Radiative neutrino masses with forbidden seesaw mechanism in an abelian extension of the Standard Model

Abstract: The seesaw mechanism is the preferred methodology to obtain light neutrino masses by the introduction of a Majorana mass matrix. Moreover, radiative corrections can be done in order to improve the predictions of the model. However, when such a Majorana mass has no inverse, radiative corrections turn out as the only mechanism to get massive neutrinos. In this letter, it is shown a nonuniversal abelian extension $\mathrm{U(1)}_{X}$ of the Standard Model in which neutrinos acquire masses completely by radiative corrections through one-loop self-energies involving heavier right-handed neutrinos. Moreover, one right-handed neutrino also gets mass through radiative corrections involving Majorana fermions. Finally, some limit cases are drafted depending on the hierarchy among vacuum expectation values and Majorana masses.