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.Comment: 19 page
