$τ$- and $μ$-physics in a general two Higgs doublet model with $μ-τ$ flavor violation

Motivated by the recent CMS excess in a flavor violating Higgs decay $h \rightarrow μτ$ as well as the anomaly of muon anomalous magnetic moment (muon g-2), we consider a scenario where both the excess in $h \rightarrow μτ$ and the anomaly of muon g-2 are explained by the $μ-τ$ flavor violation in a general two Higgs doublet model. We study various processes involving $μ$ and $τ$, and then discuss the typical predictions and constraints in this scenario. Especially, we find that the prediction of $τ\rightarrow μγ$ can be within the reach of the Belle II experiment. We also show that the lepton non-universality between $τ\rightarrow μν\barν$ and $τ\rightarrow e ν\barν$ can be sizable, and hence the analysis of the current Belle data and the future experimental improvement would have an impact on this model. Besides, processes such as $τ\rightarrow μl^+ l^-~(l=e,~μ)$, $τ\rightarrow μη$, $μ\rightarrow e γ$, $μ\rightarrow 3e$, and muon EDM can be accessible, depending on the unknown Yukawa couplings. On the other hand, the processes like $τ\rightarrow e γ$ and $τ\rightarrow e l^+ l^-~ (l=e,~μ)$ could not be sizable to observe because of the current strong constraints on the $e-μ$ and $e-τ$ flavor violations. Then we also conclude that contrary to $h \rightarrow μτ$ decay mode, the lepton flavor violating Higgs boson decay modes $h\rightarrow e μ$ and $h\rightarrow eτ$ are strongly suppressed, and hence it will be difficult to observe these modes at the LHC experiment.

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