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 $χ+ χ\to χ+ χ$ is well described by perturbation theory. We compute the scattering cross section $σ$, the transfer cross section $σ_T$, and the viscosity cross section $σ_V$ 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.