Precise predictions for the Higgs production in association with a W-boson pair at ILC

The Higgs-boson production in association with a W-boson pair at $e^+e^-$ linear colliders is one of the important processes in probing the coupling between Higgs-boson and vector gauge bosons and discovering the signature of new physics. We describe the impact of the complete electroweak(EW) radiative corrections of ${\cal O}(\alpha_{ew})$ to this process in the standard model(SM) at the International Linear Collider(ILC), and investigate the dependence of the lowest-order(LO) and EW next-to-leading order(NLO) corrected cross sections on colliding energy $\sqrt{s}$ and Higg-boson mass. The LO and NLO EW corrected distributions of the invariant mass of W-boson pair and the transverse momenta of final $W$- and Higgs-boson are presented. Our numerical results show that the relative EW radiative correction($\delta_{ew}$) varies from -19.4% to 0.2% when $m_H=120 GeV$ and $\sqrt{s}$ goes up from $300 GeV$ to $1.2 TeV$.