Bimaximal neutrino mixing and small U-e3 from Abelian flavor symmetry

Atmospheric neutrino data strongly suggest a near-maximal ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ mixing and also solar neutrino data can be nicely explained by another near-maximal ${\ensuremath{\nu}}_{e}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ or ${\ensuremath{\nu}}_{e}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ mixing. We examine the possibility that this bimaximal mixing of atmospheric and solar neutrinos arises naturally, while keeping ${U}_{e3}$ and $\ensuremath{\Delta}{m}_{\mathrm{sol}}^{2}/\ensuremath{\Delta}{m}_{\mathrm{atm}}^{2}$ small enough, as a consequence of Abelian flavor symmetry. Two simple scenarios of Abelian flavor symmetry within the supersymmetric framework are considered to obtain the desired form of the neutrino mass matrix and the charged lepton mass matrix parametrized by the Cabibbo angle $\ensuremath{\lambda}\ensuremath{\approx}0.2.$ Future experiments at a neutrino factory measuring the size of ${U}_{e3}$ and the sign of $\ensuremath{\Delta}{m}_{32}^{2}$ could discriminate between those scenarios as they predict distinctive values of ${U}_{e3}$ in connection with $\ensuremath{\Delta}{m}_{\mathrm{sol}}^{2}/\ensuremath{\Delta}{m}_{\mathrm{atm}}^{2}$ and also with the order of the neutrino mass eigenvalues.