Antiproton constraints on the GeV gamma-ray excess: a comprehensive
  analysis
  A GeV gamma-ray excess has possibly been individuated in Fermi-LAT data from
the Galactic Center and interpreted in terms of Dark Matter (DM) annihilations,
either in hadronic (essentially $b\bar{b}$) or leptonic channels. In order to
test this tantalizing interpretation, we address two issues: (i) we improve the
computation of secondary emission from DM (Inverse Compton and Bremsstrahlung)
with respect to previous works, confirming it to be very relevant for
determining the DM spectrum in the leptonic channels, so that any conclusion on
the DM nature of the signal critically depends on this contribution; (ii) we
consider the constraints from antiprotons on the DM hadronic channel, finding
that the uncertainties on the propagation model, and in particular on the halo
height, play a major role. Moreover, we discuss the role of solar modulation,
taking into account possible charge dependent effects whose importance is
estimated exploiting detailed numerical tools. The limits that we obtain
severely constrain the DM interpretation of the excess in the hadronic channel,
for standard assumptions on the Galactic propagation parameters and solar
modulation. However, they considerably relax if more conservative choices are
adopted.
