Anomalous U(1)-mediated supersymmetry breaking, fermion masses, and natural suppression of FCNC andCP-violating effects

We construct realistic supergravity models where supersymmetry breaking arises from the $D$ terms of an anomalous U(1) gauge symmetry broken at the Planck scale. The model has the attractive feature that the gaugino masses, the $A$ terms, and the mass splittings between the like-charged squarks of the first two generations compared to their average masses (i.e., $\Delta m_{\tilde{q}}^2{/m}_{\tilde{q}}^2)$ are all suppressed. As a result, the electric dipole moment of the neutron as well as the flavor-changing neutral current effects are predicted to be naturally small. We show how some versions of these models can lead to the expected value of the $\mu$ and $B\mu$ terms and qualitatively explain the observed mass hierarchy among quarks and leptons.