On thermal production of self-interacting dark matter

We consider thermal production mechanisms of self-interacting dark matter in models with gauged $Z_3$ symmetry. A complex scalar dark matter is stabilized by the $Z_3$, that is the remnant of a local dark $U(1{)}_d$. Light dark matter with large self-interaction can be produced from thermal freeze-out in the presence of SM-annihilation, SIMP and/or forbidden channels. We show that dark photon and/or dark Higgs should be relatively light for unitarity and then assist the thermal freeze-out. We identify the constraints on the parameter space of dark matter self-interaction and mass in cases that one or some of the channels are important in determining the relic density.