  The thermal decoupling description of dark matter (DM) and co-annihilating
partners is reconsidered. If DM is realized at around the TeV-mass region or
above, even the heaviest electroweak force carriers could act as long-range
forces, leading to the existence of meta-stable DM bound states. The formation
and subsequent decay of the latter further deplete the relic density during the
freeze-out process on top of the Sommerfeld enhancement, allowing for larger DM
masses. While so far the bound-state formation was described via the emission
of an on-shell mediator ($W^{\pm}$, $Z$, $H$, $g$, photon or exotic), we point
out that this particular process does not have to be the dominant
scattering-bound state conversion channel in general. If the mediator is
coupled in a direct way to any relativistic species present in the Early
Universe, the bound-state formation can efficiently occur through particle
scattering, where a mediator is exchanged virtually. To demonstrate that such a
virtually stimulated conversion process can dominate the on-shell emission even
for all temperatures, we analyze a simplified model where DM is coupled to only
one relativistic species in the primordial plasma through an electroweak-scale
mediator. We find that the bound-state formation cross section via particle
scattering can exceed the on-shell emission by up to several orders of
magnitude.
