$\tau$- and $\mu$-physics in a general two Higgs doublet model with $\mu -\tau$ flavor violation

Abstract

Motivated by the recent CMS excess in a flavor violating Higgs decay $h\to \mu \tau$ as well as the anomaly of muon anomalous magnetic moment (muon g-2), we consider a scenario where both the excess in $h\to \mu \tau$ and the anomaly of muon g-2 are explained by the $\mu -\tau$ flavor violation in a general two Higgs doublet model. We study various processes involving $\mu$ and $\tau$, and then discuss the typical predictions and constraints in this scenario. Especially, we find that the prediction of $\tau \to \mu \gamma$ can be within the reach of the Belle II experiment. We also show that the lepton non-universality between $\tau \to \mu \nu \bar{\nu }$ and $\tau \to e\nu \bar{\nu }$ 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 $\tau \to \mu l^{+}{l}^{-}(l=e,\mu )$, $\tau \to \mu \eta$, $\mu \to e\gamma$, $\mu \to 3e$, and muon EDM can be accessible, depending on the unknown Yukawa couplings. On the other hand, the processes like $\tau \to e\gamma$ and $\tau \to e{l}^{+}{l}^{-}(l=e,\mu )$ could not be sizable to observe because of the current strong constraints on the $e-\mu$ and $e-\tau$ flavor violations. Then we also conclude that contrary to $h\to \mu \tau$ decay mode, the lepton flavor violating Higgs boson decay modes $h\to e\mu$ and $h\to e\tau$ are strongly suppressed, and hence it will be difficult to observe these modes at the LHC experiment.

35 pages, 17 figures, 1 table

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