Reinterpreting the ATLAS HHH$\to 6b$ Search with CheckMATE and Rivet: Validation, TRSM Benchmarks, and HL-LHC Prospects

This paper presents a validated implementation of the ATLAS triple Higgs to six $b$-jets search in CheckMATE and Rivet, utilizing it to establish exclusion limits for Standard Model and TRSM benchmarks and to project High Luminosity LHC sensitivity under various systematic uncertainty scenarios.

The Gist

Imagine the Large Hadron Collider (LHC) as a massive, high-speed particle smasher. When protons crash into each other, they sometimes create a very rare and heavy particle called the Higgs boson. Scientists are particularly interested in seeing if the LHC can produce three of these Higgs bosons at the exact same time. This is like trying to catch three rare, elusive butterflies in a single net; it's incredibly difficult, but if you do, it tells us a lot about the fundamental rules of the universe.

This paper is about a team of physicists who took a specific search conducted by the ATLAS experiment (one of the giant detectors at the LHC) and rebuilt it using two different "digital simulation tools" called CheckMATE and Rivet. Think of these tools as two different types of high-tech video game engines. The goal was to see if they could perfectly mimic the ATLAS experiment's results and then use them to look for new physics that the original team might have missed.

Here is a breakdown of what they did, using simple analogies:

1. The "Six-B-Jet" Puzzle

When three Higgs bosons are created, they almost immediately decay (break apart) into pairs of particles called b-quarks. Since each Higgs makes two, three Higgses make six b-quarks. In the detector, these look like six jets of energy.

• The Challenge: The background noise (other particle collisions) is like a crowded, noisy party. Finding six specific jets in that noise is like trying to find six specific people wearing red hats in a stadium full of people.
• The Solution: The ATLAS team used a Deep Neural Network (DNN). Think of this as a super-smart AI referee that looks at the shape, speed, and position of those six jets to decide: "Is this the rare triple-Higgs signal, or just background noise?"

2. The "Re-creation" (Validation)

The authors of this paper wanted to make sure they could replicate the ATLAS team's work perfectly using their own tools (CheckMATE and Rivet).

• The "Recipe" Check: They took the "recipe" (the data and the AI model) provided by ATLAS and tried to cook the same dish in their own kitchens.
• The Discovery: They found a few small mistakes in the "recipe book" (the published paper). For example, the paper said the AI looked at the jets in one way, but the actual AI had actually rotated the jets into a different perspective before looking at them. It was like realizing the chef was measuring ingredients from the bottom of the bowl instead of the top.
• The Fix: Once they corrected these details, their simulations matched the ATLAS results almost perfectly. This proved that their tools were reliable and that the original experiment was solid.

3. Testing New Theories (The "What If" Scenarios)

The Standard Model (our current best theory of physics) predicts how often these triple-Higgs events should happen. But what if there is New Physics?

• The TRSM Model: The authors tested a specific new theory called the Two Real Scalar Model (TRSM). Imagine the Standard Model is a standard deck of cards. This new theory suggests there are two extra, hidden cards in the deck that change how the game is played.
• The "Benchmark" Points: They tested 140 different versions of this new theory (like testing 140 different ways the extra cards could be shuffled).
• The Result for Now: Using the data we have right now (from the last few years of the LHC), none of these 140 new theories were ruled out. The signal was too weak to see them yet. It's like looking for a whisper in a hurricane; the current data isn't loud enough to hear them.

4. Looking into the Future (The HL-LHC)

The LHC is getting an upgrade called the High-Luminosity LHC (HL-LHC), which will run for many more years and collect much more data.

• The Projection: The authors used their validated tools to simulate what would happen if the LHC collected 3 to 6 times more data than it has now.
• The Good News: With this massive amount of new data, the "noise" of the party would be drowned out, and the "whisper" of the new physics would become audible.
  • In a "best-case" scenario (where we assume we can perfectly control all measurement errors), they found that almost half of the 140 new theories could be confirmed or ruled out.
  • Even in a more realistic scenario, they could rule out a few of the most extreme versions of these theories.

5. Why This Matters

This paper is a "quality control" and "future forecasting" report.

• Quality Control: They proved that independent scientists can rebuild complex experiments using open tools, ensuring the results are trustworthy.
• Future Forecasting: They showed that while we can't see these new theories today, the upgraded LHC in the future will likely be powerful enough to find them (or prove they don't exist).

In short: The authors took a complex particle physics search, rebuilt it with their own tools to ensure it was perfect, and then used it to predict that the next generation of the LHC will finally have the power to detect these rare, triple-Higgs events and potentially discover new laws of physics.

Technical Summary

Technical Summary: Reinterpreting the ATLAS HHH→6b Search with CheckMATE and Rivet

Problem and Motivation
The measurement of Higgs boson self-couplings ($\lambda_3$ and $\lambda_4$) is a primary objective for the Large Hadron Collider (LHC), as deviations from Standard Model (SM) predictions would signal Beyond Standard Model (BSM) physics. While Higgs pair production has provided constraints, triple Higgs production ($HHH$) offers crucial independent sensitivity to the quartic coupling. The ATLAS collaboration recently published a search for $HHH \to 6b$ (HIGP-2024-32) utilizing advanced machine learning techniques, specifically Deep Neural Networks (DNNs), and a statistical model based on the HS3 format. However, the complexity of these analyses—particularly the reliance on proprietary neural network inputs and statistical likelihoods—poses challenges for independent reinterpretation. This paper addresses the need for a robust, validated implementation of the ATLAS $HHH \to 6b$ search in two widely used reinterpretation frameworks: CheckMATE and Rivet.

Methodology
The authors implemented the ATLAS analysis in both CheckMATE and Rivet, following a rigorous validation protocol enabled by the extensive auxiliary material provided by ATLAS (including ONNX neural networks, HS3 statistical models, and validation histograms).

1. Event Generation and Simulation: Signal events for the SM and the Two Real Scalar Model (TRSM) were generated using MadGraph5_aMC@NLO at $\sqrt{s}=13$ TeV and 14 TeV, interfaced with Pythia 8 for parton showering and hadronization. Detector simulation was performed using Delphes 3.5 (for CheckMATE) and Rivet's smearing functions (for Rivet), incorporating the DL1d b-tagging algorithm.
2. Implementation Details:
   • CheckMATE: Utilized the ONNX Runtime C++ library for DNN inference and a new interface for HS3-format likelihoods using XRooFit.
   • Rivet: Employed a standalone Python script to read YODA and HS3 files for statistical inference, as the standard Contur package does not yet support HS3 likelihoods directly.
3. Validation Process: The authors performed a granular comparison of the ten kinematic input variables for three distinct DNNs (non-resonant, resonant, and heavy-resonant) against ATLAS reference distributions. Crucially, they identified and corrected discrepancies in the definition of input variables, specifically:
   • Sphericity/Aplanarity: The original analysis calculated these observables after boosting the six leading jets into the rest frame of the triple-Higgs system, a detail initially missed in the implementation.
   • RMS($\eta$): Corrected to reflect the root-mean-square of the six leading b-jets before pairing, rather than the three Higgs candidates.
4. Statistical Analysis: The implementations were validated by comparing exclusion limits against ATLAS results for over 60 benchmark points. The study then applied these validated tools to a new set of 140 "Optimised Double-Resonant Benchmark" (ODRB) points from Ref. [25], which satisfy perturbativity constraints and offer enhanced cross-sections compared to previous benchmarks.

Key Contributions

• First Full Validation of ML Inputs: This work presents the first instance where all input distributions and outputs of a reinterpreted LHC neural network have been individually validated against the original experiment, confirming the necessity of detailed auxiliary plots for ML reinterpretation.
• HS3 Likelihood Integration: It demonstrates the first usage of HS3-format likelihoods within the CheckMATE framework and a custom workflow for Rivet, validating the utility of this format for external reinterpretation studies.
• Correction of Analysis Details: The paper identifies specific technical discrepancies between the published analysis description and the actual implementation (e.g., frame boosting for sphericity), providing a corrected methodology for future reinterpretations.
• New Physics Projections: The study extends the analysis to the ODRB benchmark points, which were not covered in the original ATLAS publication, and projects sensitivity to the High-Luminosity LHC (HL-LHC).

Results

• Validation: After correcting the input variable definitions, both CheckMATE and Rivet implementations showed excellent agreement with ATLAS data for input distributions and DNN scores. Statistical exclusion limits for the original ATLAS benchmarks were reproduced within uncertainty bands, with minor deviations attributed to the exclusion of certain signal-specific systematic uncertainties in the recasting workflow.
• Run 2 Sensitivity: Applying the validated tools to the 140 ODRB points at $\sqrt{s}=13$ TeV (Run 2), the authors found that none of the benchmark points are excluded by the current dataset. The strongest observed signal strength limit ($\mu$) is approximately 4.
• HL-LHC Prospects: Extrapolating to the HL-LHC ($\sqrt{s}=14$ TeV, 3 ab$^{-1}$ and 6 ab$^{-1}$) under various systematic uncertainty scenarios:
  • In a "baseline" scenario, no points are excluded.
  • In a "reduced background uncertainty" scenario, 3 points become accessible with a combined ATLAS+CMS dataset (6 ab$^{-1}$).
  • In a "no systematics" scenario, 25 points are accessible with 3 ab$^{-1}$, and 67 points (nearly half the set) are accessible with 6 ab$^{-1}$.
  • The resonant DNN provides the strongest limits for the majority of points, though the non-resonant DNN becomes dominant for higher $m_3$ values.

Significance
The paper demonstrates that with sufficient auxiliary material (ONNX models, HS3 likelihoods, and detailed validation plots), complex machine-learning-based LHC searches can be successfully and accurately recast. The successful validation of the HS3 format for statistical inference in external tools marks a significant step toward more transparent and reproducible BSM physics searches. While the current Run 2 data is insufficient to probe the new ODRB benchmarks, the study establishes that the HL-LHC has the potential to exclude a significant portion of these physically motivated models, provided systematic uncertainties are managed and, potentially, if neural networks are re-optimized for the specific kinematics of these new benchmarks. The authors emphasize that their results serve as a proof-of-concept for the utility of HS3 and the importance of detailed validation in the era of advanced machine learning in particle physics.