Self-Interacting Forbidden Dark Matter under a Cannibally Co-Decaying Phase

In a usual dark matter (DM) model without a huge mass difference between the DM and lighter mediator, using the coupling strength suitable for having the correct relic density, the resulting self-interaction becomes several orders of magnitude smaller than that required to interpret the small scale structures. We present a framework that can offer a solution for this point. We consider a model that contains the vector DM and a heavier but unstable Higgs-like scalar in the hidden sector. When the temperature drops below $\sim m_{\rm DM}$, the hidden sector, which is thermally decoupled from the visible sector, enters a cannibal phase, during which the DM density is depleted with the out-of-equilibrium decay of the scalar. The favored parameter region, giving the correct relic density and the proper size of self-interactions, shows the scalar-to-DM mass ratio $\in [1.1,1.33]$ and the scalar mass $\in[9,114]\,{\rm MeV}$. A sizable parameter space still survives the most current constraints and can be further probed by the near future NA62 beam dump experiment.