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 $\chi$ coupled to a scalar or vector mediator, such that the reaction $\chi +\chi \to \chi +\chi$ is well described by perturbation theory. We compute the scattering cross section $\sigma$, the transfer cross section ${\sigma }_T$, and the viscosity cross section ${\sigma }_V$ 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.

15 pages, 10 figures

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