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Combination of searches for heavy vector boson resonances in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Based on 138 fb $^{-1}$ of proton-proton collision data at 13 TeV collected by the CMS experiment, this paper presents a combined statistical analysis of searches for heavy vector boson resonances that finds no deviation from the Standard Model and sets the most stringent constraints to date on the Heavy Vector Triplet model, excluding resonance masses up to 5.5 TeV depending on the coupling scenario.

Original authors: CMS Collaboration

Published 2026-07-10

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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 Large Hadron Collider (LHC) as the universe's most powerful particle-smashing blender. For years, scientists have been tossing protons into this blender at speeds close to light, hoping to see if the debris reveals any "new ingredients" that don't belong in the standard recipe of physics. This new report from the CMS experiment is like a massive, super-organized cleanup crew that has just finished sorting through 138 fb⁻¹ of collision data collected between 2016 and 2018.

Their mission? To hunt for "heavy vector boson resonances." Think of these as mysterious, super-heavy cousins of the familiar W and Z bosons (the messengers of the weak force). In the world of particle physics, these heavy cousins are often called W′ and Z′. The scientists were looking for them by checking if they popped into existence and then immediately split apart into pairs of other particles: pairs of W, Z, or Higgs bosons; pairs of quarks (like top or bottom quarks); or pairs of leptons (like electrons, muons, or taus).

The Big Reveal: The Search Continues
After crunching the numbers with a sophisticated statistical toolkit, the team found no significant deviation from what the Standard Model predicts. In plain English: the blender didn't spit out any new, heavy particles. The data looks exactly like what we expected if only the known particles exist.

Because they didn't find the particles, the scientists didn't just throw up their hands. Instead, they set up a series of "fences" to say, "We know these heavy particles aren't hiding below these heights." They used a framework called the Heavy Vector Triplet (HVT) to draw these lines in the sand.

The Fences They Built
The paper sets strict limits on how heavy these hypothetical particles could be before we would have definitely seen them. If they exist, they must be heavier than these thresholds:

5.5 TeV if they are "weakly coupled" (Model A).
4.8 TeV if they are "strongly coupled" (Model B).
2.0 TeV if they are created through a specific process called "vector boson fusion" (Model C).

To put those numbers in perspective, 1 TeV is roughly the mass of a thousand protons. So, they are saying, "If these heavy cousins exist, they are at least 4,800 to 5,500 times heavier than a proton." Anything lighter than that has been effectively ruled out by this search.

What About the "Ghost" Signals?
You might wonder: "Did they see anything weird?" The paper mentions that in some individual channels, there were small, localized bumps in the data—tiny excesses of events that looked slightly interesting. For example, one search saw a bump at 2.1 TeV and another at 2.9 TeV with a local significance of 3.6 standard deviations. Another search saw a bump at 1.5 TeV.

However, when the scientists combined all the different searches together, these bumps didn't line up. They were like different people in a crowd shouting about seeing a ghost in different corners of the room; when you look at the whole room, the ghosts disappear. The combined analysis showed that these fluctuations were just random noise, not evidence of new physics. The largest remaining "excitement" in the combined data was only about 2.4 standard deviations, which is far too low to claim a discovery.

Why This Matters
Even though they didn't find the new particles, this paper is a huge success because it provides the most stringent constraints to date. It's like sweeping a room with a finer broom than ever before. By combining data from dozens of different search channels (looking at everything from pure leptons to messy jets of quarks), they have squeezed the possible hiding spots for these heavy particles tighter than ever before.

The results are interpreted within the HVT framework, which acts like a map for where these particles might be. The map now says: "If you are looking for a weakly coupled W′ or Z′, you can stop looking below 5.5 TeV. If you are looking for a strongly coupled one, stop below 4.8 TeV."

In summary, the universe, at least in the energy range explored by the CMS experiment up to 138 fb⁻¹ of data, remains stubbornly standard. No new heavy vector bosons were found. But by proving they aren't hiding in the lower mass ranges, the scientists have cleared the path for future searches to look even higher, perhaps at energies where the next great discovery might be waiting.

Technical Summary: Combination of Searches for Heavy Vector Boson Resonances in Proton-Proton Collisions at $\sqrt{s} = 13$ TeV

Problem and Motivation
The search for heavy resonances decaying into two-body final states remains a central component of the physics program at the CERN Large Hadron Collider (LHC), aimed at uncovering physics beyond the Standard Model (BSM). While the discovery of the $W$ , $Z$ , and Higgs bosons confirmed the Standard Model (SM) and the electroweak symmetry breaking mechanism, the existence of heavy spin-1 partners ( $W'$ and $Z'$ , collectively $V'$ ) is predicted by various BSM scenarios, including composite Higgs models, little Higgs models, and sequential extensions of the SM. These resonances could couple predominantly to SM fermions or bosons, or act as portals to dark matter sectors.

Individual searches for these resonances have occasionally reported localized excesses of events (e.g., in fully hadronic final states or specific diboson channels) with local significances reaching up to 3.6 standard deviations (SD). However, these deviations have not been statistically significant enough to claim evidence for BSM physics. A combined statistical analysis is essential to maximize sensitivity, fully exploit the outcomes of individual searches, and provide a robust assessment of potential deviations from SM expectations, particularly given the complementary nature of different decay channels and production mechanisms.

Methodology
This paper presents a combined statistical analysis of CMS searches for heavy spin-1 resonances decaying into pairs of $W$ , $Z$ , or Higgs bosons, as well as into quark pairs ($qq, bb, tt, tb$) or lepton pairs ( $\ell^+\ell^-, \ell\nu$ , where $\ell = e, \mu, \tau$ ). The analysis utilizes proton-proton collision data collected by the CMS experiment from 2016 to 2018 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb $^{-1}$ .

Signal Model: The results are interpreted within the simplified Heavy Vector Triplet (HVT) framework, a phenomenological parameterization that encompasses a broad class of models predicting heavy vector bosons. The framework defines three benchmark scenarios:
- Model A: A weakly coupled extension based on extended gauge symmetry, where $V'$ production is dominated by quark-antiquark annihilation (Drell-Yan process).
- Model B: A strongly coupled scenario (e.g., composite Higgs), also dominated by Drell-Yan production but with different coupling strengths favoring bosonic decays.
- Model C: A scenario where production occurs exclusively via vector boson fusion (VBF), with the $V'$ boson decoupled from SM fermions.
Input Channels: The combination includes the most sensitive channels for spin-1 resonance decays, categorized by final state:
- Leptonic: $Z' \to \ell^+\ell^-$ , $W' \to \ell\nu$ , $Z' \to \tau^+\tau^-$ , $W' \to \tau\nu$ .
- Hadronic/Fermionic: $V' \to qq'$ , $W' \to tb$ (0 $\ell$ and 1 $\ell$ ), $Z' \to t\bar{t}$ (1 $\ell$ ).
- Bosonic: $W' \to WZ$ , $Z' \to ZH$ , $V' \to WV/WH$ , and $V' \to VV/VH$ (fully hadronic).
- Reconstruction: For high-mass resonances, decay products are often highly boosted. Small-radius jets ( $R=0.4$ ) and large-radius jets ( $R=0.8$ ) are reconstructed using the anti- $k_T$ algorithm. Jet substructure techniques (e.g., soft-drop) and machine-learning-based taggers are employed to identify boosted $W/Z/H$ bosons and top quarks.
Statistical Combination: The combination is performed using a simultaneous maximum likelihood fit across all individual analyses using the CMS COMBINE tool. To ensure statistical independence, overlapping phase spaces are handled by retaining only the channel with the highest expected sensitivity for a given signal model and mass hypothesis. Systematic uncertainties (theoretical, experimental, and background modeling) are treated as nuisance parameters, with correlations applied where appropriate (e.g., jet energy scale, luminosity).

Key Contributions

Comprehensive Combination: This work represents the most comprehensive combination of CMS searches for heavy vector bosons to date, integrating results from 16 distinct search channels covering a wide range of final states and production modes.
Improved Sensitivity: By combining channels with complementary sensitivities (e.g., leptonic channels dominating in weakly coupled scenarios and hadronic bosonic channels in strongly coupled scenarios), the analysis achieves tighter constraints than any single channel or previous combinations.
Handling of Excesses: The analysis addresses previously reported localized excesses (e.g., the 3.6 SD excess at 2.1 and 2.9 TeV in fully hadronic channels). The combination demonstrates that these excesses are not consistent across different channels, leading to a reduction in their significance when viewed globally.
Parameter Space Exploration: Beyond setting mass limits, the analysis explores the HVT coupling parameter space ( $g_F$ vs. $g_H$ ) and investigates non-universal couplings to third-generation quarks ( $g_{q3}$ vs. $g_{q12}$ ), providing constraints that no single channel could achieve alone.

Results

Observation: No significant deviation from the Standard Model expectations is observed in the combined analysis. The global goodness-of-fit yields a $p$ -value of approximately 34% under the background-only hypothesis.
Exclusion Limits: The analysis sets 95% confidence level (CL) upper limits on the production cross sections and coupling strengths:
- Model A (Weakly Coupled): Resonances with masses below 5.5 TeV are excluded.
- Model B (Strongly Coupled): Resonances with masses below 4.8 TeV are excluded.
- Model C (VBF Production): Resonances with masses up to 2.0 TeV are excluded (specifically, 1.2–1.4 TeV for $g_H=3$ and below 2 TeV for $g_H=6$ ).
Coupling Constraints: The combination provides the most stringent constraints to date on the HVT coupling parameter space. Compared to results using only the 2016 dataset, the sensitivity is improved by a factor of 1.7 to 3.6 for the strongly coupled scenario and 4.4 to 7.7 for the weakly coupled scenario.
Excesses: The largest local excesses observed in the combination are 2.4 SD at 2.6 TeV and 2.1 SD at 3.4 TeV for Model A, and 2.3 SD at 2.9 TeV and 2.4 SD at 3.0 TeV for Model B. These are significantly reduced compared to individual channel results and do not constitute evidence for new physics. The combination also does not confirm a previously reported ATLAS excess around 1.5 TeV.

Significance
The paper claims that this combination provides the most stringent and comprehensive constraints to date on the production of heavy vector triplet resonances. The results represent a significant improvement over previous constraints, driven by the inclusion of the full Run 2 dataset (138 fb $^{-1}$ ) and advances in the underlying analyses, particularly the use of advanced jet substructure tagging techniques and three-dimensional signal extraction strategies in fully hadronic channels. While the results do not confirm the existence of heavy vector bosons, they effectively rule out large portions of the parameter space predicted by the HVT framework, thereby guiding future theoretical and experimental efforts in the search for BSM physics.

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