The Higgs ﬁelds φ and ψ are obtained by expanding Φ and Ψ as
Φ =

 0
1
√
2 (v+ φ)

, (5)
Ψ = 1
√
2(v′ + ψ), (6)
around the true vacuum with the vacuum expectation values v and v′. These are related
with the mass eigenstates h and H through

h
H

=

cos θ − sin θ
sin θ cos θ



φ
ψ

, (7)
with θ being the mixing angle. Their masses are given by
M2
h = 2 λ1v2 cos2 θ+ 2λ2v′2 sin2 θ− 2λ3vv′ sin θcos θ, (8)
M2
H = 2 λ1v2 sin2 θ+ 2λ2v′2 cos2 θ+ 2λ3vv′ sin θcos θ. (9)
The mass of the new neutral gauge boson Z′ arises by the U(1)B−L gauge symmetry
breaking,
M2
Z′ = 4 g2
B−Lv′2. (10)
Associated with the U(1)B−L gauge symmetry breaking, the RH neutrinos Ni acquire masses
MNi = −λRi
v′
√
2. (11)
From LEP experiment, the current lower bound on the Z′ boson mass has been found to
be [10, 11]
MZ′
gB−L
= 2 v′ ≳ 6 − 7 TeV. (12)
Two Z2-even RH neutrinos N1 and N2 are responsible for light neutrino masses via the
seesaw mechanism,
mναβ = −
∑
i=1, 2
yαi yiβ
v2
2MNi
. (13)
Note that the rank of this mass matrix is two, so that the lightest ne utrino is massless.
III. RIGHT-HANDED NEUTRINO DARK MATTER
Due to the Z2 parity, one of RH neutrino N3 (we denote it as N hereafter) in our model
can be the DM candidate. We ﬁrst estimate its relic abundance and ide ntify the model
4