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One-loop electroweak corrections to the annihilation cross-sections of darkmatter in the Higgs resonance region of the inert doublet model (IDM) areinvestigated. The procedure of how to implement the width of the Higgs in orderto regularise the amplitude both at tree-level and at one-loop together withthe renormalisation of a key parameter of the model, are thoroughlyscrutinised. The discussions go beyond the application to the relic densitycalculation and also beyond the IDM so that addressing these technical issuescan help in a wider context. We look in particular at the dominant channelswith the $b \bar b$ final state and the more involved 3-body final state, $W f\bar f^\prime$, where both a resonance and an anti-resonance, due tointerference effects, are present. We also discuss how to integrate over suchconfigurations when converting the cross-sections into a calculation of therelic density.

Relic density of dark matter in the inert doublet model beyond leading order for the low mass region: 4. The Higgs resonance region