Full ${\cal O}(\alpha_{ew})$ electroweak corrections to $e^+e^- \to H H Z$

We calculate the full ${\cal O}(\alpha_{ew})$ electroweak corrections to the Higgs pair production process $e^+ e^- \to H H Z$ at an electron-positron linear collider in the standard model, and analyze the dependence of the Born cross section and the corrected cross section on the Higgs boson mass $m_H$ and the c.m. energy $\sqrt{s}$. To see the origin of some of the large corrections clearly, we calculate the QED and genuine weak corrections separately. The numerical results show that the corrections significantly suppress or enhance the Born cross section, depending on the values of $m_H$ and $\sqrt{s}$. For the c.m. energy $\sqrt{s} = 500 GeV$, which is the most favorable colliding energy for $H H Z$ production with intermediate Higgs boson mass, the relative correction decreases from -5.3% to -11.5% as $m_H$ increases from 100 to 150 GeV. For the range of the c.m. energy where the cross section is relatively large, the genuine weak relative correction is small, less than 5%.