Anomalous U(1) Gauge Symmetry and Lepton Flavor Violation

In recent years, many people have studied the possibility that the anomalous U(1) gauge symmetry is a trigger of SUSY breaking and/or an origin of the fermion mass hierarchy. Though it is interesting that the anomalous U(1) symmetry may explain these two phenomena simultaneously, it causes a negative stop mass squared or a severe fine-tuning in order to avoid the FCNC problem. Recently, it was pointed out that the F-term contribution of the dilaton field can dominate the flavor-dependent contribution from the anomalous U(1) D-term, so that the FCNC problem may be naturally avoided. In this paper, we study the case in which the dilaton is stabilized by the deformation of the K\"ahler potential for the dilaton and find that the order of the ratio of the F-term to the D-term contributions is generally determined. This implies that the branching ratio of \mu \to e \gamma can be found around the present experimental bound.