ℓ − ℓ − ℓ + ℓ + δ −− δ ++ S$_{D}$ ℓ − ν ¯ ν ℓ + δ − δ + S$_{D}$ ν ν ¯ ν ¯ ν δ 0 δ 0 S$_{D}$ FIG. 1: Feynman diagrams for DM particle S$_{D}$ decaying into charged leptons and neutrinos through intermediate SU (2)$_{L}$ triplets δ ++ L δ −− L , δ + $_{L}$δ − L and δ 0 $_{L}$δ 0 $_{L}$. 7 where Y$_{ℓℓ}$ is the Yukawa coupling between δ ++ L and charged lepton ℓ $^{+}$. For the typical case v$_{L}$ ∼ O (10 − $^{9}$) GeV and m$_{δ}$$_{L}$ ∼ O (10 $^{3}$) GeV, Γ( δ ++ L → ℓ $^{+}$ℓ$^{+}$) is always dominant over Γ( δ ++ L → W $^{+}$W$^{+}$) as long as the Yukawa coupling is not too small, namely, Y$_{ℓℓ}$ ≳ 10 − $^{10}$. An important consequnce of the smallness of v$_{L}$ is that the couplings between left-handed triplets and SM gauge bosons W ± and Z 0 are strongly suppressed, as δ ±± L W $^{∓}$W $^{∓}$, δ ± $_{L}$W $^{∓}$Z 0 and δ 0 $_{L}$Z $^{0}$Z0 couplings are all proportional to v$_{L}$ . For instance, the ratio between the decay width of δ ++ L → ℓ $^{+}$ℓ+ and δ ++ L → W $^{+}$W+ is given by with ( M$_{L}$$_{(}$$_{R}$$_{)}$ )$_{ij}$ = y$_{ij}$v$_{L}$$_{(}$$_{R}$$_{)}$$_{/}$√$_{2 and (}$$_{M}$$_{D}$$_{)}$$_{ij}$ = ( h$_{ij}$κ$_{1}$ + ˜ h$_{ij}$κ ∗ 2 + g$_{ij}$ξ$_{1}$ + ˜ g$_{ij}$ξ ∗ $_{2}$) $_{/}$√$_{2. The upper}$ bound for v$_{L}$ from neutrino masses is around a few eV, and that from the ρ -parameter in electroweak precision measurements is about 1 GeV. The absence of W$_{R}$ from collider searches sets a lower bound of v$_{R}$ ≳ O (TeV). Thus the hierarchies in neutrino masses, SM gauge boson masses and the right-handed gauge boson masses require that which leads to the following seesaw formula for left-handed neutrino mass matrix The triplets with non-zero lepton number do not couple to quarks directly. The Yukawa interaction between the scalars and leptons is L Y = − ¯ ℓ$_{Li}$ ( h$_{ij}$φ + ˜ h$_{ij}$ ˜ φ + g$_{ij}$χ + ˜ g$_{ij}$ ˜ χ ) ℓ$_{Rj}$ − y$_{ij}$ $^{(}$ℓ c $_{Li}$iτ$_{2}$ Δ$_{L}$ ℓ$_{Lj}$ + ℓ c $_{Ri}$iτ$_{2}$ Δ$_{R}$ ℓ$_{Rj}$ $^{)}$+ h.c, (10) M$_{ν}$ = M$_{L}$ − M$_{D}$ 1 M$_{R}$ M T D (11) v$_{L}$ ≪ κ ≪ v$_{R}$ . (12) Γ( δ ++ L → W $^{+}$W$^{+}$) Γ( δ ++ L ℓ $^{+}$ℓ$^{+}$) ≈ g 4 16$^{(}$ v$_{L}$m$_{δ}$$_{L}$ Y$_{ℓℓ}$m 2 W ) 2 , (13)