Abstract
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 $\sim ab^{-1}$.
Highlights
The Standard Model (SM) of particle physics based on the gauge group SUð3Þ × SUð2Þ × Uð1Þ is spectacularly successful in explaining current data
We have discussed the case in which two out of the three SM lepton generations have opposite Uð1Þl charges, ζ1 1⁄4 −ζ2, as in Refs. [10,11], and the remaining one with Uð1Þl charge ζ3 has its anomalies canceled with four exotic leptons, L1;2 and E1;2, as introduced in Refs. [8,9]
To the best of our knowledge, this solution requires the least number of new degrees of freedom to solve the anomalies for all three generations
Summary
The Standard Model (SM) of particle physics based on the gauge group SUð3Þ × SUð2Þ × Uð1Þ is spectacularly successful in explaining current data It contains two accidental symmetries associated with lepton- and baryon-number conservation. The three SM lepton generations were given different names or quantum numbers, e, μ, τ, and were taken to be conserved.. We shall refer to them as the first, second, and third generations, and reserve the flavor labeling e, μ, τ to denote the charged leptons in the mass basis with the eigenvalues me, mμ, mτ, 1Different conserved electron and muon quantum numbers were first introduced in Ref. We further note that if two generations have equal and opposite lepton charges, e.g., ζ2 1⁄4 −ζ1, the anomaly cancellation can be achieved with a significantly reduced number of new leptons required.
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