Gauging U(1)U(1) symmetries and the number of right-handed neutrinos

In this Letter we consider that assuming: (a) that the only left-handed neutral fermions are the active neutrinos, (b) that B−LB−L is a gauge symmetry, and (c) that the L   assignment is restricted to the integer numbers, the anomaly cancellation imply that at least three right-handed neutrinos must be added to the minimal representation content of the electroweak standard model. However, two types of models arise: (i) the usual one where each of the three identical right-handed neutrinos has total lepton number L=1L=1; (ii) and the other one in which two of them carry L=4L=4 while the third one carries L=−5L=−5.