Comment on "New Freezeout Mechanism for Strongly Interacting Dark Matter"

Inspired by our recent paper "reshuffled SIMP dark matter", we notice that the reaction rate of the two-loop induced $2 \to 2$ process may dominate over or be comparable with that of the $3 \to 2$ process at the chemical freezeout of Co-SIMP dark matter [Phys. Rev. Lett. 125, 131301 (2020)], especially when the Co-SIMP mass is close to the standard model particle mass (called the edge case). To check our point, we then derive the Boltzmann equation with all relevant annihilation cross sections in an electrophilic model and numerically solve it to obtain the cosmological evolution of Co-SIMP dark matter. Our result shows that the two-loop induced $2 \to 2$ process does modify the parameter space of the coupling for the edge case in the Co-SIMP mechanism and has to be taken into account in UV completion models.