ELECTROWEAK BREAKING AND THE MU-PROBLEM IN SUPERGRAVITY MODELS WITH AN ADDITIONAL U(1)

We consider electroweak symmetry breaking in supersymmetric models wit h an extra nonanomalous U(1)' gauge symmetry and an extra standard-mod el singlet scalar S. For appropriate charges the U(1)' forbids an elem entary mu term, but an effective mu is generated by the VEV of S, lead ing to a natural solution to the mu problem. There are a variety of sc enarios leading to acceptably small Z-Z' mixing and other phenomenolog ical consequences, all of which involve some but not excessive fine-tu ning. One class, driven by a large trilinear soft supersymmetry-breaki ng term, implies small mixing, a light Z' (e.g., 200 GeV), and an elec troweak phase transition that may be first order at the tree level. In another class, with m(S)(2) < 0 (radiative breaking), the typical sca le of dimensional parameters, including M-Z' and the effective mu, is similar to 1 TeV, but the electroweak scale is smaller due to cancella tions. We relate the soft supersymmetry-breaking parameters at the ele ctroweak 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 m ass parameters at the string scale and no exotic multiplets contributi ng to the renormalization group equations. However, either scenario is possible when the assumption of universal soft breaking is relaxed. R adiative breaking can also be generated by exotics, which are expected in most string models.