The structure of quark mass corrections in the $gg \rightarrow HH$ amplitude at high-energy

The leading and next-to-leading order QCD predictions for Higgs boson pair production at hadron colliders suffer from a significant mass renormalisation scheme uncertainty related to the choice of the top-quark mass. The functional dependence of the result on the value of the intermediate quark mass can be understood in the high-energy limit using the Method of Regions and the tools of Soft-Collinear Effective Theory. In this work, we study the origin of the sizeable logarithmic mass corrections in the $gg \to HH$ amplitudes at leading and next-to-leading power in the limit $s,|t|,|u| \gg m_t^2 \gg m_H^2$. We argue that the mass corrections follow a predictable factorised pattern that can be exploited to simplify their computation. We present results for the leading power leading logarithmic corrections, our analysis leads to a significant reduction in the theoretical uncertainty of the double Higgs production amplitudes at high-energy due to the top-quark mass scheme.