Abstract
The seesaw mechanism is the preferred method to obtain light neutrino masses by introducing a Majorana mass matrix. Moreover, radiative corrections can be made to improve the predictions of the model. However, when such a Majorana mass matrix has no inverse, radiative corrections are the only mechanism to get massive neutrinos. Here, we show a non-universal abelian extension 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. Besides, the right-handed neutrino ν2R also gets mass through radiative corrections involving Majorana fermions. Finally, some limit cases are formulated depending on the hierarchy among vacuum expectation values and Majorana masses.
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