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Combination of vector boson scattering measurements in leptonic final states 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 detector, this paper presents a statistical combination of vector boson scattering measurements in various leptonic final states, which confirms Standard Model predictions and enables a charge-separated analysis of W boson production asymmetry.

Original authors: CMS Collaboration

Published 2026-08-04

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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

Imagine the universe as a giant, cosmic dance floor where the most fundamental particles are the dancers. For decades, physicists have been trying to understand the rules of this dance, specifically how particles get their mass. In 2012, they found the "mass-giver," a particle called the Higgs boson, which confirmed a theory about how the universe works. But just because you found the DJ doesn't mean you understand every move the dancers make. There are still gaps in our knowledge, particularly regarding how heavy particles called "vector bosons" (think of them as the heavyweight champions of the particle world) interact with each other at super-high speeds.

When these heavy particles smash into each other, they should theoretically scatter in a way that breaks the laws of physics unless the Higgs boson steps in to save the day. This process is called "Vector Boson Scattering" (VBS). It's like watching two bowling balls collide in mid-air; if they just bounce off, everything is fine. But if they start doing something weird, like passing through each other or creating a black hole, it means our understanding of the universe's rulebook is incomplete. Scientists care deeply about this because finding a glitch in the dance could reveal "new physics"—hidden forces or particles that we haven't discovered yet, which would change everything we know about reality.

Now, enter the CMS Collaboration, a massive team of scientists working with a giant particle detector called CMS at the Large Hadron Collider (LHC) in Europe. They have been watching billions of collisions between protons (tiny packets of matter) zooming around at nearly the speed of light. In this new paper, they decided to stop looking at just one type of collision at a time and instead took a "group selfie" of all the different ways these heavy particles scatter. They analyzed a massive dataset collected between 2016 and 2018, which corresponds to a record-breaking amount of data: 138 inverse femtobarns (a unit of measurement for how many collisions they saw).

The team focused on events where two heavy particles (W or Z bosons) were created and then scattered off each other, leaving behind a trail of other particles, specifically two jets (clumps of particles) and at least one pair of leptons (lightweight particles like electrons or muons). They looked at several different "dance moves": same-sign W bosons (two Ws with the same electric charge), opposite-sign W bosons (one positive, one negative), and combinations involving Z bosons. They even looked at cases where one of the heavy particles decayed into a jet of particles, adding more complexity to the mix.

To make sense of this chaos, the scientists built two different statistical models. The first model treated the W bosons as a single group, regardless of their electric charge, measuring four main types of scattering. The second model was more picky, separating the W bosons by their charge (positive vs. negative) to see if nature prefers one charge over the other, resulting in six different measurements. They used powerful computer algorithms, including deep neural networks (a type of artificial intelligence), to sift through the noise and find the rare signal of the scattering event hiding among billions of background collisions.

The results? The universe is behaving exactly as the Standard Model predicts. When the scientists measured how often these scattering events happened, the numbers matched the theoretical predictions almost perfectly. For the same-sign W bosons, the signal was so strong that the chance of it being a fluke is less than one in a billion (more than 5 standard deviations of certainty). For the other channels, the results were also consistent with the Standard Model, with statistical significances ranging from about 4 to 7 standard deviations.

Crucially, the paper does not find any evidence of "new physics" or deviations from the expected rules. The "dance" is happening exactly as the Higgs boson and the known laws of physics say it should. The team also confirmed that there is a slight asymmetry in the production of positively charged versus negatively charged W bosons, which is exactly what we expect because protons are made of different types of quarks.

In short, this paper is a massive stress test of our current understanding of the universe. By combining all these different measurements into one giant, coherent picture, the scientists have tightened the screws on the Standard Model. While they didn't find the "smoking gun" of new physics this time, they have proven that the current rulebook is incredibly robust. It's like checking the blueprint of a skyscraper against the actual building and finding that every beam and bolt is exactly where it should be. This gives physicists a solid foundation to keep searching for the tiny cracks that might one day lead to a revolution in how we understand the cosmos.

Technical Summary: Combination of Vector Boson Scattering Measurements in Leptonic Final States

Problem and Motivation
The discovery of the Higgs boson confirmed the Brout–Englert–Higgs mechanism as the source of electroweak symmetry breaking (EWSB). However, the understanding of the Yukawa and scalar sectors remains incomplete. Vector boson scattering (VBS) serves as a critical probe of the high-energy behavior of electroweak (EW) interactions. In the Standard Model (SM), the scattering amplitude for longitudinally polarized weak bosons increases with energy, threatening unitarity at center-of-mass energies around 1 TeV. The inclusion of the SM Higgs boson restores unitarity through a delicate cancellation. Deviations from SM predictions in VBS could indicate new physics, such as modified Higgs couplings to gauge bosons or altered triple and quartic self-interactions of gauge bosons. While individual VBS channels (same-sign $WW$, opposite-sign $WW$, $WZ$, and $ZZ$) have been observed, a global, coherent statistical combination of these processes was lacking to provide a comprehensive test of the EW sector.

Methodology
This analysis presents a statistical combination of VBS measurements using proton-proton collision data at a center-of-mass energy of $\sqrt{s} = 13$ TeV, collected by the CMS detector during 2016–2018, corresponding to an integrated luminosity of 138 fb $^{-1}$ .

Input Analyses: The combination integrates seven distinct analyses targeting VBS topologies where two heavy vector bosons ( $W$ $W$ or $Z$ $Z$ ) scatter and are accompanied by two forward jets. The final states include:
- Fully leptonic decays: Same-sign $WW $($ SSWW$) with $\ell^\pm\ell^\pm 2\nu$ and $\ell^\pm\tau_h^\pm 2\nu$ ; Opposite-sign $WW $($ OSWW$) with $\ell^+\ell^- 2\nu$ ; $WZ$ with $3\ell\nu$ ; and $ZZ$ with $4\ell$ .
- Semi-leptonic decays: $WV $($ \ell\nu jj$) and $ZV $($ 2\ell jj$), where one boson decays hadronically.
Event Selection and Orthogonality: Events are selected based on lepton multiplicity (electrons, muons, or hadronic taus) and kinematic requirements characteristic of VBS: high invariant mass of the dijet system ( $m_{jj} > 100$ or $500$ GeV) and large pseudorapidity separation ( $|\Delta\eta_{jj}| > 2.5$ ). To prevent double-counting, mutually exclusive regions are defined primarily by charged-lepton multiplicity and vetoes, refined by kinematic observables and object properties (e.g., $b$ -tagging, jet resolution).
Signal Extraction: Advanced discriminants are employed to separate EW-induced VBS signals from QCD-induced backgrounds. These include Deep Neural Networks (DNN) for $SSWW(\tau_h)$ , $OSWW$, and $WV/ZV$ channels; a Boosted Decision Tree (BDT) for $WZ$; and a matrix element-based discriminant (KD) for $ZZ$. The $SSWW(e, \mu)$ channel utilizes differential kinematic observables.
Statistical Framework: A profile likelihood ratio test statistic is used to extract signal strengths ( $\mu = \sigma_{obs}/\sigma_{SM}$ $μ = σ_{o b s} / σ_{S M}$ ). Two combination models are constructed:
1. 4-Parameter Model: Simultaneously measures signal strengths for $SSWW$, $OSWW$, $WZ$, and $ZZ$.
2. 6-Parameter Model: Disaggregates the $WW$ channels by electric charge ( $W^+W^+$ , $W^-W^-$ , $W^+W^-$ ) and $WZ$ by charge ( $W^+Z$ , $W^-Z$ ), alongside $ZZ$, to probe production charge asymmetry arising from proton parton distribution functions.
Systematics: The fit incorporates 1525 bins across 48 phase space regions. Systematic uncertainties from experimental sources (luminosity, lepton/jet energy scales, pileup) and theoretical sources (scale variations, PDFs, parton shower modeling) are treated as nuisance parameters with appropriate correlations across analyses and years.

Key Contributions

Global Combination: This work constitutes the most comprehensive statistical combination of VBS measurements to date, integrating results from seven analyses into a single coherent framework.
Charge-Asymmetry Sensitivity: By distinguishing the electric charge of the $W$ bosons in the 6-parameter model, the analysis explicitly probes the expected production charge asymmetry, a feature not accessible in previous single-channel measurements.
Enhanced Sensitivity: The combination leverages correlations between channels and constrains background normalizations using control regions, improving the precision of signal strength measurements compared to individual inputs.

Results
The analysis yields signal strength measurements for all considered VBS production modes.

4-Parameter Model: The measured signal strengths are $\mu_{SSWW} = 1.05^{+0.15}_{-0.14}$ , $\mu_{OSWW} = 1.11^{+0.20}_{-0.20}$ , $\mu_{WZ} = 1.21^{+0.28}_{-0.25}$ , and $\mu_{ZZ} = 1.15^{+0.44}_{-0.37}$ . All results are consistent with the SM prediction ( $\mu=1$ ) within the 68.3% confidence level. The statistical significance of the EW VBS signal exceeds $5\sigma$ for $SSWW$, $OSWW$, and $WZ$, and reaches $4.0\sigma$ for $ZZ$.
6-Parameter Model: The charge-separated measurements are also consistent with the SM. Specifically, $\mu_{W^+W^+} = 1.13^{+0.17}_{-0.16}$ , $\mu_{W^-W^-} = 0.84^{+0.28}_{-0.24}$ , $\mu_{W^+W^-} = 1.10^{+0.20}_{-0.20}$ , $\mu_{W^+Z} = 1.16^{+0.32}_{-0.27}$ , $\mu_{W^-Z} = 1.31^{+0.47}_{-0.40}$ , and $\mu_{ZZ} = 1.16^{+0.44}_{-0.38}$ .
Precision Improvement: The combination improves the uncertainty on signal strengths by up to 15% for the $OSWW$ and $WZ$ channels relative to the best individual CMS measurements.
Correlations: Two-dimensional fits reveal mild correlations among the signal strengths, and all results remain in agreement with SM expectations.

Significance
The paper claims that this combination provides a unique and rigorous stress test of the SM electroweak sector. By simultaneously constraining all VBS processes involving massive vector bosons, including charge-separated channels, the analysis enables a coherent test of the EW gauge structure that was previously inaccessible. The results, which are in agreement with SM predictions, improve the precision of VBS measurements and establish a benchmark for future VBS studies at the LHC. The work demonstrates the capability of the CMS experiment to perform complex, multi-channel statistical combinations to probe the fundamental mechanisms of electroweak symmetry breaking.

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