An $SU(2)_{L} imes U(1)_{Y} imes S_{3} imes D$ model for atmospheric and solar neutrino deficits

摘要

Motivated by the recent Super-Kamiokande experiment on atmospheric and solarneutrino oscillation we propose a see-saw model of three generations ofneutrinos based on the gauge group $SU(2)_{L}\times U(1)_{Y}$ with discretesymmetries $(S_{3} \times D)$ and three right handed singlet neutrinos so thatthis model can accommodate the recent Super-Kamiokande data on atmospheric andsolar neutrino oscillations. The model predicts maximal mixing between$\nu_{\mu}$ and $\nu_{\tau}$ with $sin^{2}2{\theta_{\mu\tau}}$ = 1 as requiredby the atmospheric neutrino data and small mixing between $\nu_{e}$ and$\nu_{\mu}$ with $sin^{2}2{\theta_{e\mu}} \sim (10^{-2}-10^{-3})$ as a possibleexplanation of the solar neutrino deficit through the MSW mechanism. The modeladmits two mass scales of which one breaks the electroweak symmetry and theother is responsible for the breaking of the lepton number symmetry at GUTscale leading to small Majorana mass of the left handed doublet neutrinos.