Can LSND be included in a 3-Neutrino framework?

Abstract

We study the special features emerging from a three lepton generation analysis of the available neutrino oscillation data (solar, atmospheric and LSND). First we find that it is possible to explain all three sets of data in terms of the standard left handed neutrinos without the need of sterile neutrinos. Second we find a significant difference in the mass matrix extracted from the data, depending on the analysis (without or with LSND), if the mass of the lightest neutrino, which cannot be determined from the neutrino oscillation data alone, is relatively small, i.e $\leq$0.1 eV. To compare with other processes we used the R-parity violating Minimal Supersymmetric Standard Model (\rp-MSSM) for the theoretical description of the neutrino masses. Using the oscillation data we were able to constrain the parameters of the model. In particular we were able to obtain values for the coupling constants of the \rp-MSSM.