Eur. Phys. J. C (2025) 85:738 https://doi.org/10.1140/epjc/s10052-025-14078-0 Regular Article - Experimental Physics Cross-section measurements for the production of a W -boson in association with high-transverse-momentum jets in pp collisions at √ s = 13 TeV with the ATLAS detector ATLAS Collaboration� CERN, 1211 Geneva 23, Switzerland Received: 17 December 2024 / Accepted: 14 March 2025 © CERN for the benefit of the ATLAS Collaboration 2025 Abstract A set of measurements for the production of a W -boson in association with high-transverse-momentum jets is presented using 140 fb−1 of proton–proton collision data at a centre-of-mass energy of √ s = 13 TeV collected by the ATLAS detector at the LHC. The measurements are per- formed in final states in which the W -boson decays into an electron or muon plus a neutrino and is produced in associ- ation with jets with pT > 30 GeV, where the leading jet has pT > 500 GeV. The angular separation between the lepton and the closest jet with pT > 100 GeV is measured and used to define a collinear phase space, wherein measurements of kinematic properties of the W -boson and the associated jet are performed. The collinear phase space is populated by dijet events radiating a W -boson and events with a W -boson produced in association with several jets and it serves as an excellent data sample to probe higher-order theoretical pre- dictions. Measured differential distributions are compared with predictions from state-of-the-art next-to-leading order multi-leg merged Monte Carlo event generators and a fixed- order calculation of the W + 1-jet process computed at next- to-next-to-leading order in the strong coupling constant. Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . 2 ATLAS detector . . . . . . . . . . . . . . . . . . . . 3 Data and simulated event samples . . . . . . . . . . . 4 Event reconstruction . . . . . . . . . . . . . . . . . . 5 Event selection . . . . . . . . . . . . . . . . . . . . 6 Background estimation . . . . . . . . . . . . . . . . . 7 Unfolding . . . . . . . . . . . . . . . . . . . . . . . 8 Systematic uncertainties . . . . . . . . . . . . . . . . 9 Results . . . . . . . . . . . . . . . . . . . . . . . . . 10 Conclusions . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . � e-mail: atlas.publications@cern.ch 1 Introduction Measurements of electroweak (EW) bosons in the electron or muon decay modes provide a clean experimental signa- ture to test the EW sector of the Standard Model (SM) and perturbative quantum chromodynamics (QCD) in high jet- multiplicity final states. The large production cross-section for a single W -boson provides a very large data sample with which to explore the modelling of kinematic variables in the high-momentum phase space. Moreover, the W+ jets pro- cess represents a significant irreducible background to a wide range of analyses within the Large Hadron Collider (LHC) physics programme, such as Higgs boson [1–4] and top quark measurements [5–8], and searches for new physics phenom- ena beyond the Standard Model (BSM) [9–14]. Therefore, an accurate description of this process across a large energy range is critical to the success of the LHC physics pro- gramme. At next-to-leading order (NLO) in αs, new partonic scat- tering topologies emerge that can contribute very large enhancements to the overall production rate (Fig. 1b). Of particular importance are diagrams where dijet production is accompanied by the emission of a real W -boson from the incoming or outgoing quarks, as shown in Fig. 1. These contributions lead to large enhancements in the produc- tion rate that are proportional to αs ln2 pclosest jet T /mW , where pclosest jet T is the transverse momentum of the closest jet, and mW is the W -boson mass. This results in an overall cross- section enhancement at small values in the distribution of the angular separation between the W -boson and the closest jet in events with high-pT jets, referred to as collinear enhance- ment. The collinear region also contains contributions where the W -boson is produced in association with larger numbers of jets. An accurate description of W -bosons produced in association with many jets demands theoretical predictions computed at the highest possible order in both the strong and electroweak couplings. 0123456789().: V,-vol 123 http://crossmark.crossref.org/dialog/?doi=10.1140/epjc/s10052-025-14078-0&domain=pdf mailto:atlas.publications@cern.ch 738 Page 2 of 35 Eur. Phys. J. C (2025) 85:738 Fig. 1 Representative Feynman diagrams for the production of a W -boson in association with jets. The t-channel diagram shown in a typically leads to large angular separation between the recoiling jet and the lepton, while the s-channel diagram shown in b can lead to small angular separations between the lepton and the outgoing quark Measurements ofW -bosons emitted from high-momentum partons in the muon channel only were reported in proton–proton collisions at a centre-of-mass energy of 8 TeV by the ATLAS Collaboration using a data sample with 20.3 fb−1 [15] of integrated luminosity, and a more inclusive measurement by the CMS Collaboration using a data sam- ple with 19.6 fb−1 [16]. CMS performed an initial measure- ment of W+ jets events in a high-momentum region using 2.2 fb−1 of proton–proton collision data at a centre of mass energy of 13 TeV in the muon decay channel [17]. This paper presents an extension of those measurements using the full Run 2 data sample corresponding to 140 fb−1 of proton–proton collision data at a centre-of-mass energy of 13 TeV, via a combination of the cross-section measure- ments from the electron and muon channels. The large data sample allows the measurement of kinematic variables typ- ically probed in searches for new phenomena beyond the 1 TeV energy scale. ATLAS also performed a measurement of Z + jets events in the high-momentum region with the full Run 2 data sample [18]. The measurement presented here is complementary to the Z + jets measurement, and is able to probe higher energy regimes due to the nearly ten times larger production cross-section. This paper presents inclusive and differential cross-section measurements of a W -boson produced in asso- ciation with high-pT jets. It targets events where theW -boson decays into a lepton (electron or muon) in association with jets with pT > 30 GeV and |η| < 2.5, where the leading jet has pT > 500 GeV. This phase space is referred to as the inclusive region, and measurements of the differential cross-section for observables sensitive to collinear enhance- ment in the production rate are performed: • �Rmin(�, jet100 i ): angular separation1 between the lep- ton and closest jet with transverse momentum greater than 100 GeV. Events with �Rmin(�, jet100 i ) > 2.6 (for each jet i in the event) are expected to be dominated by leading-order W +1-jet production and referred to as the back-to-back region. The opposing selection �Rmin(�, jet100 i ) < 2.6, expected to be dominated by W+≥ 2-jet processes, is referred to as the collinear region. • p�ν T /pclosest jet T : the ratio of the transverse momentum of the lepton–neutrino system (p�ν T ) to the transverse momentum of the jet that is closest to the lepton. Val- ues around one represent events where the W -boson and closest jet have similar momentum, and therefore are expected to be dominated by leading-order W + 1-jet production. Values away from one are expected to be dominated by W+≥ 2-jets production. • mjj: the invariant mass of the highest momentum pair of jets. This observable is measured in the inclusive 2-jet region where at least two jets are required. This is an observable often explored in EW induced measure- ments [19] or BSM searches [20–22], but is difficult to model in the multi-TeV kinematic range. In addition, differential measurements are performed of observables sensitive to W -boson production in association with many jets in the collinear region. These observables are: 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upwards. Polar coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2) and is equal to the rapidity y = 1 2 ln ( E+pz E−pz ) in the relativistic limit. Angular distance is measured in units of �R ≡ √ (�y)2 + (�φ)2. 123 Eur. Phys. J. C (2025) 85:738 Page 3 of 35 738 • the transverse momentum of the leading jet, • the transverse momentum of the lepton–neutrino system (p�ν T ), • the jet multiplicity for jets with pT > 30 GeV, and • the total scalar sum of the transverse momentum of all jets (ST). State-of-the-art event generator programs that are multi- leg matrix element accurate to NLO in αs merged with parton-shower models to emulate the higher missing orders are compared with the measured data. In addition, fixed- order predictions for W + 1-jet production computed at next-to-next-to-leading order (NNLO) inαs using the MCFM program [23], are compared with the measured data. The data from this publication will be publicly provided through both HEPData [24] and Rivet [25] and can be used to improve the theoretical description of these high-energy events. The paper is organised as follows. The ATLAS detector is described in Sect. 2. Section 3 presents the data sample and simulated samples used in the measurement, while Sect. 4 details the reconstruction of leptons, jets, and the miss- ing transverse momentum. The event selection is described in Sect. 5, and the estimation of background processes to the measurement are explained in Sect. 6. The unfolding of detector effects is described in Sect. 7, and systematic uncer- tainties in Sect. 8. The final results are presented in Sect. 9, with concluding remarks in Sect. 10. 2 ATLAS detector The ATLAS detector [26] at the LHC covers nearly the entire solid angle around the collision point. It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and a muon spectrometer incorporating three large superconduct- ing air-core toroidal magnets. The inner-detector system (ID) is immersed in a 2T axial magnetic field and provides charged-particle tracking in the range |η| < 2.5. The high-granularity silicon pixel detector covers the vertex region and typically provides four measure- ments per track, the first hit generally being in the insertable B-layer (IBL) installed before Run 2 [27,28]. It is followed by the SemiConductor Tracker (SCT), which usually pro- vides eight measurements per track. These silicon detectors are complemented by the transition radiation tracker (TRT), which enables radially extended track reconstruction up to |η|=2.0. The TRT also provides electron identification infor- mation based on the fraction of hits (typically 30 in total) above a higher energy-deposit threshold corresponding to transition radiation. The calorimeter system covers the pseudorapidity range |η| < 4.9. Within the region |η| < 3.2, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) calorimeters, with an additional thin LAr presampler covering |η| < 1.8 to correct for energy loss in material upstream of the calorimeters. Hadronic calorime- try is provided by the steel/scintillator-tile calorimeter, seg- mented into three barrel structures within |η| < 1.7, and two copper/LAr hadronic endcap calorimeters. The solid angle coverage is completed with forward copper/LAr and tung- sten/LAr calorimeter modules optimised for electromagnetic and hadronic energy measurements respectively. The muon spectrometer (MS) comprises separate trigger and high-precision tracking chambers measuring the deflec- tion of muons in a magnetic field generated by the super- conducting air-core toroidal magnets. The field integral of the toroids ranges between 2.0 and 6.0 T m across most of the detector. Three layers of precision chambers, each con- sisting of layers of monitored drift tubes, cover the region |η| < 2.7, complemented by cathode-strip chambers in the forward region, where the background is highest. The muon trigger system covers the range |η| < 2.4 with resistive-plate chambers in the barrel, and thin-gap chambers in the endcap regions. The luminosity is measured mainly by the LUCID–2 [29] detector that records Cherenkov light produced in the quartz windows of photomultipliers located close to the beampipe. Events are selected by the first-level trigger system imple- mented in custom hardware, followed by selections made by algorithms implemented in software in the high-level trigger [30]. The first-level trigger accepts events from the 40 MHz bunch crossings at a rate below 100 kHz, which the high-level trigger further reduces in order to record complete events to disk at about 1 kHz. A software suite [31] is used in data simulation, in the reconstruction and analysis of real and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment. 3 Data and simulated event samples The data used in this analysis were recorded with the ATLAS detector from 2015 to 2018 in proton–proton col- lisions at √ s = 13 TeV and correspond to a total integrated luminosity of 140 fb−1. The uncertainty in the combined 2015–2018 integrated luminosity is 0.83% [32], obtained using the LUCID-2 detector for the primary luminosity mea- surements, complemented by measurements using the inner detector and calorimeters. The mean number of proton– proton interactions per bunch crossing, including hard scat- tering events and other interactions in the same and neigh- bouring bunch crossings (pile-up), was 〈μ〉 = 34. Monte Carlo (MC) simulated samples are used to estimate various background processes, to unfold the data to particle 123 738 Page 4 of 35 Eur. Phys. J. C (2025) 85:738 Table 1 Overview of Monte Carlo simulated samples used to model signal and background processes. The perturbative accuracy of the QCD calculation in the matrix element is given in the last column level, to estimate systematic uncertainties and for the compar- ison with the unfolded data distributions. Generated events were processed using a full detector simulation [33] based on Geant4 [34] for the detector response to final-state parti- cles. Simulated events were processed and then reconstructed with the same reconstruction algorithms as used for the data. To account for pile-up, multiple overlaid inelastic pp colli- sions were simulated with Pythia8.186 [35] using the A3 set of tuned parameters (tune) [36] and the NNPDF2.3lo set of parton distribution functions (PDFs) [37]. The sim- ulated events are reweighted so that the mean number of proton–proton interactions in simulation matches that observed in each of the data-taking periods. A summary of the simulated samples is provided in Table 1. All simulated samples are normalised to the cross-section predicted by the generator unless otherwise specified. The nominal modelling for theW+ jets signal process uses the Sherpa2.2.11 event generator [38–40]. Matrix elements accurate to NLO in both the strong and EW couplings (vir- tual corrections only, denoted NLO EWvirt) for up to two jets were computed by OpenLoops [41,42], while LO-accurate matrix elements for up to five jets were calculated with the Comix [43] library. The matrix elements were merged with the Sherpa parton shower following the MEPS@NLO prescription [44] and used the tune developed by the Sherpa authors. The NNPDF3.0nnlo set of PDFs [45] was used. The default Sherpa parton shower [46] based on Catani–Seymour dipoles and the cluster hadronisation model [47] was used. The phase space was statistically enhanced using the max(ST, pVT ) variable using an ana- lytic enhancement technique, where ST is the scalar sum of the transverse momenta of all outgoing particles and pVT is the transverse momentum of the vector boson. The NLO EWvirt corrections are available as alternative generator weights in three different schemes for the combination with the QCD matrix elements: additive, multiplicative and expo- nentiated [40]. Nominal predictions were obtained without the NLO EWvirt corrections, but results are also presented with these corrections using the multiplicative scheme as default and an uncertainty computed from the envelope of all other combination schemes. Scale and PDF uncertainties were evaluated on-the-fly [48] using 7-point variations of the factorisation and renormalisation scales in the matrix ele- ments and parton shower and using the Hessian PDF eigen- vector variations for the NNPDF3.0nnlo set of PDFs. The scales were varied coherently in the matrix element and par- ton shower by factors of 0.5 and 2 relative to the nominal scale, but avoiding combinations where renormalisation and factorisation scales are varied in opposite directions. A second multijet merged configuration with NLO accu- racy in αs was provided using MadGraph5_aMC@NLO interfaced with Pythia8. Samples were produced using the MadGraph5_aMC@NLO v2.6.5 [49] program to gener- ate matrix elements for vector-boson production with up 123 Eur. Phys. J. C (2025) 85:738 Page 5 of 35 738 to three additional jets in the final state to NLO accuracy in αs. The showering and subsequent hadronisation were performed using Pythia8.240 [50] with the A14 tune [51], using the NNPDF2.3lo PDF set with αs = 0.130. The different jet multiplicities were merged using the FxFx prescription [52]. The PDF set used for event generation was NNPDF3.1luxQED [53] computed at NNLO with αs = 0.118. The samples were generated with additional weights for the PDF eigenvector variations as well as varia- tions of the renormalisation and the factorisation scales [54]. Electroweak production of W+jj (with W → �ν) and Z+jj (with Z → �� or νν) final states was simulated with Sherpa2.2.11 using LO matrix elements with up to two additional parton emissions. The matrix elements were merged with the Sherpa parton shower following the MEPS@LO prescription [44] and used the tune devel- oped by the Sherpa authors. The NNPDF3.0nnlo set of PDFs was employed. The samples were produced using the VBF approximation, which avoids overlap with semileptonic diboson topologies by requiring a t-channel colour-singlet exchange. The EW production of �νjj is treated as a back- ground and is subtracted from the data before unfolding. Interference between EW and QCD induced vector-boson processes was neglected. The production of t t̄+jets events was modelled using the Sherpa2.2.12 event generator. In the Sherpa2.2.12 sam- ples NLO-accurate matrix elements, for up to one additional jet and LO-accurate matrix elements, for up to four addi- tional jets, were calculated with the Comix and OpenLoops libraries. Aside from this, the same general configuration as the signal W+ jets described above was used. Single-top quark production (single-top) included s- and t-channel dia- grams and the associated production of a single top quark with a W -boson (tW ). All single-top processes were mod- elled using the PowhegBoxv2 [55–58] generator that pro- vides matrix elements at NLO in αs. TheNNPDF3.0nloPDF set was used in the matrix element and events were interfaced with Pythia8.230 using the A14 tune and the NNPDF2.3lo set of PDFs. The inclusive cross-section for single-top was normalised to the theory prediction calculated at NNLO in QCD with next-to-leading logarithmic (NNLL) soft-gluon corrections [59–62]. The PowhegBoxv2 [56–58] generator was used to sim- ulate diboson (WW , WZ and Z Z ) production at NLO accu- racy in αs [63]. The effect of singly resonant amplitudes and interference effects due to Z/γ ∗ and same-flavour lep- ton combinations in the final state were included, where appropriate. Events were interfaced with Pythia8.210 for the modelling of the parton shower, hadronisation, and underlying event, with parameters set according to the AZNLO tune [64]. The CT10 PDF set [65] was used for the hard-scattering processes, whereas the CTEQ6L1 PDF set [66] was used for the parton shower. The EvtGen1.2.0 pro- gram [67] was used to decay bottom and charm hadrons. The factorisation and renormalisation scales were set to the invari- ant mass of the boson pair. An invariant mass ofm�� > 4 GeV was required at matrix element level for any pair of same- flavour charged leptons. Multijet production was simulated using Pythia8.230 with LO matrix elements matched to the parton shower. The renormalisation and factorisation scales were set to the geo- metric mean of the squared transverse masses of the two outgoing particles in the matrix element. The NNPDF2.3lo PDF set was used in the matrix element generation, the par- ton shower, and the simulation of the multi-parton interac- tions. The A14 set of tuned parameters was used. Perturbative uncertainties were estimated through event weights [68] that encompass variations of the scales at which αs is evaluated in the initial- and final-state shower as well as the PDF uncer- tainty in the shower and the non-singular part of the splitting functions. All simulated event samples are corrected to compensate for small efficiency differences between data and simulation. These include correction factors relating to the efficiency of b-tagging for b-, c- and light-jets, lepton trigger, recon- struction, identification, and isolation, and the efficiency for jet-to-vertex association requirements. Further details on the event reconstruction can be found in Sect. 4. 4 Event reconstruction Events are required to satisfy a set of quality requirements that ensures the detector was in good operating condi- tion [73]. In addition, events are required to have a recon- structed primary vertex with two or more associated tracks, where the primary vertex is chosen as the vertex with the highest scalar sum of the p2 T of associated tracks [74]. The data sample was collected using either a single-electron or single-muon trigger with different transverse momentum, isolation and identification criteria, which depended on the data-taking periods, each characterised by a different instan- taneous luminosity [75–77]. Baseline electrons are reconstructed by algorithms that combine ID tracks and clusters of energy deposits in the elec- tromagnetic calorimeter. The track associated to the electron candidate is required to have a longitudinal impact param- eter (|z0 sin θ |) less than 0.5 mm and the significance of the transverse impact parameter (|d0/σd0 |) is required to be less then 5.0 to ensure the electron candidate originates from the primary vertex. Baseline electron candidates are required to have pT > 10 GeV and |η| < 2.47. Addition- ally, electrons reconstructed in the transition region between the calorimeter barrel and endcap regions, which contains a relatively large amount of inactive material, are removed by excluding electrons with 1.37 < |η| < 1.52. Baseline 123 738 Page 6 of 35 Eur. Phys. J. C (2025) 85:738 electron candidates are identified using the electromagnetic shower shape, calorimeter energy to tracker momentum ratio, and other discriminating variables that are combined into likelihood-based parameters; they are selected if they satisfy the TightLLH quality criterium [78]. The signal electron can- didates must additionally satisfy the Tight_VarRad isolation requirement [78], which uses the calorimeter isolation and track-based isolation cones around the electron candidate. Unlike muon candidates defined below, the isolation cones for electrons are variable-radius. The electron energy scale and resolution is determined using electrons from Z -boson decays in data and applied to simulation [79]. Baseline muon candidates are reconstructed by combining tracks from the ID and MS sub-detectors via a global refit. Baseline muons are required to be of at least Medium qual- ity [80] with transverse momentum greater than 10 GeV and |η| < 2.4. To ensure signal muon candidates are well isolated from other tracks, they are required to satisfy a combination of calorimeter and track-based isolation criteria implemented into the Loose_FixedRad isolation working point [80]. The associated ID track is required to satisfy |z0 sin θ | < 0.5 mm and |d0/σd0 | < 3.0 to be consistent with the primary vertex. The muon energy scale and resolution is determined using muons from Z -boson decays in data and applied to simula- tion [81]. Jets are clustered using the anti-kt algorithm [82] imple- mented in the FastJet package [83] with a radius param- eter of R = 0.4. The jets are clustered from particle flow objects [84], which are charged-particle tracks matched to the hard-scatter vertex and calorimeter energy clusters following an energy subtraction algorithm that removes the calorimeter deposits associated with good-quality tracks from any ver- tex. Different MC-based calibration steps are applied to the reconstructed jets [85], including an area-based correction to account for energy contributions from pile-up interactions, a pT- and η-dependent calibration to match the generator- level energy scale of the jets, and the ‘global sequential cali- bration’ to minimize energy calibration differences between quark- and gluon-initiated jets. Finally, an in situ calibration is applied to jets in data to match the energy scale in simu- lation. All calibrated jets are required to have pT > 30 GeV and |y| < 2.5. Jets with pT < 60 GeV and |y| < 2.4 must also satisfy a requirement based on the output of the multi- variate ‘jet vertex tagger’ (JVT) algorithm, which is used to identify and reject jets from pile-up vertices [86]. The Tight (default) working point is used and jets failing to satisfy the JVT requirements are discarded. These remaining jets are categorised as baseline jets. Baseline jets originating from b-quarks need to be rejected to suppress background contributions from processes involv- ing top quarks. Jets containing a b-hadron (b-jets) are identi- fied using the DL1r b-tagging procedure [87], a deep learning multivariate algorithm trained using information on tracks and secondary vertices. Jets are rejected if they satisfy the DL1r working points tuned to have a 60% efficiency on aver- age for jets associated with generated b-hadrons in simulated t t̄ events. This working point is chosen to improve the purity of the t t̄ control region described in Sect. 6. At the chosen working point, the light-jet (charm-jet) rejection measured in t t̄ MC simulation is about a factor of 1155 (29) on average. The missing transverse momentum (with magnitude Emiss T ) is estimated as the negative vector sum of the trans- verse momentum of all identified electrons, photons, jets and muons [88]. All electrons, muons and jets described above are used as input to the reconstruction. Tracks not associated with any such object are included in the so-called soft term. An overlap-removal procedure is applied to uniquely iden- tify signal lepton candidates and signal jet candidates in an event. Baseline electrons are removed if they share an ID track with a baseline muon. Baseline jets within �R < 0.2 of a baseline electron are removed, then any remaining base- line electrons with 0.2 < �R < 0.4 of a baseline jet are removed. Finally, baseline muons closer than �R = 0.4 to any remaining baseline jets are removed. 5 Event selection Events are required to contain a single electron or muon satisfying the criteria described in Sect. 4 and summarised in the first section of Table 2. The leading (highest pT) lepton is required to be matched to the single lepton that triggered the event and have transverse momentum pT> 30 GeV. In addition, the angular separation between the lep- ton and any selected jet is required to be �R(�, jet) > 0.4. To enrich the selected data sample in events where the W -boson is produced in association with many jets, events are required to contain at least one jet with transverse momen- tum pT> 500 GeV. Contributions from Z + jets and di- leptonic t t̄ processes are suppressed by imposing a veto on any additional leptons in the event. To further suppress the contribution of top-quark backgrounds to the measurement region, a b-jet veto is applied. The event selection is sum- marised in the second section of Table 2. The selection described above forms the inclusive region. Three additional regions that are subsets of the inclusive selection are defined. The first is the inclusive-2 jets region, where a requirement of at least two jets is applied. The second region is the collinear region, where the angular separation between the lepton and the closest jet with pT > 100 GeV is required to be �Rmin(�, jet100 i ) < 2.6. The final region is the back-to-back region, where the angular separation require- ment is inverted relative to the collinear region and so that �Rmin(�, jet100 i ) > 2.6. A summary of the region selection criteria can be found at the bottom section of Table 2. 123 Eur. Phys. J. C (2025) 85:738 Page 7 of 35 738 Table 2 Detector-level selections used to define the signal regions at reconstruction level (see text for details) 6 Background estimation Several SM processes can give rise to a signature similar to theW+ jets signal process. These background processes need to be estimated and subtracted from data before performing the unfolding procedure. The dominant prompt-lepton back- grounds arise from processes involving the decay of an EW boson to final states with leptons, and are therefore primarily associated with t t̄ and Z + jets processes. The t t̄ and Z + jets backgrounds contribute up to 8% of the total expected event yield across the four regions. They contribute equally to both the electron and muon channels. Backgrounds can also arise from multijet events for which the leptons are either non- prompt (i.e. arising from heavy-quark decays), or jets mis- identified as leptons, collectively referred to as ‘fake lep- tons’. The latter contribution represents a significant back- ground in the back-to-back region of the electron selection (up to 20%), while the contribution of fake leptons in the muon channel is a sub-dominant background. Multijet back- grounds in all other regions contribute up to 8% (3%) for elec- trons (muons), respectively. The single-top-quark and dibo- son processes represent sub-dominant backgrounds. Their contributions are estimated directly from simulation, and are expected to account for up to 2% (3%) for electrons (muons). The EW production of V+jj contributes up to 10% of the total expected event yield for large invariant jet mass in the inclusive-2 jets region. The dominant backgrounds, namely t t̄ , Z + jets, and mul- tijet are estimated by using a semi-data-driven technique separately for each background. The normalisation of these background contributions is extracted from data in dedicated control regions enriched in their respective processes. The goal of this method is to extract normalisation factors for each of the backgrounds without introducing a bias from the contributions of other backgrounds that are known to be mis- modelled in the high momentum region of phase space. The control regions are constructed such that they are kinemati- cally similar to the inclusive measurement region, except for a few selections that allow the control region to be enriched in the targeted background process. These factors are statis- tically compatible with normalisation factors derived within each individual signal region. Since the perturbative accu- racy of the t t̄ and Z + jets samples varies with additional QCD emissions, the normalisation factors are parameterised as a function of the number of jets (njet). The multijet nor- malisation factor is parameterised as a function of lepton pT and |η| to capture the variations of the fake-lepton compo- sition as a function of detector geometry and momentum of the fake leptons. The t t̄ and Z + jets normalisation factors are determined first using the MC predictions for multijets, and then applied to the multijets control region where the multijet normalisation factor is subsequently derived. This approach is valid because of the small contribution of the multijets process in the t t̄ and Z + jets control regions. 123 738 Page 8 of 35 Eur. Phys. J. C (2025) 85:738 The t t̄ control region is defined in the same way as the inclusive region, except the b-jet veto is replaced with the requirement of at least two b-tagged jets. The purity of this region in terms of t t̄ events is more than 80%, with small contributions from single-top and W+ jets processes. In both the electron and muon channels, the extracted normalisation factors are 0.8 ± 0.1 for the 2-jet and 3-jet bins and close to unity for the higher jet multiplicities. The background con- tribution to the 1-jet bin is less than 1% of the total expected event yield for all samples. Good agreement between the background model with the normalisation factors applied and data is observed as a function of all observables measured. The only exception is themjj distribution, where the expected event yield is 1σ higher than the data for mjj > 1 TeV, where σ is the total uncertainty. An additional mjj modelling uncertainty is applied to account for this mis-modelling as described in Sect. 8. Most of the Z + jets contribution in the signal region con- sists of events where one of the two leptons fails the kine- matic or geometric requirements, resulting in a single-lepton event. The remaining Z + jets contributions arise from one of the leptons being mis-identified as a jet. The Z + jets control region is defined in the same way as the inclu- sive region, except the single-lepton requirement is replaced by requiring exactly two same-flavour opposite-sign leptons with an invariant mass between 60 < m�� < 120 GeV. In the Z + jets control region, the purity of the Z + jets pro- cess is approximately 90% with the remaining contributions arising primarily from diboson production. The average nor- malisation factor for Z + jets events with up to three jets is 1.05 ± 0.05 and decreases to 0.80 ± 0.05 for events with greater than five jets. Mis-identified jets that are matched to generator-level electrons from the Z -boson decay are excluded from the jet-multiplicity-dependent normalisation factor in the signal region to match the jet counting in the control region, where both electrons are reconstructed. The corrected background model provides an excellent descrip- tion of the data in the control region as a function of all measurement observables, except for mjj. As for the t t̄ pro- cess, an additional modelling uncertainty is applied to the Z + jets of the mjj distribution in the signal region. The multijet control region is defined in the same phase space as each of the signal regions, but the lepton is instead required to fail to satisfy the impact parameter or the isolation lepton criteria. The purity of this region in terms of multijet events is more than 80%, with small contributions from top and W+ jets processes. The normalisation factor is roughly independent of lepton pT for the electron and muon channels, but ranges from 0.3±0.1 to 0.8±0.1 for high to low electron |η|. After the application of the lepton pT and |η| correction factors to the multijet MC sample, an excellent description of the data is observed for all observables measured. The modelling of the multijet estimate is additionally checked in a region where the lepton signal criteria are satisfied, but the missing transverse momentum is below 100 GeV. This validation region has a small 8% overlap with the measure- ment signal region while the multijet background accounts for more than half of the total event yield. Good agreement is found between the simulated events and observed data in the validation region for the full set of measured observables; therefore, no additional uncertainties are assigned to the mul- tijet normalisation factors. The event yields in each measured signal region, after the corrections extracted from the control regions as described above, are summarised in Table 3 with signal theory uncer- tainties included. The W+ jets signal prediction is obtained from the Sherpa2.2.11 simulation. The large pT require- ment on the leading jet selects high jet multiplicity events, so the total uncertainty in the number of W+ jets is dominated by LO matrix elements for Sherpa2.2.11. Overall, the total signal-plus-background predictions are in good agreement with the observed data across all regions for both the electron and muon channels. Differential distributions in the electron and muon channels are shown in Fig. 2 for �Rmin(�, jet100 i ), p�ν T /pclosest jet T , p�ν T , and leading jet pT. The combined signal plus background predictions are in good agreement with the observed data for the full set of observables, except for themjj distribution where the combined signal plus background pre- diction is about 1–2σ higher than the data including all signal and all background uncertainties, similar to that observed in the t t̄ and Z + jets control regions. 7 Unfolding The cross-section are unfolded to particle level using an iter- ative Bayesian unfolding technique [89] to account for object and selection inefficiencies, small acceptance corrections, and resolution effects. The data are unfolded to particle-level regions that closely match the reconstruction-level object and phase-space selections shown in Table 2. Final-state pho- tons radiated from the leptons are added to the lepton four- momentum within a cone of �R = 0.1. These leptons are referred to as ‘dressed leptons’. The anti-kt jet clustering algorithm is used to cluster all final state particles with a life- time greater than 30 ps into jets, excluding the neutrino and the electron or muon from the W -boson decay and any pho- ton included in the dressed lepton. The missing transverse momentum is computed from the final-state neutrino from the W -boson decay. Events are then selected to contain at least one particle-level jet with transverse momentum greater than 500 GeV and exactly one dressed lepton with transverse momentum greater than 30 GeV and |η| < 2.5. The lepton η requirements are harmonised between the electron and muon channels to unfold to a common fiducial region. All other 123 Eur. Phys. J. C (2025) 85:738 Page 9 of 35 738 Table 3 Event yields in the electron and muon channels for the different signal regions after the application of the background normalisation factors. The uncertainties in the predictions include statistical and systematic uncertainties added in quadrature. The nominal Sherpa2.2.11 signal prediction is used to compare with the data. Theoretical uncertainties are also included for signal requirements are applied that define the regions in Table 2, except for the b-jet veto requirement to keep the particle- level measurement inclusive in jet flavour. The unfolding algorithm implemented in the RooUnfold toolkit [90] is used with two iterations. The electron and muon channels are unfolded separately and then combined as discussed in Sect. 9. The signal event yields are determined by subtracting the estimated background contributions from the data satisfy- ing the detector-level selection. The resulting distributions are corrected for detector-level effects to the fiducial phase space at particle level. The Sherpa2.2.11 generator is used as the nominal signal prediction in the unfolding procedure. Simulated signal events, satisfying both the detector-level and particle-level selections, are used to generate a response matrix for each distribution and the particle-level distribu- tion is used as the initial prior to determine the first esti- mate of the unfolded data distribution. For the second itera- tion, the new estimate of unfolded data is obtained using the background-subtracted data and an unfolding matrix, which is derived using Bayes’ theorem, from the response matrix and the current prior. Before entering the iterative unfolding, the background-subtracted data are corrected for the expected fraction of events that satisfy the detector-level selection, but not the particle-level one (unmatched-events). For each bin of each differential distribution, the unfolded event yields are divided by the integrated luminosity of the data sample and by the bin width, to obtain the measured cross-section. A �R-matching procedure is applied to fill the matrices and the unmatched-events fraction is defined accordingly. The lepton and highest pT jet at reconstruction and generator level are required to be matched within an angular cone of �R = 0.4. Moreover the reconstructed jet that is found to be closest to the lepton is required to be matched to the closest particle-level jet within an angular cone of �R = 0.4. In the case of the inclusive-2 jets region, the sub-leading jet at reconstruction level is also required to be matched to the sub-leading jet at particle level. If the matching criteria fail, the corresponding event does not enter the response matrix calculation and is considered as an unmatched fake object that is subtracted from the data alongside other backgrounds before unfolding. Jets that satisfy the generator-level selection on the leading jet of pT> 500 GeV may fail this requirement at reconstruc- tion level due to the finite jet energy resolution. To account for these migration effects, an additional underflow bin is added for all observables, where the selection on the recon- struction level leading jet transverse momentum is relaxed to 400 < pT < 500 GeV. These migrations account for less than 10% of the total events in the fiducial region. 123 738 Page 10 of 35 Eur. Phys. J. C (2025) 85:738 Fig. 2 Differential distributions at reconstruction level in the a, c elec- tron or b, d muon channel for a, b inclusive and c, d collinear signal regions after the application of the background normalisation factors. The signal process is stacked above all background predictions. The bottom panel shows the ratio of the data to the total signal plus back- ground prediction. The shaded band includes statistical and systematic uncertainties from signal and background processes added in quadrature 8 Systematic uncertainties Several sources of experimental and theoretical uncertain- ties are considered during the unfolding process. System- atic uncertainties are derived for each observable by prop- agating changes from each systematic source through the MC unfolding inputs and the subtracted background in the unfolded data. For all sources of uncertainty that affect the background model, the background estimate is recalculated with the modified background model and propagated to the subtracted background before unfolding. For experimental uncertainties affecting the reconstructed signal and back- ground in a similar way, the unfolding response matrices, reconstruction efficiencies and the unmatched events correc- tions are adjusted alongside the subtracted background in the unfolded data. Uncertainties are assessed separately for the electron and muon channels, with correlations taken into account as necessary. Systematic uncertainties relating to the lepton triggering, reconstruction, identification, and isolation are included [78, 80,91]. Muon reconstruction uncertainties include variations in muon momentum scale, the ID and MS resolution, and the sagitta-bias corrections [81]. Variations of the electron energy scale and resolution are included and arise from mate- rial interactions, in situ calibrations, shower shapes, and pile- up modelling [92]. Electron and muon identification uncer- tainties account for variations of the efficiency scale factors by varying the statistical and systematic components of the scale factors. The jet energy scale (JES) and resolution (JER) uncertain- ties are derived as a function of the jet transverse momen- tum, rapidity, and flavour [85]. A reduction scheme is applied resulting in 29 nuisance parameters for the JES and 13 nui- 123 Eur. Phys. J. C (2025) 85:738 Page 11 of 35 738 sance parameters for the JER. Aspects of the JES/JER uncer- tainty that rely on the relative fraction of quark- to gluon- initiated jets are estimated as a function of the jet momentum and rapidity from simulation. The uncertainty in the effi- ciency corrections for the JVT requirement that is used to mitigate the impact of pile-up jets is evaluated by shifting the scale factors by the corresponding uncertainties. Uncertain- ties in the correction factors for the b-tagging efficiency are applied to the MC samples using dedicated flavour-enriched samples in data and an additional term is included to extrap- olate the measured uncertainties to the very high-pT phase space using MC-based uncertainties [93–95]. Variations in the energy scale and resolution of all physics objects are also propagated to the reconstruction of the miss- ing transverse momentum. Sources of uncertainty relating to the background estima- tion include statistical uncertainties in the background nor- malisation factors, theoretical uncertainties including vari- ations of the renormalisation and factorisation scales and PDF eigenvector variations for each background. Additional uncertainties are applied to the mjj background model for t t̄ and Z + jets processes. Residual mis-modelling of the mjj distribution in the control regions persists at the 1–2σ level for mjj > 1 TeV. No additional uncertainties are added to the multijet process as described in Sect. 6 given the good modelling observed in the corresponding multijet validation region. The difference between the nominal prediction and the data is symmetrised and taken as a conservative uncer- tainty. Due to the small contributions of these backgrounds in the mjj > 1 TeV measurement regions, this uncertainty has a very small impact on the final results. The uncertainty in the combined 2015–2018 integrated luminosity is 0.83% [32]. The uncertainty in pile-up effects is assessed by varying the average number of pile-up inter- actions. Several additional sources of uncertainties are assigned to the unfolding procedure, which account for possible simula- tion or theoretical biases: • Prior-related unfolding bias: These assess the sensi- tivity of the unfolded data to the choice of the ini- tial prior from the nominal Sherpa2.2.11 signal model. The Sherpa2.2.11 sample is reweighted at generator level such that it matches the background-subtracted data at reconstruction level for each measured observable. This pseudo-data sample is unfolded with the nominal response matrix, and the basic unfolding bias uncertainty is obtained from the difference between the unfolded dis- tribution and the reweighted generator-level distribution. • Uncertainty in migrations, efficiencies and fakes mod- elling: The alternative MadGraph5_aMC@NLO +Pythia8 sample is used to assess the uncertainty due to the mis-modelling of the migrations, the reconstruction efficiency and the fake corrections. In this procedure, first the alternative signal sample is reweighted to match the nominal Sherpa2.2.11 sample at generator level to avoid double-counting with the prior-related uncertainty. Then the reweighted sample is used to unfold the data and the difference between that and the nominal unfolding result is taken as the systematic error. • Signal modelling uncertainty: An uncertainty in the mea- sured cross-section is assessed from signal theory uncer- tainties. The scale and PDF variations in the nominal Sherpa2.2.11 prediction are varied in the unfolding MC inputs, and the unfolded data are compared with the nom- inal unfolded cross-section in data to derive an uncer- tainty. This uncertainty is negligible compared to the two other uncertainties. The statistical uncertainty in the unfolded measurement and its bin-by-bin correlations are assessed using the boot- strap method [96] with an ensemble of 10,000 replicas of the original data sample for each measured observable. Measurements in the electron and muon channels are combined and an average value is reported, as described in Sect. 9. During the combination, common sources of uncertainties are correlated across the channels, while those uniquely affecting the electron or muon channel are treated as uncorrelated. The statistical and systematic uncertainties in the unfolded inclusive cross-sections after the combina- tion are shown in Table 4. Uncertainties in the inclusive cross-sections across all regions are approximately 3%–4% and dominated by systematic uncertainties, while statistical uncertainties constitute less than 0.5% of the uncertainty in the measured cross-section. The dominant sources of system- atic uncertainty arise from the background modelling driven by the statistical uncertainty in the normalisation factors, JES/JER, b-tagging, and unfolding uncertainties. The ‘Oth- ers’ category contains sub-dominant sources of uncertainties arising from missing transverse momentum reconstruction and the jet-to-vertex fraction uncertainties. Differential distributions of the relative statistical and systematic uncertainties in the unfolded cross-section for �Rmin(�, jet100 i ) and p�ν T in the inclusive region; p�ν T /pclosest jet T and leading jet pT in the collinear region are shown in Fig. 3. The total uncertainty is up to 10% in the inclusive region and up to 15% in the collinear region. The background mod- elling uncertainties are the dominant source of uncertainty and contribute at a similar level to the statistical uncertainty across most distributions. In the back-to-back region and highest energy bins of the leading jet pT and the W -boson pT the statistical uncertainties are one of the leading sources of uncertainty and are around 10–15%. All other sources of uncertainty contribute at the few percent level across all dis- tributions. 123 738 Page 12 of 35 Eur. Phys. J. C (2025) 85:738 Table 4 Relative uncertainties (in %) in the measured integrated cross-sections. Statistical uncertainties from the data and sources of systematic uncertainties are shown separately. The ‘Others’ category contains sub-dominant uncertainties arising from missing transverse momentum reconstruction and the jet-to-vertex fraction uncertainties Uncertainty source Regions Inclusive Inclusive 2-jet Collinear Back-to-back Background modelling 2.0 2.1 2.0 2.3 JES/JER 1.3 1.2 1.1 1.6 b-tagging 1.2 1.4 1.5 0.7 Lepton 0.8 0.8 0.7 1.2 Unfolding 0.34 0.4 0.6 0.05 Luminosity 0.8 0.8 0.8 0.8 Pile-up 0.19 0.15 0.22 0.18 Others 0.14 0.19 0.20 0.03 Data statistical 0.4 0.5 0.5 0.8 Total uncertainty 3.3 3.4 3.4 4 Fig. 3 Relative systematic uncertainties in the averaged cross-section for various differential distributions in the a, b inclusive and c, d collinear phase spaces. The upper solid line shows the total uncer- tainty in the measured cross-section in data, and includes correlations between the systematic components. The ’Others’ category contains sub-dominant uncertainties arising from missing transverse momentum reconstruction and the jet-to-vertex fraction uncertainties 123 Eur. Phys. J. C (2025) 85:738 Page 13 of 35 738 9 Results The cross-sections in the electron and muon channels are measured separately and an average cross-section is obtained using a χ2 likelihood fit with the Combiner [97] package. In this method, all uncertainties are treated as correlated between the electron and muon channels, except for sta- tistical uncertainties and lepton-specific systematic uncer- tainties such as unfolding uncertainties, lepton triggering, and the lepton energy and momentum resolution. Addition- ally, uncertainties in the multijet backgrounds are consid- ered uncorrelated since the two channels are dominated by different fake-lepton processes. All systematic uncertain- ties are symmetrised before the combination. The combined cross-section is found to be consistent with the individual electron and muon channels for the full set of regions and observables. The measured data is compared with several state-of- the-art theoretical predictions, including two NLO multi- jet merged generator predictions: the Sherpa2.2.11 and MadGraph5_aMC@NLO+Pythia8 samples described in Sect. 3. The Sherpa2.2.11 predictions are shown with and without NLO EWvirt corrections to demonstrate their impact on the measured distributions. Additionally, a fixed-order prediction of W + 1-jet was generated at NNLO in αs using the MCFM program [23,98,99] and is compared with the data. The NNLO calculation relies on the N -jettiness sub- traction formalism and the event shape variable N -jettiness τ [100]. For all results presented in this paper, a require- ment of τcut = 10−4 is used and found to impact the final results at the sub-percent level for all differential distri- butions measured. A dynamic scale choice is used where μ = √ m2 �ν + ∑ jets p 2 T, where m�ν is the invariant mass of the lepton–neutrino system and the second term contains the scalar sum of the transverse momentum squared of all jets with pT > 30 GeV. The NNPDF3.0nnlo set of PDFs was used. The PDF uncertainties from the MCFM calculation are expected to be similar in size to Sherpa2.2.11 NLO calculations and shown in Table 5. The renormalisation and factorisation scales are varied coherently by a factor of two, avoiding asymmetric variations. Non-perturbative effects in the high-momentum phase space of this analysis were found to be negligible for all measured observables. The effects of higher-order EW corrections on the MCFM prediction are assessed by extrapolating from the Sherpa prediction. A bin-by-bin correction factor computed from the ratio of the Sherpa QCD with EWvirt prediction to the QCD-only pre- diction is applied to the MCFM prediction and displayed sep- arately throughout all results. This procedure was discussed with the MCFM authors and also done in the corresponding Z + jets analysis [18]. The combined inclusive cross-sections in the inclusive, inclusive 2-jet, collinear, and back-to-back regions are shown in Fig. 4 and tabulated in Table 5. For results showing pre- dictions accurate to QCD, uncertainties include scale and PDF uncertainties added in quadrature, while the results reported with EW virtual corrections display uncertainties arising from the different EW combination schemes only. The measurement uncertainties are significantly smaller than the uncertainties in the signal predictions from the Sherpa2.2.11 and MadGraph5_aMC@NLO+Pythia8 event generators, which are dominated by variations in the renormalisation and factorisation scale uncertainties. In particular, Sherpa2.2.11 uncertainties are larger than the MadGraph5_aMC@NLOuncertainties due to the 3-5j@LO calculations of the matrix element for Sherpa. The uncer- tainty shown in Fig. 4 is the total uncertainty in the prediction which is very large in comparison to the EW corrections and scale uncertainties in the QCD predictions. The fixed-order MCFM W +1-jet prediction computed at NNLO accuracy is found to be in good agreement with the data across all regions with a precision comparable to that of the measured cross- sections from data. The NLO EWvirt corrections lead to an overall decrease in the inclusive cross-section by 10%–12%, in agreement with fixed-order calculations computed for V+2-jet in Ref. [101]. This improves the agreement of the Sherpa prediction with the data in the collinear region, but leads to an approximate 10% underestimate of the cross- sections for the MCFM prediction. Measurements of the differential cross-section for all observables are shown in Figs. 5, 6 and 7. The measured differential distributions are compared with the same three signal predictions as described above. For all figures, the main panel shows the various theoretical predictions that do not include NLO EW corrections, while the two lower pan- els additionally show the effect of NLO EWvirt as computed from Sherpa2.2.11. The uncertainties in the QCD accurate predictions contain uncertainties due to scale and PDF uncer- tainties added in quadrature, while the predictions includ- ing NLO EWvirt corrections display only the uncertainty due to different EW correction combination schemes. The mea- sured cross-sections in data and their statistical uncertainty are shown by the solid dots and error bars, while the shaded band shows the systematic and statistical uncertainties added in quadrature. Figure 5 shows the differential cross-sections as a func- tion of �Rmin(�, jet100 i ) and p�ν T /pclosest jet T in the inclu- sive phase space. These observables can be used to dis- tinguish W -boson emission from a high-momentum jet, referred to as the collinear events, from events where the W -boson recoils against a single initial-state-radiation jet, referred to as back-to-back events. Due to the leading jet pT > 500 GeV requirement, these back-to-back topologies 123 738 Page 14 of 35 Eur. Phys. J. C (2025) 85:738 Table 5 Measured fiducial cross-section (σfid) in each signal region with theoretical predictions from Sherpa2.2.11, Mad- Graph5_aMC@NLO+Pythia8, and MCFM W+1-jet@NNLO. Systematic uncertainties in the measured cross-sections are separated into statistical and non-statistical sources, while theoretical predictions show uncertainties arising from scale and PDF variations separately. For results showing predictions accurate to QCD, uncertainties include scale and PDF uncertainties added in quadrature, while the results reported with EW virtual corrections display uncertainties arising from the different EW combination schemes only Inclusive σfid (fb) Total �σfid (fb) Data 778 ±3 (stat.) ±25 (syst.+stat.) Sherpa2.2.11 823 +8−10 (PDF) +360−210 (scale) +360−210 Sherpa2.2.11 QCD+EW 733 +32−32 (EW virt) +360−210 MadGraph5_aMC@NLO+Pythia8 851 +6−6 (PDF) +90−130 (scale) +90−130 MCFM 765 +26−26 (scale) MCFM QCD+EW 680 +30−30 (EW virt) +40−40 Inclusive 2-jet σfid (fb) Total �σfid (fb) Data 684 ±3 (stat.) ±23 (syst.+stat.) Sherpa2.2.11 728 +7−10 (PDF) +340−200 (scale) +350−200 Sherpa2.2.11 QCD+EW 649 +28−28 (EW virt) +350−200 MadGraph5_aMC@NLO+Pythia8 754 +5−5 (PDF) +76−110 (scale) +76−110 MCFM 693 +28−28 (scale) MCFM QCD+EW 620 +30−30 (EW virt) +40−40 Collinear σfid (fb) Total �σfid (fb) Data 532 ±3 (stat.) ±18 (syst.+stat.) Sherpa2.2.11 574 +6−8 (PDF) +290−170 (scale) +300−170 Sherpa2.2.11 QCD+EW 521 +18−18 (EW virt) +300−170 MadGraph5_aMC@NLO+Pythia8 578 +4−4 (PDF) +50−90 (scale) +50−90 MCFM 530 +31−31 (scale) MCFM QCD+EW 480 +17−17 (EW virt) +35−35 Back-to-back σfid (fb) Total �σfid (fb) Data 247 ±2 (stat.) ±9 (syst.+stat.) Sherpa2.2.11 249 +2−3 (PDF) +60−40 (scale) +60−40 Sherpa2.2.11 QCD+EW 210 +10−10 (EW virt) +60−40 MadGraph5_aMC@NLO+Pythia8 273 +2−2 (PDF) +40−40 (scale) +40−40 MCFM 235 +5−5 (scale) MCFM QCD+EW 200 +13−13 (EW virt) +14−14 typically lead to high-momentum W -boson events contain- ing a lepton whose angular separation with the leading jet is �R(�, jetleading) ∼ π . Furthermore, these single-jet events contain a W -boson with momentum that balances the leading jet in the transverse plane, leading to p�ν T /pclosest jet T close to one. In contrast, events where the W -boson is emitted from a high-momentum jet receive an overall collinear enhance- ment in the distribution of the angular distance between the W -boson and the closest jet. Moreover, the largest contri- bution occurs when the W -boson momentum is relatively soft and leads to p�ν T /pclosest jet T close to zero. For larger p�ν T /pclosest jet T where the W -boson is not quite as soft, this disagreement with the MCFM prediction is more notice- able in light of the smaller uncertainties. These features can be clearly seen in Fig. 5. The multijet merged Sherpa and MadGraph5_aMC@NLO+Pythia8 event generators pro- vide an excellent description of the data across both vari- ables. The inclusion of NLO EW corrections in the Sherpa prediction generally improve the agreement with the data in the collinear regions, but lead to an underestimate of the cross-sections in the back-to-back region while remaining consistent within uncertainties of the Sherpa prediction. The fixed-order MCFM W + 1-jet NNLO prediction provides a good description of the data, except for back-to-back regions with �Rmin(�, jet100 i ) > π . In these regions, the MCFM pre- diction undershoots the data well beyond measurement and prediction uncertainties. Figure 6 shows the differential cross-section as a function of the invariant mass of the leading two jets (mjj) in the inclu- sive 2-jet region. As discussed above, the cross-section due to a relatively soft W -boson emitted from an outgoing quark 123 Eur. Phys. J. C (2025) 85:738 Page 15 of 35 738 Fig. 4 Measured fiducial cross-sections in each signal region. The measured cross-sections in data and their total uncertainty are shown by the solid dots and error band. Various theoretical predictions are overlaid and compared with the data in the lower panel. The small error bars inside the markers are the statistical uncertainties. The large shaded areas are the theoretical systematic uncertainties. Uncertainties in pre- dictions accurate to NLO precision include QCD scale and PDF uncer- tainties, while predictions that add NLO EWvirt (electroweak) correc- tions show uncertainties only due to different electroweak combination schemes. Uncertainties in predictions accurate at fixed-order NNLO precision are derived primarily from MCFM, do not include PDF vari- ations, with an additional extrapolation from the Sherpa QCD with EWvirt prediction to assess the effects of higher-order electroweak cor- rections. On predictions with EWvirt corrections, the total uncertainty is shown as a shaded region, while the electroweak correction is overlaid with an error bar line contributes significantly to the overall production rate in the inclusive phase space. Due to the leading jet pT > 500 GeV requirement, this leads to an overall enhancement in the rate for mjj around 1 TeV since the W -boson carries only a small amount of the momentum. Events with large mjj are domi- nated by extremely high momentum jets with large opening angles. This variable is an important observable for a range of BSM searches and EW-induced measurements that have his- torically been difficult to model [19–22]. Since the MCFM prediction is computed at NNLO precision for the process W +1-jet, it provides NLO precision for the mjj variable due to the two-jet requirement. All theoretical predictions over- estimate the cross-section around mjj > 2 TeV beyond their corresponding systematic uncertainties. In the collinear selection, defined by the requirement of �Rmin(�, jet100 i ) < 2.6, the differential cross-section as a function of the leading-jet transverse momentum, the inclu- sive jet multiplicity, the scalar sum of jet momenta, and the W -boson candidate transverse momentum are measured. These measurements are shown in Fig. 7. The leading jet pT distribution is shown in Fig. 7a and probes jet momenta up to the 1.5 TeV scale. The Mad- Graph5_aMC@NLO+Pythia8 and Sherpa predictions provide an excellent description of the data across the entire measured range. There remain large uncertainties associated with the Sherpa predictions even though the Sherpa NLO EWvirt corrections improve the agreement of the central value with the data. The fixed-order MCFM provides an excellent description of the data with precision that matches or exceeds that of the measured data in the highest measured bins. The application of the NLO EWvirt corrections to the MCFM reduces the cross-section in all bins and generally leads to a ∼10% underestimate of the cross-section. Measurements of the differential cross-section as a func- tion of the inclusive jet multiplicity and the scalar sum of all the jet momenta are shown in Fig. 7b, c. Similar to the leading jet pT measurement, the multijet merged predictions provide an excellent description of the data across all measured val- ues. For the most extreme ST bins, the scale uncertainties in the Sherpa prediction exceed 50% due to large contributions from the leading-order matrix elements in this region of phase space. The fixed-order MCFM provides a good description of the data for ST < 1.4 TeV but underestimates the cross- section for more extreme values. For such extreme regions, the dominant contribution comes from events with three or 123 738 Page 16 of 35 Eur. Phys. J. C (2025) 85:738 Fig. 5 Differential cross-section measurement in the inclusive phase space as function of a the minimum angular separa- tion between the lepton and any jet with transverse momentum greater than 100 GeV (�Rmin(�, jet100 i )), and b the ratio of W - boson pT to the closest-jet pT (p�ν T /pclosest jet T ). The measured cross-sections in data and their statistical uncertainty are shown by the solid dots and error bars, while the shaded band shows the systematic and statistical uncertainties added in quadrature. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text. The bins around p�ν T /pclosest jet T equal to 1 are merged to be insensitive to the singularity that exists in the fixed-order MCFM calculation. Additionally, in b, the central two bins from the MCFM prediction are merged due to a singularity in fixed-order cal- culations, which requires pT resummation of the W+ jets system. The two lower panels show the effect of NLO EWvirt as computed from Sherpa2.2.11 Fig. 6 Differential cross-section as a function of the invariant mass of the leading two jets (mjj) in the inclusive, 2-jet phase space. The mea- sured cross-sections in data and their statistical uncertainty are shown by the solid dots and error bars, while the shaded band shows the sys- tematic and statistical uncertainties added in quadrature. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text. The two lower panels show the effect of NLO EWvirt as computed from Sherpa2.2.11 more jets, beyond the formal accuracy of the MCFM calcu- lation. The differential distribution of the measured cross-section as a function of p�ν T is shown in Fig. 7d. The QCD-only pre- dictions agree well with the data at low p�ν T values but lead to a small overestimate in the high p�ν T regime that is improved with inclusion of NLO EW corrections. At high p�ν T , the NLO EWvirt corrections show the standard Sudakov behaviour and lead to large negative corrections over the QCD-only cross- section at high transverse momentum. The size of these cor- rections can be as large as 30% and exceed uncertainties in the fixed-order MCFM NNLO prediction in the highest momentum jet bins. The application of the NLO EWvirt cor- rections significantly improves the agreement of the MCFM prediction with data in the highest p�ν T bins. Towards softer W -boson emissions, the Sherpa prediction is dominated by many jet events that are described by its LO accurate matrix elements and leads to large scale uncertainties for smaller p�ν T values. 10 Conclusions A measurement of cross-sections for a W -boson produced in association with at least one high-transverse-momentum 123 Eur. Phys. J. C (2025) 85:738 Page 17 of 35 738 Fig. 7 Differential cross-section as a function of a the leading pjet T , b the inclusive jet multiplicity, c ST, and d p�ν T in the collinear phase- space. The measured cross-sections in data and their statistical uncer- tainty are shown by the solid dots and error bars, while the shaded band shows the systematic and statistical uncertainties added in quadrature. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text. The two lower panels show the effect of NLO EWvirt as computed from Sherpa2.2.11 jet is presented. This measurement utilises 140 fb−1 of proton–proton collision data collected at a centre-of-mass energy of √ s = 13 TeV by the ATLAS detector at the LHC. Measurements are performed on events containing a single electron or muon from the W → �ν decay and at least one high-momentum jet with pT> 500 GeV. This paper focuses on events where the angular separation between the lepton and a high-momentum jet is small to define a collinear phase space. This region is populated either by dijet events radiating a W -boson or events with a W -boson produced in association with several jets and it serves as an excellent data sample to probe higher-order theoretical predictions. Measurements of the inclusive and differential cross-sections in the collinear phase space as a function of a variety of observables sensi- tive to the emission of W -bosons from high-momentum jets are presented. Measurements probe W -bosons produced in association with jets with transverse momentum above the TeV scale. The background-subtracted data distributions are unfolded to the particle level and compared with several multijet 123 738 Page 18 of 35 Eur. Phys. J. C (2025) 85:738 generator predictions and to a fixed-order calculation. The Sherpa and MadGraph5_aMC@NLO +Pythia8 multi- jet merged predictions, accurate to NLO in αs, provide an excellent description of the data across all measured dis- tributions. The scale uncertainties in the Sherpa predic- tions are found to be significantly larger than those from MadGraph5_aMC@NLO, due to the extra leading-order matrix elements in the Sherpa sample used to describe the high-jet-multiplicity final states. The fixed-order calculation for W + 1-jet from MCFM, computed to NNLO in αs, pro- vides a good description of the data with a precision that is comparable to the measurement uncertainties. In regions of phase space with large angular separations between the lep- ton and leading jet, the MCFM prediction underestimates the cross-section. The impact of NLO EW virtual corrections is assessed using the Sherpa event generator, the size of the corrections is found to be larger than the scale uncertainties in the MCFM prediction. NLO EW corrections improve the agreement of the theory prediction with measured data in regions of phase space with highly-boosted W -bosons. Acknowledgements We thank CERN for the very successful oper- ation of the LHC and its injectors, as well as the support staff at CERN and at our institutions worldwide without whom ATLAS could not be operated efficiently. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF/SFU (Canada), NDGF (Den- mark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [ATL-SOFT-PUB-2025-001]. We gratefully acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC, China; Minciencias, Colombia; MEYS CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA- DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Ger- many; GSRI, Greece; RGC and Hong Kong SAR, China; ICHEP and Academy of Sciences and Humanities, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW, Poland; FCT, Portugal; MNE/IFA, Romania; MSTDI, Serbia; MSSR, Slovakia; ARIS and MVZI, Slovenia; DSI/NRF, South Africa; MICIU/AEI, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; NSTC, Taipei; TENMAK, Türkiye; STFC/UKRI, United Kingdom; DOE and NSF, United States of America. Individual groups and members have received support from BCKDF, CANARIE, CRC and DRAC, Canada; CERN- CZ, FORTE and PRIMUS, Czech Republic; COST, ERC, ERDF, Horizon 2020, ICSC-NextGenerationEU and Marie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex, Investisse- ments d’Avenir Idex and ANR, France; DFG and AvH Foundation, Ger- many; Herakleitos, Thales and Aristeia programmes co-financed by EU- ESF and the Greek NSRF, Greece; BSF-NSF and MINERVA, Israel; NCN and NAWA, Poland; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stif- telse, Sweden; The Royal Society and Leverhulme Trust, United King- dom. In addition, individual members wish to acknowledge support from Armenia: Yerevan Physics Institute (FAPERJ); CERN: Euro- pean Organization for Nuclear Research (CERN DOCT); Chile: Agen- cia Nacional de Investigación y Desarrollo (FONDECYT 1230812, FONDECYT 1230987, FONDECYT 1240864); China: Chinese Min- istry of Science and Technology (MOST-2023YFA1605700, MOST- 2023YFA1609300), National Natural Science Foundation of China (NSFC - 12175119, NSFC 12275265, NSFC-12075060); Czech Repub- lic: Czech Science Foundation (GACR - 24-11373 S), Ministry of Edu- cation Youth and Sports (FORTE CZ.02.01.01/00/22_008/0004632), PRIMUS Research Programme (PRIMUS/21/SCI/017); EU: H2020 European Research Council (ERC - 101002463); European Union: European Research Council (ERC - 948254, ERC 101089007, ERC, BARD, 101116429), European Union, Future Artificial Intelligence Research (FAIR-NextGenerationEU PE00000013), Italian Center for High Performance Computing, Big Data and Quantum Computing (ICSC, NextGenerationEU); France: Agence Nationale de la Recherche (ANR-20-CE31-0013, ANR-21-CE31-0013, ANR-21-CE31-0022, ANR-22-EDIR-0002); Germany: Baden-Württemberg Stiftung (BW Stiftung-Postdoc Eliteprogramme), Deutsche Forschungsgemeinschaft (DFG - 469666862, DFG - CR 312/5-2); Italy: Istituto Nazionale di Fisica Nucleare (ICSC, NextGenerationEU), Ministero dell’Università e della Ricerca (PRIN - 20223N7F8K - PNRR M4.C2.1.1); Japan: Japan Society for the Promotion of Science (JSPS KAKENHI JP22H01227, JSPS KAKENHI JP22H04944, JSPS KAKENHI JP22KK0227, JSPS KAKENHI JP23KK0245); Netherlands: Netherlands Organisation for Scientific Research (NWO Veni 2020 - VI.Veni.202.179); Norway: Research Council of Norway (RCN-314472); Poland: Ministry of Sci- ence and Higher Education (IDUB AGH, POB8, D4 no 9722), Pol- ish National Agency for Academic Exchange (PPN/PPO/2020/1/00002 /U/00001), Polish National Science Centre (NCN 2021/42/E/ST2/00350, NCN OPUS 2023/51/B/ST2/02507, NCN OPUS nr 2022/47/B/ST2/ 03059, NCN UMO-2019/34/E/ST2/00393, NCN & H2020 MSCA 945339, UMO-2020/37/B/ST2/01043, UMO-2021/40/C/ST2/00187, UMO-2022/47/O/ST2/00148, UMO-2023/49/B/ST2/04085, UMO- 2023/51/B/ST2/00920); Slovenia: Slovenian Research Agency (ARIS grant J1-3010); Spain: Generalitat Valenciana (Artemisa, FEDER, IDIFEDER/2018/048), Ministry of Science and Innovation (MCIN & NextGenEU PCI2022-135018-2, MICIN & FEDER PID2021- 125273NB, RYC2019-028510-I, RYC2020-030254-I, RYC2021-0312 73-I, RYC2022-038164-I); Sweden: Carl Trygger Foundation (Carl Trygger Foundation CTS 22:2312), Swedish Research Council (Swedish Research Council 2023-04654, VR 2018-00482, VR 2021-03651, VR 2022-03845, VR 2022-04683, VR 2023-03403), Knut and Alice Wallenberg Foundation (KAW 2018.0458, KAW 2019.0447, KAW 2022.0358); Switzerland: Swiss National Science Foundation (SNSF - PCEFP2_194658); United Kingdom: Leverhulme Trust (Leverhulme Trust RPG-2020-004), Royal Society (NIF-R1-231091); United States of America: U.S. Department of Energy (ECA DE-AC02-76SF00515), Neubauer Family Foundation. Data Availability Statement My manuscript has associated data in a data repository. [Authors’ comment: All ATLAS scientific output is published in journals, and preliminary results are made available in Conference Notes. All are openly available, without restriction on use by external parties beyond copyright law and the standard conditions agreed by CERN. Data associated with journal publications are also made available: tables and data from plots (e.g. cross section values, likelihood profiles, selection efficiencies, cross section limits,...) are stored in appropriate repositories such as HEPDATA (http://hepdata. cedar.ac.uk/). ATLAS also strives to make additional material related to the paper available that allows a reinterpretation of the data in the context of new theoretical models. For example, an extended encap- sulation of the analysis is often provided for measurements in the framework of RIVET (http://rivet.hepforge.org/). This information is taken from the ATLAS Data Access Policy, which is a public docu- ment that can be downloaded from http://opendata.cern.ch/record/413 [opendata.cern.ch]. 123 http://hepdata.cedar.ac.uk/ http://hepdata.cedar.ac.uk/ http://rivet.hepforge.org/ http://opendata.cern.ch/ record/413 Eur. Phys. J. C (2025) 85:738 Page 19 of 35 738 Code Availability Statement My manuscript has associated code/ software in a data repository. [Authors’ comment: ATLAS collabo- ration software is open source, and all code necessary to recreate an analysis is publicly available. The Athena (http://gitlab.cern.ch/atlas/ athena) software repository provides all code needed for calibration and uncertainty application, with configuration files that are also publicly available via Docker containers and cvmfs. The specific code and con- figurations written in support of this analysis are not public; however, these are internally preserved.] Open Access This article is licensed under a Creative Commons Attri- bution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, pro- vide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indi- cated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permit- ted use, you will need to obtain permission directly from the copy- right holder. To view a copy of this licence, visit http://creativecomm ons.org/licenses/by/4.0/. 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Zwalinski37 1 Department of Physics, University of Adelaide, Adelaide, Australia 2 Department of Physics, University of Alberta, Edmonton, AB, Canada 3 (a)Department of Physics, Ankara University, Ankara, Turkey; (b)Division of Physics, TOBB University of Economics and Technology, Ankara, Turkey 4 LAPP, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France 5 APC, Université Paris Cité, CNRS/IN2P3, Paris, France 6 High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA 7 Department of Physics, University of Arizona, Tucson, AZ, USA 8 Department of Physics, University of Texas at Arlington, Arlington, TX, USA 9 Physics Department, National and Kapodistrian University of Athens, Athens, Greece 10 Physics Department, National Technical University of Athens, Zografou, Greece 11 Department of Physics, University of Texas at Austin, Austin, TX, USA 12 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan 13 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain 14 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China 15 Physics Department, Tsinghua University, Beijing, China 16 Institute of Physics, University of Belgrade, Belgrade, Serbia 17 Department for Physics and Technology, University of Bergen, Bergen, Norway 18 (a)Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA; (b)University of California, Berkeley, CA, USA 19 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany 123 http://orcid.org/0000-0001-5551-5456 http://orcid.org/0000-0003-2482-711X http://orcid.org/0000-0001-9116-055X http://orcid.org/0000-0002-8487-8480 http://orcid.org/0000-0003-3952-8139 http://orcid.org/0000-0002-5246-5497 http://orcid.org/0000-0002-1024-0687 http://orcid.org/0000-0001-7613-5997 http://orcid.org/0000-0001-9839-608X http://orcid.org/0000-0001-8530-6487 http://orcid.org/0000-0002-5821-4875 http://orcid.org/0000-0001-7477-4955 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Phys. J. C (2025) 85:738 Page 31 of 35 738 20 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland 21 School of Physics and Astronomy, University of Birmingham, Birmingham, UK 22 (a)Department of Physics, Bogazici University, Istanbul, Turkey; (b)Department of Physics Engineering, Gaziantep University, Gaziantep, Turkey; (c)Department of Physics, Istanbul University, Istanbul, Turkey 23 (a)Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia; (b)Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia 24 (a)Dipartimento di Fisica e Astronomia A. Righi, Università di Bologna, Bologna, Italy; (b)INFN Sezione di Bologna, Bologna, Italy 25 Physikalisches Institut, Universität Bonn, Bonn, Germany 26 Department of Physics, Boston University, Boston, MA, USA 27 Department of Physics, Brandeis University, Waltham, MA, USA 28 (a)Transilvania University of Brasov, Brasov, Romania; (b)Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania; (c)Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania ; (d)National Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj-Napoca, Romania; (e)National University of Science and Technology Politechnica, Bucharest, Romania; (f)West University in Timisoara, Timisoara, Romania; (g)Faculty of Physics, University of Bucharest, Bucharest, Romania 29 (a)Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia; (b)Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 30 Physics Department, Brookhaven National Laboratory, Upton, NY, USA 31 Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, y CONICET, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires, Argentina 32 California State University, Long Beach, CA, USA 33 Cavendish Laboratory, University of Cambridge, Cambridge, UK 34 (a)Department of Physics, University of Cape Town, Cape Town, South Africa; (b)iThemba Labs, Cape Town, Western Cape, South Africa; (c)Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa; (d)National Institute of Physics, University of the Philippines Diliman (Philippines), Quezon City, Philippines; (e)University of South Africa, Department of Physics, Pretoria, South Africa; (f)University of Zululand, KwaDlangezwa, South Africa; (g)School of Physics, University of the Witwatersrand, Johannesburg, South Africa 35 Department of Physics, Carleton University, Ottawa, ON, Canada 36 (a)Faculté des Sciences Ain Chock, Université Hassan II de Casablanca, Casablanca, Morocco; (b)Faculté des Sciences, Université Ibn-Tofail, Kenitra, Morocco; (c)Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech, Marrakech, Morocco; (d)LPMR, Faculté des Sciences, Université Mohamed Premier, Oujda, Morocco; (e)Faculté des sciences, Université Mohammed V, Rabat, Morocco; (f)Institute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir, Morocco 37 CERN, Geneva, Switzerland 38 Affiliated with an Institute Formerly Covered by a Cooperation Agreement with CERN, Geneva, Switzerland 39 Affiliated with an Institute Covered by a Cooperation Agreement with CERN, Geneva, Switzerland 40 Affiliated with an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland 41 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA 42 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France 43 Nevis Laboratory, Columbia University, Irvington, NY, USA 44 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 45 (a)Dipartimento di Fisica, Università della Calabria, Rende, Italy; (b)INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Frascati, Italy 46 Physics Department, Southern Methodist University, Dallas, TX, USA 47 National Centre for Scientific Research “Demokritos”, Agia Paraskevi, Greece 48 (a)Department of Physics, Stockholm University, Stockholm, Sweden; (b)Oskar Klein Centre, Stockholm, Sweden 49 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany 50 Fakultät Physik , Technische Universität Dortmund, Dortmund, Germany 51 Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany 52 Department of Physics, Duke University, Durham, NC, USA 53 SUPA-School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK 123 738 Page 32 of 35 Eur. Phys. J. C (2025) 85:738 54 INFN e Laboratori Nazionali di Frascati, Frascati, Italy 55 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany 56 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 57 Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland 58 (a)Dipartimento di Fisica, Università di Genova, Genoa, Italy; (b)INFN Sezione di Genova, Genoa, Italy 59 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 60 SUPA-School of Physics and Astronomy, University of Glasgow, Glasgow, UK 61 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France 62 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA 63 (a)Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China; (b)Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China; (c)School of Physics and Astronomy, Shanghai Jiao Tong University, Key Laboratory for Particle Astrophysics and Cosmology (MOE), SKLPPC, Shanghai, China; (d)Tsung-Dao Lee Institute, Shanghai, China; (e)School of Physics, Zhengzhou University, Zhengzhou, China 64 (a)Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany; (b)Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 65 (a)Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong; (b)Department of Physics, University of Hong Kong, Pok Fu Lam, Hong Kong; (c)Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 66 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 67 IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405 Orsay, France 68 Centro Nacional de Microelectrónica (IMB-CNM-CSIC), Barcelona, Spain 69 Department of Physics, Indiana University, Bloomington, IN, USA 70 (a)INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy; (b)ICTP, Trieste, Italy; (c)Dipartimento Politecnico di Ingegneria e Architettura, Università di Udine, Udine, Italy 71 (a)INFN Sezione di Lecce, Lecce, Italy; (b)Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy 72 (a)INFN Sezione di Milano, Milan, Italy; (b)Dipartimento di Fisica, Università di Milano, Milan, Italy 73 (a)INFN Sezione di Napoli, Naples, Italy; (b)Dipartimento di Fisica, Università di Napoli, Naples, Italy 74 (a)INFN Sezione di Pavia, Pavia, Italy; (b)Dipartimento di Fisica, Università di Pavia, Pavia, Italy 75 (a)INFN Sezione di Pisa, Pisa, Italy; (b)Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy 76 (a)INFN Sezione di Roma, Rome, Italy; (b)Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy 77 (a)INFN Sezione di Roma Tor Vergata, Rome, Italy; (b)Dipartimento di Fisica, Università di Roma Tor Vergata, Rome, Italy 78 (a)INFN Sezione di Roma Tre, Rome, Italy; (b)Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy 79 (a)INFN-TIFPA, Povo, Italy; (b)Università degli Studi di Trento, Trento, Italy 80 Universität Innsbruck, Department of Astro and Particle Physics, Innsbruck, Austria 81 University of Iowa, Iowa City, IA, USA 82 Department of Physics and Astronomy, Iowa State University, Ames, IA, USA 83 Istinye University, Sariyer, Istanbul, Turkey 84 (a)Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil ; (b)Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil; (c)Instituto de Física, Universidade de São Paulo, São Paulo, Brazil; (d)Rio de Janeiro State University, Rio de Janeiro, Brazil; (e)Federal University of Bahia, Bahia, Brazil 85 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 86 Graduate School of Science, Kobe University, Kobe, Japan 87 (a)AGH University of Krakow, Faculty of Physics and Applied Computer Science, Krakow, Poland; (b)Marian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland 88 Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland 89 Faculty of Science, Kyoto University, Kyoto, Japan 90 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan 91 L2IT, Université de Toulouse, CNRS/IN2P3, UPS, Toulouse, France 92 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 123 Eur. Phys. J. C (2025) 85:738 Page 33 of 35 738 93 Physics Department, Lancaster University, Lancaster, UK 94 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK 95 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia 96 School of Physics and Astronomy, Queen Mary University of London, London, UK 97 Department of Physics, Royal Holloway University of London, Egham, UK 98 Department of Physics and Astronomy, University College London, London, UK 99 Louisiana Tech University, Ruston, LA, USA 100 Fysiska institutionen, Lunds universitet, Lund, Sweden 101 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain 102 Institut für Physik, Universität Mainz, Mainz, Germany 103 School of Physics and Astronomy, University of Manchester, Manchester, UK 104 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France 105 Department of Physics, University of Massachusetts, Amherst, MA, USA 106 Department of Physics, McGill University, Montreal, QC, Canada 107 School of Physics, University of Melbourne, Melbourne, VIC, Australia 108 Department of Physics, University of Michigan, Ann Arbor, MI, USA 109 Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA 110 Group of Particle Physics, University of Montreal, Montreal, QC, Canada 111 Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany 112 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany 113 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 114 (a)Department of Physics, Nanjing University, Nanjing, China; (b)School of Science, Shenzhen Campus of Sun Yat-sen University, Shenzhen, China; (c)University of Chinese Academy of Science (UCAS), Beijing, China 115 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA 116 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University/Nikhef, Nijmegen, The Netherlands 117 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands 118 Department of Physics, Northern Illinois University, DeKalb, IL, USA 119 (a)New York University Abu Dhabi, Abu Dhabi, United Arab Emirates; (b)United Arab Emirates University, Al Ain, United Arab Emirates 120 Department of Physics, New York University, New York, NY, USA 121 Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan 122 Ohio State University, Columbus, OH, USA 123 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA 124 Department of Physics, Oklahoma State University, Stillwater, OK, USA 125 Palacký University, Joint Laboratory of Optics, Olomouc, Czech Republic 126 Institute for Fundamental Science, University of Oregon, Eugene, OR, USA 127 Graduate School of Science, Osaka University, Osaka, Japan 128 Department of Physics, University of Oslo, Oslo, Norway 129 Department of Physics, Oxford University, Oxford, UK 130 LPNHE, Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, France 131 Department of Physics, University of Pennsylvania, Philadelphia, PA, USA 132 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA 133 (a)Laboratório de Instrumentação e Física Experimental de Partículas-LIP, Lisbon, Portugal; (b)Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal; (c)Departamento de Física, Universidade de Coimbra, Coimbra, Portugal; (d)Centro de Física Nuclear da Universidade de Lisboa, Lisbon, Portugal; (e)Departamento de Física, Escola de Ciências, Universidade do Minho, Braga, Portugal; (f)Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, Spain; (g)Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal 134 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 135 Czech Technical University in Prague, Prague, Czech Republic 136 Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic 137 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK 123 738 Page 34 of 35 Eur. Phys. J. C (2025) 85:738 138 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France 139 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA 140 (a)Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile; (b)Millennium Institute for Subatomic physics at high energy frontier (SAPHIR), Santiago, Chile; (c)Instituto de Investigación Multidisciplinario en Ciencia y Tecnología y Departamento de Física, Universidad de La Serena, La Serena, Chile; (d)Department of Physics, Universidad Andres Bello, Santiago, Chile; (e)Instituto de Alta Investigación, Universidad de Tarapacá, Arica, Chile ; (f)Departamento de Física, Universidad Técnica Federico Santa María, Valparaiso, Chile 141 Department of Physics, Institute of Science, Tokyo, Japan 142 Department of Physics, University of Washington, Seattle, WA, USA 143 Department of Physics and Astronomy, University of Sheffield, Sheffield, UK 144 Department of Physics, Shinshu University, Nagano, Japan 145 Department Physik, Universität Siegen, Siegen, Germany 146 Department of Physics, Simon Fraser University, Burnaby, BC, Canada 147 SLAC National Accelerator Laboratory, Stanford, CA, USA 148 Department of Physics, Royal Institute of Technology, Stockholm, Sweden 149 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA 150 Department of Physics and Astronomy, University of Sussex, Brighton, UK 151 School of Physics, University of Sydney, Sydney, Australia 152 Institute of Physics, Academia Sinica, Taipei, Taiwan 153 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia; (b)High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia; (c)University of Georgia, Tbilisi, Georgia 154 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel 155 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 156 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece 157 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan 158 Department of Physics, University of Toronto, Toronto, ON, Canada 159 (a)TRIUMF, Vancouver, BC, Canada; (b)Department of Physics and Astronomy, York University, Toronto, ON, Canada 160 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan 161 Department of Physics and Astronomy, Tufts University, Medford, MA, USA 162 Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA 163 University of West Attica, Athens, Greece 164 University of Sharjah, Sharjah, United Arab Emirates 165 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden 166 Department of Physics, University of Illinois, Urbana, IL, USA 167 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia-CSIC, Valencia, Spain 168 Department of Physics, University of British Columbia, Vancouver, BC, Canada 169 Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada 170 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany 171 Department of Physics, University of Warwick, Coventry, UK 172 Waseda University, Tokyo, Japan 173 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel 174 Department of Physics, University of Wisconsin, Madison, WI, USA 175 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany 176 Department of Physics, Yale University, New Haven, CT, USA 177 Yerevan Physics Institute, Yerevan, Armenia a Also Affiliated with an Institute Covered by a Cooperation Agreement with CERN, Geneva, Switzerland b Also at An-Najah National University, Nablus, Palestine c Also at Borough of Manhattan Community College, City University of New York, New York, NY, USA d Also at Center for High Energy Physics, Peking University, Beijing, China e Also at Center for Interdisciplinary Research and Innovation (CIRI-AUTH), Thessaloniki, Greece 123 Eur. Phys. J. C (2025) 85:738 Page 35 of 35 738 f Also at CERN, Geneva, Switzerland g Also at CMD-AC UNEC Research Center, Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan h Also at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland i Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain j Also at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece k Also at Department of Mathematical Sciences, University of South Africa, Johannesburg, South Africa l Also at Department of Physics, California State University, Sacramento, USA m Also at Department of Physics, King’s College London, London, UK n Also at Department of Physics, Stanford University, Stanford, CA, USA o Also at Department of Physics, Stellenbosch University, Stellenbosch, South Africa p Also at Department of Physics, University of Fribourg, Fribourg, Switzerland q Also at Department of Physics, University of Thessaly, Volos, Greece r Also at Department of Physics, Westmont College, Santa Barbara, USA s Also at Faculty of Physics, Sofia University, ’St. Kliment Ohridski’, Sofia, Bulgaria t Also at Hellenic Open University, Patras, Greece u Also at Henan University, Kaifeng, China v Also at Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia w Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain x Also at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany y Also at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Sofia, Bulgaria z Also at Institute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir, Morocco aa Also at Institute of Particle Physics (IPP), Toronto, Canada ab Also at Institute of Physics and Technology, Mongolian Academy of Sciences, Ulaanbaatar, Mongolia ac Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan ad Also at National Institute of Physics, University of the Philippines Diliman (Philippines), Quezon City, Philippines ae Also at Technical University of Munich, Munich, Germany af Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China ag Also at TRIUMF, Vancouver, BC, Canada ah Also at Università di Napoli Parthenope, Naples, Italy ai Also at University of Colorado Boulder, Department of Physics, Colorado, USA aj Also at University of the Western Cape, Cape Town, South Africa ak Also at Washington College, Chestertown, MD, USA al Also at Yeditepe University, Physics Department, Istanbul, Turkey ∗ Deceased 123 Cross-section measurements for the production of a W-boson in association with high-transverse-momentum jets in pp collisions at sqrts = 13 TeV with the ATLAS detector Abstract 1 Introduction 2 ATLAS detector 3 Data and simulated event samples 4 Event reconstruction 5 Event selection 6 Background estimation 7 Unfolding 8 Systematic uncertainties 9 Results 10 Conclusions Acknowledgements References