A Novel Implementation of the Matrix Element Method at Next-to-Leading Order for the Measurement of the Higgs Self-Coupling ${\lambda}_{3H}$

The determination of the Higgs boson trilinear self-coupling ${\lambda}_{3H}$ is a key goal of the LHC physics programme. Its precise measurement will provide unique insight into the scalar potential and the mechanism of electroweak symmetry breaking. Higgs boson pair production in the ${gg}\to{HH}$ process, and particularly in the ${HH}\to{b}\bar{b}{\gamma}{\gamma}$ final state, offers direct sensitivity to ${\lambda}_{3H}$. We present the first implementation of the Matrix Element Method at Next-to-Leading Order (MEM@NLO) for this process, which is publicly available. The MEM is a statistically optimal approach that maximises information extraction from collision events. Extending it to NLO represents a major methodological challenge, which we address with a new formalism integrated into the MoMEMta framework. Results with simulated pseudo-experiments demonstrate, in a proof-of-principle study, the strong discriminating power of the method and its ability to extract the coupling modifier ${\kappa}_{\lambda}$=${\lambda}_{3H}$/${\lambda}_{3H}^{SM}$ with high precision.