Maximizing Returns: Optimizing Experimental Observables at the LHC

TL;DR

This work tackles the challenge of designing EFT-sensitive observables at the LHC under finite data and resource constraints. It develops a unified framework that combines analytic (matrix-element) calculations with machine-learning approximations to build near-optimal, low-dimensional observables, supported by a novel Likelihood Operating Characteristic (LOC) framework and the LoC metric for robust performance in the presence of interference and multiple hypotheses. A key contribution is the MiLoMerge binning tool, which achieves substantial dimensionality reduction (e.g., from tens of thousands of bins to around 1k or 100) with minimal loss in discriminatory power, enabling practical data preservation and global data combination. Demonstrated on Higgs production processes H→4ℓ and VH, the approach yields near-optimal sensitivity to eight EFT parameters and provides a scalable pathway for comprehensive EFT analyses at the HL-LHC, with broad applicability to other LHC observables and data-analysis pipelines.

Abstract

We introduce a framework that integrates both analytical and machine-learning approaches for calculating observables optimal for EFT and broader applications at the LHC. A new metric for evaluating the performance of these approaches has been introduced. In addition, we demonstrate how the majority of relevant information can be effectively stored in a limited number of bins, allowing for efficient data analysis, data preservation, and global data combination, while also providing tools to achieve these benefits. A key feature of this approach is the reduction in the dimensionality of the observable information, which enhances both the effectiveness and practicality of the data analysis while maximizing gains within limited resources. These features have been demonstrated through simulated analyses of the Higgs boson production and decay processes at the LHC.

Figures (17)

• Figure 1: Diagrams illustrating the $H$ boson production and decay processes at the LHC: $q\bar{q}\to (Z/\gamma^*) \to H(Z/\gamma^*) \to H(\ell^+\ell^-)$ and $H\to(Z/\gamma^*)(Z/\gamma^*) \to 4\ell$ with angular observables defined in the rest frames of $H$ and $V=Z$ or $\gamma^*$Gao:2010qxBolognesi:2012mmAnderson:2013afp.
• Figure 2: Left: A schematic view of event analysis in an LHC experiment for a set of parameters $\vec{\theta}$ that define a fundamental process in proton collisions at the LHC, characterized by the partonic kinematic quantities $\vec{x}_\mathrm{part}$. Right: The sequence of MC modeling of the probability density ${\cal P}(\vec{x}_\mathrm{reco}|\vec{\theta})$ which depends on the reconstructed observables $\vec{x}_\mathrm{reco}$ and the test parameters $\vec{\theta}_i$. Refer to the text for further details.
• Figure 3: The distribution of simulated proton-proton collision events at the LHC for the process $q\bar{q}\to (Z/\gamma^*) \to H(Z/\gamma^*) \to H(\ell^+\ell^-)$ is shown for the three optimal observables, ${\cal D}_\mathrm{opt,2}$, ${\cal D}_\mathrm{opt,1}^{(1)}$, and $\mathcal{D}_{\text{opt,1}}^{(0)}$ computed using the matrix-element MELA approach Anderson:2013afp according to Eqs. (\ref{['eq:optimized2']}) and (\ref{['eq:optimized1']}). The coupling $\tilde{c}_{zz}$ is taken as the alternative hypothesis, with a $0.5$ contribution to the process cross section in the middle panel, where the sign indicates the relative coupling sign.
• Figure 4: The distribution of simulated proton-proton collision events at the LHC for the process $q\bar{q}\to (Z/\gamma^*) \to H(Z/\gamma^*) \to H(\ell^+\ell^-)$ is presented for the three optimal observables, ${\cal D}_\mathrm{opt,2}$, ${\cal D}_\mathrm{opt,1}^{(1)}$, and $\mathcal{D}_{\text{opt,1}}^{(0)}$, closely following the presentation of Fig. \ref{['fig:MELA_d0m']}, but using the machine-learning approach instead of MELA.
• Figure 5: Distributions of $m_2$ (left) and $\Phi$ (right) in $H \to ZZ \to 2e2\mu$ decay are shown for both the SM and the scenario driven by the $\tilde{c}_{zz}$ coupling, as discussed in the text.