Alternative Perspective on Gauged Lepton Number and Implications for Collider Physics

A new anomaly-free gauged $U(1)_\ell$ lepton-number model is studied. Two standard model lepton generations acquire the same but oppositive sign $U(1)_\ell$ charges, while four exotic chiral leptons cancel the anomalies of the remaining lepton family. We discuss a simplified case which has the universal Yukawa couplings. It agrees with all the experimental constraints and predicts $m_e, m_\mu \ll m_\tau$, and the latter is of the electroweak scale. Due to the interference between the SM and $U(1)_\ell$ gauge interactions, this model robustly predicts that $e,\mu,\tau$ have distinctive forward-backward asymmetries at the $e^+e^-$ colliders. It can be searched for at the $e^+e^-$ machine with $\sim$ TeV center-of-mass energy and an integrated luminosity $\sim ab^{-1}$.