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.
Highlights
Dark matter (DM) with long-range interactions, mediated by a light or massless force carrier, appears in diverse theories motivated on various grounds
The formation of bound states affects the phenomenology of dark matter in a variety of ways
Computing the rates for bound-state formation and other related processes is essential in calculating the cosmology of DM and accurately estimating the expected DM
Summary
Dark matter (DM) with long-range interactions, mediated by a light or massless force carrier, appears in diverse theories motivated on various grounds. If the interaction is attractive, the Sommerfeld effect enhances the cross-section for any process the two particles may participate in, including the formation of bound states. It follows that, cosmologically, DM bound states form most efficiently after the temperature of the dark plasma drops below the binding energy. We emphasise that BSF is distinct from processes such as the direct annihilation into mediators or elastic scattering, in which particles coupled to a long-range interaction may participate While all these processes are influenced by the Sommerfeld effect, the final-state particles are obviously different. Field-theoretic treatments of the annihilation processes, analogous to the formalism presented here for BSF and discrete level transitions, have been presented in refs. [65, 66]
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