Current status and future prospects of the singlet-doublet dark matter model with $CP$ violation

We discuss the singlet-doublet fermion dark matter model with $CP$-violation. In this model, the $CP$ violation generates a pseudoscalar interaction of dark matter with the standard model-Higgs boson. Thanks to the pseudoscalar interaction, the model can evade the strong constraint from the dark matter direct detection experiments while keeping the success of the thermal relic scenario. The $CP$ violation also predicts signals in dark matter indirect detection experiments and electric dipole moments (EDM) that can be as large as the current upper bound. We investigate the constraints and prospects of the direct detection experiments, the indirect detection experiment, and the electron EDM. We also investigate the stability of the Higgs potential. Combining these observables, we find that heavy dark matter is disfavored. We also find it is possible to probe the Higgs funnel region by the combination of the direct detection experiments and the measurements of the electron EDM if experiments for the electron EDM reach to $\mathcal{O}({10}^{-32})e\mathrm{cm}$ in future.

Figure 1

The schematic view of the UV completion from the effective theory to the singlet-doublet model.

Figure 2

The fermion dark matter with $m_{\mathrm{DM}}=55$ (upper left), 100 (upper right), 300 (lower left), and 1000 GeV (lower right). The relic abundance $\mathrm{\Omega }{h}^2=0.1198$ on the red lines. The right region of the blue lines is excluded by the XENON1T experiment [2].

Figure 3

The spin-independent cross section for the DM-nucleon scattering. The current upper bound on ${\sigma }_{\mathrm{SI}}$ from the XENON1T experiment [2] is shown by the black solid line. For $m_{\mathrm{SM}}>1\mathrm{TeV}$, we extrapolate the result given in Ref. [2], and show it by the black dashed line. We also show the future prospects for the XENONnT experiment [44] and LZ experiment [45] by the red solid line. The other lines are the prediction of the effective theory given in Eq. (2.1).

Figure 4

The constraint on the effective theory from the measurements of the $\gamma$-ray flux from the dSphs by the Fermi-LAT experiment. In the upper panel, we use the 19 dSphs whose J-factors were measured kinematically.

Figure 5

Current situation (upper panels) and prospects (lower panels)of the singlet-doublet model for $M_2=1\mathrm{TeV}$ and $r=1$. The gray, green, and blue shaded regions are excluded by the XENON1T [2], ACME [40], and Fermi-LAT experiment [37], respectively. The cyan region is excluded by the measurement of the Higgs invisible decay at the LHC experiments [67, 68]. For the prospect, we used LZ [45] and $|d_e|={10}^{-30}e\mathrm{cm}$ [61, 62].

Figure 6

The cutoff scale from the stability bound. The upper (lower) panels are for $M_2=1(3)\mathrm{TeV}$ and $r=1$. In the red, orange, and yellow regions, $\mathrm{\Lambda }<50\mathrm{TeV}$, $50\mathrm{TeV}<\mathrm{\Lambda }<500\mathrm{TeV}$, and $500\mathrm{TeV}<\mathrm{\Lambda }$, respectively. The gray regions are excluded by the XENON1T experiment [2].

Figure 7

Current situation (upper panels) and prospects (lower panels) of the singlet-doublet model for $M_2=3\mathrm{TeV}$ and $r=1$. The color notation is the same as Fig. 5.

Figure 8

The current and prospects of the direct detection experiments on the Higgs funnel region.

Figure 9

The branching ratio of the Higgs boson decaying to the DM pairs for $M_2=1\mathrm{TeV}$ and $r=1$. The gray and cyan shaded regions are excluded by the XENON1T experiment [2], and the LHC experiment [67, 68], respectively.

Figure 10

The eEDM for $M_2=1\mathrm{TeV}$, $r=1$. The gray and cyan shaded regions are excluded by the XENON1T experiment [2], and the LHC experiment [67, 68], respectively. The green region in the right panel is excluded by the ACME experiment [40] The blue dashed line is the prospects by [61, 62]. We take $\varphi =0.5\pi$ in the right panel.