Relic density of dark matter in the inert doublet model beyond leading order for the low mass region. II. Coannihilation

Shankha Banerjee,Fawzi Boudjema,Hao Sun,Nabarun Chakrabarty

doi:10.1103/physrevd.104.075003

Abstract

We examine the relic density of the light mass dark matter region in the inert doublet model (IDM) when the dominant process is due to co-annihilation between the lightest neutral scalars of the model. The full one-loop electroweak corrections are computed in an on-shell scheme and are found to be well approximated as an effective cross-section expressed in terms of $Z$-observables. The electroweak corrections to the subdominant process which consists of an annihilation into an on-shell $W$ and an off-shell $W$, that is calculated as a annihilation into a 3-body final state, is also performed. The latter reveals an important dependence on a parameter that describes the self-interaction of the new scalars (solely within the dark sector), a parameter which is not accessible in tree-level calculations of standard model (SM)-IDM interactions.

Highlights

In the very thorough analysis we have conducted in the parent paper [1] of this series on the available parameter space of the inert doublet model (IDM) [2,3] for the low mass dark matter (DM), we have confirmed the survival of a very small region with a DM mass of 55–60 GeV, which has been unraveled [4,5] only recently
We examine the relic density of the light mass dark matter region in the inert doublet model (IDM) when the dominant process is due to coannihilation between the lightest neutral scalars of the model
The electroweak corrections to the subdominant process, which consists of an annihilation into an on shell W and an off shell W, that is calculated as a annihilation into a three-body final state, is performed

Summary

INTRODUCTION

In the very thorough analysis we have conducted in the parent paper [1] of this series on the available parameter space of the inert doublet model (IDM) [2,3] for the low mass dark matter (DM) (below the W mass, MW), we have confirmed the survival of a very small region with a DM mass of 55–60 GeV, which has been unraveled [4,5] only recently. The annihilations are essentially P wave with a very small S-wave contribution that is noticeable only for extremely small velocities in the case of the heaviest final state fermion, the b quark For such 2 → 2 processes, the cross section can be described by a transparent analytical formula. Despite our P-wave appellation, note that the s (and v) dependence contained in σfv2fis not small for the two scenarios that we are studying; see Fig. 2 This s-dependent factor in the expression of σ ffv explains that for the same value of the relative velocity, the coannihilation processes are about 20% larger for P58 as compared to P60. The effective corrective factor misses only about −0.5% for the benchmark point P58 (almost independent of the nature of the fermion) of the full one-loop corrections and about −1% for P60 These small corrections are the effect of the box contributions. As soon as the P-wave contribution kicks in, the tiny λ2 dependence in the S-wave contribution is totally swamped, such that the one-loop

Tree-level considerations

One-loop results

EFFECT ON THE RELIC DENSITY

Findings

CONCLUSIONS