The inert doublet model of dark matter revisited

TL;DR

The paper addresses the inert doublet model by incorporating the three-body annihilation channel $H^0H^0 o WW^*$ into relic-density and detection calculations. By computing the cross section $\sigma(H^0H^0 o WW^*)$ and its interference with Higgs-mediated amplitudes, it shows that the 3-body process can dominate over traditional two-body channels in a large portion of parameter space, especially near the $W$ threshold and for certain Higgs masses. This leads to substantial revisions of the relic density predictions and a contraction of the genuine viable parameter space, with direct-detection cross sections reduced by up to two orders of magnitude. The work also highlights broader implications for indirect detection and Higgs phenomenology, underscoring that three-body annihilation must be included for accurate IDM predictions and realistic prospects for discovery.

Abstract

The inert doublet model, a minimal extension of the Standard Model by a second higgs doublet with no direct couplings to quarks or leptons, is one of the simplest scenarios that can explain the dark matter. In this paper, we study in detail the impact of dark matter annihilation into three-body final state on the phenomenology of the inert doublet model. We find that this new annihilation mode dominates, in a relevant portion of the parameter space, over those into two-body final states considered in previous analysis. As a result, the computation of the relic density is modified and the viable regions of the model are displaced. After obtaining the genuine viable regions for different sets of parameters, we compute the direct detection cross section of inert higgs dark matter and find it to be up to two orders of magnitude smaller than what is obtained for two-body final states only. Other implications of these results, including the modification to the decay width of the higgs and to the indirect detection signatures of inert higgs dark matter, are also briefly considered. We demonstrate, therefore, that the annihilation into three-body final state can not be neglected, as it has a important impact on the entire phenomenology of the inert doublet model.

Figures (14)

• Figure 1: The Feynman diagrams that contribute, in the unitary gauge, to the $H^0H^0$ annihilation into the three-body final state $WW^*\to Wf\bar{f}'$ within the inert doublet model. For the $H^+$-mediated diagram the exchange diagram (not shown) must also be taken into account.
• Figure 2: Comparison between the three-body and the two-body annihilation rate, $\sigma\mathrm{v}$, as a function of the dark matter mass for the two possible signs of $\lambda_L$. In the left panel $m_h=120$ GeV whereas in the right panel $m_h=150$ GeV. The other parameters were taken as $\Delta m_{A^0}=\Delta m_{H^\pm}=50$ GeV, $|\lambda_L|=10^{-2}$.
• Figure 3: This figure illustrates the dependence on $m_h$ of the ratio between the three-body and the two-body annihilation rate. For the other parameters, we take $\Delta m_{A^0}=\Delta m_{H^\pm}=50$ GeV and $\lambda_L=10^{-2}$.
• Figure 4: This figure illustrates the dependence on $\lambda_L$ of the ratio between the three-body and the two-body annihilation rate. It shows $\sigma(\text{3-body})/\sigma(\text{2-body})$ as a function of $m_{H^0}$ for two values of $\lambda_L$ ($10^{-2}$ and $10^{-3}$) and two different higgs masses ($120$ and $150\,\mathrm{GeV}$). For the other parameters, we take $\Delta m_{A^0}=\Delta m_{H^\pm}=50$ GeV.
• Figure 5: This figure illustrates the dependence on the sign of $\lambda_L$ of the ratio between the three-body and the two-body annihilation rate. It shows $\sigma(\text{3-body})/\sigma(\text{2-body})$ as a function of $m_{H^0}$ for the possible signs of $\lambda_L$ and two different higgs masses ($120$ and $150\,\mathrm{GeV}$). For the other parameters, we take $\Delta m_{A^0}=\Delta m_{H^\pm}=50$ GeV and $|\lambda_L|=10^{-2}$.