Not so Coy Dark Matter explains DAMA (and the Galactic Center excess)

We study a Dirac Dark Matter particle interacting with ordinary matter via the exchange of a light pseudo-scalar, and analyze its impact on both direct and indirect detection experiments. We show that this candidate can accommodate the long-standing DAMA modulated signal and yet be compatible with all exclusion limits at ${99}_S$ % CL. This result holds for natural choices of the pseudo-scalar-quark couplings (e.g.~flavor-universal), which give rise to a significant enhancement of the Dark Matter-proton coupling with respect to the coupling to neutrons. We also find that this candidate can accommodate the observed 1-3 GeV gamma-ray excess at the Galactic Center and at the same time have the correct relic density today. The model could be tested with measurements of rare meson decays, flavor changing processes, and searches for axion-like particles with mass in the MeV range.