Neutrino oscillations in supersymmetry without lepton number conservation andRparity

Abstract

With the on-shell renormalization scheme, we discuss neutrino masses up to the one-loop approximation in the supersymmetry without lepton number conservation and R parity. It is shown that in this model with experimentally allowed parameters, $\ensuremath{\Delta}{m}_{32}^{2},$ $\ensuremath{\Delta}{m}_{12}^{2},$ and the mixing angles $|\mathrm{sin}\ensuremath{\theta}23|,$$|\mathrm{sin}{\ensuremath{\theta}}_{12}|$ which are consistent with the present observation values can be produced. We find that a small neutrino mass (\ensuremath{\leqslant}1 eV) sets a loose constraint on the R-parity violation parameters in the soft breaking terms.