b. Annihilation into νs, ν s (heavy sterile-like neutrinos)
|M|2 =
32
⏐
⏐
⏐
⏐
g2
B−Lqf qN
s− M2
Z′ + iMZ′ ΓZ′
⏐
⏐
⏐
⏐
2
(s− 4m2
N)
( 3
8s− 1
2
( s
2 + m2
νs
)
+ 1
2
( s
4 + m2
νs
)
cos2 θ
)
+4λ2
Nλ2
νs
⏐
⏐
⏐
⏐
∂Ψ
∂h
i
s− M2
h + iMhΓh
∂Ψ
∂h + ∂Ψ
∂H
i
s− M2
H + iMH ΓH
∂Ψ
∂H
⏐
⏐
⏐
⏐
2
(s− 4m2
N)(s− 4m2
νs ).
(B3)
3. Annihilation into W +W −
|M|2 = 8 λ2
N
( 1
2g2v
) 2 ⏐
⏐
⏐
⏐
∂Ψ
∂h
1
s− M2
h + iMhΓh
∂φ
∂h + ∂Ψ
∂H
1
s− M2
H + iMH ΓH
∂φ
∂H
⏐
⏐
⏐
⏐
2
(s− 4m2
N)
(
1 + 1
2M4
W
( s
2 − M2
W
) 2)
. (B4)
4. Annihilation into ZZ
|M|2 = 8 λ2
N
( 1
4(g2 + g′2)v
) 2 ⏐
⏐
⏐
⏐
∂Ψ
∂h
1
s− M2
h + iMhΓh
∂φ
∂h + ∂Ψ
∂H
1
s− M2
H + iMH ΓH
∂φ
∂H
⏐
⏐
⏐
⏐
2
(s− 4m2
N)
(
1 + 1
2M4
Z
( s
2 − M2
Z
) 2)
. (B5)
5. Annihilation into hh
M1 denotes the amplitude by s-channel Higgs bosons hand H exchange, while M2 does
that for t(u)-channel N exchange diagram. The formulas for NN → hH and HH can be
obtained by appropriate replacement of the vertexes, e.g., λhhh → λhhH .
|M|2 = |M1 + M2|2, (B6)
|M1|2 = λ2
N
( s
2 − 2m2
N
)
⏐
⏐
⏐
⏐
∂Ψ
∂h
i
s− M2
h + iMhΓh
iλhhh + ∂Ψ
∂H
i
s− M2
H + iMH ΓH
iλHhh
⏐
⏐
⏐
⏐
2
, (B7)
11