Updated cosmic-ray and radio constraints on light dark matter: Implications for the GeV gamma-ray excess at the Galactic Center

The apparent gamma-ray excess in the Galactic center region and inner Galaxy has attracted considerable interest, notably because both its spectrum and its radial distribution are consistent with an interpretation in terms of annihilating dark matter particles with a mass of about 10-40 GeV. We confront such an interpretation with an updated compilation of various indirect dark matter detection bounds, which we adapt to the specific form required by the observed signal. We find that cosmic-ray positron data strongly rule out dark matter annihilating to light leptons, or "democratically" to all leptons, as an explanation of the signal. Cosmic-ray antiprotons, for which we present independent and significantly improved limits with respect to previous estimates, are already in considerable tension with dark matter (DM) annihilation to any combination of quark final states; the first set of AMS-02 data will thus be able to rule out or confirm the DM hypothesis with high confidence. For reasonable assumptions about the magnetic field in the Galactic center region, radio observations independently put very severe constraints on a DM interpretation of the excess, in particular for all leptonic annihilation channels.