Non-universal gauge bosons $Z^{\mathrm{\prime }}$ and rare top decays

We study a new method for detecting non-universal gauge bosons $Z^{\mathrm{\prime }}$ via considering their effects on rare top decays. We calculate the contributions of the non-universal gauge bosons $Z^{\mathrm{\prime }}$ predicted by topcolor-assisted technicolor (TC2) models and flavor-universal TC2 models on the rare top decays $t⟶cV(V=g,\gamma ,Z)$ and $t\longrightarrow cl_{i}l_{j}(l_{i}, l_{j}=\tau, \mu$,or$e)$. We show that the branching ratios of these processes can be significantly enhanced. Over a sizable region of the parameter space, we have $Br(t⟶cg)\sim {10}^{-5}$ and $Br(t\longrightarrow c\tau\tau)\sim10^{-7}$, which may approach the observable threshold of near future experiments. Non-universal gauge bosons $Z^{\mathrm{\prime }}$ may be detected via the rare top decay processes at the top-quark factories such as the CERN LHC.