Neutrino Masses and Mixing in Supersymmetric Models without $R$ Parity

Abstract

We study neutrino masses and mixing in Supersymmetric Models without $R$ parity and with generic soft Supersymmetry breaking terms. Neutrinos acquire mass from various sources: tree level neutrino--neutralino mixing, loop effects and non--renormalizable operators. Abelian horizontal symmetries (invoked to explain the smallness and hierarchy in quark parameters) replace $R$ parity in suppressing neutrino masses. We find lower bounds on the mixing angles: $\sin {\theta }_{ij}\text{gsim}m({\ell }_i^{-})/m({\ell }_j^{-})$ ($i<j$) and unusual order of magnitude predictions for neutrino mass ratios: $m({\nu }_e)/m({\nu }_{\mu })\sim {\sin }^2{\theta }_{12}$; $m({\nu }_i)/m({\nu }_{\tau })\sim 10^{-7}{\sin }^2{\theta }_{i3}$ ($i=1,2$). Bounds from laboratory experiments exclude $m_{{\nu }_{\tau }}\text{gsim}3MeV$ and the cosmological constraint that excludes $m_{{\nu }_{\tau }}\text{gsim}100eV$ is not evaded. Neither the solar nor the atmospheric neutrino problems are likely to be solved by ${\nu }_{\mu }-{\nu }_e$ oscillations. These conclusions can be evaded if holomorphy plays an important role in the lepton Yukawa couplings.

Comments: 16 pages, harvmac, no figures; Version to appear in Phys. Lett. B