Lepton flavor violating semileptonic τ decays τto lP(V) in a topcolor scenario

The contributions of the neutral top-pion $\pi_{t}^{0}$ and the non-universal gauge boson $Z'$ predicted by topcolor scenario to the lepton flavor violating $(LFV)$ semileptonic $\tau$ decays $\tau\to lP(V)$ $(P=\pi^{0}, \eta, \eta' $ and $ V=\rho^{0}, \phi)$ are discussed. We find that the contributions of $Z'$ to these decay processes are generally larger than those from $\pi_{t}^{0}$. $\pi_{t}^{0}$ can only make the value of the branching ratio $Br(\tau\to lP)$ in the range of 1$\times10^{-11}$ $\sim$ 1$\times10^{-16}$, which is far below the sensitivity of foreseeable experiments. With reasonable values of the free parameters, the non-universal gauge boson $Z'$ can make the value of the branching ratio $Br(\tau^{-}\to \mu^{-}\phi)$ reach 1$\times10^{-7}$, which might approach the observable threshold of near-future experiments.