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Searches for resonant and nonresonant multi-Higgs production in ATLAS and CMS

This paper presents recent results from the ATLAS and CMS experiments at the LHC on searches for resonant and nonresonant multi-Higgs production, which are crucial for measuring Higgs self-couplings and probing physics beyond the Standard Model.

Original authors: Emmanouil Vourliotis (on behalf of the ATLAS,CMS Collaborations)

Published 2026-06-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Emmanouil Vourliotis (on behalf of the ATLAS,CMS Collaborations)

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is built like a giant, complex Lego set. For a long time, scientists have been trying to understand the rules of how these Lego bricks snap together. The "Higgs boson" is a special, rare brick that gives other bricks their weight. But there's a deeper mystery: How does this special brick interact with itself? Does it like to hang out alone, or does it prefer to form pairs or even groups of three?

This paper is a report from two massive teams of scientists, ATLAS and CMS, who are working at the world's biggest particle collider (the LHC). Their goal is to catch these Higgs bricks in the act of forming groups, specifically looking for two Higgs bosons (a "di-Higgs") or even three Higgs bosons (a "tri-Higgs") appearing at the same time.

Here is a breakdown of their hunt, explained simply:

1. The Big Challenge: Finding a Needle in a Haystack

Finding a single Higgs boson is already like finding a needle in a haystack. Finding two of them at once is 1,000 times harder, and finding three is 500,000 times harder.

The Analogy: Imagine you are at a massive concert (the particle collider). Seeing one famous singer (a single Higgs) is easy. Seeing two singers show up on stage at the exact same time is rare. Seeing three is almost impossible.
Why it matters: If we see these groups, it tells us the shape of the "energy landscape" of the universe. If the groups look different than our current theories predict, it means there are hidden rules or new particles we haven't discovered yet.

2. The Hunt for Pairs (Di-Higgs)

The teams looked for pairs of Higgs bosons in several different ways, like looking for a specific pair of shoes in a giant lost-and-found bin.

The "Golden" Search (bbγγ): They looked for a pair where one Higgs turned into two photons (light) and the other turned into two bottom quarks (heavy particles).
- ATLAS used data from 2015–2024. They used smart computer programs (called "Boosted Decision Trees") to sort through the noise. They found the results matched the "Standard Model" (our current best guess) perfectly. They didn't see anything strange, but they set a very strict rule: "If there is a new type of pair production, it can't be more than 3.8 times stronger than we expect."
- CMS used data from 2022–2023. They tried two different math tricks to find the signal. They also found no new pairs, but they narrowed down the possible "weirdness" of the Higgs interaction significantly.
The "Heavy" Search (Top Quarks): They also looked for Higgs pairs that appear alongside top quarks (the heaviest known particles).
- ATLAS used a new type of AI called "Transformer Neural Networks" (the same tech behind advanced chatbots) to spot these rare events. They found nothing unusual, but they tightened the rules on how these heavy particles interact.
The Team-Up: In a major move, ATLAS and CMS combined their separate results. By pooling their data, they created the strongest search yet. They now say that if there is any extra Higgs pair production, it is less than 2.5 times what we expect. This is the tightest net cast so far.

3. The Hunt for Trios (Tri-Higgs)

This is the "Holy Grail" of the current search. Finding three Higgs bosons at once is incredibly difficult because the signal is so faint.

The Challenge: In the data CMS looked at, only about 25% of the events actually had three Higgs bosons fully visible. The rest were messy or incomplete.
The Solution: They used a sophisticated AI tool called SPANet. Think of this like a detective who can look at a messy crime scene and figure out exactly which three suspects were there, even if some evidence is missing.
The Result: They found no evidence of tri-Higgs production. They set a limit: if it happens, it's extremely rare (less than 588 times the expected rate). This is the best limit ever set for this specific search.

4. Looking for Heavy Resonances (The "New" Particles)

So far, the teams have been looking for Higgs bosons appearing out of nowhere (nonresonant). But they also looked for a "messenger" particle.

The Analogy: Imagine you are looking for two people meeting in a park. You might see them just walking up to each other. But maybe they are meeting because a giant bus (a heavy new particle) dropped them off.
The Search: ATLAS and CMS looked for a heavy, invisible bus (called "X" or "Y") that decays into Higgs bosons. They scanned through a huge range of possible weights for this bus.
The Result: No buses were found. No heavy new particles were spotted dropping off Higgs pairs.

5. What's Next? (The Outlook)

The paper concludes that while they haven't found any "new physics" yet, they are getting much better at the hunt.

The Future: By using better data from the latest runs of the collider and smarter AI tools, they are preparing for the "High-Luminosity LHC" (a future upgrade).
The Prediction: They project that by the end of the current program, they will have enough data to see Higgs pairs with a confidence level of 7 sigma (which is the gold standard in physics for a discovery). In other words, they are confident they will eventually see these pairs clearly, even if they haven't found any surprises yet.

In Summary:
The ATLAS and CMS teams are playing a high-stakes game of "Where's Waldo?" with the Higgs boson. They are using supercomputers and advanced AI to find pairs and trios of these particles. So far, the universe is behaving exactly as the Standard Model predicts—no surprises, no new heavy particles, and no weird interactions. However, the search is tightening, and the next few years promise to finally reveal the true nature of how the Higgs boson interacts with itself.

Technical Summary: Searches for Resonant and Nonresonant Multi-Higgs Production in ATLAS and CMS

Problem and Motivation
The measurement of the Higgs boson self-couplings is a primary physics objective of the Large Hadron Collider (LHC) program, as these couplings define the shape of the Higgs potential and offer sensitivity to physics beyond the Standard Model (BSM). The trilinear self-coupling is probed via di-Higgs ($HH$) production, which has a cross-section approximately $10^3$ times smaller than single Higgs production. The quartic coupling is accessible through tri-Higgs ($HHH$) production, with a cross-section roughly $5 \times 10^2$ times smaller than di-Higgs production. Additionally, resonant searches for heavy scalars decaying to Higgs pairs or a Higgs and a new scalar are motivated by various BSM models. The paper presents recent results from the ATLAS and CMS collaborations covering both resonant and nonresonant multi-Higgs production across diverse final states, utilizing data from LHC Run 2 ( $\sqrt{s} = 13$ TeV) and early Run 3 ( $\sqrt{s} = 13.6$ TeV).

Methodology
The analyses employ advanced machine learning techniques and optimized strategies to separate rare signal processes from dominant backgrounds. Key methodological approaches include:

Di-Higgs ($HH$) Searches:
- $HH \to b\bar{b}\gamma\gamma$ : ATLAS utilized a combination of full Run 2 and partial Run 3 data (308 fb $^{-1}$ ), employing Boosted Decision Trees (BDTs) trained in kinematic regions defined by the $b\bar{b}\gamma\gamma$ invariant mass. Signal regions (SRs) were defined based on BDT outputs, and a simultaneous fit of the $m_{\gamma\gamma}$ distribution across 14 exclusive SRs was performed. CMS analyzed 62 fb $^{-1}$ of Run 3 data using two approaches: a 1D fit ( $m_{\gamma\gamma}$ only) and a 2D fit ( $m_{\gamma\gamma}$ and $m_{b\bar{b}}$ ). Both utilized multiclass multivariate methods to construct "resolved" and "boosted" SRs.
- $HH \to WWbb$ : CMS analyzed 62 fb $^{-1}$ of Run 3 data, categorizing gluon-gluon fusion (ggF) and vector boson fusion (VBF) signals into resolved and boosted SRs based on $b$ -tagged jet counts. Binary and multiclass neural networks (NNs) were used to separate signal from backgrounds ( $t\bar{t}$ , $t$ , $DY$).
- $t\bar{t}HH$ Production: ATLAS performed the first search for this process using 196 fb $^{-1}$ (2015–2023 data). Three signatures were targeted: single-lepton ( $1L$ ), same-sign/multilepton ($SSML$), and $b\bar{b}\gamma\gamma$ . Transformer NNs were applied to the $1L$ and $SSML$ categories, while BDTs were used for the $b\bar{b}\gamma\gamma$ category. Signal extraction involved simultaneous fits of NN outputs and $m_{\gamma\gamma}$ distributions.
- Combinations: Independent analyses from ATLAS and CMS were combined to maximize sensitivity, resulting in the most stringent limits to date.
Tri-Higgs ($HHH$) Searches:
- CMS searched for $HHH \to 6b$ using 138 fb $^{-1}$ of Run 2 data. Given the low reconstruction efficiency (only $\sim25\%$ of events have three reconstructed Higgs bosons), the analysis utilized SPANet to classify events into signal ($HHH$) and background ($HH$, $t\bar{t}$ , QCD). An additional SPANet layer categorized signal events into SRs based on the number of resolved ( $h$ ) or boosted ($bh$) Higgs bosons.
Resonant Searches:
- ATLAS ( $X \to S(bb)H(\gamma\gamma)$ ): Analyzed Run 2 and Run 3 data (140 + 59 fb $^{-1}$ ) using parametrized NNs (PNNs) in regions with one or two $b$ -tagged jets to cover a wide mass parameter space for heavy scalars $X$ and $S$ .
- CMS ( $X \to H(ZZ)H(bb)$ and $X \to Y(ZZ)H(bb)$ ): Used Run 2 data (138 fb $^{-1}$ ) with parametrized BDTs in SRs with 0, 1, or 2 large-radius jets to probe various mass hypotheses for $X$ and $Y$ .

Key Results

Nonresonant Di-Higgs ($HH$):
- ATLAS ( $b\bar{b}\gamma\gamma$ ): The signal strength was measured as $\mu_{HH} = 0.9^{+1.3}_{-1.0}(\text{stat.})^{+0.6}_{-0.5}(\text{syst.})$ , consistent with the Standard Model (SM). The observed (expected) significance was 0.84 (1.01) $\sigma$ . Upper limits were set at $\mu_{HH} < 3.8$ (observed) and $\mu_{HH} < 3.7$ (expected). Constraints on coupling modifiers were $\kappa_\lambda = 2.7^{+2.3}_{-3.0}$ and $\kappa_{2V} = 1.6^{+0.6}_{-1.9}$ .
- CMS ( $b\bar{b}\gamma\gamma$ ): Using the 2D-fit approach, observed (expected) upper limits were $\mu_{HH} < 11$ (7.3). The $\kappa_\lambda$ modifier was constrained to the range $-6.1 < \kappa_\lambda < 12.8$ .
- CMS ($WWbb$): Observed (expected) upper limit on signal strength was 12.7 (18.6). Constraints were $\kappa_\lambda \in [-9.7, 15.8]$ and $\kappa_{2V} \in [-0.27, 2.32]$ .
- ATLAS ( $t\bar{t}HH$ ): Observed (expected) upper limit on signal strength was $\mu_{HH} < 20$ (21). The Wilson coefficient $c_{t\bar{t}HH}$ was constrained to $[-3.9, 3.4]$ .
- Combined ATLAS/CMS: The combination of independent analyses yielded the most stringent limits to date: $\mu_{HH}^{\text{observed(expected)}} < 2.5(1.7)$ , with tightest constraints on $\kappa_\lambda$ and $\kappa_{2V}$ .
Nonresonant Tri-Higgs ($HHH$):
- CMS ( $6b$ ): The analysis provided the best limit to date on tri-Higgs production, with $\mu_{HHH}^{\text{observed(expected)}} < 588(572)$ . The quartic coupling modifier was constrained as $|\kappa_4| < 190$ .
Resonant Searches:
- ATLAS ( $X \to S(bb)H(\gamma\gamma)$ ): No significant excesses were reported; the highest local significance was of the order of 2 $\sigma$ .
- CMS ( $X \to H(ZZ)H(bb)$ and $X \to Y(ZZ)H(bb)$ ): Upper limits on production cross-sections were set, found to be comparable to those in more sensitive final states like $H \to \gamma\gamma$ and $H \to \tau\tau$ .

Significance and Outlook
The paper highlights that the ATLAS and CMS collaborations have reached a level of maturity in Run 2 analyses, enabling comprehensive combinations that significantly improve sensitivity. The integration of Run 3 data and the application of cutting-edge machine learning (including transformer NNs, SPANet, and PNNs) have enhanced the ability to probe these rare processes. While current results are consistent with the Standard Model, the ongoing efforts are paving the way for High-Luminosity LHC projections, which anticipate an expected significance exceeding 7 $\sigma$ for the observation of di-Higgs production by the end of the Phase 2 running program.