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Combination of searches for nonresonant Higgs boson pair production in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb $^{-1}$ of proton-proton collision data at 13 TeV collected by the CMS experiment, this paper presents a combined search for nonresonant Higgs boson pair production that sets the most stringent limits to date on the inclusive production cross section, constrains the Higgs trilinear self-coupling and vector boson coupling modifiers, and explores various new physics scenarios within the Higgs effective field theory framework.

Original authors: CMS Collaboration

Published 2026-09-09

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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

In the heart of the universe, a fundamental force gives mass to the particles that make up everything we see. This force is carried by a field that permeates all of space, and the particle associated with this field is the Higgs boson. Discovered in 2012, this particle confirmed a decades-old theory about how the universe acquired its structure. However, while scientists have measured how the Higgs boson interacts with other particles, one crucial aspect of its nature remains a mystery: how it interacts with itself. Just as a magnet has a north and south pole, the Higgs field has a self-interaction that determines the shape of the universe's energy landscape. Understanding this self-interaction is vital because it reveals the stability of the universe and how it evolved from the Big Bang. If the Higgs boson behaves differently than predicted, it could point to entirely new laws of physics beyond our current understanding.

A researcher working with the Compact Muon Solenoid, or CMS, experiment at the Large Hadron Collider in Switzerland has taken a massive step toward solving this puzzle. By analyzing a vast collection of data from proton-proton collisions recorded between 2016 and 2018, they searched for a rare event where two Higgs bosons are created at the same time. This process, known as nonresonant pair production, is the most direct way to measure the strength of the Higgs boson's self-interaction. The researcher examined 138 units of collision data, a volume equivalent to the total energy output of the collider over three years, looking for specific patterns where the Higgs bosons decay into other particles like bottom quarks, tau leptons, photons, or W bosons. Because this event is incredibly rare, they had to sift through billions of collisions to find the handful of candidates that might signal the presence of two Higgs bosons.

The search covered multiple pathways, or "channels," depending on how the two Higgs bosons broke apart after being created. Some analyses focused on the decay into four bottom quarks, which is the most common outcome but also the most difficult to distinguish from background noise. Others looked for cleaner signatures, such as two Higgs bosons decaying into two photons and two bottom quarks, or into pairs of tau leptons. The researcher combined the results from all these different approaches to create a single, powerful measurement. They found no evidence of a new, unexpected signal that would indicate a deviation from the standard model of physics. Instead, the data aligns closely with the predictions made by the standard model, though the statistical precision is not yet high enough to rule out all possible variations.

The researcher set strict boundaries on how much the Higgs boson's self-interaction could differ from the standard model. They determined that the strength of this interaction, represented by a specific modifier, must fall within a range of negative 1.35 to positive 6.37 times the standard value. While this range is still broad, it represents the most precise constraint achieved to date using data from the Large Hadron Collider. Furthermore, the study examined how the Higgs boson interacts with other force-carrying particles, specifically the vector bosons. The data strongly suggests that the interaction between two vector bosons and two Higgs bosons exists and behaves as expected, excluding the possibility that this interaction is zero with a high degree of statistical certainty. This finding confirms a specific type of four-particle interaction that is essential for the mathematical consistency of the theory.

Beyond the standard model, the researcher also looked for signs of "new physics" by testing various theoretical scenarios where the Higgs boson might have unusual connections to other particles, such as top quarks or gluons. They found no evidence for these exotic couplings, effectively ruling out several specific theoretical models that predicted such behavior. The study also projected what might happen when the Large Hadron Collider is upgraded to a high-luminosity version in the coming years. With significantly more data, the researcher estimates they could reach a level of sensitivity that would allow them to see the Higgs boson pair production process clearly, potentially confirming the standard model's predictions with high confidence or revealing a crack in the foundation of current physics. For now, the Higgs boson remains a stubbornly standard particle, holding its secrets just out of reach, but the path forward is becoming increasingly clear.

Technical Summary: Combination of Searches for Nonresonant Higgs Boson Pair Production in Proton-Proton Collisions at $\sqrt{s} = 13$ TeV

Problem and Motivation
While the discovery of the Higgs boson (H) in 2012 confirmed the mechanism of electroweak symmetry breaking, the nature of the Higgs boson self-interaction remains an open question. Measurements of the trilinear ( $\lambda_3$ ) and quartic ( $\lambda_4$ ) self-couplings are essential for validating the Brout–Englert–Higgs mechanism and probing potential new physics scenarios, such as extended Higgs sectors. Although the quartic coupling is difficult to access at the Large Hadron Collider (LHC), the trilinear coupling can be directly probed through nonresonant Higgs boson pair (HH) production. This paper presents a combination of searches for nonresonant HH production using the full Run 2 dataset collected by the CMS experiment at $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 138 fb $^{-1}$ .

Methodology
The analysis combines results from multiple decay channels and production mechanisms to maximize sensitivity to the Higgs boson trilinear self-coupling modifier ( $\kappa_\lambda = \lambda_3/\lambda_3^{\text{SM}}$ ) and the coupling modifier governing the interaction between two vector bosons and two Higgs bosons ( $\kappa_{2V}$ ).

Channels and Topologies: The combination includes searches in the following final states:
- $HH \to bbbb$ (resolved and boosted topologies, including VHH production).
- $HH \to bb\tau\tau$ .
- $HH \to bb\gamma\gamma$ .
- $HH \to bbWW$ (including $WW \to \ell\nu qq/2\ell2\nu$ and $WW \to 4q$ ).
- $HH \to \text{multilepton}$ ( $4W, 2W2\tau, 4\tau$ ).
- $HH \to \tau\tau\gamma\gamma$ .
- $HH \to bbZZ$ ( $4\ell$ ).
- $HH \to WW\gamma\gamma$ .
- New channels introduced in this combination include $bbWW$ (all-hadronic and semi-leptonic) and $WW\gamma\gamma$ .
Signal Modelling: The analysis utilizes the Higgs Effective Field Theory (HEFT) framework. Signal samples for gluon-gluon fusion (ggF) are modeled using a reweighting method that parametrizes differential cross-sections as a function of the invariant mass of the HH pair and angular separation, allowing for scans over coupling modifiers ( $\kappa_\lambda, \kappa_t, c_2, c_g, c_{2g}$ ). Vector boson fusion (VBF) and associated production (VHH) are modeled using linear combinations of simulated samples with varying coupling modifiers.
Statistical Combination: A global maximum likelihood fit is performed using the profile likelihood ratio test statistic. Systematic uncertainties (theoretical and experimental) are treated as nuisance parameters. Correlations between analyses are fully accounted for, and specific overlap removal strategies are applied to prevent double-counting of events.
Projections: The results are extrapolated to the High-Luminosity LHC (HL-LHC) conditions, considering integrated luminosities up to 3000 fb $^{-1}$ and three scenarios for systematic uncertainties.

Key Contributions

First Combination of Multiple Channels: This work supersedes previous results by combining a broader set of final states, including the first searches for $HH \to bbWW$ in the all-hadronic channel and the inclusion of VHH production in the $bbbb$ final state.
HEFT and UV-Complete Model Constraints: Beyond standard coupling modifiers, the analysis constrains anomalous couplings ( $c_2, c_g, c_{2g}$ ) within the HEFT framework. These constraints are mapped to specific ultraviolet (UV) complete models, including singlet extensions, Two-Higgs-Doublet Models (2HDM), and Minimal Composite Higgs Models (MCHM).
Exclusion of $\kappa_{2V} = 0$ : The analysis provides a definitive exclusion of the scenario where the quartic Higgs-vector boson coupling is zero.

Results

Cross Section Limits: The observed (expected) upper limit on the inclusive nonresonant HH production cross section is 3.5 (2.5) times the Standard Model (SM) prediction at 95% confidence level (CL). For VBF production alone, the limit is 79 (91) times the SM prediction.
Coupling Modifiers:
- $\kappa_\lambda$ : Assuming SM values for other couplings, $\kappa_\lambda$ is constrained to the range $[-1.35, 6.37]$ at 95% CL (expected: $[-2.24, 7.89]$ ). The best-fit value is 1.51.
- $\kappa_{2V}$ : The value $\kappa_{2V} = 0$ is excluded with a significance of 6.6 standard deviations. At 95% CL, $\kappa_{2V}$ is constrained to $[0.64, 1.40]$ (expected: $[0.62, 1.41]$ ).
- Anomalous Couplings ( $c_2$ ): The coupling modifier $c_2$ (interaction between two top quarks and two Higgs bosons) is constrained to $[-0.29, 0.63]$ at 95% CL (expected: $[-0.27, 0.56]$ ).
Model Constraints:
- Singlet Extensions: Constraints are placed on the mixing angle $\alpha$ and effective trilinear coupling $\lambda_{\text{eff}}$ .
- 2HDM: Exclusion contours are derived in the $(m_H, \tan\beta)$ and $(|\cos(\beta-\alpha)|, \tan\beta)$ planes for Type-I, II, X, and Y models.
- MCHM: The compactness parameter $\xi$ is constrained to $[0, 0.45]$ for MCHM4 and $[0, 0.26]$ for MCHM5 at 95% CL.
HL-LHC Projections: The analysis projects that with an integrated luminosity of 2000 fb $^{-1}$ , the CMS experiment could achieve evidence for HH production (3.5 $\sigma$ significance) assuming SM-like signal and nominal systematic uncertainties. At 3000 fb $^{-1}$ , the expected significance rises to 4.2 $\sigma$ .

Significance
This work represents the most stringent limits and constraints obtained to date from nonresonant HH production searches using the LHC Run 2 dataset. The exclusion of $\kappa_{2V} = 0$ at more than 5 standard deviations marks a decisive step in establishing the presence of quartic Higgs-vector boson interactions in nature. The results are consistent with SM predictions, and no significant deviations from the SM are observed. The paper concludes that with the anticipated data from the HL-LHC, the observation of HH production is within reach, offering a critical path to understanding the Higgs potential and the stability of the electroweak vacuum.

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