Minimal Gauged U(1)$_{L_\alpha - L_\beta}$ Models Driven into a Corner

Understand

It is well known that the differences between the lepton numbers can be gauged with the Standard Model matter content.

• Such extended gauge theories, dubbed as the gauged U(1)$_{L_\alpha - L_\beta}$ models, have been widely discussed so far as potential candidates for physics beyond the Standard Model.
• In this work, we study the minimal versions of these gauge theories, where three right-handed neutrinos as well as a single U(1)$_{L_\alpha - L_\beta}$ symmetry breaking Higgs field---an SU(2)$_L$ singlet or doublet---are introduced.
• In these minimal models, the neutrino mass terms are constrained by the gauge symmetry, which result in the two-zero texture or two-zero minor structure of neutrino mass matrices.