Can the relic density of self-interacting dark matter be due to   annihilations into Standard Model particles?
  Motivated by the hypothesis that dark matter self-interactions provide a solution to the small-scale structure formation problems, we investigate the possibilities that the relic density of a self-interacting dark matter candidate can proceed from the thermal freeze-out of annihilations into Standard Model particles. We find that scalar and Majorana dark matter in the mass range of $10-500$ MeV, coupled to a slightly heavier massive gauge boson, are the only possible candidates in agreement with multiple current experimental constraints. Here dark matter annihilations take place at a much slower rate than the self-interactions simply because the interaction connecting the Standard Model and the dark matter sectors is small. We also discuss prospects of establishing or excluding these two scenarios in future experiments. 
Xiaoyong Chu, Camilo Garcia-Cely and Thomas Hambye
hep-ph