Effective field theory and keV lines from dark matter

We survey operators that can lead to a keV photon line from dark matter decay or annihilation. We are motivated in part by recent claims of an unexplained 3.5 keV line in galaxy clusters and in Andromeda, but our results could apply to any hypothetical line observed in this energy range. We find that given the amount of flux that is observable, explanations in terms of decay are more plausible than annihilation, at least if the annihilation is directly to Standard Model states rather than intermediate particles. The decay case can be explained by a scalar or pseudoscalar field coupling to photons suppressed by a scale not far below the reduced Planck mass, which can be taken as a tantalizing hint of high-scale physics. The scalar case is particularly interesting from the effective field theory viewpoint, and we discuss it at some length. Because of a quartically divergent mass correction, naturalness strongly suggests the theory should be cut off at or below the 1000 TeV scale. The most plausible such natural UV completion would involve supersymmetry. These bottom-up arguments reproduce expectations from top-down considerations of the physics of moduli. A keV line could also arise from the decay of a sterile neutrino, in which case a renormalizable UV completion exists and no direct inference about high-scale physics is possible.