Predictions from an anomalous U(1) model of Yukawa hierarchies

Abstract

We present a supersymmetric standard model with three gauged Abelian symmetries of a type commonly found in superstrings. One is anomalous; the other two are ${E}_{6}$ family symmetries. It has a vacuum in which only these symmetries are broken by stringy effects. It reproduces all observed quark and charged lepton Yukawa hierarchies and the value of the Weinberg angle. It predicts three massive neutrinos, with mixing that can explain both the small angle MSW effect and the atmospheric neutrino anomaly. The Cabibbo angle is expressed in terms of the gauge couplings at unification. It conserves $R$ parity and proton decay is close to experimental bounds.