# A Practical and Consistent Parametrization of Dark Matter Self-Interactions

## TL;DR

This paper introduces a simple, model-independent parametrization for dark matter self-interactions that accurately captures their velocity dependence across different theoretical scenarios, aiding astrophysical analysis.

## Contribution

It presents a two-parameter effective-range formalism to approximate dark matter self-interaction cross sections, applicable to various models including Yukawa, Breit-Wigner, and bound states.

## Key findings

- The parametrization accurately models velocity-dependent cross sections.
- It provides a unified interpretation across multiple dark matter interaction models.
- The approach can be refined for specific regimes where it initially performs poorly.

## Abstract

Self-interacting dark matter has been proposed to explain the apparent mass deficit in astrophysical small-scale halos, while observations from galaxy clusters suggest that the corresponding cross section depends on the velocity. Accounting for this is often believed to be highly model-dependent with studies mostly focusing on scenarios with light mediators. Based on the effective-range formalism, in this work we point out a model-independent approach which accurately approximates the velocity dependence of the self-interaction cross section with only two parameters. We illustrate how this parameterization can be simultaneously interpreted in various well-motivated scenarios, including self-interactions induced by Yukawa forces, Breit-Wigner resonances and bound states. We investigate the astrophysical implications and discuss how the approximation can be improved in certain special regimes where it works poorly.