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 pseudo-scalar interaction of dark matter with the SM-Higgs boson. Thanks to the pseudo-scalar 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 $O(10^{ -32})$ e cm in future.