Neutrino anomalies in a gauge mediated model with trilinear $R$ violation

The structure of neutrino masses and mixing resulting from trilinear R violating interactions is studied in the presence of gauge mediated supersymmetry breaking. Neutrino masses arise in this model at the tree level through the renormalization-group-induced vacuum expectation values of the sneutrinos and also through direct contribution at one loop. The relative importance of these contributions is determined by the values of the strong- and weak-coupling constants. In the case of purely ${\lambda }^{\prime }$ couplings, the tree contribution dominates over the one-loop diagram. In this case, one simultaneously obtains atmospheric neutrino oscillations and quasivacuum oscillations of the solar neutrinos if all the ${\lambda }^{\prime }$ couplings are assumed to be of similar magnitudes. If R parity violation arises from the trilinear λ couplings, then the loop-induced contribution dominates over the tree level. One cannot simultaneously explain the solar and atmospheric deficit in this case if all the λ couplings are of similar magnitude. This, however, becomes possible with hierarchical λ and we give a specific example of this.