Vacuum solutions of neutrino anomalies through a softly broken U (1) symmetry

Abstract

We discuss an extended SU(2)×U(1) model which naturally leads to mass scales and mixing angles relevant for understanding both the solar and atmospheric neutrino anomalies in terms of the vacuum oscillations of the three known neutrinos. The model uses a softly broken L_e-L_μ-L_τ symmetry and contains a heavy scale M_H ~10¹⁵ GeV. The L_e-L_μ-L_τ symmetric neutrino masses solve the atmospheric neutrino anomaly while breaking of L_e-L_μ-L_τ generates highly suppressed radiative mass scale Δ_S ~10⁻¹⁰ eV² needed for the vacuum solution of the solar neutrino problem. All the neutrino masses in the model are inversely related to M_H, thus providing seesaw-type of masses without invoking any heavy right-handed neutrinos. Possible embedding of the model into an SU(5) grand unified theory is discussed.