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. In the context of general two Higgs doublet model, the discrepancy can be explained via 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 Yukawa coupling, $\lambda_\tau$. Taking $\rho_{\ell\ell^\prime}\sim \lambda_{ \rm min(\ell, \ell^\prime)}$, we show that the above solution to muon $g-2$ then predicts enhanced rates of various charged lepton flavor violating processes, which should be accessible at upcoming experiments. We cover muon related processes such as $\mu \to e \gamma$, $\mu \to eee$ and $\mu N \to e N$, and $\tau$ decays $\tau \to \mu \gamma$ and $\tau \to \mu\mu\mu$. A similar one-loop diagram with $\rho_{e\tau}= \rho_{\tau e} = {\cal O}(\lambda_e)$ induces $\mu \to e\gamma$, bringing the rate right into the sensitivity of the MEG~II experiment. The $\mu e\gamma$ dipole can be probed further by $\mu \to 3e$ and $\mu N \to e N$. With its promised sensitivity range and ability to use different nuclei, the $\mu N \to eN$ conversion experiments can not only make discovery, but access the extra diagonal quark Yukawa couplings $\rho_{qq}$. For the $\tau$ lepton, we find that $\tau \to \mu\gamma$ would probe $\rho_{\tau\tau}$ down to $\lambda_\tau$ or lower, while $\tau \to 3\mu$ would probe $\rho_{\mu\mu}$ to ${\cal O}(\lambda_{\mu})$.