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The new particles predicted by the topcolor-assisted technicolor ($TC2$)model and the littlest Higgs model with T-parity (called $LHT$ model) caninduce the lepton flavor violation ($LFV$) couplings at tree level or one looplevel, which might generate large contributions to some $LFV$ processes. Takinginto account the constraints of the experimental data on the relevant freeparameters, we calculate the branching ratios of the $LFV$ decay processes$\tau^-\to\mu^- P_1 P_2 $ with $P_1 P_2$ = $\pi^+\pi^-$, $K^+K^-$ and$K^0\bar{K^0}$ in the context of these two kinds of new physics models. We findthat the $TC2$ model and the $LHT$ model can indeed produce significantcontributions to some of these $LFV$ decay processes.

Lepton flavor violation decays $\tau^-\to \mu^- P_1 P_2$ in the topcolor-assisted technicolor model and the littlest Higgs model with $T$ parity