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A two Higgs doublet model (2HDM) is one of the minimal extensions of theStandard Model (SM), and it is well-known that the general setup predicts theflavor-violating phenomena, mediated by neutral Higgs interactions. Recentlythe CMS collaboration has reported an excess of the lepton-flavor-violatingHiggs decay in $h \rightarrow \mu \tau$ channel with a significance of 2.5 $\sigma$. We investigate the CMS excess in a general 2HDM with tree-level FlavorChanging Neutral Currents (FCNCs), and discuss its impact on the other physicalobservations. Especially, we see that the FCNCs relevant to the excess canenhance the neutral Higgs contributions to the muon anomalous magnetic moment,and can resolve the discrepancy between the measured value and the SMprediction. We also find that the couplings to be consistent with the muon g-2anomaly as well as the CMS excess in $h\rightarrow \mu\tau$ predict the sizablerate of $ \tau \rightarrow \mu \gamma$, which is within the reach of future Bfactory.

Lepton-flavor-violating Higgs decay $h \to \mu\tau$ and muon anomalous magnetic moment in a general two Higgs doublet model