A dark matter model that reconciles tensions between the cosmic-ray $e^\pm$ excess and the gamma-ray and CMB constraints

The cosmic-ray (CR) $e^\pm$ excess observed by AMS-02 can be explained by dark matter (DM) annihilation. However, the DM explanation requires a large annihilation cross section which is strongly disfavored by other observations, such as the Fermi-LAT gamma-ray observation of dwarf galaxies and the Planck observation of the cosmic microwave background (CMB). Moreover, the DM annihilation cross section required by the CR $e^\pm$ excess is also too large to generate the correct DM relic density with thermal production. In this work we use the Breit-Wigner mechanism with a velocity dependent DM annihilation cross section to reconcile these tensions. If DM particles accounting for the CR $e^\pm$ excess with $v\sim \mathcal{O}(10^{-3})$ are very close to a resonance in the physical pole case, their annihilation cross section in the Galaxy reaches a maximal value. On the other hand, the annihilation cross section would be suppressed for DM particles with smaller relative velocities in dwarf galaxies and at recombination, which may affect the gamma-ray and CMB observations, respectively. We find a proper parameter region that can simultaneously explain the AMS-02 results and the thermal relic density, while satisfying the Fermi-LAT and Planck constraints.