Measurement of the Higgs self-coupling using the Matrix Element Method at Next-to-Leading Order (NLO) in the gg→HH→ $b\bar{b}\gamma \gamma$ channel for the ATLAS experiment at the LHC

This thesis delivers the first implementation of the Matrix Element Method at Next-to-Leading Order (MEM@NLO) for the gg→HH→bb̄γγ channel in ATLAS, targeting a precise determination of the Higgs self-coupling λ_3H (or its corresponding coupling modifier κ_λ). This work introduces a new NLO framework featuring an analytic matrix elements with full top-mass dependence, an infrared-safe treatment of real emission, and an automated “MEM factory” integrated within MoMEMta for large-scale event processing. It motivates the powerful potential of the Matrix Element Method to exploit the full kinematic information of each event for precision measurements of rare Higgs processes at the LHC.

The method is validated on realistic NLO pseudo-datasets and on fully simulated ATLAS bb̄γγ n-tuples.
It achieves κ_λ = 1.14 ± 0.50 on NLO (ISR) samples and κ_λ = 1.22 ± 0.41 on full-simulation datasets, with the three main background sources (tt̄H, single-Higgs, and QCD diphoton processes), while removing the long-standing mirror solution near κ_λ ≈ 4 via the full kinematic information of MEM@NLO. Our framework modular design enables straightforward extensions to other HH final states (e.g. bb̄τ⁺τ⁻, bbbb) and to SMEFT interpretations at full NLO accuracy.

This thesis document provides methodology, validation, performance results, and a transferable implementation for present (LHC) and future (HL-LHC) analyses using the Matrix Element Method (up to NLO accuracy).