Due to the presence of extra top quark T in the little Higgs models, the $CKM$ matrix is not unitary and the flavor changing neutral currents may exist at the tree level. In the context of the Littlest Higgs(LH) model, we discuss the top-charm production at the high-energy linear $e^{ +}e^{ -}$ collider $(LC)$ via the processes $e^{ +}e^{ -}\to \bar{ t}c +t\bar{ c}$, $e^{ +}e^{ -}\to (\bar{ t}c +t\bar{ c})\nu_{ e}\bar{ \nu_{ e}}$, and $e^{ -}\gamma\to e^{ -}\bar{ t}c$. We find that the resonance production cross section for the process $e^{ +}e^{ -}\to \bar{ t}c+ t\bar{ c} $ is significantly larger, which can be detected in future $LC$ experiments.
Categories: hep-ph