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We attempt to reconcile large trilinear R-parity violating interactions in asupersymmetric (SUSY) theory with the observed pattern of neutrino masses andmixing. We show that, with a restricted number of such interaction terms withthe $\lambda'$-type couplings in the range (0.1-1.0), it is possible to forbidone-loop contributions to the neutrino mass matrix. This is illustrated withthe help of a `working example' where an econnomic choice of SUSY parameters ismade, with three non-vanishing and `large' R-parity violating terms in thesuperpotential. The two-loop contributions in such a case can not only generatethe masses in the requisite order but can also lead us to specific allowedregions of the parameter space.

Two-loop neutrino masses with large R-parity violating interactions in supersymmetry