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Cross-section measurements for the production of a $W$ -boson in association with high-transverse-momentum jets in $pp$ collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

This paper presents cross-section measurements of $W$ -boson production in association with high-transverse-momentum jets using 140 fb $^{-1}$ of 13 TeV proton-proton collision data from the ATLAS detector, focusing on a collinear phase space to test state-of-the-art multi-leg merged Monte Carlo and fixed-order theoretical predictions.

Original authors: ATLAS Collaboration

Published 2026-08-19

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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

The Large Hadron Collider is a machine built to smash protons together at speeds close to the speed of light, recreating the intense energy that existed just moments after the universe began. When these tiny particles collide, they do not simply bounce off one another; they shatter into a spray of new, often fleeting particles. Among the most common products of these collisions are W bosons, heavy particles that act as messengers for the weak nuclear force, one of the four fundamental forces of nature. These W bosons are unstable and decay almost instantly, usually transforming into a charged particle like an electron or a muon, and a nearly invisible particle called a neutrino. Because the neutrino escapes detection, physicists infer its presence by measuring what is missing from the total energy balance of the collision.

To understand how the universe works at its most fundamental level, scientists must be able to predict exactly how often these particles are created and how they behave. This requires a precise understanding of the strong force, which binds the quarks and gluons inside protons. When a W boson is produced alongside high-speed jets of particles, the event becomes a complex laboratory for testing the mathematical theories that describe these forces. If the predictions made by these theories do not match what is observed in the detector, it could signal a flaw in our current understanding or the presence of new, unknown physics.

A researcher using the ATLAS detector at the LHC has now taken a closer look at these specific events, analyzing a massive collection of data equivalent to 140 inverse femtobarns of proton-proton collisions. This dataset, gathered over several years of operation, allowed the researcher to study W bosons produced in association with jets of particles that carry extremely high momentum. The researcher focused on a specific scenario where the W boson and a jet are produced so close together in direction that they appear almost aligned, a configuration known as the collinear region. This area of physics is particularly challenging to model because it involves complex interactions where multiple jets of particles are created simultaneously, pushing the limits of current theoretical calculations.

The researcher measured how often these events occurred and examined the detailed properties of the particles involved, such as the angle between the visible charged particle and the nearest jet, and the ratio of their momenta. They compared their real-world measurements against the most advanced computer simulations available, which use complex mathematical frameworks to predict particle behavior. The study found that the simulations which combine different levels of theoretical accuracy generally describe the data very well across the entire range of energies tested. However, the researcher also noted that in certain high-energy regions, the predictions were slightly higher than what was actually observed in the data.

A key part of the analysis involved accounting for the effects of the detector itself. Because the machinery used to catch these particles is not perfect, the raw data must be mathematically "unfolded" to reveal the true properties of the particles as they existed before hitting the detector. After this correction, the results showed that the measured rates of W boson production matched the predictions of the best available theories, though with some small deviations in the most extreme energy ranges. The study also confirmed that including corrections for electroweak interactions—subtle effects from the weak force and electromagnetism—improved the agreement between theory and data in the most energetic collisions.

This work provides a rigorous test of the Standard Model of particle physics in a regime where particles carry energies far beyond what is seen in everyday life. By confirming that our current theories can accurately describe these high-momentum events, the research strengthens the foundation upon which future discoveries will be built. The data has been made publicly available, allowing other scientists to use these precise measurements to refine their own models and search for any subtle signs of new physics that might lie just beyond the reach of current predictions. The findings serve as a benchmark, ensuring that when the next unexpected signal appears, it will be distinguished from the known behavior of the universe with greater confidence.

Technical Summary: Cross-section measurements for the production of a W-boson in association with high-transverse-momentum jets in pp collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

Problem and Motivation
The production of a $W$ -boson in association with jets ( $W$ +jets) represents a significant irreducible background for a wide range of analyses at the Large Hadron Collider (LHC), including Higgs boson and top quark measurements, as well as searches for physics beyond the Standard Model (BSM). Accurate theoretical modeling of this process across a large energy range is critical for the success of the LHC physics programme. While leading-order (LO) descriptions suffice for some regimes, the production of a $W$ -boson in association with high-momentum jets involves complex QCD dynamics. At next-to-leading order (NLO), new partonic scattering topologies emerge, particularly those involving dijet production accompanied by the emission of a real $W$ -boson. These contributions lead to "collinear enhancements" in the production rate, proportional to $\alpha_s \ln^2(p_T^{\text{closest jet}}/m_W)$ , which are difficult to model in the multi-TeV kinematic range. Previous measurements at 8 TeV and initial 13 TeV data were limited in statistics or phase space coverage. This paper addresses the need for precise measurements in the high-momentum regime using the full Run 2 dataset to probe higher-order theoretical predictions and improve the modeling of kinematic variables typically explored in new physics searches.

Methodology
The analysis utilizes 140 fb $^{-1}$ of proton–proton collision data collected by the ATLAS detector at a center-of-mass energy of $\sqrt{s}=13$ TeV. The study focuses on events where the $W$ -boson decays into an electron or muon plus a neutrino, produced in association with jets having transverse momentum $p_T > 30$ GeV, with the leading jet required to have $p_T > 500$ GeV.

Event Selection and Regions: The analysis defines an "inclusive" region and three sub-regions based on the angular separation $\Delta R_{\min}(\ell, \text{jet}_{100})$ between the lepton and the closest jet with $p_T > 100$ GeV. The "collinear" region ( $\Delta R < 2.6$ ) is dominated by $W$ + $\ge$ 2-jet processes and dijet events radiating a $W$ , while the "back-to-back" region ( $\Delta R > 2.6$ ) is dominated by LO $W$ +1-jet production. An "inclusive 2-jet" region is also defined.
Background Estimation: Dominant backgrounds ( $t\bar{t}$ , $Z$ +jets, and multijets) are estimated using semi-data-driven techniques. Normalization factors are extracted from dedicated control regions enriched in these specific processes (e.g., requiring $b$ -tagged jets for $t\bar{t}$ or same-flavor opposite-sign dileptons for $Z$ +jets). Multijet backgrounds are estimated using a data-driven method based on lepton isolation and impact parameter failures.
Unfolding: Detector effects are unfolded to the particle level using an iterative Bayesian technique. The particle-level definition includes "dressed" leptons (leptons plus radiated photons within $\Delta R=0.1$ ) and jets clustered from final-state particles. The unfolding corrects for inefficiencies, acceptance, and resolution effects.
Theoretical Comparisons: Measured differential distributions are compared against state-of-the-art predictions:
- Multi-leg merged Monte Carlo generators: Sherpa 2.2.11 (NLO in $\alpha_s$ for up to 2 jets, LO for up to 5) and MadGraph5_aMC@NLO (NLO for up to 3 jets) interfaced with Pythia8.
- Fixed-order calculations: $W$ +1-jet computed at next-to-next-to-leading order (NNLO) in $\alpha_s$ using the MCFM program.
- Electroweak corrections: The impact of NLO electroweak virtual (EW $_{\text{virt}}$ ) corrections is assessed using Sherpa predictions.

Key Contributions and Results
The paper presents inclusive and differential cross-section measurements for $W$ +jets production in the high- $p_T$ regime.

Inclusive Cross-sections: The measured fiducial cross-sections in the inclusive, inclusive 2-jet, collinear, and back-to-back regions are found to be in good agreement with data. The total uncertainties on the measurements are approximately 3%–4%, dominated by systematic uncertainties (background modeling, jet energy scale, and $b$ -tagging).
Differential Distributions:
- Collinear vs. Back-to-Back: The measurements of $\Delta R_{\min}(\ell, \text{jet}_{100})$ and the ratio $p_T^{\ell\nu}/p_T^{\text{closest jet}}$ successfully distinguish between collinear and back-to-back topologies. The multijet merged generators (Sherpa and MadGraph5_aMC@NLO) provide an excellent description of the data across these variables.
- High- $p_T$ Regime: Differential measurements of the leading jet $p_T$ (up to 1.5 TeV), jet multiplicity, scalar sum of jet transverse momenta ( $S_T$ ), and the $W$ -boson candidate $p_T$ ( $p_T^{\ell\nu}$ ) are presented.
- Fixed-Order vs. Merged: The fixed-order NNLO MCFM prediction for $W$ +1-jet provides a good description of the data with precision comparable to the measurement uncertainties in the back-to-back region. However, in regions with large angular separations or high jet multiplicities (where $W$ + $\ge$ 2-jet processes dominate), the MCFM prediction underestimates the cross-section, as expected given its formal accuracy.
- Electroweak Corrections: The inclusion of NLO EW $_{\text{virt}}$ corrections in the Sherpa prediction leads to an overall decrease in the inclusive cross-section by 10%–12%. These corrections significantly improve the agreement between theory and data in the collinear region and for high- $p_T^{\ell\nu}$ bins, where Sudakov logarithms induce large negative corrections. Conversely, they lead to an underestimation of the cross-section in the back-to-back region.
- Invariant Mass ( $m_{jj}$ ): In the inclusive 2-jet region, all theoretical predictions overestimate the cross-section for $m_{jj} > 2$ TeV beyond their systematic uncertainties.

Significance
The paper claims that the presented measurements serve as an excellent data sample to probe higher-order theoretical predictions in a phase space populated by both dijet events radiating a $W$ -boson and events with a $W$ -boson produced in association with several jets. The results demonstrate that:

State-of-the-art multi-leg merged Monte Carlo generators provide a robust description of $W$ +jets production across a wide range of observables, including high jet multiplicities.
Fixed-order NNLO calculations for $W$ +1-jet are precise and accurate in their domain of validity but require higher-multiplicity contributions to describe the full phase space.
NLO electroweak corrections are essential for accurately modeling the high-momentum tail of the distributions, particularly in the collinear regime.
The data, which is made publicly available via HEPData and Rivet, will allow for improved theoretical descriptions of these high-energy events, directly benefiting the modeling of backgrounds for future Higgs, top, and BSM searches at the LHC.

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