Cross section calculations in theories of self-interacting dark matter

Abstract

We study an asymmetric dark matter model with self-interacting dark matter consisting of a Dirac fermion χ coupled to a scalar or vector mediator, such that the reaction χ+χ→χ+χ is well described by perturbation theory. We compute the scattering cross section σ, the transfer cross section σT, and the viscosity cross section σV for this reaction. As one part of our study, we give analytic and numerical comparisons of results obtained with the inclusion of both t-channel and u-channel exchanges and results obtained in an approximation that has often been used in the literature that includes only the t-channel contribution. The velocity dependences of these cross sections are studied in detail and shown to be in accord with observational data.