  We study theoretical and experimental constraints on electroweak theories
including a new color-singlet and electrically-neutral gauge boson. We first
note that the electric charges of the observed fermions imply that any such Z'
boson may be described by a gauge theory in which the Abelian gauge groups are
the usual hypercharge along with another U(1) component in a kinetic-diagonal
basis. Assuming that the observed quarks and leptons have
generation-independent U(1) charges, and that no new fermions couple to the
standard model gauge bosons, we find that their U(1) charges form a
two-parameter family consistent with anomaly cancellation and viable fermion
masses, provided there are at least three right-handed neutrinos. We then
derive bounds on the Z' mass and couplings imposed by direct production and
Z-pole measurements. For generic charge assignments and a gauge coupling of
electromagnetic strength, the strongest lower bound on the Z' mass comes from
Z-pole measurements, and is of order 1 TeV. If the new U(1) charges are
proportional to B-L, however, there is no tree-level mixing between the Z and
Z', and the best bounds come from the absence of direct production at LEPII and
the Tevatron. If the U(1) gauge coupling is one or two orders of magnitude
below the electromagnetic one, these bounds are satisfied for most values of
the Z' mass.
