Z ′ gauge bosons at the Fermilab Tevatron

We study the discovery potential of the Tevatron for a Z{sup '} gauge boson. We introduce a parametrization of the Z{sup '} signal which provides a convenient bridge between collider searches and specific Z{sup '} models. The cross section for pp-bar{yields}Z{sup '}X{yields}l{sup +}l{sup -}X depends primarily on the Z{sup '} mass and the Z{sup '} decay branching fraction into leptons times the average square coupling to up and down quarks. If the quark and lepton masses are generated as in the standard model, then the Z{sup '} bosons accessible at the Tevatron must couple to fermions proportionally to a linear combination of baryon and lepton numbers in order to avoid the limits on Z-Z{sup '} mixing. More generally, we present several families of U(1) extensions of the standard model that include as special cases many of the Z{sup '} models discussed in the literature. Typically, the CDF and D0 experiments are expected to probe Z{sup '}-fermion couplings down to 0.1 for Z{sup '} masses in the 500-800 GeV range, which in various models would substantially improve the limits set by the LEP experiments.