can be achieved only when the annihilation processes are enhanced b y Higgs resonances.
Therefore, the mass of the RH neutrino DM should be around a half o f Higgs boson masses.
We have also calculated the elastic scattering cross section betwee n the DM particle and a
proton and found it within the reach of future experiments for the direct DM search.
Appendix A: The Higgs sector
The Higgs potential (4) contains ﬁve parameters:m2
1,m2
2,λ1,λ2 and λ3. These parameters
can be rewritten in terms of two Higgs VEVs, two physical Higgs mass es and the mixing
angle between them. The stationary conditions are
m2
1+ λ1v2 + 1
2λ3v′2 = 0 , (A1)
m2
2+ λ2v2 + 1
2λ3v′2 = 0 . (A2)
The physical Higgs masses are given by Eqs. (8) and (9) with the mixin g angle that θsatisﬁes
tan 2θ= − λ3vv′
(λ1v2 − λ2v′2). (A3)
Higgs self interaction terms are expressed as
Lint = λ1vφ3 + λ2v′ψ3 + 1
2λ3(vφψ2 + v′ψφ2) + 1
4(λ1φ4 + λ2ψ4 + λ3φ2ψ2), (A4)
in terms of φ and ψ. With Eq. (7), these are rewritten in terms of h and H with θ as
Lint
=
[
λ1vcos3 θ− λ2v′ sin3 θ+ 1
2λ3(vcos θsin2 θ− v′ sin θcos2 θ)
]
hhh
+
[
3λ1vcos2 θsin θ+ 3λ2v′ sin2 θcos θ+ 1
2λ3(v(sin3 θ− 2 cos2 θsin θ)
+v′(cos3 θ− 2 sin2 θcos θ))
]
hhH
+
[
3λ1vcos θsin2 θ− 3λ2v′ sin θcos2 θ+ 1
2λ3(v(cos3 θ− 2 sin2 θcos θ)
+v′(− sin3 θ+ 2 sin θcos2 θ))
]
hHH
+
[
λ1vsin3 θ+ λ2v′ cos3 θ+ 1
2λ3(vsin θcos2 θ+ v′ sin2 θcos θ)
]
HHH
+four point interactions . (A5)
We can read oﬀ a Higgs three point vertex from Eq. (A5).
9