Low-Energy Effective Lagrangian in Unified Theories with Non-Universal Supersymmetry Breaking Terms

Supersymmetric grand unified theories with non-universal soft supersymmetry breaking terms are studied. By integrating out the superheavy fields at an unification scale, we compute their low-energy effective Lagrangian. We find new contributions to the scalar potential specific to the non-universal supersymmetry breaking. $D$-term contribution to the scalar masses is one example. The gauge hierarchy achieved by a fine-tuning in the superpotential would be violated in general due to the non-universal SUSY breaking terms. We show, however, it is preserved for a certain class of the soft terms derived from a {\em hidden} ansatz. We also discuss some phenomenological implications of the non-universal supersymmetry breaking, including predictions of the radiative electroweak symmetry breaking scenario and of no-scale type models.