UV completions of magnetic inelastic and Rayleigh dark matter for the Fermi Line(s)

Abstract

Models that seek to produce a line at $\ensuremath{\sim}130\text{ }\text{ }\mathrm{GeV}$ as possibly present in the Fermi data face a number of phenomenological hurdles, not the least of which is achieving the high cross section into $\ensuremath{\gamma}\ensuremath{\gamma}$ required. A simple explanation is a fermionic dark matter particle that couples to photons through loops of charged messengers. We study the size of the dimension-5 dipole (for a pseudo-Dirac state) and dimension-7 Rayleigh operators in such a model, including all higher order corrections in $1/{M}_{\mathrm{mess}}$. Such corrections tend to enhance the annihilation rates beyond the naive effective operators. We find that while freeze-out is generally dominated by the dipole, the present-day gamma-ray signatures are dominated by the Rayleigh operator, except at the most strongly coupled points, motivating a hybrid approach. With this, the magnetic inelastic dark matter scenario provides a successful explanation of the lines at only moderately strong coupling. We also consider the pure Majorana weakly interacting massive particle, where both freeze-out and the Fermi lines can be explained, but only at very strong coupling with light ($\ensuremath{\sim}200--300\text{ }\text{ }\mathrm{GeV}$) messengers. In both cases there is no conflict with nonobservation of continuum photons.