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 dark matter (DM) self-scattering. We present effective self-interactions for DM in the leading order expansions with momentum transfer and DM velocity. We compare 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 DM and spin-2 particle masses for velocity-dependent self-scattering to solve small-scale problems in galaxies and to satisfy the bounds from galaxy clusters at the same time. (paper)