In Type-II seesaw model, an electroweak triplet scalar field Δ with a non-zero vacuum expectation value (vev) vΔ is introduced to facilitate the generation of small neutrino masses. A non-zero vΔ also affects the W mass through the electroweak ρ parameter, making it to be less than 1 as predicted by standard model (SM). The component fields in Δ come along introduce additional contributions to reduce the SM rare neutrino trident scattering cross section. These fields also induce new processes not existed in SM, such as li→lj‾lkll and li→ljγ. There are severe constraints on these processes which limit the effects on neutrino trident scattering and the ρ parameter and therefore the W mass. The newly measured W mass by CDF makes the central value of ρ parameter to be larger than 1, even larger than previously expected. Combining neutrinoless double beta decay, direct neutrino mass and oscillation data, we find a lower limit for vΔ as a function of the triplet scalar mass mΔ, vΔ>(6.3∼8.4)eV(100GeV/mΔ). To have significant effect on ρ in this model, vΔ needs to be in the range of a GeV or so. However this implies a very small mΔ which is ruled out by data. We conclude that the effect of triplet vev vΔ on the W mass can be neglected. We also find that at 3σ level, the deviation of the ratio for Type-II Seesaw to SM neutrino trident scattering cross section predictions is reduced to be below 1, but is restricted to be larger than 0.98.
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