# Pion dark matter in a $\theta$ vacuum: a thermal relic with sharp velocity-dependent self-interactions

## TL;DR

This paper proposes a dark matter model involving a non-zero topological angle and a dark photon portal, which explains the observed relic abundance and predicts velocity-dependent self-interactions relevant for astrophysical phenomena.

## Contribution

It introduces a novel dark matter scenario with a sharp velocity-dependent self-interaction mechanism via a Breit-Wigner resonance, connecting QCD-like theories with astrophysical observations.

## Key findings

- Accounts for observed dark matter relic abundance
- Predicts velocity-dependent self-interactions in halos
- Explains strong-lensing system observations

## Abstract

As recently proposed, a non-vanishing topological angle may play a central role in QCD-like theories of dark matter (DM). In this work, we introduce a dark photon portal to the Standard Model in order to establish thermal equilibrium in the early Universe, and discuss the ensuing phenomenological constraints, including the stability of DM. The resulting dynamics accounts for the observed DM relic abundance and yields velocity-dependent DM self-interactions in astrophysical halos. Due to the sharp velocity dependence arising from a Breit-Wigner resonance, dedicated studies are required to assess the gravothermal evolution in detail, especially in the core-collapse regime. This is particularly timely in light of self-interacting DM interpretations of strong-lensing systems such as SDSS J0946+1006, which can be naturally explained within our framework.