Simply split strongly interacting massive particles

Dark matter which interacts strongly with itself, but only feebly with the Standard Model, is a possibility that has been entertained to solve apparent small-scale structure problems that are pertinent to the noninteracting cold dark matter paradigm. In this paper, we study the simple case in which the self-scattering rate today is regulated by kinematics and/or the abundance ratio, through the mass splitting of nearly degenerate pseudo-Dirac fermions χ₁ and χ₂ or real scalars φ₁ and φ₂. We calculate the relic density of these states in a scenario where self-scattering proceeds through off-diagonal couplings with a vector particle V (dark photon) and where the abundance is set through number-depleting 4-to-2 reactions in the hidden sector, or, alternatively, via freeze-in. We study the implications of the considered models and their prospect of solving astrophysical small-scale structure problems. We also show how the introduction of the (meta)stable heavier state may be probed in future dark matter searches.