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The triplets with non-zero lepton number do not couple to quarks directly. The Yukawa interaction between the scalars and leptons is 

<img src='content_image/343778.jpg'>

which leads to the following seesaw formula for left-handed neutrino mass matrix 

<img src='content_image/343779.jpg'>

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 

<img src='content_image/343780.jpg'>

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 

<img src='content_image/343781.jpg'>

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 − $^{10}$. 

