Relic Abundance in a Secluded Dark Matter Scenario with a Massive Mediator

The relic abundance of the dark matter (DM) particle $d$ is studied in a secluded DM scenario, in which the $d$ number decreasing process dominantly occurs not through the pair annihilation of $d$ into the standard model particles, but via the $dd \to mm$ scattering process with a subsequently decaying mediator particle $m$. It is pointed out that the cosmologically observed relic abundance of DM can be accomplished even with a massive mediator having a mass $m_m$ non-negligibly heavy compared with the DM particle mass $m_d$. In the degenerated $d$-$m$ case ($m_d=m_m$), the DM relic abundance is realized by adjusting the $dd \to mm$ scattering amplitude large enough and by choosing an appropriate mediator particle life-time. The DM evolution in the early universe exhibits characteristic "terrace" behavior, or two-step number density decreasing behavior, having a "fake" freeze-out at the first step. Based on these observations, a novel possibility of the DM model buildings is introduced in which the mediator particle $m$ is unified with the DM particle $d$ in an approximate dark symmetry multiplet. A pionic DM model is proposed to illustrate this idea in a renormalizable field theory framework.