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Search for nonresonant triple Higgs boson production in the final state with six bottom quarks in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb $^{-1}$ of proton-proton collision data at 13 TeV, the CMS experiment performed a search for nonresonant triple Higgs boson production in the six-bottom-quark final state, setting the most stringent constraints to date on the signal cross section and trilinear and quartic Higgs coupling modifiers while excluding a portion of the parameter space allowed by perturbative unitarity.

Original authors: CMS Collaboration

Published 2026-07-07

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: CMS Collaboration

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

The Big Picture: Hunting for a "Ghost" Trio

Imagine the universe is built out of tiny, invisible building blocks. One of the most important blocks is the Higgs boson. Think of the Higgs boson as the "glue" that gives other particles their mass (like how a heavy backpack makes you feel heavier).

Scientists already know this glue exists. Now, they want to understand how the glue sticks to itself. Does it stick tightly? Loosely? Or does it repel itself? To find out, they need to watch the Higgs bosons interact with each other.

The most extreme interaction they are looking for is three Higgs bosons appearing at the exact same time (a "trio"). This is incredibly rare. It's like trying to win the lottery three times in a row, but with odds so low that you'd need to buy a ticket every second for thousands of years to see it happen once.

The Experiment: The Great Filter

The scientists at CERN (specifically the CMS experiment) acted like a massive, high-tech sieve. They smashed protons together at nearly the speed of light, creating a chaotic storm of particles.

The Goal: They were looking for a specific "signature": six bottom quarks. Since each Higgs boson decays into two bottom quarks, finding three Higgs bosons means finding six bottom quarks.
The Problem: The universe is messy. Every time they smash protons, they get millions of "junk" particles that look very similar to what they want. It's like trying to find three specific, rare blue marbles in a giant pile of sand, where the sand is constantly shifting and looking exactly like blue marbles.
The Solution (The AI): To separate the rare trio from the sand, the scientists used a super-smart computer program called SPANET.
- Imagine you are trying to identify a specific group of three friends in a crowded stadium. You know what they look like, but there are thousands of people.
- SPANET is like a super-observer that doesn't just look at one person; it looks at the whole group, how they are standing, how they are moving, and how they relate to each other. It learns to spot the "trio" even when they are hiding in the crowd.

The Results: Silence is the Answer

After analyzing data equivalent to 138 femtobarns (a massive amount of collision data collected over several years), the scientists looked at their results.

Did they find the trio? No.
What did they see? They saw exactly what they expected to see if the trio didn't exist: just the background "noise" of regular particle collisions.
The Conclusion: They didn't find a "ghost" trio. However, finding nothing is still a huge discovery. It tells us that if these trios do exist, they are even rarer than we thought.

The Limits: How Rare is "Rare"?

Because they didn't find the trio, they set a "limit" on how often it could be happening.

The Analogy: Imagine you are fishing in a lake. You cast your line 100 times and catch nothing. You can't say, "There are no fish in the lake." But you can say, "If there are fish, they are so rare that I would need to cast my line 1,000 times to catch one."
The Paper's Limit: The scientists calculated that if the Higgs trio exists, it happens no more than 588 times more often than the Standard Model (our current best theory) predicts.
- The Standard Model predicts this event is so rare it's almost impossible.
- The scientists are saying, "Okay, maybe it's 588 times more common than the theory says, but it can't be more than that, or we would have seen it."

Why This Matters: The "Rulebook" of the Universe

The paper isn't just about counting particles; it's about testing the "Rulebook" of the universe.

The Coupling Modifiers ( $\kappa_3$ and $\kappa_4$ ): Think of these as "knobs" on a machine.
- One knob controls how two Higgs bosons stick together.
- The other controls how three stick together.
- The Standard Model says these knobs are set to specific numbers (like 1).
The New Constraint: By not finding the trio, the scientists were able to turn those knobs and say, "The knob cannot be set to these extreme values."
The Big Win: For the first time, this experiment has ruled out a specific area of the "knob settings" that was previously allowed by mathematical rules (called "perturbative unitarity"). It's like a detective saying, "We know the suspect can't be in this specific room, even though the math said they could be."

Summary

The Hunt: Scientists looked for three Higgs bosons appearing together, which would decay into six bottom quarks.
The Tool: They used a sophisticated AI (SPANET) to filter through trillions of particle collisions to find this rare signal.
The Result: They found no evidence of the trio.
The Takeaway: They set the strictest limits yet on how often this event can happen. They also narrowed down the possible "settings" for how the Higgs boson interacts with itself, ruling out some mathematical possibilities for the first time.

In short: They didn't find the ghost, but they proved the ghost is even more elusive than we thought, and they tightened the rules on how the universe's "glue" can behave.

Technical Summary: Search for Nonresonant Triple Higgs Boson Production in the Six-Bottom Quark Final State

Problem and Motivation
Following the discovery of the Higgs boson ( $H$ ), a primary objective of the LHC physics program is to probe the structure of the Higgs potential. In the Standard Model (SM), this potential is determined by the vacuum expectation value ( $v \approx 246$ GeV) and the Higgs mass ( $m_H = 125$ GeV), which fix the trilinear ( $\lambda_3$ ) and quartic ( $\lambda_4$ ) self-couplings to $\lambda_{SM} = m_H^2/(2v^2)$ . Deviations from these predictions could have profound implications for early universe cosmology and vacuum stability. While Higgs pair ($HH$) production provides sensitivity primarily to the trilinear coupling ( $\kappa_3 = \lambda_3/\lambda_{SM}$ ), triple Higgs ($HHH$) production offers direct sensitivity to both $\kappa_3$ and the quartic coupling modifier ( $\kappa_4 = \lambda_4/\lambda_{SM}$ ). However, $HHH$ production via gluon-gluon fusion (ggF) suffers from a tiny cross section ( $\sigma_{ggF}^{HHH} \approx 0.08$ fb at $\sqrt{s}=13$ TeV) due to destructive interference among contributing diagrams. This analysis addresses the challenge of searching for this rare process in the $HHH \to 6b$ final state, which has the largest branching fraction ( $\sim 60\%$ per Higgs) but faces overwhelming QCD multijet backgrounds.

Methodology
The analysis utilizes proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the CMS experiment between 2016 and 2018, corresponding to an integrated luminosity of $138 \text{ fb}^{-1}$ .

Event Reconstruction and Selection: The signal topology involves six $b$ quarks. To accommodate the varying kinematics of the Higgs bosons, the analysis employs a hybrid reconstruction strategy using both small-radius ( $R=0.4$ ) and large-radius ( $R=0.8$ ) jets. Events are required to have at least four small-radius jets ( $p_T > 25$ GeV) and large-radius jets ( $p_T > 300$ GeV). $b$ -jet identification utilizes the PARTICLENET tagger for small-radius jets and a dedicated PARTICLENET $bb$ discriminator for large-radius jets (tagging $H \to bb$ ).
Machine Learning Strategy: A symmetry-preserving attention network (SPANET) is employed to address the jet assignment problem and distinguish signal from background. The classification proceeds in two stages:
1. Inclusive Classifier: Trained to separate $HHH \to 6b$ , $HH \to 4b$ , QCD multijet, and $t\bar{t}$ events. Events with the highest $HHH$ probability are selected.
2. Refined Classifier: Applied to the signal-enriched subset to further suppress backgrounds, particularly QCD multijet production.
3. Topology Categorization: A third network categorizes events based on the number of reconstructed Higgs bosons (resolved vs. merged), creating ten distinct categories (e.g., $3H$ resolved, $2H$ merged, etc.).
Background Modeling: The dominant background is QCD multijet production ( $\sim 95\%$ of the selected sample). Instead of relying solely on simulation, the background model in the signal regions (SR) is derived from data events that fail the inclusive $HHH$ classification. The $b$ -tagging scores of these events are replaced with scores sampled from the SR to preserve event-level correlations while maintaining the kinematic shape. A separate control region (CR) enriched in $t\bar{t}$ validates the jet-tagging calibrations.
Statistical Analysis: Signal extraction is performed via a binned maximum likelihood fit to the SPANET output distribution ( $Prob_{MultiH}$ ) in the high-purity region ( $>0.8$ ). Systematic uncertainties include theoretical variations (scales, PDFs), jet energy scale/resolution, and flavor-tagging efficiencies.

Key Contributions

Novel Reconstruction Techniques: The analysis introduces an inclusive strategy that simultaneously targets four distinct reconstruction topologies (fully resolved, partially resolved/merged, and fully merged), maximizing sensitivity across the phase space.
Advanced Deep Learning: The application of SPANET, which explicitly preserves permutation symmetry, allows for effective handling of the combinatorial complexity inherent in six-jet final states.
Data-Driven Background Estimation: The method of embedding data events with modified tagging scores to model the QCD multijet background in the SR represents a robust approach to handling the dominant systematic uncertainty.

Results
No significant excess of events over the background prediction is observed.

Cross Section Limits: The observed (expected) 95% confidence level (CL) upper limit on the nonresonant $HHH$ production cross section is $44 $($ 43$) fb. This corresponds to $588 $($ 572$) times the SM prediction.
Coupling Constraints:
- Assuming $\kappa_4 = 1$ , the trilinear coupling modifier is constrained to $-7.4 < \kappa_3 < 12.4$ (expected: $-6.4 < \kappa_3 < 11.2$ ).
- Assuming $\kappa_3 = 1$ , the quartic coupling modifier is constrained to $-177 < \kappa_4 < 185$ (expected: $-180 < \kappa_4 < 190$ ).
Two-Dimensional Scan: The simultaneous fit in the $(\kappa_3, \kappa_4)$ plane yields 68% and 95% CL contours that exclude regions of parameter space permitted by the perturbative unitarity bound for the first time in a direct search for nonresonant $HHH$ production.

Significance
This work provides the most stringent constraints to date on nonresonant $HHH$ production and on the quartic Higgs self-coupling ( $\kappa_4$ ). By excluding part of the parameter space allowed by perturbative unitarity, the analysis demonstrates the capability of current LHC data to probe the structure of the Higgs potential beyond the trilinear coupling. The results serve as a critical benchmark for future high-luminosity LHC (HL-LHC) studies, where projected sensitivities suggest further improvements in constraining these couplings.