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We construct a Minimum Supersymmetry Standard Model expanded 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. Our model also provides a counter example to the previous claim that the only U(1)′ that can give rise to realistic fermion mass hierarchy and mixing pattern must be anomalous.

Non-universal, Non-anomalous U(1)' in a Model with Anomaly-Mediated SUSY Breaking