Dark-matter bound states from Feynman diagrams

TL;DR

This paper develops a field-theoretic framework to compute dark matter bound-state formation, de-excitation, and decay rates, highlighting the importance of the Sommerfeld effect in non-relativistic regimes and its implications for dark matter phenomenology.

Contribution

It introduces a novel formalism for calculating bound-state processes in theories with long-range interactions, applicable to scalar and vector mediators and extendable to non-Abelian interactions.

Findings

Bound-state formation is enhanced by the Sommerfeld effect at low velocities.

Bound-state formation can outpace annihilation for particle-antiparticle pairs under certain conditions.

The formalism can be generalized to non-Abelian theories like electroweak interactions.

Abstract

If dark matter couples directly to a light force mediator, then it may form bound states in the early universe and in the non-relativistic environment of haloes today. In this work, we establish a field-theoretic framework for the computation of bound-state formation cross-sections, de-excitation and decay rates, in theories with long-range interactions. Using this formalism, we carry out specific computations for scalar particles interacting either via a light scalar or vector mediator. At low relative velocities of the interacting particles, the formation of bound states is enhanced by the Sommerfeld effect. For particle-antiparticle pairs, we show that bound-state formation can be faster than annihilation into radiation in the regime where the Sommerfeld effect is important. The field-theoretic formalism outlined here can be generalised to compute bound-state formation cross-sections in a variety of theories, including theories featuring non-Abelian (albeit non-confining) interactions, such as the electroweak interactions.