Single production of the top partners at high energy colliders

The left-right twin $Higgs$ ($LRTH$) model is a concrete realization of the twin $Higgs$ mechanism, which predicts the existence of the top partner $T$. In this paper, we consider production of $T$ associated with the top quark $t$ at the high energy linear $e^{+}{e}^{-}$ collider ($ILC$) and the $LHC$ experiments, and its single production in future linac-ring type $ep$ collider experiment. To compare our results with those of the littlest $Higgs$ model with $T$-parity, we also estimate production of the $T$-even top partner $T_{+}$ via the corresponding processes in these high energy collider experiments. A simply phenomenological analysis is also given.