Abstract
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.
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