SIMP dark matter with gauged Z₃ symmetry

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We consider a complex scalar field as SIMP dark matter in models with gauged Z₃ discrete symmetry appearing as a remnant of dark local U(1). Dark matter (DM) annihilates dominantly by the 3-to-2 scattering, due to the DM cubic coupling in combination with the DM quartic coupling or the Z' gauge and dark Higgs couplings. We show that a light Z' gauge boson makes DM in kinetic equilibrium with thermal plasma at freeze-out and it affects the DM relic density and perturbativity/unitarity constraints for DM self-interactions. We show that the large DM self-interactions are consistent with solving small-scale structure problems and explaining the DM halo separation recently observed in Abell 3827 cluster. Various bounds on the model from the SIMP conditions, DM self-interactions, Z' searches, DM direct/indirect detection experiments, and Higgs signals, are also discussed.