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

TL;DR

This work delivers the first Matrix Element Method at Next-to-Leading Order (MEM@NLO) for Higgs boson pair production in the $b\bar{b} γγ$ final state, enabling a more precise extraction of the Higgs self-coupling $λ_{3H}$ via the coupling modifier $κ_{λ}$. It achieves this by interfacing MoMEMta with POWHEG-BOX-V2 and introducing a novel integration block, Block N, to incorporate unresolved real emissions in a consistent, infrared-safe MEM framework. Using pseudo-experiments at $L=300\,\mathrm{fb}^{-1}$, MEM@NLO yields improved discrimination over MEM@LO and provides an unbiased, high-sensitivity measurement of $κ_{λ}$ with a typical uncertainty around $0.5$, while resolving the mirror solution near $κ_{λ} \approx 4$. The results demonstrate a robust, statistically optimal pathway to constrain the Higgs potential and pave the way for applying MEM@NLO to additional channels and HL-LHC analyses.

Abstract

The determination of the Higgs boson trilinear self-coupling $λ_{3H}$ 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 ${HH}\to{b}\bar{b}γγ$ final state, offers direct sensitivity to $λ_{3H}$. 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 $κ_λ$=$λ_{3H}$/$λ_{3H}^{SM}$ with high precision.

Figures (7)

• Figure 1: Schematic representation of the new Block N, following the conventions used by MoMEMta.
• Figure 2: ROC curve for events generated at NLO, between the $ggF$ di-Higgs signal and ttH background. The black curve corresponds to MEM@LO, and the red curve to MEM@NLO. Given our conventions, the closer the ROC curve lies to the bottom-right corner of the plot, the more powerful the method.
• Figure 3: Likelihood scan for one pseudo–experiment consisting of a combination of NLO signal events ($\kappa_{\lambda}=1$) and all main backgrounds, using MEM@NLO. The graph shows $-\log\mathcal{L}$ as a function of the hypothesis $\kappa_{\lambda}$. Black: kinematic component ($\mathcal{L}_{\text{kin}}$) with offset; Green: yield term ($\mathcal{L}_{\text{yield}}$) with offset; Red: extended likelihood ($\mathcal{L}_{\text{ext}}$); Blue: quadratic fit to $-\log\mathcal{L}_{\text{ext}}$ around its minimum.
• Figure 4: Histograms of likelihood scan results of pseudo-experiments including signal and all main backgrounds. Top: distribution of the best-fit coupling parameter $\hat{\kappa_{\lambda}}$, with Gaussian fit overlaid. Middle: distribution of the estimated uncertainty $\sigma_{\text{measured}}$. Bottom: distribution of the pull values $\omega=(\hat{\kappa_{\lambda}} - \kappa_{\lambda}^{\text{true}})/\sigma_{\text{measured}}$.
• Figure 5: Summary of likelihood scan performance for MEM@NLO on NLO Monte Carlo pseudo-experiments generated with $\kappa_\lambda=1$ in the $b\bar{b}\gamma\gamma$ final state, with 300 $fb^{-1}$. The black dot marks the mean best-fit value of $\kappa_\lambda$ for each set of pseudo-experiments, while the bands show the statistical $\pm 1\sigma$ (turquoise) and $\pm 2\sigma$ (orange) ranges. The dashed grey line is the SM prediction ($\kappa_\lambda=1$), and the red vertical line the location of the mirror solution near $\kappa_\lambda=4$.