Comment on Radiative Neutrino Mass Matrix with a Sterile Neutrino
  A mechanism of radiatively generating neutrino masses is implemented in an SU(2)_L x U(1)_Y x SU(2)'_L x U(1)'_Y model, where the first and second families respect SU(2)_L x U(1)_Y while SU(2)'_L x U(1)'_Y is specific for the third family. The fourth neutrino, nu_s, that has a U(1)_Y x U(1)'_Y coupling joins in the model to induce neutrino mixings by additional interactions with e and mu. The phenomenologically consistent oscillation of nu_s - nu_e requires a dominated coupling of nu_s to e. 
Yutaka Okamoto and Masaki Yasue