Z3 scalar singlet dark matter

We consider the minimal scalar singlet dark matter stabilised by a Z(3) symmetry. Due to the cubic term in the scalar potential, semi-annihilations, besides annihilations, contribute to the dark matter relic density. Unlike in the Z(2) case, the dark matter spin independent direct detection cross section is no more linked to the annihilation cross section. We study the extrema of the potential and show that a too large cubic term would break the Z(3) symmetry spontaneously, implying a lower bound on the direct detection cross section, and allowing the whole parameter space to be tested by XENON1T. In a small region of the parameter space the model can avoid the instability of the standard model vacuum up to the unification scale. If the semi-annihilations are large, however, new physics will be needed at TeV scale because the model becomes non-perturbative. The singlet dark matter mass cannot be lower than 53.8 GeV due to the constraint from Higgs boson decay into dark matter.