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We consider electroweak symmetry breaking in supersymmetric models with anextra non-anomalous U(1)' gauge symmetry and an extra standard-model singletscalar S. For appropriate charges the U(1)' forbids an elementary mu term, butan effective mu is generated by the VEV of S, leading to a natural solution tothe mu problem. There are a variety of scenarios leading to acceptably smallZ-Z' mixing and other phenomenological consequences, all of which involve somebut not excessive fine tuning. One class, driven by a large trilinear softsupersymmetry breaking term, implies small mixing, a light Z' (e.g., 200 GeV),and an electroweak phase transition that may be first order at tree level. Inanother class, with m_S^2 < 0 (radiative breaking), the typical scale ofdimensional parameters, including M_{Z'} and the effective mu, is O(1 TeV), butthe electroweak scale is smaller due to cancellations. We relate the softsupersymmetry breaking parameters at the electroweak scale to those at thestring scale, choosing Yukawa couplings as determined within a class of stringmodels. We find that one does not obtain either scenario for universal softsupersymmetry breaking mass parameters at the string scale and no exoticmultiplets contributing to the renormalization group equations. However, eitherscenario is possible when the assumption of universal soft breaking is relaxed.Radiative breaking can also be generated by exotics, which are expected in moststring models.

Electroweak Breaking and the mu problem in Supergravity Models with an Additional U(1)