Z' Bosons and Supersymmetry
  A broad class of supersymmetric extensions of the standard model predict a Z' vector boson whose mass is naturally in the range 250 GeV < M_Z' < 2 TeV. To avoid unacceptably large mixing with the Z, one requires either a discrete tuning of the U(1)' charges or a leptophobic Z'. Both cases are likely to arise as the low energy limits of heterotic string compactifications, but a survey of existing realistic string models provides no acceptable examples. A broken U(1)' leads to additional D-term contributions to squark, slepton, and Higgs masses, which depend on the U(1)' charge assignments and the Z' mass. The Tevatron and future colliders can discover or decisively rule out this class of models. 
Joseph D. Lykken