Low-energy effective Lagrangian in unified theories with nonuniversal supersymmetry-breaking terms

Supersymmetric grand unified theories with nonuniversal soft supersymmetry- (SUSY-) breaking terms are studied. By integrating out the superheavy fields at a unification scale, we compute their low-energy effective Lagrangian. We find new contributions to the scalar potential specific to the nonuniversal supersymmetry breaking. A 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 nonuniversal SUSY-breaking terms. We show, however, it is preserved for a certain class of the soft terms derived from a hidden ansatz. We also discuss some phenomenological implications of the nonuniversal supersymmetry breaking, including predictions of the radiative electroweak symmetry-breaking scenario and of no-scale-type models.