  The semileptonic decays $\tau^- \to \mu^- M (M=\pi^0,\eta,\eta')$ could be
sensitive probe for new physics scenarios with lepton flavor violation(LFV).
Motivated by the recent Belle measurement, we investigate these decays in type
III two-Higgs-doublet model (2HDM III), R-parity violating supersymmetric
models(RPV SUSY) and flavor changing $Z'$ models with family non-universal
couplings, respectively. In these new physics scenarios, there are LFV
couplings at tree level. Our results have shown that the decays are very
sensitive to the LFV couplings and could be enhanced to the present
experimental sensitivities. We have derived strong bounds on relevant couplings
of these models, which may be useful for further relevant studies.
