New gauge bosons from the littlest Higgs model and the process $e^{+}e^{-}\to t\bar{t}$

In the context of the littlest Higgs$(LH)$ model, we study the process $e^{+}e^{-}\to t\bar{t}$. We find that the new gauge bosons $Z_{H}$ and $B_{H}$ can produce significant correction effects on this process, which can be further enhanced by the suitably polarized beams. In most of the parameter space preferred by the electroweak precision data, the absolute value of the relative correction parameter $R_{B_{H}}$ is larger than 5%. As long as $1TeV\leq M_{Z_{H}}\leq 1.5TeV$ and $0.3\leq c\leq 0.5,$ the absolute value of the relative correction parameter $R_{Z_{H}}$ is larger than 5%. With reasonable values of the parameters of the $LH$ model, the possible signals of the new gauge bosons $B_{H}$ and $Z_{H}$ can be detected via the process $e^{+}e^{-} \to t\bar{t}$ in the future $LC$ experiments with the c.m. energy $\sqrt{S}=800GeV$. $B_{H}$ exchange and $Z_{H}$ exchange can generate significantly corrections to the forward-backward asymmetry $A_{FB}(t\bar{t})$ only in small part of the parameter space.