
The simplest unified extension of the minimal supersymmetric standard model with bilinear Rparity violation naturally predicts a hierarchical neutrino mass spectrum, in which one neutrino acquires mass by mixing with neutralinos, while the other two get mass radiatively. We have performed a full oneloop calculation of the neutralinoneutrino mass matrix in the bilinear Rp minimal supersymmetric standard model, taking special care to achieve a manifestly gauge invariant calculation. Moreover we have performed the renormalization of the heaviest neutrino, needed in order to get meaningful results. The atmospheric mass scale and maximal mixing angle arise from treelevel physics, while solar neutrino scale and oscillations follow from calculable oneloop corrections. If universal supergravity assumptions are made on the softsupersymmetry breaking terms then the atmospheric scale is calculable as a function of a single Rp violating parameter by the renormalization group evolution due to the nonzero bottom quark Yukawa coupling. The solar neutrino problem must be accounted for by the small mixing angle MikheyevSmirnovWolfenstein (MSW) solution. If these assumptions are relaxed then one can implement large mixing angle solutions. The theory predicts the lightest supersymmetic particle decay to be observable at highenergy colliders, despite the smallness of neutrino masses indicated by experiment. This provides an independent way to test this solution of the atmospheric and solar neutrino anomalies.
