Sommerfeld enhancements with vector, scalar and pseudoscalar force-carriers

The first AMS-02 measurement confirms the existence of an excess in the cosmic-ray positron fraction previously reported by the PAMELA and Fermi-LAT experiments. If interpreted in terms of thermal dark matter (DM) annihilation, the AMS-02 result still suggests that the DM annihilation cross section in the present day should be significantly larger than that at freeze out. The Sommerfeld enhancement of DM annihilation cross section as a possible explanation for the observed excesses is subject to constraint from the DM thermal relic density, mainly due to the annihilation of DM particles into force-carrier particles introduced by the mechanism. We show that the effect of the Sommerfeld enhancement and the relic density constraint depend significantly on the nature of the force-carrier. Three cases where the force-carrier is a vector boson, scalar and pseudoscalar particle are investigated and compared with each other. The results show that for the vector force-carrier, the Sommerfeld enhancement can marginally account for the AMS-02 data for $2\mu$ final states, while for scalar force-carrier the allowed Sommerfeld enhancement can be larger by a factor of two. For the case with a pesudoscalar force-carrier, the Sommerfeld enhancement can be large enough to accommodate the AMS-02 and Fermi-LAT result for a variety of DM annihilation final states.