Neutrino Masses in R Parity Violating Supersymmetry

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We discuss a model for neutrino masses and mixings based on R parity violating Yukawa couplings. The model requires no right-handed neutrinos. It accommodates the SuperKamiokande data on atmospheric neutrinos and successfully relates this data to the mass difference for solar neutrinos in the small-angle MSW solution. We obtain an unexpected testable pattern for the three neutrino flavors.
9 pages LaTeX includes one postscript figure

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