Yukawa textures with an anomalous horizontal abelian symmetry

Abstract

The observed hierarchy of quark and lepton masses and mixings may be obtained by adding an abelian family symmetry to the Minimal Supersymmetric Model and coupling quarks and leptons to an electroweak singlet scalar field. In a large class of such models, this symmetry suffers from anomalies which must be compensated by the Green-Schwarz mechanism; this in turn fixes the electroweak mixing angle to be $\sin^2 \theta_W = 3/8$ at the string scale, without any assumed GUT structure. The analysis is extended to two distinct generalisations of the Standard Model: neutrino masses and mixings and R-parity violating interactions.