Fig. 1 shows the relic density Ω N h2 as a function of the DM mass mN for a set of
parameters: ( v′,Mh,MH ,MZ′ ,sin θ) = (4000 GeV ,120 GeV ,200 GeV ,1000 GeV ,0.7), for
example. Willkinson Microwave Anisotropy Probe measured the value o f DM abundance as
Ω DM h2 ≃ 0.1 [15]. The ﬁgure shows that a desired DM relic abundance can be obta ined for
only near Higgs resonances, mN ≈ Mh/2 or MH /2.
Fig. 2 shows the relic density Ω N h2 as a function of the DM mass mN for a smaller Higgs
mixing sin θ= 0 .3 (others are the same as in Fig. 1). Compared with Fig. 1, for mN ≲ MW
where the DM particles dominantly annihilate into f ¯f, the relic density further increases
because of the small mixing angle. When the DM is heavier, the annihilat ion mode into
Higgs boson pairs is opened and the relic density slightly deceases, bu t the reduction is not
enough to reach Ω N h2 ≃ 0.1.
 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. 1: The thermal relic density of RH neutrino DM as a function of its mass for a parameter
set: (v′, M h, M H , M Z′ , sin θ) = (3000 GeV, 120 GeV, 200 GeV, 1000 GeV, 0. 7).
Our model is quite analogous to the so-called gauge singlet scalar dar k matter [16–18].
Some recent studies can be found in Refs. [19, 20]. In the gauge sing let scalar DM model, the
thermal abundance is mainly controlled by the interactions between the SM Higgs boson and
the DM particle. In our model, B− LHiggs VEV v′ can play the same role for mN <MW ,
namely a larger v′ corresponds to weaker coupling between DM and Higgs for a ﬁxed DM
mass. On the other hand, for mN > MW the diﬀerence appears. Even if the annihilation
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