High energy positrons from annihilating dark matter

Results from the PAMELA experiment indicate the presence of an excess of cosmic ray positrons above 10 GeV. In this paper, we consider the possibility that this signal is the result of dark matter annihilations taking place in the halo of the Milky Way. Rather than focusing on a specific particle physics model, we take a phenomenological approach and consider a variety of masses and two-body annihilation modes, including W+W-, Z0Z0, bb, τ+τ-, μ+μ-, and e+e-. We also consider a range of diffusion parameters consistent with current cosmic ray data. We find that the significant upturn in the positron fraction above 10 GeV can be explained by dark matter annihilation to leptons, although very large annihilation cross sections and/or boost factors arising from inhomogeneities in the local dark matter distribution are required to produce the observed intensity of the signal. We comment on explanations for the large annihilation rate needed to explain the data and additionally on constraints from gamma rays, synchrotron emission, and cosmic ray antiproton measurements.