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The new round of experiments, MEG II, COMET/Mu2e, and Mu3e, would soon startto push the $\mu \to e\gamma$, $\mu N \to eN$ conversion, and $\mu \to 3e$frontier, while Belle II would probe $\tau \to \mu\gamma$ and $\tau \to 3\mu$.In the general two Higgs doublet model with extra Yukawa couplings, we showthat all these processes probe the lepton flavor violating (LFV) dipoletransition that arises from the two loop mechanism, with scalar-induced contactterms subdominant. This is because existing data suggest the extra Yukawacouplings $\rho_{\mu e},\, \rho_{ee} \lesssim \lambda_e$, while$\rho_{\tau\mu},\, \rho_{\tau\tau} \lesssim \lambda_\tau$ and $\rho_{tt}\lesssim \lambda_t$, with $\lambda_i$ the usual Yukawa coupling of the StandardModel (SM), where $\rho_{\mu e}\rho_{tt}$ and $\rho_{\tau\mu}\rho_{tt}$ enterthe $\mu e\gamma$ and $\tau\mu\gamma$ two loop amplitudes, respectively. Withthe $B_s \to \mu\mu$ decay rate basically consistent with SM expectation,together with the $B_s$ mixing constraint, we show that $B_s \to \tau\tau$would also be consistent with SM, while $B_s \to \tau\mu$ and $B \to K\tau\mu$decays would be out of reach of projected sensitivities, in strong contrastwith some models motivated by the B anomalies.

Muon Flavor Violation in Two Higgs Doublet Model with Extra Yukawa Couplings