Charged lepton flavor violation in light of the muon magnetic moment anomaly and colliders

Any observation of charged lepton flavor violation (CLFV) implies the existence of new physics beyond the SM in charged lepton sector. The muon magnetic moment anomaly between the SM prediction and the recent muon $g-2$ precision measurement at Fermilab provides an opportunity to reveal the nature of underlying CLFV. We consider the most general SM gauge invariant Lagrangian of $\Delta L=0$ bileptons with CLFV couplings to bilinear leptonic fields. The muon $g-2$ anomaly constrains the CLFV coupling $y^{\ell\ell'} (\ell\neq \ell')$ which induces the leptonic transition with $|\Delta(L_\ell-L_{\ell'})|=4$ at tree level. We investigate the implication of the muon magnetic moment anomaly for the CLFV couplings and other relevant constraints from low-energy precision experiments. The projected sensitivity of the future muonium-antimuonium conversion experiment and colliders is evaluated to the individual CLFV couplings satisfying these constraints.