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

One-loop electroweak corrections to the annihilation cross sections of dark matter in the Higgs resonance region of the inert doublet model are investigated. The procedure of how to implement the width of the Higgs in order to regularize the amplitude both at tree level and at one loop together with the renormalization of a key parameter of the model, are thoroughly scrutinized. The discussions go beyond the application to the relic density calculation and also beyond the inert doublet model so that addressing these technical issues can help in a wider context. We look in particular at the dominant channels with the $b\overline{b}$ final state and the more involved three-body final state, $Wf{\overline{f}}^{\ensuremath{'}}$, where both a resonance and an antiresonance, due to interference effects, are present. We also discuss how to integrate over such configurations when converting the cross sections into a calculation of the relic density.