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

We consider the treatment of fermionic dark matter interacting with photons via dimension-5 and -6 effective operators, arguing that one should always use hypercharge gauge field form factors, instead of those of the photon. Beyond the simple observation that the electromagnetic form factor description breaks down at the electroweak scale, we show how the additional couplings to the Z boson predicted by the hypercharge form factors modify the relic density calculation and indirect detection limits for dark matter masses of a few tens of GeV and above. Furthermore, constraints from the invisible Z decay width can be competitive for masses below 10 GeV. We review the phenomenology of 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, namely vector boson fusion versus mono-jet constraints from the LHC, and indirect versus direct searches, 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 better than the other probes we consider.