  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.
