Constraining R Violation from Anomalous Abelian Family Symmetry

The patterns of R violation resulting from imposition of a gauged U(1) horizontal symmetry, on the minimal supersymmetric standard model are systematically analyzed. We concentrate on a class of models with integer U(1) charges chosen to reproduce the quark masses and mixings as well as charged lepton masses exactly or approximately. The U(1) charges are further restricted from the requirement that very large bilinear lepton number violating terms should not be allowed in the super-potential. It is shown that all the trilinear ${\lambda }_{ijk}^{\mathrm{\prime }}$ and all but at most two trilinear ${\lambda }_{ijk}$ couplings vanish or are enormously suppressed.