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

We construct a novel flavor-dependent gauged lepton number $U(1{)}_{\mathrm{\ell }}$ 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, $\mathrm{△}{a}_{\mu }$, be explained, but the positive (or negative) $\mathrm{△}{a}_e$ can also be accommodated in this model. Without additional discrete symmetries introduced, charged lepton flavor violation is highly suppressed by the $U(1{)}_{\mathrm{\ell }}$ symmetry. Corresponding to two equally viable $U(1{)}_{\mathrm{\ell }}$ 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 $U(1{)}_{\mathrm{\ell }}$ 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.