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Bound-state effects on dark matter coannihilation: Pushing the boundaries of conversion-driven freeze-out

Bound-state formation can have a large impact on the dynamics of dark matter freeze-out in the early Universe, in particular for colored coannihilators. We present a general formalism to include an arbitrary number of excited bound states in terms of an effective annihilation cross section, taking bound-state formation, decay and transitions into account, and derive analytic approximations in the limiting cases of no or efficient transitions. Furthermore, we provide explicit expressions for radiative bound-state formation rates for states with arbitrary principal and angular quantum numbers $n,\ell$ for a mediator in the fundamental representation of $SU(3)_c$, as well as electromagnetic transition rates among them in the Coulomb approximation. We then assess the impact of bound states within a model with Majorana dark matter and a colored scalar $t$-channel mediator. We consider the regime of coannihilation as well as conversion-driven freeze-out (or coscattering), where the relic abundance is set by the freeze-out of conversion processes. We find that the region in parameter space where the latter occurs is considerably enhanced into the multi-TeV regime. For conversion-driven freeze-out, dark matter is very weakly coupled, evading direct and indirect detection constraints but leading to prominent signatures of long-lived particles that provide great prospects to be probed by dedicated searches at the upcoming LHC runs.