Searching for HWW Anomalous Couplings with Simulation-Based Inference

Understanding the source of the universe’s asymmetry between matter and antimatter is one of the major open questions in particle physics. In this work, the sensitivity of novel machine-learning-based inference techniques to CP-odd and CP-even $HWW$ anomalous couplings is studied in the $\WH \rightarrow \ell νb\bar{b}$ channel ($\ell = e, μ$), within the Standard Model Effective Field Theory (SMEFT) framework. Two machine-learning simulation-based inference (SBI) methods are explored: a per-event likelihood-ratio estimator, which directly approximates the ratio of probability densities between competing hypotheses, is benchmarked against a per-event optimal-observable estimator optimized for sensitivity to the parameters of interest. Both approaches are also compared to traditional summary statistics, in this case histograms of kinematic and angular observables, as commonly used in experimental analyses. SBI methods provide tighter constraints than one-dimensional summary statistics, though their performance is comparable to two-dimensional histogram analysis. The optimal-observable approach remains promising for its ability to probe multiple couplings simultaneously. Restricting the analysis to a region of high $S/B$ also enhances sensitivity to CP-odd operators while preserving sensitivity to CP-even operators, which histogram analyses often lose. Although the likelihood-ratio estimator sometimes struggles with likelihood minima and shapes, optimisations that target its robustness could make it more sensitive than both the optimal-observable estimator and the histogram method. These results underscore the potential of advanced simulation-based inference techniques, encouraging further exploration with LHC Run 3 data to surpass current ATLAS and CMS sensitivities.

💡 Research Summary

The paper investigates the sensitivity of modern simulation‑based inference (SBI) techniques to anomalous H W W couplings within the Standard Model Effective Field Theory (SMEFT) framework, focusing on the WH → ℓ ν b b̄ channel (ℓ = e, μ). Two dimension‑6 operators are considered: a CP‑even operator O_HW with Wilson coefficient c_HW and a CP‑odd operator Ō_HW with coefficient c_HŴ, both normalized to a new‑physics scale Λ = 1 TeV. Traditional LHC analyses of such couplings rely on low‑dimensional summary statistics—typically one‑ or two‑dimensional histograms of kinematic or angular observables—and on optimal‑observable methods that compress information using matrix‑element calculations. While computationally cheap, these approaches inevitably discard information contained in the full multi‑dimensional event space, limiting the achievable constraints on the Wilson coefficients.

To overcome this limitation, the authors employ three SBI methods that exploit the full simulator output, including latent variables describing parton‑level kinematics, showering, hadronisation, and detector response. By constructing the joint likelihood ratio r(x,z|θ₀,θ₁) and the joint score t(x,z|θ) – quantities that are analytically tractable because the stochastic components of the simulation cancel – they can train neural networks (NNs) to approximate either the likelihood ratio or the score directly from observable data x. The three methods are:

1. SALL​Y (Score Approximate Likelihood Locally Y) – trains a NN to regress the joint score using a mean‑squared‑error loss, yielding a locally optimal observable around a reference point θ_ref.
2. ALICE (Approximate Likelihood with Improved Cross‑Entropy) – treats the problem as binary classification between two hypotheses (SM vs. BSM) and uses the likelihood‑ratio trick to obtain an estimator of the likelihood ratio.
3. ALICES (ALICE with Score) – augments the ALICE loss with an additional term that penalises deviations from the true joint score, controlled by a hyper‑parameter α, thereby aiming for a globally optimal estimator.

All methods are implemented with the MadMiner toolkit and trained on large Monte‑Carlo samples generated for SM and several benchmark values of c_HW and c_HŴ, together with the dominant backgrounds (tt̄, W+jets, Z+jets). Event selection mirrors ATLAS/CMS analyses: one isolated lepton, two b‑tagged jets, missing transverse energy, and a reconstructed Higgs candidate.

The performance of the SBI approaches is benchmarked against three conventional strategies: (i) a one‑dimensional histogram of a single discriminating variable, (ii) a two‑dimensional histogram of a pair of variables, and (iii) a traditional optimal‑observable constructed from matrix‑element information. The key findings are:

• Information gain: Both SALL​Y and ALICE/ALICES achieve significantly tighter 95 % confidence intervals than the 1‑D histogram, demonstrating that SBI recovers information lost in simple binning.
• Comparison with 2‑D histograms: The constraints from SBI are comparable to those obtained with carefully chosen 2‑D histograms, indicating that a well‑designed two‑dimensional summary can capture much of the relevant information, but SBI offers a systematic, automated way to do so without manual variable selection.
• High S/B region: Restricting the analysis to events with high signal‑to‑background ratios (e.g., high transverse momentum of the W‑H system, large missing energy) markedly improves sensitivity to the CP‑odd coefficient c_HŴ while preserving sensitivity to the CP‑even c_HW. Histogram‑based analyses tend to lose this advantage because the chosen variables may not optimally separate CP‑odd effects.
• Optimal‑observable vs. SBI: The optimal‑observable method remains attractive for simultaneous multi‑parameter fits because it naturally incorporates interference terms, but its constraints are generally weaker than those from SBI when the same data are used.
• Stability of likelihood‑ratio estimator: The ALICE/ALICES likelihood‑ratio estimator sometimes exhibits instability near likelihood minima, leading to biased or broadened confidence intervals. The authors note that careful tuning of the loss function, regularisation, and the α hyper‑parameter can mitigate these issues, potentially allowing the likelihood‑ratio approach to surpass both SALL​Y and histogram methods.

The authors conclude that SBI techniques, especially those that combine likelihood‑ratio and score information, provide a powerful and flexible framework for future Higgs coupling measurements. They advocate applying these methods to LHC Run 3 data, where increased statistics and improved detector performance should enable constraints on c_HW and c_HŴ that exceed current ATLAS and CMS limits. Further methodological developments—such as ensemble learning, uncertainty quantification, and integration with existing analysis pipelines—are identified as promising directions to fully exploit the potential of simulation‑based inference in high‑energy physics.