaon
to rho + rho. In each reaction, one or two Feynman diagrams are involved in the
Born approximation. We derive formulas for the unpolarized cross section, the
transition amplitude, and the transition potential for quark-antiquark
annihilation and creation. The unpolarized cross sections for the reactions are
calculated at six temperatures, and prominent temperature dependence is found.
It is due to differences among mesonic temperature dependence in hadronic
matter.
