Non-universal gauged lepton number for charged lepton masses hierarchy and $(g-2)_{e,\mu}$

TL;DR

This paper proposes a flavor-dependent gauged lepton number model explaining charged lepton mass hierarchy and the anomalous magnetic moments of electrons and muons, predicting testable collider signatures and deviations from Standard Model Yukawa couplings.

Contribution

It introduces a novel $U(1)_ ext{ell}$ gauge symmetry model that accounts for lepton mass hierarchy and $(g-2)$ anomalies without extra discrete symmetries.

Findings

Successfully explains muon $(g-2)$ anomaly.

Accommodates positive or negative electron $(g-2)$.

Predicts observable deviations in Yukawa couplings at colliders.

Abstract

We construct a novel flavor-dependent gauged lepton number $U(1)_\ell$ model for the hierarchical charged lepton masses and the observed $(g-2)_{e,\mu}$. Only tau participates in the tree-level Standard Model ( SM ) Yukawa interaction. At the same time, the masses of electron and muon are light due to radiative generation and(or) the heavy-mediator-suppressed Yukawa coupling to the SM Higgs. Not only can the measured anomalous magnetic dipole moment of the muon, $\triangle a_\mu$, be explained, but the positive (or negative) $\triangle a_e$ can also be accommodated in this model. Without additional discrete symmetries introduced, charged lepton flavor violation is highly suppressed by the $U(1)_\ell$ symmetry. Corresponding to two equally viable $U(1)_\ell$ charge assignments, this model predicts either $A_{FB}^\mu <A_{FB}^\tau <A_{FB}^e$ or $A_{FB}^\mu >A_{FB}^\tau >A_{FB}^e$, which can be tested at the $e^+e^-$ machines before discovering the $U(1)_\ell$ gauge boson. Moreover, the effective muon and electron Yukawa couplings can depart significantly from the SM predictions, and those deviations could be probed at future $e^+e^-$ colliders and High-Luminosity LHC.