Constraining an R-parity violating supersymmetric theory from the SuperKamiokande data on atmospheric neutrinos

The constraints on an R-parity violating supersymmetric theory arising from the recent SuperKamiokande results on atmospheric neutrinos are studied, with special reference to a scenario with bilinear R-parity violating terms. Considering both the fermionic and scalar sectors, we find that a large area of the parameter space is allowed, in terms of both the lepton-number violating entries in the superpotential and the soft R-violating terms in the scalar potential, and that no fine-tuning is required. However, the need to avoid flavour changing neutral currents puts additional restrictions on the theory, requiring either the R-violating terms in the superpotential to be smaller than the R-conserving ones, or a hierarchy in the R-violating parameters for different lepton flavours in the superpotential.