Rare weak decays and direct lepton number violating signals in a minimalR-parity violating model of neutrino mass

Abstract

Within the framework of an $R$-parity violating minimal supergravity model, at least three relatively large lepton number violating ${\ensuremath{\lambda}}^{\ensuremath{'}}$ type trilinear couplings at the grand unified theory scale, not directly related to neutrino physics, can naturally generate via renormalization group evolution and/or CKM rotation, the highly suppressed bilinear and trilinear parameters at the weak scale required to explain the neutrino oscillation data. The structure of the renormalization group equations and the CKM matrix restrict the choices of the three input couplings to only eight possible combinations, each with its own distinctive experimental signature. The relatively large input couplings may lead to spectacular low-energy signatures like rare weak decays of the $\ensuremath{\tau}$ lepton and $K$ mesons, direct lepton number violating decays of several sparticles, and unconventional decay modes (and reduced lifetime) of the lightest neutralino, assumed to be the lightest supersymmetric particle, all with sizable branching ratios. Several low background signals at the Tevatron and CERN LHC have been suggested and their sizes are estimated to be at the observable level. From the particle content of the signal and the relative rate of different final states the input couplings at the grand unified theory scale, i.e., the origin of neutrino masses and mixing angles, can be identified.