Quark mass corrections in di-Higgs production amplitude at high-energy

A large theoretical uncertainty due to the choice of the top-quark mass renormalisation scheme is present in QCD predictions for Higgs boson pair production. In these proceedings, we report on the recent progress in tackling these uncertainties for the $gg\to HH$ amplitude in the high-energy limit $s,|t|,|u| \gg m_t^2 \gg m_H^2$. Using the Method of Regions and Soft-Collinear Effective Theory, the leading power in $m_t$ behaviour of the amplitude is understood to all orders in the strong coupling expansion, and leading logarithmic resummation leads to a significant reduction in the scheme choice uncertainty in the virtual amplitude for di-Higgs production at high energies.