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

In this paper, we show that positron data from AMS seem 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.