Type-II seesaw effects on neutrino trident scattering

In this talk, we have briefly discussed the Type-II seesaw contributions to the $W$ mass, charged lepton flavor violation (CLFV), and neutrino trident scattering. Based on CLFV experimental data, we have derived a lower limit on the triplet vacuum expectation value (vev) $v_{\Delta}$ as a function of the triplet scalar mass $m_{\Delta}$: $v_{\Delta} > 6.3\ \mathrm{eV}\ (100\ \mathrm{GeV}/m_{\Delta})$. This result indicates that the effect of the triplet vev $v_{\Delta}$ on the $W$ mass could be neglected. We also find that the Type-II seesaw reduces the standard model (SM) neutrino trident scattering cross section, but the deviation ratio remains above 0.98 at the $3\sigma$ confidence level.