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

Abstract

Atmospheric neutrino data strongly suggests a near-maximal ν_μ-ν_τ mixing and also solar neutrino data can be nicely explained by another near-maximal ν_e-ν_μ or ν_e-ν_τ mixing. We examine the possibility that this bi-maximal mixing of atmospheric and solar neutrinos arises naturally, while keeping U_{e3} and Δm^2_{sol}/Δm^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 λ\approx 0.2. Future experiments at a neutrino factory measuring the size of U_{e3} and the sign of Δm^2_{32} could discriminate those scenarios as they predict distinctive values of U_{e3} in connection with Δm^2_{sol}/Δm^2_{atm} and also with the order of the neutrino mass eigenvalues.