Gauged Lepton Flavour

TL;DR

This paper explores gauging lepton flavor symmetries within the Standard Model and its extension, deriving anomaly cancellation conditions that imply Seesaw mechanisms and predicting rich phenomenological signals, especially in the mu-tau sector.

Contribution

It introduces a novel framework for gauging lepton flavor groups, linking anomaly cancellation to Seesaw mechanisms and proposing new scalar field dynamics affecting flavor physics.

Findings

Seesaw mechanisms emerge naturally from anomaly cancellation.

Scalar fields in bifundamental representations modify Yukawa couplings.

Rich phenomenological signals predicted in the mu-tau flavor sector.

Abstract

The gauging of the lepton flavour group is considered in the Standard Model context and in its extension with three right-handed neutrinos. The anomaly cancellation conditions lead to a Seesaw mechanism as underlying dynamics for all leptons; requiring in addition a phenomenologically viable setup leads to Majorana masses for the neutral sector: the type I Seesaw Lagrangian in the Standard Model case and the inverse Seesaw in the extended model. Within the minimal extension of the scalar sector, the Yukawa couplings are promoted to scalar fields in the bifundamental of the flavour group. The resulting low-energy Yukawa couplings are proportional to inverse powers of the vacuum expectation values of those scalars; the protection against flavour changing neutral currents differs from that of Minimal Flavor Violation. In all cases, the $\mu-\tau$ flavour sector exhibits rich and promising phenomenological signals.