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Gamma-ray and Radio Constraints of High Positron Rate Dark Matter Models Annihilating into New Light Particles

The possibility of explaining the positron and electron excess recently found by the PAMELA and ATIC collaborations in terms of dark matter (DM) annihilation has attracted considerable attention. Models surviving bounds from, e.g, antiproton production generally fall into two classes, where either DM annihilates directly with a large branching fraction into light leptons, or, as in the recent models of Arkani-Hamed et al., and of Nomura and Thaler, the annihilation gives low-mass (pseudo)scalars or vectors $ϕ$ which then decay into $μ^+μ^-$ or $e^+e^-$. While the constraints on the first kind of models have recently been treated by several authors, we study here specifically models of the second type which rely on an efficient Sommerfeld enhancement in order to obtain the necessary boost in the annihilation cross section. We compute the photon flux generated by QED radiative corrections to the decay of $ϕ$ and show that this indeed gives a rather spectacular broad peak in $E^2dσ/dE$, that for these extreme values of the cross section violate gamma-ray observations of the Galactic center for DM density profiles steeper than that of Navarro, Frenk and White. The most stringent constraint comes from the comparison of the predicted synchrotron radiation in the central part of the Galaxy with radio observations of Sgr A*. For the most commonly adopted DM profiles, the models that provide a good fit to the PAMELA and ATIC data are ruled out, unless there are physical processes that boost the local anti-matter fluxes more than one order of magnitude, while not affecting the gamma-ray or radio fluxes.