Higgs boson pair production process $e^+e^-to ZHH$ in the littlest Higgs model at the ILC

The physics prospect at future linear $e^{+}e^{-}$ colliders for the study of the Higgs triple self-coupling via the process of $e^{+}e^{-}to ZHH$ is investigated. In this paper, we calculate the contribution of the new particles predicted by the littlest Higgs model to the cross sections of this process in the future high energy $e^{+}e^{-}$ collider($ILC$). The results show that, in the favorable parameter spaces preferred by the electroweak precision, the deviation of the total cross sections from its $SM$ value varies from a few percent to tens percent, which may be detected at the future $ILC$ experiments with $sqrt{s}$=500GeV.