  New light vectors with dimension-4 couplings to Standard Model states have
(energy / vector mass)^2 enhanced production rates unless the current they
couple to is conserved. These processes allow us to derive new constraints on
the couplings of such vectors, that are significantly stronger than the
previous literature for a wide variety of models. Examples include vectors with
axial couplings to quarks and vectors coupled to currents (such as baryon
number) that are only broken by the chiral anomaly. Our new limits arise from a
range of processes, including rare Z decays and flavor changing meson decays,
and rule out a number of phenomenologically-motivated proposals.
