A possible link between the GeV excess and the 511 keV emission line in
  the Galactic Centre
  The morphology and characteristics of the so-called GeV gamma-ray excess
detected in the Milky Way lead us to speculate about a possible common origin
with the 511 keV line mapped by the SPI experiment about ten years ago. In the
previous version of our paper, we assumed 30 GeV dark matter particles
annihilating into $b \bar{b}$ and obtained both a morphology and a 511 keV flux
(\phi_{511 keV} ~ 10^{-3} ph/cm^2/s) in agreement with SPI observation. However
our estimates assumed a negligible number density of electrons in the bulge
which lead to an artificial increase in the flux (mostly due to negligible
Coulomb losses in this configuration). Assuming a number density greater than
$n_e > 10^{-3} cm^{-3}$, we now obtain a flux of 511 keV photons that is
smaller than \phi_{511 keV} ~ 10^{-6} ph/cm^2/s and is essentially in agreement
with the 511 keV flux that one can infer from the total number of positrons
injected by dark matter annihilations into $b \bar{b}$. We thus conclude that
-- even if 30 GeV dark matter particles were to exist-- it is impossible to
establish a connexion between the two types of signals, even though they are
located within the same 10 deg region in the galactic centre.
