The correction of the littlest Higgs model to the Higgs production process $e^{-}gammato u_{e}W^{-}H$ in $e^{-}gamma$ collisions

The littlest Higgs model is the most economical one among various little Higgs models. In the context of the littlest Higgs(LH) model, we study the process $e^{-}gammato u_{e}W^{-}H$ and calculate the contributions of the LH model to the cross section of this process. The results show that, in most of parameter spaces preferred by the electroweak precision data, the value of the relative correction is larger than 10%. Such correction to the process $e^{-}gammato u_{e}W^{-}H$ is large enough to be detected via $e^{-}gamma$ collisions in the future high energy linear $e^{+}e^{-}$ collider($LC$) experiment with the c.m energy $sqrt{s}$=500 GeV and a yearly integrated luminosity $pounds=100fb^{-1}$, which will give an ideal way to test the model.