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

Abstract

In this letter we consider that assuming: a) that the only left-handed neutral fermions are the active neutrinos, b) that $B-L$ 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=1; ii) and the other one in which two of them carry L=4 while the third one carries $L=-5$.