# Relic density of Dark Matter in the Inert Doublet Model beyond Leading Order. I) The Heavy Mass Case

## TL;DR

This paper performs a precise one-loop calculation of dark matter relic density in the Inert Doublet Model for a 500 GeV candidate, highlighting the significance of electroweak corrections and renormalisation scheme dependence.

## Contribution

It provides the first full renormalisation and one-loop electroweak correction calculation for relic density in the IDM's heavy mass regime, including co-annihilation effects.

## Key findings

- One-loop corrections significantly affect relic density predictions.
- Electroweak corrections are crucial for accurate relic density calculations.
- Renormalisation scheme dependence influences the results.

## Abstract

A full renormalisation of the Inert Doublet Model (IDM) is presented and exploited for a precise calculation of the relic density of Dark Matter (DM) at one-loop. In this first paper, we study the case of a DM candidate with $m_{\rm DM} \sim 500$ GeV. In this regime, the co-annihilation channels are important. We therefore compute, for a wide range of relative velocities, the full next-to-leading order electroweak corrections to 7 annihilation/co-annihilation processes that contribute $\sim$ 70\% to the relic density of DM. These corrected cross-sections are interfaced with {\tt micrOMEGAs} to obtain the one-loop correction to the freeze-out relic density. Due to the accurate measurement of this observable, the one-loop corrections are relevant. We discuss the one-loop renormalisation scheme dependence and point out the influence, at one-loop, of a parameter that solely describes the scattering in the dark sector. A tree-level computation of the relic density is not sensitive to this parameter.