γν→γγν and crossed processes at energies below mw -: art. no. 013005

The cross sections for the processes gamma upsilon --> gamma gamma upsilon, gamma gamma --> gamma upsilon<(upsilon)over bar> and upsilon<(upsilon)over bar> --> gamma gamma gamma are calculated for a range of center of mass energies from below m(e) to considerably above m(e), but much less than m(W). This enables us to treat the neutrino-electron coupling as a four-Fermi interaction and results in amplitudes which an electron box diagrams with three real photons and one virtual photon at their vertices. These calculations extend our previous low-energy effective interaction results to higher energies and enable us to determine where the effective theory is reliable.