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 $μ$ and $τ$ 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 $ρ_{τμ}$ and $ρ_{μτ}$ at $\sim 20$ times the usual tau Yukawa coupling, $λ_τ$. Taking $ρ_{\ell\ell^\prime}\sim λ_{ \rm min(\ell, \ell^\prime)}$, 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 $μ\to e γ$, $μ\to eee$ and $μN \to e N$, and $τ$ decays $τ\to μγ$ and $τ\to μμμ$. A similar one-loop diagram with $ρ_{eτ}= ρ_{τe} = {\cal O}(λ_e)$ induces $μ\to eγ$, bringing the rate right into the sensitivity of the MEG~II experiment. The $μeγ$ dipole can be probed further by $μ\to 3e$ and $μN \to e N$. With its promised sensitivity range and ability to use different nuclei, the $μN \to eN$ conversion experiments can not only make discovery, but access the extra diagonal quark Yukawa couplings $ρ_{qq}$. For the $τ$ lepton, we find that $τ\to μγ$ would probe $ρ_{ττ}$ down to $λ_τ$ or lower, while $τ\to 3μ$ would probe $ρ_{μμ}$ to ${\cal O}(λ_μ)$.

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