  We discuss new bounds on vectors coupled to currents whose non-conservation
is due to mass terms, such as $U(1)_{L_\mu - L_\tau}$. Due to the emission of
many final state longitudinally polarized gauge bosons, inclusive rates grow
exponentially fast in energy, leading to constraints that are only
logarithmically dependent on the symmetry breaking mass term. This exponential
growth is unique to Stueckelberg theories and reverts back to polynomial growth
at energies above the mass of the radial mode. We present bounds coming from
the high transverse mass tail of mono-lepton+missing transverse energy events
at the LHC, which beat out cosmological bounds to place the strongest limit on
Stueckelberg $U(1)_{L_\mu - L_\tau}$ models for most masses below a keV. We
also discuss a stronger, but much more uncertain, bound coming from the
validity of perturbation theory at the LHC.
