0.001
 0.01
 0.1
 1
 10
 100
 1000
 60  80  100  120  140  160  180  200
Ω N   h 2
m N   [GeV]
FIG. 2: The same as Fig. 1 but for sinθ = 0. 3.
mode into W-boson pair becomes kinematically available, it is not possible to obtain t he
desired DM abundance without the Higgs resonant annihilation becau se the bound on v′
given by Eq. (12) is stringent.
B. Direct detection of dark matter
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 giv en by
σ(p)
SI = 4
π
( mpmN
mp + mN
) 2
f2
p , (17)
with the hadronic matrix element
fp
mp
=
∑
q=u,d,s
f(p)
T q
αq
mq
+ 2
27f(p)
T G
∑
c,b,t
αq
mq
, (18)
and the eﬀective vertex (see Appendix for notations)
αq = −λN yq
( ∂Φ
∂h
1
M2
h
∂Ψ
∂h + ∂Φ
∂H
1
M2
H
∂Ψ
∂H
)
, (19)
where mq is a mass of a quark with a Yukawa coupling yq, and f(p)
T q and f(p)
T G are constants.
7