R-parity violating minimal supergravity model -: art. no. 115002

We present the minimal supersymmetric standard model with general broken R parity, focusing on minimal supergravity (MSUGRA). We discuss the origins of lepton number violation in supersymmetry. We have computed the full set of coupled one-loop renormalization-group equations for the gauge couplings, the superpotential parameters, and for all the soft supersymmetry breaking parameters. We provide analytic formulas for the scalar potential minimization conditions which may be iterated to arbitrary precision. We compute the low-energy spectrum of the superparticles and the neutrinos as a function of the small set of parameters at the unification scale in the general basis. Specializing to MSUGRA, we use the neutrino masses to set new bounds on the R-parity violating couplings. These bounds are up to five orders of magnitude stricter than the previously existing ones. In addition, new bounds on the R-parity violating couplings are also derived demanding a nontachyonic sneutrino spectrum. We investigate the nature of the lightest supersymmetric particle and find extensive regions in parameter space where it is not the neutralino. This leads to a novel set of supersymmetric signatures, which we classify.