A See-Saw Model for Atmospheric and Solar Neutrino Oscillations

We have constructed an explicit see-saw model containing two singlet neutrinos, one carrying a (B − 3Le) gauge charge with an intermediate mass scale of ∼ O(10) GeV along with a sterile one near the GUT (grand unification theory) scale of ∼ O(10) GeV. With these mass scales and a reasonable range of Yukawa couplings, the model can naturally account for the near-maximal mixing of atmospheric neutrino oscillations and the small mixing matter-enhanced oscillation solution to the solar neutrino deficit. The super-Kamiokande experiment has recently provided convincing evidence for the atmospheric neutrino oscillation [1] as well as confirmed earlier results on solar neutrino oscillation [2]. The atmospheric neutrino oscillation data seem to require a large mixing angle between νμ and ντ , sin 2θμτ > 0.82 (1) and ∆M = (0.5− 6)× 10eV. (2) On the other hand, the solar neutrino oscillation data can be explained by the small mixingangle matter-enhanced solution between νe and a combination of νμ/ντ with [3] sin 2θe−μ/τ = 10 −2 − 10 (3) and ∆m = (0.5− 1)× 10eV. (4) This represents the most conservative solution to the solar neutrino anomaly although one can get equally good solutions with large mixing-angle matter-enhanced and vacuum oscillations as well. One would naturally expect a near-maximal mixing between νμ and ντ (1), as required by the atmospheric neutrino data, if they were almost degenerate Dirac partners with a small mass difference given by (2). In the context of a three-neutrino model however, the solar neutrino solution (4) would then require the νe to show a much higher level of degeneracy with one of these states, which is totally unexpected. Therefore, it is more natural to consider the three neutrino mass states as nondegenerate with m1 = (∆M ) ≃ 0.05eV, m2 = (∆m) ≃ 0.003eV, m3 << m2. (5) There is broad agreement on this point in the current literature on neutrino physics [4], much of which is focussed on the question of reconciling this hierarchical structure of neutrino masses with at least one large mixing angle (1). The cannonical mechanism for generating neutrino masses and mixings is the so called see-saw model involving heavy right-handed singlet neutrinos [5]. It naturally leads to small hierarchical masses for the three doublet neutrinos, but with small mixing angles. Alternatively one can generate the small neutrino masses radiatively via the Zee model [6, 7] or the R-parity breaking supersymmetric model [8]. Instead of heavy right-handed neutrinos, one needs here an expanded scalar sector in the ≤ TeV region, as extra Higgs multiplets in