# Re-derived overclosure bound for the inert doublet model

## TL;DR

This paper refines the overclosure bound for the inert doublet dark matter model by incorporating thermal effects and higher-order corrections, revealing a modest increase in the bound across a broad temperature range.

## Contribution

It introduces a formalism that accounts for thermal effects and resummed corrections in calculating dark matter overclosure bounds for the inert doublet model.

## Key findings

- Resummed corrections increase the overclosure bound by 1-18%.
- Thermal effects are significant in late annihilation stages.
- The analysis covers a broad temperature range, emphasizing late-stage effects.

## Abstract

We apply a formalism accounting for thermal effects (such as modified Sommerfeld effect; Salpeter correction; decohering scatterings; dissociation of bound states), to one of the simplest WIMP-like dark matter models, associated with an "inert" Higgs doublet. A broad temperature range T ~ M/20...M/10^4 is considered, stressing the importance and less-understood nature of late annihilation stages. Even though only weak interactions play a role, we find that resummed real and virtual corrections increase the tree-level overclosure bound by 1...18%, depending on quartic couplings and mass splittings.