Nuclear Physics B40 (1972) 125-140. North-Holland Publishing Company THEORETICAL INVESTIGATION OF THE REACTION 3"Y --' ~rzr AND THE e -+ 7"Y AND f -+ 73' DECAY WIDTHS G. SCHIERHOLZ and K. SUNDERMEYER II. lnstitut fi~r Theoretische Physik der Universitdt, Hamburg, Germany Received 24 November 1971 Abstract: The 73" ~ ~r~r cross section and the e --, "r'r and f ~ "Y3" decay widths are calculated on the basis of partial-wave dispersion relations. The left hand cut integral is approximated by vector meson exchange diagrams. On the right hand cut elastic unitarity is taken into account which establishes a close correspondence between the cross section and the ~r~r phase shifts. The I = 0, J = 2 phase shift is parametrized in terms of the f(1260) and for the corresponding J = 0 phase shift a "down" and an "up" solution (e Breit-Wigner) is considered. The cross section is found to depend sensitively on the form of the ~r~r final state interaction. The obtained e --, "y'yand f ~ "r3"couplings are compared with other estimates. 1. INTRODUCTION The study of the two-photon annihilation process into single hadrons and hadron pairs has become of considerable interest since it was observed that the two-photon exchange mechanism in electron-electron and electron-positron colliding beam reac- tions as indicated in fig. 1 grows to be dominant at high energies [1 ]. This will show up in the future DESY and SLAC storage ring experiments thus providing direct experimental informations on the photon-photon interaction. Fig. 1. Colliding beam production of a neutral C = + hadron state.