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Combination of Higgs boson measurements at $\sqrt{s} =$ 13 TeV and their interpretations by the ATLAS experiment

The ATLAS experiment presents a comprehensive combination of Higgs boson production and decay measurements using up to 140 fb $^{-1}$ of 13 TeV proton-proton collision data, yielding precise determinations of the inclusive event rate, coupling modifiers, the $b$ -quark running mass, and the total Higgs width, while also probing kinematic distributions within the Standard Model Effective Field Theory framework.

Original authors: ATLAS Collaboration

Published 2026-08-10

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: ATLAS 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

Imagine the universe is a giant, chaotic construction site where everything you see—stars, planets, and even you—is built from tiny, invisible Lego bricks. For decades, scientists have been trying to figure out the blueprints for how these bricks stick together. In 2012, they found a very special, mysterious brick called the Higgs boson. Think of this brick not as a building block itself, but as the "glue" that gives other particles their weight. Without it, particles would zip around at the speed of light, and atoms (and you) couldn't form. But here's the catch: we don't know exactly how strong this glue is, or if it behaves exactly the way the "instruction manual" (called the Standard Model) says it should. If the glue is slightly different than expected, it could mean there are hidden tools or secret rules in the universe we haven't discovered yet. This paper is like a massive, high-tech inspection of that glue, checking every single way it can be used to see if the universe is following the rules or if it's breaking them.

The ATLAS experiment, a giant particle detector buried deep underground at the Large Hadron Collider (LHC) in Europe, has been smashing protons together at incredible speeds to create these Higgs bosons. In this new study, the scientists acted like a team of master chefs combining thousands of different recipes. They took data from over 140 "inverse femtobarns" of collisions (a fancy way of saying a massive amount of data collected between 2015 and 2018) and mixed together measurements of how the Higgs boson is made and how it falls apart.

The main result is a big sigh of relief for the Standard Model. The team measured the overall "strength" of the Higgs boson's production and decay and found it to be 0.990 ± 0.027. In plain English, this is almost exactly 1.0, which is the perfect score predicted by the theory. It's like throwing a dart at a bullseye and landing right in the center. The scientists are very confident in this number, though they admit the biggest uncertainty comes from the theoretical math they use to predict what should happen, rather than from the experiment itself. It's as if the recipe is perfect, but the chef's estimate of how much salt to add has a little wiggle room.

The paper also took a closer look at specific "flavors" of the Higgs boson. They measured how often it turns into different particles, like pairs of bottom quarks, tau leptons, or photons. In almost every case, the Higgs behaved exactly as the Standard Model predicted. For instance, the rate at which it turns into bottom quarks was measured to be 51% (with a small margin of error), matching the expected 58.1% very closely. They even managed to weigh the "running mass" of the bottom quark at the energy scale of the Higgs, finding it to be 2.73 GeV. This is a bit like measuring the weight of a specific ingredient while it's being cooked, rather than when it's sitting on the shelf, and the result fits the recipe perfectly.

However, the scientists didn't just check the recipe; they also looked for secret ingredients. They searched for signs that the Higgs might be decaying into "invisible" particles (ghosts that the detector can't see) or "undetected" particles. They set strict limits, saying that if the Higgs does have a secret side, it can only be doing so less than 12% of the time for invisible decays and less than 18% for undetected ones. They also checked how the Higgs interacts with itself (a property called self-coupling), which is crucial for understanding the stability of the universe. They found a value of 1.3 with a wide range of uncertainty, which is consistent with the Standard Model's prediction of 1.0, but the margin of error is still too large to say for sure if there's a deviation.

One of the most exciting parts of the paper is how they looked at the "kinematics," or the motion, of the Higgs boson. They divided the data into 44 different "bins" based on how fast the Higgs was moving and what else was flying around it. This is like watching a car race and not just counting how many cars finish, but timing them in every single corner of the track. They found that the Higgs boson's behavior in these different corners matches the Standard Model predictions with a 47% compatibility score. While this isn't a perfect match, it's close enough to say the car is driving on the right track, even if the engine is a bit noisy.

Finally, the team used all this data to test "Effective Field Theory" models, which are mathematical ways of guessing what new physics might exist at energy scales we can't reach yet. They checked 20 different "knobs" that could be turned to change the laws of physics. Every single knob they turned resulted in a setting that was consistent with the Standard Model being zero (meaning no change). The most precise measurements they made were for the Higgs interacting with muons and photons, where they could probe energy scales up to 30 TeV (tera-electronvolts). This is like checking the foundation of a skyscraper and finding no cracks, even when you look with a microscope powerful enough to see atoms.

In short, this paper is a massive, detailed audit of the Higgs boson. It confirms that, so far, the universe is playing by the rules written in the Standard Model. The Higgs boson is doing exactly what it's supposed to do, from its weight to its speed to its interactions. While this might sound boring to some, it's actually a huge victory for science because it tells us exactly where not to look for new physics. If the Higgs isn't breaking the rules, then the new, exciting physics must be hiding somewhere else, waiting for us to build even bigger microscopes to find it. The mystery isn't solved, but the map just got a lot clearer.

Technical Summary: Combination of Higgs Boson Measurements at $\sqrt{s}=13$ TeV and Their Interpretations by the ATLAS Experiment

Problem and Objective
The primary objective of this work is to perform a comprehensive combination of Higgs boson production and decay measurements using the full Run 2 dataset of proton–proton collisions collected by the ATLAS experiment at $\sqrt{s}=13$ TeV, corresponding to an integrated luminosity of up to $140 \text{ fb}^{-1}$ . While individual analyses targeting specific production and decay channels have been published previously, this paper aims to provide a unified, statistically rigorous combination of 26 input analyses. The goal is to improve the precision of Higgs boson property measurements, reduce uncertainties through the correlation of systematic effects, and provide a more robust interpretation of the data within the Standard Model (SM) and beyond, including constraints on couplings, total width, self-coupling, and Effective Field Theory (EFT) parameters.

Methodology
The combination employs a global likelihood framework constructed from the likelihood functions of 26 individual input analyses. These analyses cover a wide range of Higgs boson production mechanisms (gluon–gluon fusion, vector-boson fusion, associated production with $W/Z$ bosons, top quarks, and $b$ -quarks, and Higgs pair production) and decay channels ( $H \to \gamma\gamma, ZZ^*, WW^*, \tau\tau, bb, \mu\mu, Z\gamma, cc$ , and invisible).

Statistical Treatment: A combined likelihood model is built using the RooFit framework, incorporating approximately 6,300 nuisance parameters (NPs) to account for systematic uncertainties. Correlated uncertainties (e.g., luminosity, parton distribution functions, jet energy scales) are treated using shared NPs across analyses, while uncorrelated uncertainties are handled separately. A decorrelation procedure is applied where NPs exhibit significantly different behaviors in the combined model compared to individual fits.
Uncertainty Decomposition: Uncertainties are decomposed into statistical, experimental systematic, signal theory, and background theory components. The "shifted auxiliary observable" method is used for the total width measurement to ensure an uncorrelated decomposition, while the "conditional uncertainty" method is applied to other results.
Frameworks:
- $\kappa$ -framework: Coupling modifiers ( $\kappa$ ) are used to scale SM couplings to vector bosons and fermions. Both "resolved" (loop-induced couplings derived from tree-level couplings) and "effective" (independent loop-induced couplings) parameterizations are explored.
- Simplified Template Cross-sections (STXS): Kinematic measurements are reported in 44 non-overlapping regions defined by the Stage 1.2 scheme, adapted to the sensitivity of the specific analyses.
- Standard Model Effective Field Theory (SMEFT): Results are interpreted in the context of dimension-6 operators in the Warsaw basis, considering both linear and linear+quadratic parameterizations.

Key Contributions and Results

Inclusive Signal Strength: The inclusive Higgs boson signal strength relative to the SM prediction is measured to be $\mu = 0.990^{+0.053}_{-0.051} = 0.990 \pm 0.027 \text{ (stat.)} \pm 0.024 \text{ (exp.)} ^{+0.037}_{-0.035} \text{ (sig. theo.)} ^{+0.016}_{-0.015} \text{ (bkg. theo.)}$ . This result is in excellent agreement with the SM ( $p$ -value = 77%). The total uncertainty is reduced by approximately 15% compared to the previous ATLAS combination, with signal theory uncertainty (dominated by missing higher-order QCD terms) becoming the largest component.
Production Cross-sections and Branching Ratios:
- Production cross-sections for $ggF$, VBF, $WH$, $ZH$, $t\bar{t}H$ , and $tH$ are measured. The $tH$ cross-section shows a mild deficit but remains consistent with the SM ( $p$ -value = 20%). Uncertainties for $WH$, $ZH$, and $t\bar{t}H$ are reduced by 20–40% relative to previous results.
- Branching ratios for main decay modes ( $H \to bb, WW^*, \tau\tau, ZZ^*, \gamma\gamma$ ) are measured with relative uncertainties between 8% and 13%. The $H \to bb$ and $H \to WW^*$ uncertainties are reduced by ~20%, and $H \to \tau\tau$ by ~10%.
Coupling Modifiers ( $\kappa$ -framework):
- Couplings to weak vector bosons ( $\kappa_V$ ) and fermions ( $\kappa_F$ ) are measured as $1.002^{+0.027}_{-0.026}$ and $0.945^{+0.043}_{-0.041}$ , respectively.
- In a model with independent couplings for $W, Z, t, b, \tau, \mu$ , and effective loop couplings ( $g, \gamma, Z\gamma$ ), all measured modifiers are consistent with SM expectations.
- The charm coupling modifier is constrained to $|\kappa_c| < 4.1$ at 95% CL, representing a factor of two improvement over previous limits.
- The first ATLAS determination of the running mass of the $b$ -quark at the Higgs mass scale is obtained: $m_b(m_H) = 2.73^{+0.27}_{-0.25} \text{ GeV}$ .
Total Width and Self-Coupling:
- Combining on-shell and off-shell production rates, the total Higgs boson width is constrained to $\Gamma_H = 3.6^{+2.1}_{-1.6} \text{ MeV}$ at 68% CL, consistent with the SM prediction.
- The Higgs boson self-coupling modifier is determined to be $\kappa_\lambda = 1.3^{+3.1}_{-1.6}$ , with a 95% CL interval of $[-1.5, 6.5]$ . This result combines single-Higgs and di-Higgs production measurements, with the latter providing the dominant sensitivity.
Kinematics and EFT:
- Production kinematics are measured in 44 STXS regions, providing the most detailed description of Higgs boson production to date.
- In the SMEFT interpretation, 20 measurement parameters (linear combinations of Warsaw basis operators) are constrained. The results are consistent with the SM ( $p$ -value = 81%). Sensitivity scales reach up to $\sim 30 \text{ TeV}$ for the best-constrained parameters. The inclusion of improved $H \to cc$ and $H \to bb$ analyses allows for the first measurement of the $c_u H$ operator in LHC data.

Significance
This paper represents the culmination of Run 2 Higgs boson analyses by ATLAS, offering the most precise and comprehensive set of measurements to date. By combining diverse channels and treating systematic uncertainties with a unified approach, the analysis achieves significant improvements in precision (up to 35% in some cases) over previous individual or partial combinations. The results provide stringent tests of the Standard Model, confirming its consistency across production rates, decay branching ratios, and kinematic distributions. Furthermore, the work establishes robust constraints on potential new physics, including the Higgs self-coupling, invisible decays, and dimension-6 EFT operators, setting the stage for future precision studies in the High-Luminosity LHC era. The determination of the $b$ -quark running mass and the improved constraints on the charm coupling highlight the unique capability of Higgs boson measurements to probe fundamental parameters of the Standard Model.

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