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In these proceedings, we summarise our recent calculations of next-to-leadingorder electroweak corrections to Higgs boson pair and Higgs boson plus jetproduction. The calculations are divided into different regions. In thehigh-energy region, we analytically calculate the Higgs boson contribution tothe leading two-loop Yukawa corrections for $gg\to HH$. These corrections aregenerated by a single virtual Higgs boson exchange within the top quark loop.Our high-energy expansion yields precise predictions for the region where theHiggs boson transverse momenta $p_T > 120 $ GeV. In the low-energy region, wecompute the complete two-loop electroweak corrections to $gg\to HH$ and $gg \togH$. We obtain analytic results through the large top quark mass expansion,covering all sectors of the Standard Model.

Progress in two-loop electroweak corrections to gg -> HH and gg -> gH