Bound states of WIMP dark matter in Higgs-portal models. Part I. Cross-sections and transition rates

We investigate the role of the Higgs doublet in the thermal decoupling of multi-TeV dark matter coupled to the Weak interactions of the Standard Model and the Higgs. The Higgs doublet can mediate a long-range force that affects the annihilation processes and binds dark matter into bound states. More importantly, the emission of a Higgs doublet by a pair of dark matter particles can give rise to extremely rapid monopole bound-state formation processes and bound-to-bound transitions. We compute these effects in the unbroken electroweak phase. To this end, we consider the simplest renormalisable fermionic model, consisting of a singlet and a doublet under SUL(2) that are stabilised by a Z(2) symmetry, in the regime where the two multiplets coannihilate. In a companion paper, we use the results to show that the formation of metastable bound states via Higgs-doublet emission and their decay decrease the relic density very significantly.