parameters to be consistent with the current observations. Nex t we calculate the scattering
cross section between the DM particle and a proton and discuss the implication for the direct
DM search experiments.
A. Thermal relic density
The DM RH neutrino interacts with the SM particles through couplingswith B − L
gauge and B− L Higgs bosons. Note that neutrino Dirac Yukawa interactions are ab sent
because of the Z2 parity. The most of annihilation of the RH neutrinos occurs via Z′,H and
h exchange processes in the s-channel. In practice, the dominant contributions come from
the Higgs ( h and H) exchange diagrams, because the Z′ exchange processes are suppressed
by the inverse square of the B−LHiggs VEV v′ ≳ 3 TeV. Thus, we obtain Higgs portal DM
of RH neutrino eﬀectively. The relevant annihilation modes are the an nihilation into f ¯f,
W+W−, ZZ, and h(H)h(H). Since RH neutrino DM couples to only B− L Higgs Ψ while
a SM particle does to SM Higgs Φ, the DM annihilation occurs only throug h the mixing
between these two Higgs bosons. Although it is not so severe, the p recision electroweak
measurements [12] as well as the unitarity bound [13] give constra ints on the mixing angle
and mass spectrum of the Higgs bosons.
The thermal relic abundance of DM
Ω N h2 = 1 .1 × 109 mN /Td
√g∗MP ⟨σv⟩GeV−1, (14)
with the Planck mass MP , the thermal averaged product of the annihilation cross section
and the relative velocity ⟨σv⟩, the total number of relativistic degrees of freedom in the
thermal bath g∗, and the decoupling temperature Td, is evaluated by solving the Boltzmann
equation for the number density of RH neutrino nN ;
dnN
dt + 3HnN = −⟨σv⟩(n2
N− n2
EQ), (15)
and the Friedmann equation
H2 ≡
( ˙a
a
) 2
= 8π
3M2
P
ρ, (16)
with nEQ and a(t) being the equilibrium number density and the scale factor, under th e
radiation dominated Universe with the energy density ρ= ρrad [14].
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