Radiative decay of the lightest neutralino in an R-parity violating supersymmetric theory

In an R-parity violating supersymmetric scenario, the lightest neutralino $\tilde \chi^0_1$ is no longer a stable particle. We calculate the branching ratio for the decay mode $\tilde \chi^0_1 \longrightarrow \nu \gamma$ which occurs at the one-loop level. Taking into account bilinear as well as trilinear lepton number violating interactions as the sources of R-parity violation, we make a detailed scan of the parameter space, both with and without gaugino mass unification and including the constraints on the neutrino sector from the recent Superkamiokande results. This study enables one to suggest interesting experimental signals distinguishing between the two types of R-parity breaking, and also to ascertain whether such radiative decays can give rise to collider signals of the type $\gamma \gamma$ + $\not {\rm E}$ from pair-produced neutralinos.