  We revise the treatment of fermionic dark matter interacting with photons via
dimension-5 and -6 effective operators. We show how the application of the
effective operators beyond their validity introduces unphysical, gauge
violating effects that are relevant for current experimental searches.
Restoring gauge invariance by coupling dark matter to the hypercharge gauge
field has implications for the parameter space above and below the electroweak
scale. We review the phenomenology of these hypercharge form factors at the LHC
as well as for direct and indirect detection experiments. We highlight where
the electromagnetic and hypercharge descriptions lead to wildly different
conclusions about the viable parameter space and the relative sensitivity of
various probes. These include a drastic weakening of vector bosons fusion
versus mono-jet searches at the LHC, and the incorrect impression that indirect
searches could lead to better constraints than direct detection for larger dark
matter masses. We find that the dimension-5 operators are strongly constrained
by direct detection bounds, while for dimension-6 operators LHC mono-jet
searches are competitive or performing better than the other probes we
consider.
