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

TL;DR

This paper explores the implications of gauging U(1) symmetries, specifically B-L, on the number and lepton number assignments of right-handed neutrinos, revealing two distinct model types based on anomaly cancellation.

Contribution

It demonstrates that anomaly cancellation conditions necessitate at least three right-handed neutrinos with specific lepton number assignments, leading to two possible model classes.

Findings

At least three right-handed neutrinos are required for anomaly cancellation.

Two model types emerge: one with all neutrinos having L=1, another with mixed lepton numbers (L=4 and L=-5).

The lepton number assignments influence neutrino mass models and gauge symmetry structure.

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 $L=-5$.