Consequences of an Abelian Family Symmetry

Abstract

The addition of an Abelian family symmetry to the Minimal Supersymmetric Standard Model reproduces the observed hierarchies of quark and lepton masses and quark mixing angles, only if it is anomalous. Green-Schwarz compensation of its anomalies requires the electroweak mixing angle to be $\sin^2\theta_w=3/8$ at the string scale, without any assumed GUT structure, suggesting a superstring origin for the standard model. The analysis is extended to neutrino masses and the lepton mixing matrix.