U(1) symmetry and R parity violation

The patterns of R violation resulting from the 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 by the requirement that very large bilinear lepton number violating terms should not be allowed in the superpotential. It is shown that this leads to severely constrained patterns of trilinear interactions. Specifically, the only choice compatible with phenomenological restrictions is the one in which all the trilinear ${\lambda }_{\mathrm{ijk}}^{\prime }$ and all but at most two trilinear ${\lambda }_{\mathrm{ijk}}$ couplings vanish or are enormously suppressed. The U(1) symmetry can allow the effective generation of bilinear lepton number violating parameters through terms in the Kähler potential. The resulting models are identified and the structure of neutrino masses in some of these is briefly discussed.