Diffuse MeV gamma rays and galactic 511 keV line from decaying WIMP dark matter

The origin of both the diffuse high-latitude MeV gamma-ray emission and the 511 keV line flux from the Galactic bulge are uncertain. Previous studies have invoked dark matter physics to independently explain these observations, though as yet none has been able to explain both of these emissions within the well-motivated framework of weakly-interacting massive particles (WIMPs). Here we use an unstable WIMP dark matter model to show that it is in fact possible to simultaneously reconcile both of these observations, and in the process show a remarkable coincidence: decaying dark matter with MeV mass splittings can explain both observations if positrons and photons are produced with similar branching fractions. We illustrate this idea with an unstable branon, which is a standard WIMP dark matter candidate appearing in brane-world models with large extra dimensions. We show that because branons decay via three-body final states, they are additionally unconstrained by searches for Galactic MeV gamma-ray lines. As a result, such unstable long-lifetime dark matter particles provide novel and distinct signatures that can be tested by future observations of MeV gamma rays.