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

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 $K^0\overline{K^0}$ 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.