Z(3) WIMP and SIMP Dark Matter from a Global U(1) Breaking

We propose and study a scalar extension of the Standard Model which respects a Z(3) symmetry remnant of the spontaneous breaking of a global U(1)D-M symmetry. The model has a dark matter candidate whose relic density is determined by three classes of processes: the usual self-annihilation, semi-annihilation and purely dark matter 3 -> 2 processes. The latter has been subject of recent interest leading to the so-called 'Strongly Interacting Massive Particle' (SIMP) scenario. We show under which conditions the model can lead to a concrete realization of such scenario and study the possibility that the dark matter self-interactions could address the small scale structure problems. In particular, we find that in order for the SIMP scenario to work, the dark matter mass must be in the range of 100 MeV, with the global symmetry energy breaking scale in the TeV range.