Self-Interaction of Super-Resonant Dark Matter

The $\Lambda$CDM model, while successful on large cosmological scales, faces challenges on small scales. A promising solution posits that dark matter (DM) exhibits strong self-interaction, enhanced through the narrow resonance or Sommerfeld effects. We demonstrate that the ``super-resonance" phenomenon, combining these effects, significantly amplifies the DM self-scattering cross section, enabling strong self-interactions for DM candidates in the $\mathcal{O}(100)$ GeV mass range. This mechanism also enhances the DM annihilation cross section, causing early kinetic decoupling that renders the standard Boltzmann equation inadequate. By implementing coupled Boltzmann equations, we achieve precise calculations of the relic density for super-resonant DM, aligning with observational constraints.