AnomalousU(1), holomorphy, supersymmetry breaking, and dilaton stabilization

Abstract

We show that in models with family symmetries, the implementation of the alignment mechanism for the suppression of the flavor changing neutral currents requires specific mass matrices, necessarily with holomorphic zeros in the down quark sector. Holomorphic zeros open flat directions that spoil the uniqueness of the supersymmetric vacuum, making alignment models less attractive. We are thus unavoidably lead to the recently found, unique, anomalous $U(1)$ model without holomorphic zeros in the quark sector that can reproduce all the mass hierarchies, provided that $\mathrm{tan}\ensuremath{\beta}$ is of order one. To avoid undesired flavor changing neutral currents, we propose a supersymmetry breaking mechanism and a dilaton stabilization scenario that result in degenerate squarks at $M\ensuremath{\sim}{M}_{\mathrm{GUT}}$ and a calculable low energy spectrum. We present the numerical predictions of this model for the Higgs boson mass for different values of M and $\mathrm{tan}\ensuremath{\beta}$.