Lepton-flavor violation and muon $(g-2)$ in the flavor-dependent $U(1)_F$ model
Lepton flavor violation (LFV) processes are forbidden in the standard model (SM), hence the observation of LFV transitions would represent a clear signal of new physics beyond the SM. In this work, we investigate the muon anomalous magnetic dipole moments (MDM) and LFV processes $l_{j}^{-}\to l_{i}^{-}\gamma $ and $l_{j}^{-}\to l_{i}^{-}l_{i}^{-}l_{i}^{+}$ in the extension of the SM with $U(1)_F$ local gauge symmetry (FDM). The muon anomalous MDM is one of the most precisely measured quantities in particle physics, which can be used to constrain the contributions from new couplings in the FDM. The newly incorporated $U(1)_F$ charges are correlated with the flavor properties of fermions, hence the newly added Yukawa couplings make contributions to these LFV processes. Considering the latest experimental constraints on the muon anomalous MDM, the new interactions in the FDM can make significant contributions to the LFV processes $l_{j}^{-}\to l_{i}^{-}\gamma $ and $l_{j}^{-}\to l_{i}^{-}l_{i}^{-}l_{i}^{+}$, the predicted branching ratios can well reach the future experimental sensitivity.