Michel parameters for $\tau$ decays $\tau \rightarrow l\nu\bar{\nu}~(l=e,~\mu)$ in a general two Higgs doublet model with $\mu-\tau$ flavor violation

In a general two Higgs doublet model (2HDM), the anomaly of muon anomalous magnetic moment (muon g-2) can be explained by $\mu-\tau$ flavor violating Yukawa couplings, motivated by the recent CMS excess in Higgs boson decay $h\rightarrow \mu \tau$. We study Michel parameters for $\tau$ decays $\tau \rightarrow l \nu \bar{\nu}~(l=e,~\mu)$ in the 2HDM with the lepton flavor violation, and show that they can be sensitive to the flavor structure as well as the Lorentz and chiral structures of the model. We find that the correction to the Michel parameter $\xi_\mu$ in $\tau \rightarrow \mu \nu\bar{\nu}$ is correlated to the contribution to the muon g-2, and it can be as large as $10^{-4}-10^{-2}$ in the parameter region where the $\mu-\tau$ flavor violating Yukawa couplings explain the muon g-2 anomaly. Therefore the precision measurement of the Michel parameter at the level of $10^{-4}-10^{-2}$ would significantly probe the interesting parameter space for the solution to the muon g-2 anomaly.