Bounds onR-parity violating couplings at the grand unification scale from neutrino masses

Abstract

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 ${\mathrm{B}}_{3}$ 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 $\mathcal{O}({10}^{\ensuremath{-}6})$ 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 one-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.