Atmospheric and solar neutrinos with a heavy singlet

Abstract

We follow a minimalistic approach to neutrino masses, by introducing a single heavy singlet N into the standard model (or supersymmetric standard model) with a heavy Majorana mass M, which couples as a single right-handed neutrino in a Dirac fashion to leptons, and induces a single light see-saw mass m ν ∼5×10 −2 eV, leaving two neutrinos massless. This trivial extension to the standard model may account for the atomospheric neutrino data via ν μ → ν τ oscillations with near maximal mixing angle θ 23∼ π/4 and Δ m μτ 2∼2.5×10 −3 eV 2. In order to account for the solar neutrino data the model is extended to SUSY GUT/ string-inspired type models which can naturally yield an additional light tau neutrino mass m ν τ ∼few×10 −3 eV leading to ν eL →(cos θ 23 ν μL −sin θ 23 ν τL ) oscillations with Δ m e1 2∼10 −5 eV 2 and a mixing angle sin 22 θ 1≈10 −2 in the correct range for the small angle MSW solution to the solar neutrino problem. The model predicts ν eL →(sin θ 23 ν μL +cos θ 23 ν τL ) oscillations with a similar angle but a larger splitting Δ m e2 2∼2.5×10 −3 eV 2.