A family-dependent U(1)_{Lμ-Lτ} gauge boson adds a one-loop term to the Weinberg-operator RGE that can raise the rank of the neutrino mass matrix, generating a lightest neutrino mass even if it starts at zero.
Feynman rules for fermion number violating interactions
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Quantum effects on neutrino parameters from a flavored gauge boson
A family-dependent U(1)_{Lμ-Lτ} gauge boson adds a one-loop term to the Weinberg-operator RGE that can raise the rank of the neutrino mass matrix, generating a lightest neutrino mass even if it starts at zero.