Electroweak breaking and the [Formula presented] problem in supergravity models with an additional U(1)

We consider electroweak symmetry breaking in supersymmetric models with an extra nonanomalous [Formula presented] gauge symmetry and an extra standard-model singlet scalar [Formula presented]. For appropriate charges the [Formula presented] forbids an elementary [Formula presented] term, but an effective [Formula presented] is generated by the VEV of [Formula presented], leading to a natural solution to the [Formula presented] problem. There are a variety of scenarios leading to acceptably small [Formula presented]-[Formula presented] mixing and other phenomenological consequences, all of which involve some but not excessive fine-tuning. One class, driven by a large trilinear soft supersymmetry-breaking term, implies small mixing, a light [Formula presented] (e.g., 200 GeV), and an electroweak phase transition that may be first order at the tree level. In another class, with [Formula presented] (radiative breaking), the typical scale of dimensional parameters, including [Formula presented] and the effective [Formula presented], is [Formula presented], but the electroweak scale is smaller due to cancellations. We relate the soft supersymmetry-breaking parameters at the electroweak scale to those at the string scale, choosing Yukawa couplings as determined within a class of string models. We find that one does not obtain either scenario for universal soft supersymmetry-breaking mass parameters at the string scale and no exotic multiplets contributing to the renormalization group equations. However, either scenario is possible when the assumption of universal soft breaking is relaxed. Radiative breaking can also be generated by exotics, which are expected in most string models.