Search for Higgs boson pair production in association with top-quark pairs using 196 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=$ 13 and 13.6 TeV with the ATLAS detector

Using 196 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=$ 13 and 13.6 TeV collected by the ATLAS detector, this paper presents the first search for non-resonant Higgs boson pair production in association with top-quark pairs ($t\bar{t}HH$), setting a 95% confidence-level upper limit of 20 times the Standard Model prediction on the production cross-section and constraining the corresponding Higgs effective field theory Wilson coefficient.

The Gist

Imagine the Large Hadron Collider (LHC) as the world's most powerful, high-speed particle collision machine. It smashes protons together at nearly the speed of light, creating a chaotic, microscopic "soup" of particles. For decades, physicists have been trying to understand the rules of this soup, specifically looking for the Higgs boson—the particle that gives other particles their mass.

We know how the Higgs boson is made alone. But the big mystery is: How does it interact with itself? Does it have a "self-coupling"? Think of it like this: If you throw a ball, you know how it flies. But if you throw two balls at each other, do they bounce off, stick together, or explode? Understanding how two Higgs bosons interact (Higgs pair production) is crucial to understanding the stability of the entire universe.

This paper is the first-ever search by the ATLAS experiment (one of the giant detectors at the LHC) for a very specific, rare event: Two Higgs bosons being created at the same time, accompanied by a pair of top quarks.

Here is the breakdown of this complex scientific hunt in simple terms:

1. The "Holy Grail" Event: $t\bar{t}HH$

In the Standard Model (our current rulebook for physics), creating two Higgs bosons at once is incredibly rare. It's like winning the lottery twice in a row.

• The Top Quark: This is the heaviest known elementary particle. It's the "sumo wrestler" of the particle world.
• The Process: The scientists are looking for a scenario where the collision creates a "sumo wrestler" pair (top and anti-top quarks) plus a "Higgs pair."
• Why it matters: This specific combination acts as a magnifying glass. It allows physicists to measure a specific "knob" in the laws of physics (called a Wilson coefficient) that tells us if the Higgs boson behaves exactly as the Standard Model predicts, or if there is some "new physics" hiding in the shadows.

2. The Detective Work: Three Different "Crime Scenes"

Since this event is so rare and the particles decay (break apart) instantly, the detectors can't see the Higgs bosons directly. They have to look for the "debris" left behind. The team looked for three distinct patterns of debris, like looking for a suspect's fingerprints in three different rooms:

• Room 1: The "Heavy Metal" Room (1L Channel)
  • The Clue: One electron or muon (a type of light, fast particle) and at least five "bottom quarks" (heavy particles that leave a specific trail).
  • The Analogy: Imagine walking into a room and seeing one shiny coin and five heavy anvils. That's a very specific, heavy signature.
• Room 2: The "Same-Sign" Room (SSML Channel)
  • The Clue: Two or more electrons/muons that have the same electric charge (like two positive charges repelling each other) or three or more leptons in total.
  • The Analogy: In nature, positive and negative usually cancel out. Finding two positives together is like finding two north poles of magnets stuck together—it's unusual and points to a specific, complex event.
• Room 3: The "Flashy" Room ($b\bar{b}\gamma\gamma$ Channel)
  • The Clue: Two photons (particles of light) and two bottom quarks.
  • The Analogy: This is the "cleanest" room. The two photons act like a bright flash of light that is very easy to spot, but it's also the hardest to find because there are so few events here.

3. The Tools: AI and Data

The LHC produces billions of collisions every second. Most of them are boring background noise (like static on a radio).

• The Filter: The team used advanced Machine Learning (AI), specifically a type called a "Transformer" (the same tech behind modern chatbots), to act as a super-smart filter. It learned to distinguish the tiny signal of the Higgs pair from the massive mountain of background noise.
• The Data: They analyzed data from 2015–2018 (Run 2) and 2022–2023 (Run 3), totaling a massive amount of information (196 "inverse femtobarns"—a unit of data volume).

4. The Results: The "Silence" is the Story

After all the searching, the big news is: They didn't find it.

• The Verdict: The data looked exactly like what we would expect if only background noise was present. There was no "excess" of events that would indicate the Higgs pair was there.
• The Limit: While they didn't find the particle, they set a very strict rule. They can say with 95% confidence that if this event does happen, it happens less than 20 times more often than the Standard Model predicts.
• The "Knob" Measurement: They also measured the "knob" (the Wilson coefficient $c_{ttHH}$). The result is consistent with the Standard Model (the knob is set to zero), but the range of uncertainty is still quite wide (between -3.9 and 3.3).

5. Why This Matters (The "So What?")

You might ask, "If they didn't find anything, why write a paper?"

• Ruling Out the Impossible: In science, proving something doesn't exist in a certain range is just as important as finding it. This paper tells theorists: "If you have a theory that predicts this event happens 50 times more often than the Standard Model, you are wrong."
• The Next Step: The LHC is still running. As they collect more data in the future, they will be able to tighten these limits. If the Higgs boson does have weird self-interactions, this paper proves we need to look even harder.

In Summary:
This paper is like a team of detectives searching a massive city for a specific, rare criminal (the Higgs pair with top quarks). They used high-tech AI to scan millions of surveillance tapes (collision data) across three different neighborhoods. They didn't catch the criminal, but they proved that if the criminal is out there, they are much rarer than previously suspected. This helps the rest of the physics community narrow down where to look next.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics successfully describes fundamental particles and interactions, yet the mechanism of electroweak symmetry breaking (EWSB) relies on the Higgs potential, which is governed by the Higgs boson's self-couplings (trilinear and quartic). These couplings remain poorly constrained experimentally.

• The Gap: While gluon-gluon fusion (ggF) and vector-boson fusion (VBF) are the dominant Higgs pair ($HH$) production modes, they are sensitive to multiple couplings simultaneously, making it difficult to isolate specific deviations.
• The Target: The associated production of a Higgs boson pair with a top-quark pair ($t\bar{t}HH$) is the third-largest $HH$ production mode in the SM. Crucially, this process is sensitive to the quartic coupling between two Higgs bosons and two top quarks ($t\bar{t}HH$), which can be parameterized by the Wilson coefficient $c_{t\bar{t}HH}$ in the Higgs Effective Field Theory (HEFT).
• The Goal: This paper presents the first search for non-resonant $t\bar{t}HH$ production using the full Run 2 (2015–2018) and partial Run 3 (2022–2023) datasets from the ATLAS detector at the Large Hadron Collider (LHC).

2. Methodology

Data and Simulation

• Dataset: The analysis utilizes an integrated luminosity of 196 fb⁻¹, comprising 140 fb⁻¹ at $\sqrt{s}=13$ TeV (Run 2) and 56 fb⁻¹ at $\sqrt{s}=13.6$ TeV (Run 3).
• Signal Modeling: Signal samples ($t\bar{t}HH$) were generated using MadGraph5_aMC@NLO at Leading Order (LO) with Pythia8 for parton showering. The cross-section is normalized to Next-to-Leading Order (NLO) QCD predictions.
• Background Modeling: Dominant backgrounds include $t\bar{t}$+jets, $t\bar{t}W$, $t\bar{t}Z$, $t\bar{t}H$, and multi-top processes. These were modeled using various generators (PowhegBox, Sherpa, MG5_aMC) at NLO or LO, normalized to state-of-the-art theoretical cross-sections.

Analysis Strategy and Event Selection

The search targets three distinct final states based on the decay modes of the $W$ bosons (from top quarks) and the Higgs bosons:

1. 1L Channel (Single Lepton):

   • Signature: Exactly one lepton ($e$ or $\mu$), $\ge 5$ $b$-tagged jets, and significant missing transverse momentum ($E_T^{miss}$).
   • Selection: Requires $p_T > 27$ GeV for the lepton, $E_T^{miss} > 20$ GeV, $\ge 6$ jets total, and $\ge 4$ $b$-tagged jets (85% working point).
   • Background Estimation: Uses a hybrid approach where $t\bar{t}$+jets normalizations are constrained by Control Regions (CRs) using a profile likelihood fit.

2. SSML Channel (Same-Sign Multilepton):

   • Signature: Two or more leptons with the same electric charge (SS2L) or $\ge 3$ leptons (3L), accompanied by $\ge 2$ $b$-tagged jets.
   • Selection: Requires $p_T > 15$ GeV for sub-leading leptons and $> 27$ GeV for the leading lepton.
   • Background Estimation: Physics backgrounds (e.g., $t\bar{t}W$) are constrained via CRs. Instrumental backgrounds (charge misidentification, fake/non-prompt leptons) are estimated using data-driven methods and template fits.

3. $b\bar{b}\gamma\gamma$ Channel (Diphoton):

   • Signature: Two photons with an invariant mass $105 < m_{\gamma\gamma} < 160$ GeV and $\ge 2$ $b$-tagged jets.
   • Selection: Targets the $HH \to b\bar{b}\gamma\gamma$ decay.
   • Background Estimation: The continuum background is fully data-driven, extracted from the diphoton mass sidebands ($105-120$ GeV and $130-160$ GeV) using an exponential function fit. Resonant backgrounds are modeled via simulation.

Multivariate Analysis

• 1L and SSML Channels: A Transformer-based neural network (utilizing self-attention mechanisms) is employed to distinguish signal from background.
  • Inputs include kinematic variables ($p_T, \eta, \phi$) of leptons, jets, and $E_T^{miss}$, along with $b$-tagging scores and charge information.
  • The output is a discriminant score used in the final statistical fit.
• $b\bar{b}\gamma\gamma$ Channel: A set of Boosted Decision Trees (BDTs) trained with XGBoost defines Signal Regions (SRs) of varying purity based on the separation between signal and specific background processes ($\gamma\gamma b\bar{b}$, $t\bar{t}\gamma\gamma$, etc.).

Statistical Analysis

• A simultaneous maximum-likelihood fit is performed across all Signal Regions (SRs) and Control Regions (CRs).
• The parameter of interest (POI) is the signal strength modifier $\mu_{t\bar{t}HH}$ (ratio of observed to SM cross-section).
• Systematic uncertainties (experimental, theoretical, and modeling) are incorporated as nuisance parameters.

3. Key Contributions

• First Search: This is the inaugural search for non-resonant $t\bar{t}HH$ production by the ATLAS collaboration.
• Machine Learning Integration: The application of Transformer architectures for signal-background discrimination in high-multiplicity final states (1L and SSML) represents a significant methodological advancement in ATLAS analyses.
• Combined Run 2 and Run 3: The analysis combines data from two distinct LHC energy periods (13 TeV and 13.6 TeV), providing the first constraints on this process with the highest available luminosity.
• HEFT Interpretation: The results are interpreted within the Higgs Effective Field Theory framework to constrain the quartic $t\bar{t}HH$ coupling, offering a complementary constraint to the more sensitive but model-dependent ggF $HH$ channel.

4. Results

• Observation: No significant excess of events over the Standard Model background expectation was observed in any of the three channels.
• Signal Strength: The combined measured signal strength is:
  $$\mu_{t\bar{t}HH} = -3^{+11}_{-12}$$
  This result is consistent with the SM prediction ($\mu = 1$) within uncertainties.
• Upper Limits:
  • The observed 95% Confidence Level (CL) upper limit on the production cross-section is 20 times the SM prediction.
  • The expected limit is 21 times the SM prediction.
  • Individual channel limits: 1L (26), SSML (40), $b\bar{b}\gamma\gamma$ (75).
• HEFT Constraints:
  • The Wilson coefficient $c_{t\bar{t}HH}$ is constrained to the range:
    $$-3.9 < c_{t\bar{t}HH} < 3.3 \quad (95\% \text{ CL})$$
  • The expected range is $-4.0 < c_{t\bar{t}HH} < 3.5$.
  • The likelihood scan shows a double-minimum structure due to the quadratic dependence of the cross-section on $c_{t\bar{t}HH}$, though the observed data results in a nearly flat region between the minima.

5. Significance

• Probing New Physics: While the SM prediction for $t\bar{t}HH$ is small ($\sim 0.76$ fb at 13 TeV), this process is uniquely sensitive to the quartic coupling between the Higgs and top sectors. Constraints on $c_{t\bar{t}HH}$ are crucial for testing the nature of the Higgs potential and potential Beyond-the-Standard-Model (BSM) physics.
• Complementarity: Unlike the ggF $HH$ channel, which requires assumptions about other couplings (like $c_{ggH}$) to isolate $c_{t\bar{t}HH}$, the $t\bar{t}HH$ channel provides a more direct and robust constraint on the quartic interaction in weakly interacting theories.
• Future Prospects: Although the current limits are roughly an order of magnitude weaker than those from the ggF channel, this analysis establishes the necessary framework (including advanced ML techniques and combined Run 2/3 data strategies) for future high-luminosity LHC runs, where the sensitivity to this rare process will significantly improve.