# Bound States of Pseudo-Dirac Dark Matter

## TL;DR

This paper analyzes the bound-state spectrum of pseudo-Dirac dark matter, highlighting how mass splitting affects bound-state formation and resonances, and provides an analytic method validated for different dark matter models.

## Contribution

It introduces a simple analytic approach to estimate bound-state spectra in systems with mass splitting, applicable to pseudo-Dirac and wino dark matter, and relates capture rates to Sommerfeld enhancement.

## Key findings

- Bound-state spectrum is significantly affected by mass splitting.
- Capture rates into bound states are related to Sommerfeld enhancement.
- Analytic estimates match numerical results for different dark matter models.

## Abstract

We study the bound-state spectrum in a simple model of pseudo-Dirac dark matter, and examine how the rate of bound-state formation through radiative capture compares to Sommerfeld-enhanced annihilation. We use this model as an example to delineate the new features induced by the presence of a mass splitting between the dark matter and a nearly-degenerate partner, compared to the case where only a single dark-matter-like state is present. We provide a simple analytic prescription for estimating the spectrum of bound states in systems containing a mass splitting, which in turn allows characterization of the resonances due to near-zero-energy bound states, and validate this estimate both for pseudo-Dirac dark matter and for the more complex case of wino dark matter. We demonstrate that for pseudo-Dirac dark matter the capture rate into deeply bound states is, to a good approximation, simply related to the Sommerfeld enhancement factor.