In the expression of annihilation cross section, we used the following notations : ∂ Φ ∂h = 1 √$_{2}$ cos θ, ∂ Φ ∂H = 1 √$_{2}$ sin θ, ∂ Ψ ∂h = − 1 √$_{2}$ sin θ, ∂ Ψ ∂H = 1 √$_{2}$ cos θ. (A6) |M| 2 = 32 ∣ g 2 $^{B}$−$_{L}$q$_{f}$ q$_{N}$ s − M 2 Z ′ + iM$_{Z}$ ′ Γ$_{Z}$ ′ ∣ ∣$^{2}$$^{(}$$^{s}$ − 4 m 2 $_{N}$) ( 3 8 s − 1 2 ( s 2 − m 2 f ) + 1 2 ( s 4 − m 2 f ) cos 2 θ ) +16 λ 2 N ∣ ∣$^{y$_{f}$}$ ( ∂ Φ ∂h i s − M 2 h + iM$_{h}$ Γ$_{h}$ ∂ Ψ ∂h + ∂ Φ ∂H i s − M 2 H + iM$_{H}$ Γ$_{H}$ ∂ Ψ ∂H )∣ ∣ ∣$^{2}$ ( s − 4 m 2 $_{N}$) ( s 4 − m 2 f ) . (B1) Appendix B: Amplitude We give explicit formulas of the invariant amplitude squared for the pair annihilation processes of the RH neutrinos. 1. Annihilation into charged fermions 2. Annihilation into neutrinos a. Annihilation into ν$_{a}$, ν$_{a}$ (light active-like neutrinos) |M| 2 = 32 ∣ g 2 $^{B}$−$_{L}$q$_{f}$ q$_{N}$ s − M 2 Z ′ + iM$_{Z}$ ′ Γ$_{Z}$ ′ ∣ ∣$^{2}$$^{(}$$^{s}$ − 4 m 2 $_{N}$) ( 3 8 s − 1 2 ( s 2 + m 2 ν$_{a}$ ) + 1 2 ( s 4 + m 2 ν$_{a}$ ) cos 2 θ ) . (B2) 10