Fitting the Fermi-LAT GeV excess: On the importance of including the propagation of electrons from dark matter

An excess of gamma rays at GeV energies has been pointed out in the Fermi-LAT data. This signal comes from a narrow region centred around the Galactic center and has been interpreted as possible evidence for light dark matter particles annihilating either into a mixture of leptons-antileptons and b-bbar or into b-bbar only. Focusing on the prompt gamma-ray emission, previous works found that the best fit to the data corresponds to annihilations proceeding predominantly into b-bbar. However, here we show that omitting the photon emission originating from primary and secondary electrons produced in dark matter annihilations, and undergoing diffusion through the Galactic magnetic field, can actually lead to the wrong conclusion. Accounting for this emission, we find that not only are annihilations of ~ 10 GeV particles into a purely leptonic final state allowed, but the democratic scenario actually provides a better fit to the spectrum of the excess than the pure b-bbar channel. We conclude our work with a discussion on constraints on these leptophilic scenarios based on the AMS data and the morphology of the excess.