Velocity-dependent self-interacting dark matter from thermal freeze-out and tests in direct detections

A small fraction of millicharged dark matter (DM) is considered in the literature to give an interpretation of the enhanced 21-cm absorption at the cosmic dawn. Here we focus on the case that the main component of DM is self-interacting dark matter (SIDM), motivated by the small-scale problems. For self-interactions of SIDM being compatible from dwarf to cluster scales, velocity-dependent self-interactions mediated by a light scalar $$\phi $$ϕ are considered. For fermionic SIDM $$\Psi $$Ψ, the main annihilation mode $$\Psi \bar{\Psi } \rightarrow \phi \phi $$ΨΨ¯→ϕϕ is a p-wave process. The thermal transition of SIDM $$\rightleftarrows \phi \rightleftarrows $$⇄ϕ⇄ standard model (SM) particles in the early universe sets a lower bound on couplings of $$\phi $$ϕ to SM particles, which has been excluded by direct detections of DM, and here we consider SIDM in thermal equilibrium via millicharged DM. For $$m_\phi>$$mϕ> twice millicharged DM mass, $$\phi $$ϕ could decay quickly and avoid excess energy injection to big bang nucleosynthesis. Thus, the $$\phi $$ϕ–SM particle couplings could be very tiny and evade direct detections of DM. The picture of weakly interacting massive particle (WIMP)–nucleus scattering with contact interactions fails for SIDM–nucleus scattering with a light mediator, and a method is explored in this paper with which a WIMP search result can be converted into the hunt for SIDM in direct detections.