Electroweak radiative corrections to $e^+e^- \to t \bar{t} h$ at linear colliders

We calculate the ${\cal O}(\alpha_{{\rm ew}})$ electroweak radiative corrections to $e^+ e^- \to t \bar{t} h$ at a electron-positron linear collider (LC) in the standard model. We analyze the dependence of the ${\cal O}(\alpha_{{\rm ew}})$ corrections on the Higgs boson mass $m_{h}$ and colliding energy $\sqrt{s}$, and find that the corrections significantly decrease or increase the Born cross section depending on the colliding energy. The numerical results show that the ${\cal O}(\alpha_{{\rm ew}})$ relative correction is strongly related to the Higgs boson mass when $\sqrt{s}=500 GeV$, and for $m_h = 150 GeV$ the relative correction ranges from -31.3% to 2.3% as the increment of the colliding energy from 500 GeV to 2 TeV.