A conservative assessment of the current constraints on dark matter annihilation from Cosmic Rays and CMB observations

In view of the current interest in combining different observations to constraint annihilating WIMP dark matter, we examine the relation between the Sommerfeld effect at the recombination epoch and in the galactic halo. By considering an up-to-date collection of interpolations of cosmic rays lepton data (AMS-02 2014, Fermi and PAMELA), as dark matter annihilation signals, we show that current cosmic rays measurements and recent Planck 2015 constraints from CMB anisotropies almost overlap for dark matter masses of the order of few $TeV$, although great theoretical uncertainties afflict cosmic rays and dark matter descriptions. Combining cosmic rays fits we obtain proper minimal regions allowed by CMB observations, especially for $\mu$ and $\tau$ annihilation channels, once assumed viable values of the efficiency factor for energy absorption at recombination: the results are consistent with those obtained by the Planck collaboration but allow a slightly larger overlap between Cosmic Rays constraints from the lepton sector and CMB. Incoming AMS-02 measurements of cosmic rays antiprotons will help to clarify the conundrum.