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A scheme of neutrino mass generation is proposed by [arXiv:2003.12069], inwhich the small nonzero neutrino masses come from nonzero vacuum expectationvalue (VEV) of the charged Higgs field in the Higgs doublet in the StandardModel of particle physics (SM). However, the introduction of nonzero VEV forthe charged Higgs field implies broken ${\rm U}(1)$ symmetry in the electroweaktheory, which leads to non-conservation of electric charge and nonzero mass ofphoton. By comparing the predicted ratio of VEVs of charged Higgs field andneutral Higgs field in [1] with the ratio constrained by the presentexperimental upper bound of photon mass, we show that this scheme does notwork.

Why Neutrino Masses Cannot Arise from Nonzero VEV of Charged Higgs Field in the Only Higgs Doublet