Single Higgs boson production at $e^{+}e^{-}$ colliders in the Littlest Higgs Model with T-parity

In this work, we investigate the Higgs-boson production processes $e^{+}e^{-}\rightarrow ZH$, $e^{+}e^{-}\rightarrow \nu_{e}\bar{\nu_{e}}H$ and $e^{+}e^{-}\rightarrow e^{+}e^{-}H$ in the littlest Higgs model with T-parity. We present the production cross sections, the relative corrections and some distributions of the final states. In the allowed parameter space, we find that the relative corrections of the three production channels are negative, the relative correction of the $ZH$ production can reach $-7.5\%$ and the relative corrections of the $\nu_{e}\bar{\nu_{e}}H$ and $e^{+}e^{-}H$ production can both reach $-6.5\%$ for $\sqrt{s}=500$ GeV with the scale $f=$694 GeV.