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Effective Interaction of Electroweak-Interacting Dark Matter with Higgs Boson and Its Phenomenology

We study phenomenology of electroweak-interacting fermionic dark matter (DM) with a mass of $\mathcal{O}(100)$ GeV. Constructing the effective Lagrangian that describes the interactions between the Higgs boson and the SU(2)$_L$ isospin multiplet fermion, we evaluate the electric dipole moment (EDM) of electron, the signal strength of Higgs boson decay to two photons and the spin-independent elastic-scattering cross section with proton. As representative cases, we consider the SU(2)$_L$ triplet fermions with zero/nonzero hypercharges and SU(2)$_L$ doublet fermion. It is found that the electron EDM gives stringent constraints on those model parameter spaces. In the cases of the triplet fermion with zero hypercharge and the doublet fermion, the Higgs signal strength does not deviate from the standard model prediction by more than a few % once the current DM direct detection constraint is taken into account, even if the CP violation is suppressed. On the contrary, $\mathcal{O}(10$-$20)$ % deviation may occur in the case of the triplet fermion with nonzero hypercharge. Our representative scenarios may be tested by the future experiments.