Bi-maximal neutrino mixing and small U_{e3} from Abelian flavor symmetry

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