Single vector-like top partner production in the Left-Right Twin Higgs model at TeV energy $e\gamma$ colliders

The left-right twin Higgs model contains a new vector-like heavy top quark, which mixes with the SM-like top quark. In this work, we studied the single vector-like top partner production via process $e^{-}\gamma \rightarrow \nu_{e}\bar{T}b$ at the International Linear Collider. We calculated the production cross section at tree level and displayed the relevant differential distributions. The result shows that there will be 125 events produced each year with $\sqrt{s}$=2TeV and the integrated luminosity $\mathcal L_{int}\simeq 500fb^{-1}$, and the b-quark tagging and the relevant missing energy $\met$ cut will be helpful to detect this new effect.