Froggatt-Nielsen models with a residual Z4R symmetry

The Froggatt-Nielsen mechanism provides an elegant explanation for the hierarchies of fermion masses and mixings in terms of a U(1) symmetry. Promoting such a family symmetry to an R symmetry, we explicitly construct supersymmetric Froggatt-Nielsen models which are gauged, family-dependent U(1)(R) completions of the Z(4)(R) symmetry proposed by Lee, Raby, Ratz, Ross, Schieren, Schmidt-Hoberg and Vaudrevange in 2010. Forbidden by Z(4)(R), the mu term is generated around the supersymmetry breaking scale m(3/2) from either the Kahler potential or the superpotential. Neutrinos acquire their mass via the type-I seesaw mechanism with three right-handed neutrino superfields. Taking into account the Green-Schwarz anomaly cancellation conditions, we arrive at a total of 3 x 34 distinct phenomenologically viable charge assignments for the standard model fields, most of which feature highly fractional charges.