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

TL;DR

This paper demonstrates that generating neutrino masses via a nonzero VEV of the charged Higgs field in the Standard Model leads to violations of electric charge conservation and predicts a photon mass inconsistent with experimental bounds, invalidating the scheme.

Contribution

The paper critically analyzes a proposed neutrino mass generation mechanism involving charged Higgs VEVs and shows it is incompatible with experimental constraints.

Findings

Charged Higgs VEVs break U(1) symmetry and induce photon mass.

Predicted VEV ratios conflict with experimental photon mass bounds.

The proposed scheme for neutrino mass generation is invalid.

Abstract

A scheme of neutrino mass generation is proposed by [arXiv:2003.12069], in which the small nonzero neutrino masses come from nonzero vacuum expectation value (VEV) of the charged Higgs field in the Higgs doublet in the Standard Model of particle physics (SM). However, the introduction of nonzero VEV for the charged Higgs field implies broken ${\rm U}(1)$ symmetry in the electroweak theory, which leads to non-conservation of electric charge and nonzero mass of photon. By comparing the predicted ratio of VEVs of charged Higgs field and neutral Higgs field in [1] with the ratio constrained by the present experimental upper bound of photon mass, we show that this scheme does not work.