Scalar and Fermion Two-component SIMP Dark Matter with an Accidental $\mathbb{Z}^{}_4$ Symmetry

In this paper, we construct for the first time a two-component strongly interacting massive particles (SIMP) dark matter (DM) model, where a complex scalar and a vector-like fermion play the role of the SIMP DM candidates. These two particles are stable due to an accidental $\mathbb{Z}^{}_4$ symmetry after the breaking of a $\text{U}(1)^{}_\textsf{D}$ gauge symmetry. By introducing one extra complex scalar as a mediator between the SIMP particles, this model can have $3 \to 2$ processes that determine the DM relic density. On the other hand, the SIMP DM particles can maintain kinetic equilibrium with the thermal bath until the DM freeze-out temperature via the $\text{U}(1)^{}_\textsf{D}$ gauge couplings. Most importantly, we find an unavoidable two-loop induced $2 \to 2$ process tightly connecting to the $3 \to 2$ process that would redistribute the SIMP DM number densities after the chemical freeze-out of DM. Moreover, this redistribution would significantly modify the predictions of the self-interacting cross section of DM compared with other SIMP models. It is crucial to include the two-loop induced $2 \to 2$ annihilations to obtain the correct DM phenomenology.