 0.001  0.01  0.1  1  10  100  1000  60  80  100  120  140  160  180  200 N h 2 m$_{N}$ [GeV] FIG. 2: The same as Fig. 1 but for sin θ = 0 . 3. mode into W -boson pair becomes kinematically available, it is not possible to obtain the desired DM abundance without the Higgs resonant annihilation because the bound on v ′ given by Eq. (12) is stringent. Our RH neutrino DM can elastically scatter off with nucleon, unlike another RH neutrino DM model has been proposed by Krauss et. al. [21] and studied [22, 23]. The main process is Higgs exchange and the resultant cross section for a proton is given by with the hadronic matrix element and the effective vertex (see Appendix for notations) where m$_{q}$ is a mass of a quark with a Yukawa coupling y$_{q}$ , and f ( p ) Tq and f ( p ) TG are constants. σ ( p ) SI = 4 π ( m$_{p}$m$_{N}$ m$_{p}$ + m$_{N}$ ) 2 f 2 $_{p}$, (17) f$_{p}$ m$_{p}$ = ∑ q = u,d,s f ( p ) Tq α$_{q}$ m$_{q}$ + 2 27 f ( p ) TG ∑ c,b,t α$_{q}$ m$_{q}$ , (18) α$_{q}$ = − λ$_{N}$y$_{q}$ ( ∂ Φ ∂h 1 M 2 h ∂ Ψ ∂h + ∂ Φ ∂H 1 M 2 H ∂ Ψ ∂H ) , (19) B. Direct detection of dark matter 7