Charged lepton flavor violation in light of Muon $g-2$

The recent confirmation of the muon $g-2$ anomaly by the Fermilab g-2 experiment may harbinger a new era in $\mu$ and $\tau$ physics. As is known, the effect can arise from one-loop exchange of sub-TeV exotic scalar and pseudoscalars, namely $H$ and $A$, that have flavor changing neutral couplings $\rho_{\tau\mu}$ and $\rho_{\mu\tau}$ at $\sim 20$ times the usual tau Weinberg coupling, $\lambda_\tau$. A similar diagram induces $\mu \to e\gamma$, where $\rho_{e\tau}= \rho_{\tau e} = {\cal O}(\lambda_e)$ brings the rate right into the sensitivity of the MEG II experiment, and the $\mu e\gamma$ dipole can be probed further by $\mu \to 3e$ and $\mu N \to eN$. With its promised sensitivity range and ability to use different nuclei, the $\mu N \to e N$ conversion experiments can not only make discovery, but access the extra diagonal quark Weinberg couplings $\rho_{qq}$. For the $\tau$ lepton, $\tau \to \mu\gamma$ would probe $\rho_{\tau\tau}$ down to $\lambda_\tau$ or lower, while $\tau \to 3\mu$ would probe $\rho_{\mu\mu}$ to ${\cal O}(\lambda_{\mu})$.