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Combined measurements and interpretations of Higgs boson production and decay in proton-proton collisions at $\sqrt{s}$ = 13 TeV

The CMS Collaboration presents a comprehensive combined analysis of Higgs boson production and decay using 138 fb $^{-1}$ of proton-proton collision data at 13 TeV, measuring signal yields across multiple channels and theoretical frameworks that show strong compatibility with Standard Model predictions.

Original authors: CMS Collaboration

Published 2026-08-13

📖 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

Imagine the universe as a giant, invisible web that holds everything together. Without this web, particles would zip around at the speed of light, never slowing down to stick together and form atoms, stars, or even you. This web is called the Higgs field, and the particle that proves it exists is the Higgs boson. Think of the Higgs boson as a tiny, energetic ripple in that web. When scientists first spotted this ripple in 2012, it was like finding the first clue to a massive mystery: "Does the universe work exactly the way our best rulebook, the Standard Model, says it should?"

The Standard Model is like a massive instruction manual for how the universe is built. It predicts how particles should behave, how heavy they should be, and how they should interact. But scientists have always suspected there might be more to the story—maybe hidden particles, extra dimensions, or secret forces that the manual doesn't mention. To find out, they need to check the manual's instructions with extreme precision. They do this by smashing protons together at mind-boggling speeds in a giant ring called the Large Hadron Collider (LHC). When these protons collide, they create a shower of new particles, including the elusive Higgs boson. By watching how the Higgs is born and how it falls apart, scientists can see if it follows the rules or if it's breaking them, which would be the biggest discovery in physics since the manual was written.

The Great Higgs Check-Up

In this new paper, the CMS Collaboration—a massive team of scientists working with a giant detector called CMS at CERN—has performed the most comprehensive "check-up" of the Higgs boson ever done. They didn't just look at the Higgs once; they gathered data from 2016 to 2018, representing a colossal amount of information (138 fb⁻¹ of integrated luminosity, which is like having a library of collision data that would take a supercomputer years to read). They looked at the Higgs boson in seven different ways, watching it decay into pairs of photons, Z bosons, W bosons, tau particles, bottom quarks, muons, and even a Z boson and a photon. They also searched for the Higgs disappearing into "invisible" particles and checked how it behaves when it's produced at very high energies.

The big question was: Does the Higgs act exactly like the Standard Model predicts? The answer is a resounding "mostly yes." When the scientists measured the total number of Higgs bosons they found compared to what the manual predicted, the result was 1.014 times the expected amount. The uncertainty on this number is tiny (about ±0.055), meaning the Higgs is behaving almost exactly as the rulebook says it should. It's like if you ordered a pizza and the delivery guy brought you a pizza that was 1.014 times the size of the picture on the menu—it's a perfect match within the margin of error.

However, science is never just about saying "it matches." The scientists also looked for tiny cracks in the armor. They found a few small "tensions" or bumps in the data. For instance, when they looked at how often the Higgs is produced alongside a single top quark (a process called tH), the data showed a value about 2.2 standard deviations higher than expected. While this sounds like a big deal, in the world of particle physics, a "standard deviation" is a measure of how surprised you should be. A 2.2-sigma bump is like flipping a coin and getting heads five times in a row; it's unusual, but not impossible by pure chance. It's a hint, not a proof of new physics. Similarly, the Higgs produced with a W or Z boson at very high speeds seemed a bit more frequent than the manual predicted, but again, the data isn't strong enough to say the manual is wrong.

The team also used this data to test specific theories about what might be hiding "beyond the Standard Model." They checked if the Higgs could be decaying into invisible particles (like dark matter) or if its interactions were being tweaked by new, heavy particles we can't see yet. They found that the Higgs is not hiding any significant amount of invisible stuff, and its interactions with other particles (like the top quark or the bottom quark) are sticking very closely to the predicted values. For example, the strength of the Higgs' connection to the top quark was measured to be 0.91 times the expected strength, and its connection to the W boson was 1.05 times expected. These numbers are so close to 1.0 that they confirm the Standard Model is doing an incredible job describing our universe.

In short, this paper is a massive victory for the Standard Model. The Higgs boson is behaving exactly as the theory predicted, with no major surprises. While there are a few tiny, intriguing wiggles in the data that scientists will keep watching, the overall picture is one of a universe that, so far, follows the rules perfectly. It's a bit like checking a master clock: every gear turns exactly as it should, and while a few ticks might sound slightly different, the time is still correct. For now, the mystery of the Higgs is solved, but the hunt for what lies beyond the clock continues.

Technical Summary: Combined Measurements and Interpretations of Higgs Boson Production and Decay in Proton-Proton Collisions at $\sqrt{s} = 13$ TeV

Problem and Scope
This paper presents the most comprehensive study of Higgs boson properties conducted by the CMS Collaboration to date. It reports a statistical combination of measurements regarding Higgs boson production and decay rates using proton-proton collision data collected between 2016 and 2018 at a center-of-mass energy of $\sqrt{s} = 13$ TeV, corresponding to an integrated luminosity of 138 fb $^{-1}$ . The analysis aims to characterize the Higgs boson's interactions with Standard Model (SM) particles with high precision, test the validity of the SM, and constrain potential Beyond-the-Standard-Model (BSM) physics. The study covers seven decay channels ( $H \to \gamma\gamma, ZZ, WW, \tau\tau, bb, \mu\mu, Z\gamma$ ), searches for invisible decays, and measurements of off-shell production.

Methodology
The statistical combination integrates up to 1951 event categories from 19 input analyses. These analyses target various production mechanisms: gluon fusion (ggH), vector boson fusion (VBF), associated production with vector bosons (VH), associated production with top quarks (ttH), and associated production with a single top quark (tH).

Statistical Framework: The combination employs a profile likelihood ratio test statistic. The likelihood function is constructed as a product of likelihoods over mutually exclusive analysis regions (signal and control regions), constrained by nuisance parameters (NPs) representing systematic uncertainties.
Signal Parametrization: The study utilizes multiple parametrization models to extract results:
- Signal Strengths ( $\mu$ ): Measured at inclusive, per-production, per-decay, and per-production-and-decay levels.
- Simplified Template Cross Sections (STXS): Measurements are performed at two levels of granularity. Stage 0 defines cross sections for inclusive production processes within a fiducial region ( $|y_H| < 2.5$ ). Stage 1.2 partitions the phase space based on kinematic properties (e.g., $p_T^H$ , jet multiplicity, dijet mass) to isolate regions sensitive to BSM effects and reduce theoretical uncertainties.
- Coupling Modifiers ( $\kappa$ ): Interpretations are provided in the $\kappa$ -framework, scaling production cross sections and decay widths. Both "resolved" loop models (distinguishing top and bottom quark contributions) and "effective" loop models are tested.
- Effective Field Theory (SMEFT): Constraints are placed on Wilson coefficients (WCs) using linear and linear-plus-quadratic parametrizations. A Principal Component Analysis (PCA) is used to identify linear combinations of WCs that can be simultaneously constrained.
Systematic Uncertainties: Theoretical uncertainties (QCD/EW corrections, PDFs, $\alpha_S$ ) and experimental uncertainties (luminosity, lepton/jet energy scales, b-tagging, pileup) are treated as NPs. A pruning strategy is applied to reduce model complexity without significantly affecting results.
Input Data: The combination includes new measurements not present in previous CMS combinations, such as VBF $H \to bb$ , high- $p_T$ $H \to bb$ , off-shell $H \to ZZ \to 4\ell$ , and invisible decays via ttH/VH.

Key Contributions

First CMS STXS Combination: This paper presents the first combined STXS measurement from CMS, providing granular cross-section measurements across 32 kinematic regions at Stage 1.2.
Expanded Decay Channels: It incorporates the first measurements of $H \to bb$ via VBF and high- $p_T$ production, and includes searches for invisible decays and off-shell production to constrain the total decay width.
Comprehensive Interpretations: The results are interpreted within the coupling modifier framework (including constraints on the Higgs trilinear self-coupling via NLO EW corrections) and the SMEFT framework, providing constraints on 43 Wilson coefficients and 17 principal components.

Results

Inclusive Signal Strength: The best fit inclusive signal yield is measured to be $1.014^{+0.055}_{-0.053}$ times the SM expectation. The result shows good compatibility with the SM ( $p_{SM} = 0.80$ ).
Production and Decay Channels:
- Per-production measurements show a small tension with the SM ( $p_{SM} = 0.02$ ), primarily driven by an excess in the $tH$ production process ( $\mu_{tH} \approx 5.9$ ) and elevated values for $WH$ and $ZH$.
- Per-decay measurements show better compatibility ( $p_{SM} = 0.33$ ), with the largest deviations in $\mu_{\tau\tau}$ and $\mu_{Z\gamma}$ , though consistent with SM within 95% CL.
- The precision on the $H \to bb$ signal strength has improved significantly (68% CL interval of $\pm 15\%$ ) compared to previous combinations.
STXS Measurements:
- Stage 0 cross sections show a tension with the SM ( $p_{SM} = 0.012$ ), driven by excesses in $tH$ and $VH$ leptonic high- $p_T$ regions.
- Stage 1.2 measurements reveal deviations in specific kinematic regions, notably $WH$ and $ZH$ leptonic production at $p_T^V > 250$ GeV (exceeding SM by $\sim 2.1-2.2\sigma$ ) and the $ggH$ high- $p_T$ bin ( $450 < p_T^H < 650$ GeV). The overall compatibility for Stage 1.2 is $p_{SM} = 0.06$ .
Coupling Modifiers:
- Resolved loop fits yield coupling modifiers consistent with the SM ( $p_{SM} = 0.12$ ). Vector boson couplings ( $\kappa_W, \kappa_Z$ ) are measured with $\sim 6\%$ precision; third-generation fermion couplings ( $\kappa_t, \kappa_b, \kappa_\tau$ ) with $\sim 6-12\%$ ; and $\kappa_\mu$ with $\sim 20\%$ .
- The data constrain the Higgs boson total width and place limits on invisible branching fractions.
SMEFT Constraints:
- Individual Wilson coefficients are constrained, with the tightest limits on $c_{HG}$ and $c_{HB}$ (probing new physics scales $\Lambda \sim 15$ TeV).
- A deviation from the SM is observed in the $c^{(3)}_{Hq}$ coefficient ( $p_{SM} = 0.01$ ), correlating with the excesses in high- $p_T$ VH production.
- PCA identifies 17 constrained eigenvectors, with the most sensitive direction driven by $ggH$ in the $H \to \gamma\gamma$ channel. The overall SMEFT results are compatible with the SM ( $p_{SM} = 0.11$ ).

Significance
The paper claims to represent the most comprehensive and granular characterization of the Higgs boson by the CMS Collaboration. By combining a wide array of decay channels and production modes, including rare processes and off-shell contributions, the analysis significantly reduces statistical uncertainties and provides a robust test of the SM. The introduction of STXS Stage 1.2 measurements allows for a more differential view of Higgs properties, isolating regions where BSM effects might manifest. The results generally support the SM predictions, though specific kinematic excesses (particularly in $tH$ and high- $p_T$ VH) warrant further investigation. The provided constraints on coupling modifiers and SMEFT parameters serve as critical inputs for global fits and theoretical model building. All tabulated results are made available via HEPData to facilitate reinterpretation.

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