Light and Darkness: consistently coupling dark matter to photons via effective operators

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.