Di-Higgs and Effective Field Theory: Signal Reweighting Beyond $m_{hh}$

Di-Higgs ($hh$) production is crucial for probing the Higgs boson self-interaction and understanding the electroweak phase transition. Deviations from Standard Model predictions in $hh$ gluon-gluon fusion (ggF) can be systematically parameterized using effective field theories (EFT), such as Higgs Effective Field Theory (HEFT) and Standard Model Effective Field Theory (SMEFT), as long as the conditions of the EFT are fulfilled. This note presents an improved EFT signal reweighting method that addresses the limitations of approaches that rely solely on the invariant mass of the di-Higgs system $m_{hh}$, which fail to capture variations in kinematic variables such as the Higgs boson transverse momentum. We show that these limitations are particularly pronounced in scenarios involving strong destructive interference. The proposed method is developed for both EFTs for $hh$ ggF at $\sqrt{s} = 13$ and $13.6$ TeV at next-to-leading order in QCD. We demonstrate a reweighting technique that combines more than one EFT reference sample while incorporating multiple key variables of ggF. These enhancements improve accuracy across phase space, particularly in capturing variation of the Higgs boson transverse momentum. The method employs a convex combination of the reference samples, with weights parametrized by a distance measure, to achieve a more precise reweighting. In principle, this approach can be extended to other processes, provided that suitable reference samples and distance measure are carefully chosen.