Next-to-leading order electroweak corrections to $gg \to HH$ and $gg \to gH$ in the large-$m_t$ limit

Abstract: We compute two-loop electroweak corrections to Higgs boson pair and Higgs plus jet production, taking into account all sectors of the Standard Model. All diagrams with virtual top quarks are computed in an expansion for large top quark mass up to order $1/m_t^8$ or more. We present analytic results for the form factors and discuss the convergence properties. For the process $gg\to gH$ we also consider QCD corrections in the large-$m_t$ limit.