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 -> 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 -> 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 -> mu gamma can be within the reach of the Belle II experiment. We also show that the lepton nonuniversality between tau -> mu nu(nu) over bar and tau -> e nu(nu) over bar 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 -> mu l(+)l(-) (l = e, mu), tau -> mu eta, mu -> mu gamma, mu -> 3e and the muon electric dipole moment can be accessible, depending on the unknown Yukawa couplings. On the other hand, the processes like tau -> e gamma and tau -> el(+)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 the h -> mu tau decay mode, the lepton flavor violating Higgs boson decay modes h -> e mu and h -> e tau are strongly suppressed, and hence it will be difficult to observe these modes at the LHC experiment.