Reconciling neutrino anomalies in a simple four-neutrino scheme with R-parity violation

We propose a simple extension of the MSSM based on extra compact dimensions which includes an SU(2) x U(1) singlet superfield. The fermion present in this superfield is the sterile neutrino, which combines with one linear com bination of nu (e) - nu (mu) - nu (tau) to form a Dirac pair whose mass acc ounts for the LSND anomaly. Its small mass can be ascribed to a volume supp ression factor associated with extra compact dimensions. On the other hand the sterile neutrino scalar partner can trigger the spontaneous violation o f R-parity, thereby inducing the necessary mass splittings to fit also the solar and atmospheric neutrino data. Thus the model can explain all neutrin o oscillation data. It leads to four predictions for the neutrino oscillati on parameters and implies that the atmospheric neutrino problem must includ e at least some nu (mu) --> nu (S) oscillations, which will be testable in the near future. Moreover, it also predicts that the lightest supersymmetri c particle (LSP) decays visibly via lepton number violating modes, which co uld be searched for at present and future accelerators. (C) 2000 Elsevier S cience B.V. All rights reserved