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 $\sqrt{s}$. The numerical results show that the corrections significantly suppress or enhance the Born cross section, depending on the values of $m_H$ and $\sqrt{s}$, especially 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 -32.9% as $m_H$ increases from 100 to 200 GeV