Lepton flavor violation decays τ^-to μ^- P₁ P₂ in the topcolor-assisted technicolor model and the littlest Higgs model with T parity

The new particles predicted by the topcolor-assisted technicolor ($TC2$) model and the littlest Higgs model with T-parity (called $LHT$ model) can induce the lepton flavor violation ($LFV$) couplings at tree level or one loop level, which might generate large contributions to some $LFV$ processes. Taking into account the constraints of the experimental data on the relevant free parameters, 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 find that the $TC2$ model and the $LHT$ model can indeed produce significant contributions to some of these $LFV$ decay processes.