Simply split SIMPs

Abstract: 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 non-interacting 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 $\chi_1$ and $\chi_2$ or real scalars $\phi_1$ and $\phi_2$. 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.