Single production of the vector-like top quark in the littlest Higgs model at TeV energy $e^{-}gamma$ colliders

The new colored vector-like heavy fermion $T$ is a crucial prediction in little Higgs models, which plays a key role in breaking the electroweak symmetry. The littlest Higgs model is the most economical one among various little Higgs models. In the context of the littlest Higgs model, we study single production of the new heavy vector-like quark via $e^{-}gamma$ collisions and discuss the possibility of detecting this new particle in the TeV energy $e^{+}e^{-}$ collider(LC). We find that the production cross section can vary in a wide range($10^{-3}-10^{1}fb$) in most parameter spaces. For the favorable parameter spaces, the possible signals of the vector-like top quark $T$ can be detected via $e^{-}gamma$ collisions in future $LC$ experiment with $sqrt{s}=3TeV$ and $pounds=500fb^{-1}$.