Neutral top-pion and the rare top decays $t\to c l_{i} l_{j}$

Abstract

We study the rare top decays $t\to c l_{i} l_{j}(l=τ,μ,or e)$ in the framework of topcolor-assisted technicolor($TC2$) models. We find that the neutral top-pion $π_{t}^{0}$ can produce significant contributions to these processes via the flavor changing couplings $π_{t}^{0} \bar{t} c$ and $π_{t}^{0} l_{i} l_{j}$. For the $π_{t}^{0}$ mass $m_{π_{t}}=150 GeV$ and the parameter $ε=0.08$, the branching ratio $Br$(t$\to c ττ)$ can reach $7.1\times10^{-7}$. Taking into account the constraints of the present experimental limit of the process $μ\to e γ$ on the free parameters of $TC2$ models, we find that the value of $Br$($t\to c τμ$)$\approx$$Br$($t\to c τe$) is in the range of 1.8$\times10^{-10}\sim1.7\times10^{-8}$.