Note on the dark matter explanation of the ARCADE excess and AMS data

Abstract: In this paper we show that positron data from AMS seems to rule out the explanation of the ARCADE isotropic radio background excess in terms of self-annihilating dark matter. In earlier works it was found that leptonic annihilation channels of light dark matter provide a good fit to the excess due to synchrotron emission of the final state particles. However, limits on the self-annihilation cross-section derived from the positron data of AMS now severely constrain light self-annihilating dark matter and cross-sections below that of a thermal relic are already tested for leptonic annihilation channels. Combining these two results, we conclude that an explanation of the excess in the radio background in terms of self-annihilating dark matter is excluded.