Anomalous $U(1)$ Mediated SUSY Breaking, Fermion Masses and Natural Suppression of FCNC and CP 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 $A$ and $B$ terms and the mass splittings between the like-charged squarks of the first two generations compared to their average masses 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. These models predict naturally the expected value of the $\mu$-term and also have the potential to qualitatively explain the observed mass hierarchy among quarks and leptons.