  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.
