Lifting Slepton Masses with a Non-universal, Non-anomalous U(1)'_{NAF} in Anomaly Mediated SUSY breaking

We extend the Minimum Supersymmetry Standard Model by a non-anomalous family (NAF) U(1)'_{NAF} gauge symmetry. All gauge anomalies are cancelled with no additional exotics other than the three right-handed neutrinos. The FI D-terms associated with the U(1)'_{NAF} symmetry lead to additional positive contributions to slepton squared masses. In a RG invariant way, this thus solves the tachyonic slepton mass problem in Anomaly Mediated Supersymmetry Breaking. In addition, the U (1)'_{NAF} symmetry naturally gives rise to the fermion mass hierarchy and mixing angles, and determines the mass spectrum of the sparticles.