Lepton flavor violating signals of the neutral top-pion in future lepton colliders

The presence of the top-pions $\pi_{t}^{0,\pm}$ in the low-energy spectrum is an inevitable feature of the topcolor scenario. Taking into account the constraints of the present experimental limit of the lepton flavor violating($LFV$) process $\mu\to e\gamma$ on the free parameters of topcolor-assisted techicolor(TC2) models, we study the contributions of the neutral top-pion $\pi^{0}_{t}$ to the $LFV$ processes $\mu^{+}\mu^{-}\to\tau \mu$ (or $\tau e$), $ \gamma \gamma\to\tau \mu$ (or $\tau e$), $e^{+} e^{-}\to\tau \mu $, and $e \gamma\to e \pi_{t}^{0}\to e \tau \mu(e)$ via the flavor changing ($FC$) couplings $\pi_{t}^{0}l_{i}l_{j}$ and discuss the possibility of searching for the $LFV$ signals via these processes in future lepton colliders.