Probing signals of the littlest Higgs model via the $WW$ fusion processes at the high energy $e^{+}{e}^{-}$ collider

In the framework of the littlest Higgs($LH$) model, we consider the processes $e^{+}{e}^{-}\to \nu \bar{\nu }{H}^0$ and $e^{+}e^{-}\to W^{}W^{}\nu\bar{\nu}\to\nu\bar{\nu}t\bar{t}$, and calculate the contributions of new particles to the cross sections of these processes in the future high energy $e^{+}{e}^{-}$ collider($ILC$) with $\sqrt{S}=1TeV$. We find that, with reasonable values of the free parameters, the deviations of the cross sections for the processes $e^{+}{e}^{-}\to \nu \bar{\nu }{H}^0$ from its $SM$ value might be comparable to the future $ILC$ measurement precision. The contributions of the light Higgs boson $H^0$ to the process $e^{+}e^{-}\to W^{}W^{}\nu\bar{\nu}\to\nu\bar{\nu}t\bar{t}$ are significant large in all of the parameter space preferred by the electroweak precision data, which might be detected in the future $ILC$ experiments. However, the contributions of the new gauge bosons $B_H$ and $Z_H$ to this process are very small.