  The formation of meta-stable dark matter bound states in coannihilating
scenarios could efficiently occur through the scattering with a variety of
Standard Model bath particles, where light bosons during the electroweak cross
over or even massless photons and gluons are exchanged in the t-channel. The
amplitudes for those higher-order processes, however, are divergent in the
collinear direction of the in- and out-going bath particles if the mediator is
massless. To address the issue of collinear divergences, we derive the
bound-state formation collision term in the framework of non-equilibrium
quantum field theory. The main result is an expression for a more general cross
section, which allows to compute higher-order bound-state formation processes
inside the primordial plasma background in a comprehensive manner. Based on
this result, we show that next-to-leading order contributions, including the
bath-particle scattering, are i) collinear finite and ii) generically dominate
over the on-shell emission for temperatures larger than the absolute value of
the binding energy. Based on a simplified model, we demonstrate that the impact
of these new effects on the thermal relic abundance is significant enough to
make it worthwhile to study more realistic coannihilation scenarios.
