Can LSND be included in a three-neutrino framework?

We constrain the neutrino mass matrix considering the following sets of experimental input. (a) Neutrino oscillations in a three-generation scenario, which includes the LSND, the super-Kamiokande and the solar neutrino experiments. (b) The CHARM II constraint on the vector interaction of neutrinos. In this way one is able to construct the neutrino mass matrix, up to a mass scale and the Majorana neutrino CP eigenvalues. The latter are, of course, constrained by the CHARM II results. From a theoretical point of view the neutrino mass matrix is constructed in the context of the R-p-MSSM model with no need to introduce the right-handed neutrino. Since the data are not sufficient to completely determine the required theoretical parameters entering the R-p-MSSM superpotential, we imposed constraints on the cubic couplings employing an additional U(1)(x) flavour symmetry. This procedure, which has been very successful in the study of the Yukawa couplings, reduces the number of required parameters to just five, which can be fixed by the data. Some phenomenological implications of our model are then examined. We find, in particular, that including the LSND result in a three-family mixing scheme leads to an averaged Majorana neutrino mass of /<m >/ similar or equal to 0.2 eV, while excluding the LSND result leads to /<m >/ < 0.06 eV. These predictions can be tested by the next generation of neutrinoless double-beta-decay experiments.