Effects of Bound States on Dark Matter Annihilation

TL;DR

This paper investigates how bound state formation influences dark matter annihilation signals, revealing significant effects for indirect detection but negligible impact during early universe epochs.

Contribution

It derives a comprehensive cross section for bound state formation in dark matter models with a light mediator, highlighting its velocity and mediator mass dependence.

Findings

Bound states can significantly enhance dark matter annihilation signals in galaxies.

Bound state effects are negligible during freeze out and recombination epochs.

Fermi gamma ray constraints are more stringent when bound states are considered.

Abstract

We study the impact of bound state formation on dark matter annihilation rates in models where dark matter interacts via a light mediator, the dark photon. We derive the general cross section for radiative capture into all possible bound states, and point out its non-trivial dependence on the dark matter velocity and the dark photon mass. For indirect detection, our result shows that dark matter annihilation inside bound states can play an important role in enhancing signal rates over the rate for direct dark matter annihilation with Sommerfeld enhancement. The effects are strongest for large dark gauge coupling and when the dark photon mass is smaller than the typical momentum of dark matter in the galaxy. As an example, we show that for thermal dark matter the Fermi gamma ray constraint is substantially increased once bound state effects are taken into account. We also find that bound state effects are not important for dark matter annihilation during the freeze out and recombination epochs.