Supersymmetric resolution of solar and atmospheric neutrino puzzles

Renormalizable lepton number violating interactions that break $R$ parity can induce a Majorana mass for neutrinos. Based on this, we show that it is possible to obtain a phenomenologically viable neutrino mass matrix that can accommodate atmospheric neutrino data via ${\nu }_{\mu }-{\nu }_{\tau }$ mixing and the solar neutrino data via either the large or small angle MSW effect. We argue that such a mass matrix could result from an approximate discrete symmetry of the superpotential that forbids renormalizable baryon number violating couplings.