Cross Section Calculations in Theories of Self-Interacting Dark Matter

TL;DR

This paper analyzes self-interacting dark matter models with Dirac fermions and mediators, computing scattering cross sections and comparing different calculation methods to match observational data.

Contribution

It provides detailed calculations of scattering cross sections including both $t$- and $u$-channel exchanges, improving upon common approximations.

Findings

Cross sections computed with full $t$- and $u$-channel contributions match observational velocity dependence.

Analytic and numerical comparisons highlight the importance of including both channels.

Results support the viability of self-interacting dark matter models with specific velocity-dependent cross sections.

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.