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.

20 pages, 3 figures; v3: Fixed factor of 4 error in Eq 14, CHARM bounds, and updated Fig 1 and Fig 3 accordingly