Supersymmetric models with anomalous U(1) mediated supersymmetry breaking

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 effective action for these theories at sub-Planck energies (including higher dimensional terms in the superpotential) is severely restricted by the U(1) symmetry and by the assumption, it arises from an underlying renormalizable theory at a higher scale. The phenomenological consequences of these models are studied. It is found that they have 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 can all be naturally 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 also predict the value of the $\mu$ term to be naturally small and have the potential to qualitatively explain the observed mass hierarchy among quarks and leptons. We then discuss examples of high scale renormalizable theories that can justify the choice of the the effective action from naturalness point of view.