Bounds on R-parity Violating Couplings at the Grand Unification Scale from Neutrino Masses

We consider the embedding of the supersymmetric Standard Model with broken R-parity in the minimal supergravity (mSUGRA) model. We restrict ourselves to the case of broken lepton number, the B3 mSUGRA model. We first study in detail how the tree-level neutrino mass depends on the mSUGRA parameters. We find in particular a strong dependence on the trilinear supersymmetry breaking A-parameter, even in the vicinity of the mSUGRA SPS1a point. We then reinvestigate the bounds on the trilinear R-parity violating couplings at the unification scale from the low-energy neutrino masses including dominant one-loop contributions. These bounds were previously shown to be very strict, as low as O(10^{-6}) for SPS1a. We show that these bounds are significantly weakened when considering the full mSUGRA parameter space. In particular the ratio between the tree-level and 1-loop neutrino masses is reduced such that it may agree with the observed neutrino mass hierarchy. We discuss in detail how and in which parameter regions this effect arises.