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Measurements of the electroweak production of a $W$ boson in association with two jets at $\sqrt{s}=13\,\mathrm{TeV}$ with the ATLAS detector

Using 140 fb⁻¹ of 13 TeV proton-proton collision data, the ATLAS collaboration measures the electroweak production of a W boson in association with two jets, determining integrated and differential cross-sections in a fiducial region enhanced for vector-boson fusion and deriving stringent limits on anomalous triple-gauge-boson couplings within an effective field theory framework.

Original authors: ATLAS Collaboration

Published 2026-07-24

📖 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 as a giant, cosmic construction site where the fundamental rules of physics are the blueprints. For decades, scientists have been testing these blueprints, looking for tiny cracks that might hint at a bigger, hidden structure underneath. One of the most exciting places to look for these cracks is in the "electroweak" force, a cosmic glue that holds particles together. To understand this force, physicists often study how particles smash into each other at incredible speeds, creating a shower of debris. In this specific story, the stars of the show are the W boson (a heavy messenger particle that carries the weak force) and jets (sprays of smaller particles that act like cosmic shrapnel).

The big question scientists are asking is: Do these particles interact exactly as the current "Standard Model" of physics predicts, or is there something weird happening? Specifically, they are looking for signs of "anomalous" interactions—moments where the particles might be breaking the rules, perhaps due to new, undiscovered forces or particles lurking just beyond our view. It's like watching a game of billiards; if the balls bounce off each other in a way that defies the laws of physics we know, it suggests there's a hidden magnet or a secret rulebook we haven't found yet. This paper is a massive, high-stakes experiment designed to watch these collisions with extreme precision to see if the universe is playing by the rules or pulling a fast one.

The Cosmic Billiard Match: Catching a Sneaky W Boson

In the heart of the Large Hadron Collider (LHC) at CERN, protons are smashed together at nearly the speed of light, creating a chaotic explosion of particles. The ATLAS detector, a giant, multi-layered camera the size of a cathedral, watches this chaos unfold. In this study, the ATLAS team looked at a very specific, rare event: a W boson being born alongside two high-energy jets of particles.

Why is this specific event special? Usually, when particles interact, they exchange "color charge" (a property of the strong nuclear force), which is like a sticky glue that makes the debris clump together. However, in the rare "electroweak" process this paper studies, the W boson is produced via Vector Boson Fusion (VBF). Imagine two protons zooming past each other, and instead of crashing head-on, they exchange a ghostly, invisible force carrier that spawns a W boson. The two protons recoil, shooting off two jets in opposite directions. Because they didn't touch directly, there's a "quiet zone" (a rapidity gap) between the jets where no other messy debris appears. It's like two cars speeding past each other on a highway, and instead of a crash, they just flick a lightbulb (the W boson) into the air, leaving the space between them perfectly clear.

The Great Hunt: Separating Signal from Noise

The challenge for the scientists was like trying to hear a single violin solo in the middle of a roaring stadium. The "signal" they wanted (the clean VBF event) is drowned out by a much louder "background" noise: the QCD Wjj process. In this background, the W boson and jets are produced by the strong force, which is messy and crowded.

To find the quiet violin, the team used a clever set of filters:

The "Tag" Jets: They looked for two jets with huge energy (over 80 GeV and 60 GeV) that were far apart from each other, like two flags planted on opposite sides of a field.
The "Quiet Zone": They checked the space between these jets. If there was too much extra junk (other particles) in the middle, they discarded the event. They wanted that clean, empty gap.
The W Boson: They looked for the W boson decaying into a charged lepton (an electron or a muon) and a missing neutrino. Since the neutrino is invisible, they measured the "missing energy" to confirm it was there.

Using 140 inverse femtobarns of data (a massive amount of collision records from 2015 to 2018), the team successfully isolated these rare events. They didn't just count them; they measured how they moved and interacted in six different ways, looking at the angles and speeds of the jets and the lepton.

The Results: The Rules Hold Up (For Now)

After all the filtering and complex math (including "unfolding" the data to remove the blurring effects of the detector itself), the team found a clear picture. The measured rate of these events was 480 ± 12 (statistical) ± 39 (experimental) ± 53 (theoretical) femtobarns.

When they compared this number to the predictions made by the Standard Model, the results were a perfect match. The data danced right in step with the theoretical music.

Did they find new physics? No. The paper explicitly states that the data is well-described by current theories.
Did they rule out anything? They didn't rule out the existence of new physics entirely, but they placed very tight limits on how "weird" the interactions could be. They tested for "anomalous triple-gauge-boson couplings"—essentially, they checked if the W boson was interacting with other force carriers in a way that shouldn't happen.

The "What-If" Test: Effective Field Theory

To be absolutely sure, the scientists played a "what-if" game using a framework called Effective Field Theory (EFT). They asked: "What if there were new, heavy particles influencing these collisions?" They simulated how the data would look if certain "Wilson coefficients" (numbers that describe the strength of these new interactions) were non-zero.

They found that if these new interactions existed, they would have to be incredibly weak. The paper sets some of the most stringent limits to date on these coefficients.

For the linear terms of the extended Lagrangian (a fancy way of saying the basic math describing these forces), the limits on the coefficients $c_W/\Lambda^2$ and $\tilde{c}_W/\Lambda^2$ are extremely tight.
Specifically, the observed 95% confidence intervals for $c_W/\Lambda^2$ are between -0.17 and 0.12 TeV⁻².

In plain English: If there is a new force messing with these particles, it's so weak that our current detectors can barely feel its whisper. The universe, at least in this specific corner, seems to be sticking very closely to the known rulebook.

Why This Matters

This paper is a triumph of precision. It didn't find a new particle, but in science, proving that the universe behaves exactly as predicted is just as important as finding something new. It tells us that if there is "new physics" hiding in the shadows, it's hiding very well. The ATLAS team has drawn a tighter boundary around the unknown, showing that any future discoveries will need to be even more subtle to slip past these rigorous tests. For now, the Standard Model remains the champion of the ring, having successfully defended its title against the challenge of the electroweak W boson and its two jet partners.

Technical Summary: Measurements of the electroweak production of a W boson in association with two jets at $\sqrt{s}=13$ TeV with the ATLAS detector

Problem and Motivation
This paper addresses the measurement of the electroweak (EW) production of a $W$ boson in association with two jets ( $EW\ Wjj$ ) in proton–proton collisions at a center-of-mass energy of $\sqrt{s}=13$ TeV. This process is of significant interest for probing the non-Abelian nature of electroweak interactions and setting limits on anomalous weak-boson self-interactions. Specifically, the study focuses on the vector-boson fusion (VBF) production mode, where a $W$ boson is produced via the fusion of two vector bosons radiated from quarks. Direct measurement of pure VBF- $W$ is impossible due to interference with other EW $Wjj$ processes; therefore, the analysis targets a kinematic region where the VBF contribution is enhanced. The primary challenge lies in distinguishing this signal from the dominant background: mixed strong-and-electroweak $Wjj$ production (QCD $Wjj$), which involves at least two QCD vertices and shares the same final state.

Methodology
The analysis utilizes a dataset corresponding to an integrated luminosity of $140\ \text{fb}^{-1}$ collected by the ATLAS detector during LHC Run 2 (2015–2018). The signal is defined by a fiducial region requiring a $W$ boson decaying leptonically (to an electron or muon and a neutrino) in association with at least two jets.

Event Selection and Categorization: Candidate events must contain exactly one signal lepton ( $p_T > 27$ GeV), missing transverse momentum ( $p_T^{miss} > 30$ GeV), and a transverse mass $m_T^W > 50$ GeV. Crucially, the analysis requires two "tag" jets with high transverse momenta ( $p_T^{j1} > 80$ GeV, $p_T^{j2} > 60$ GeV), a large dijet invariant mass ( $m_{jj} > 1$ TeV), and a large rapidity separation ( $|\Delta y_{jj}| > 2$ ).
Region Definition: To separate signal from background, the inclusive phase space is subdivided into four mutually exclusive regions based on the centrality of the lepton and additional jets relative to the tag jets:
- Signal Region (SR): Lepton is central ( $C_\ell < 0.4$ ) and no additional central jets ( $N_{jets}^{cent} = 0$ ). This region is enriched in EW $Wjj$.
- Control Regions (CR0, CR1, CR2): Defined by varying lepton centrality and the presence of central jets. These regions are used to constrain the normalization and shape of the dominant QCD $Wjj$ background.
Background Estimation:
- Multijet Background: Estimated using data-driven methods (template-fit and matrix method) to account for misidentified or non-prompt leptons.
- QCD $Wjj$ Background: Modeled using Monte Carlo (MC) simulations (Powheg+Pythia 8) but constrained by data in the control regions via an extended binned maximum-likelihood fit. This fit simultaneously determines the EW signal strength and corrects the QCD background shape and normalization.
- Other Backgrounds: Estimated using MC simulations for processes like $Z$ +jets, top-quark production, and diboson production.
Unfolding: Measured differential cross-sections are unfolded to the particle level using an iterative Bayesian unfolding (IBU) procedure to correct for detector effects. The response matrix is constructed using the Powheg+Pythia 8 EW $Wjj$ prediction.
Theoretical Interpretation: Results are interpreted within the Standard Model Effective Field Theory (SMEFT) framework, specifically testing dimension-six operators related to triple-gauge-boson couplings ( $c_W, c_{HWB}$ and their CP-odd counterparts).

Key Contributions

First Differential Measurements at 13 TeV: This work presents the first differential cross-section measurements for EW $Wjj$ production in 13 TeV proton–proton collisions.
Six Observables: The analysis provides unfolded differential cross-sections as functions of six observables characterizing the signal: the dijet invariant mass ( $m_{jj}$ ), the dijet transverse momentum ( $p_T^{jj}$ ), the absolute rapidity difference of the jets ( $|\Delta y_{jj}|$ ), the azimuthal angle difference of the jets ( $\Delta \phi_{jj}$ ), the leading jet transverse momentum ( $p_T^{j1}$ ), and the charged lepton transverse momentum ( $p_T^\ell$ ).
Robust Background Constraint: The methodology employs a simultaneous fit across signal and control regions to constrain the QCD $Wjj$ background directly from data, reducing systematic uncertainties associated with theoretical modeling.
EFT Limits: The paper derives 95% confidence interval limits on Wilson coefficients for anomalous triple-gauge-boson couplings, combining low and high lepton $p_T$ regions to enhance sensitivity.

Results

Cross-Section: The fiducial cross-section for EW $Wjj$ production at the particle level is measured to be:
$\sigma_{EW} = 480 \pm 12\ (\text{stat.}) \pm 39\ (\text{exp.}) \pm 53\ (\text{theory})\ \text{fb}$
This result is in agreement with theoretical predictions from Powheg+Pythia 8 ( $431 \pm 7$ fb), Powheg+Herwig 7.2.1 ( $420 \pm 6$ fb), and Sherpa 2.2.11 ( $402 \pm 60$ fb).
Differential Distributions: The measured differential cross-sections are generally well-described by NLO QCD predictions from Powheg+Pythia 8 and Powheg+Herwig 7.2.1. The LO prediction from Sherpa 2.2.11 also agrees with data but exhibits larger theoretical uncertainties. Discrepancies are noted in the extreme tails of distributions (e.g., low $|\Delta y_{jj}|$ , central $\Delta \phi_{jj}$ , and high energy regions), where statistical fluctuations are more pronounced.
EFT Constraints:
- For the CP-even coefficient $c_W/\Lambda^2$ , the observed "linear-only" 95% confidence interval is $[-0.17, 0.12]\ \text{TeV}^{-2}$ .
- For the CP-odd coefficient $\tilde{c}_W/\Lambda^2$ , the observed "linear-only" interval is $[-0.083, 0.25]\ \text{TeV}^{-2}$ .
- The limits on $c_W/\Lambda^2$ are among the most stringent to date for linear terms of the extended Lagrangian. The limits on $\tilde{c}_W/\Lambda^2$ are complementary to existing bounds from other ATLAS and CMS analyses.

Significance
The paper claims that these measurements provide a rigorous test of the Standard Model's electroweak sector, specifically the non-Abelian gauge structure. By isolating the EW component of $Wjj$ production and constraining the QCD background with data, the analysis offers a precise benchmark for theoretical calculations. The derived limits on anomalous triple-gauge-boson couplings represent some of the most stringent constraints on linear EFT terms to date, demonstrating the sensitivity of the VBF-enhanced topology to physics beyond the Standard Model. The results also serve as a validation for NLO QCD generators in modeling complex multi-jet final states with electroweak bosons.

The Cosmic Billiard Match: Catching a Sneaky W Boson

The Great Hunt: Separating Signal from Noise

The Results: The Rules Hold Up (For Now)

The "What-If" Test: Effective Field Theory

Why This Matters

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