Abstract
One-loop electroweak corrections to the annihilation cross-sections of dark matter in the Higgs resonance region of the inert doublet model (IDM) are investigated. The procedure of how to implement the width of the Higgs in order to regularise the amplitude both at tree-level and at one-loop together with the renormalisation of a key parameter of the model, are thoroughly scrutinised. The discussions go beyond the application to the relic density calculation and also beyond the IDM so that addressing these technical issues can help in a wider context. We look in particular at the dominant channels with 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 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.
Highlights
The discussions go beyond the application to the relic density calculation and beyond the inert doublet model so that addressing these technical issues can help in a wider context
In the accompanying parent paper [1] we have seen that here is a fine-tuned region in the parameter space of the inert doublet model (IDM) [2,3] where if the mass of the lightest neutral scalar of the model X is such that 2MX ≃ Mh 1⁄4 125 GeV [h is the Standard Model (SM) Higgs], a good value of the relic density is obtained within the freeze-out mechanism
The contribution of the ZZ final state is below 3%, which is too small a contribution for any correction to make an impact on the relic density calculation, especially in view of the results we find in the WW channel
Summary
In the accompanying parent paper [1] we have seen that here is a fine-tuned region in the parameter space of the inert doublet model (IDM) [2,3] where if the mass of the lightest neutral scalar of the model X is such that 2MX ≃ Mh 1⁄4 125 GeV [h is the Standard Model (SM) Higgs], a good value of the relic density is obtained within the freeze-out mechanism This is possible thanks to the efficient annihilation of the DM pair through, essentially, the SM Higgs resonance. With λL 1⁄4 0, the relic density is almost as much as 20 times larger This huge increase is due to the extremely small residual gauge contribution from XX → WW⋆ðZZ⋆Þ through the t-channel exchange of HÆðAÞ, which we study at length in Ref.
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