Effective theory for self-interacting dark matter and massive spin-2 mediators

We consider the effective theory for self-interacting dark matter with arbitrary spin and go beyond the previous discussion in the literature by introducing a massive spin-2 particle as the mediator for the dark matter self-scattering. We present the effective self-interactions for dark matter in the leading order expansions with the momentum transfer and the dark matter velocity. We compare between the Born cross section and the non-perturbative cross section in the leading order approximation of the effective Yukawa interaction. As a result, we find that there is a wide range of dark matter and spin-2 particle masses for a velocity-dependent self-scattering to solve small-scale problems at galaxies as well as satisfy the bounds from galaxy clusters at the same time.