Measurements of W+W− production in decay topologies inspired by searches for electroweak supersymmetry

Eur. Phys. J. C (2023) 83:718 https://doi.org/10.1140/epjc/s10052-023-11508-9 Regular Article - Experimental Physics Measurements of W+W−production in decay topologies inspired by searches for electroweak supersymmetry ATLAS Collaboration CERN, 1211 Geneva 23, Switzerland Received: 1 July 2022 / Accepted: 9 October 2022 © CERN for the benefit of the ATLAS collaboration 2023 Abstract This paper presents a measurement of fiducial and differential cross-sections for W+W−production in proton–proton collisions at √s=13 TeV with the ATLAS experiment at the Large Hadron Collider using a dataset corresponding to an integrated luminosity of 139 fb−1. Events with exactly one electron, one muon and no hadronic jets are studied. The fiducial region in which the measurements are performed is inspired by searches for the electroweak production of supersymmetric charginos decaying to twolepton final states. The selected events have moderate values of missing transverse momentum and the ‘stransverse mass’ variable mT2, which is widely used in searches for supersymmetry at the LHC. The ranges of these variables are chosen so that the acceptance is enhanced for direct W+W−production and suppressed for production via top quarks, which is treated as a background. The fiducial cross-section and particle-level differential cross-sections for six variables are measured and compared with two theoretical SM predictions from perturbative QCD calculations. 1 Introduction Measurements of W+W−(referred to hereafter as WW)production provide important tests of the electroweak (EWK) gauge structure of the Standard Model (SM) of particle physics, and WW production is also an important background process in searches for physics beyond the SM (BSM physics). In searches for supersymmetry [1–6] (SUSY) where WW events are a significant background, a semidata-driven approach is often taken, that involves normalising the simulated Monte Carlo (MC) samples to data in a control region (CR), designed to be kinematically similar to the search regions but enriched in SM WW production. Significantdeviations of these scaling factorsfromunitysuggest mismodelling in the phase space targeted by the search, but it can be difficult to make comparisons with the level of agreement observed in precision SM measurements because e-mail: [email protected] the scaling factors refer to detector-level quantities which are subject to mis-measurement and inefficiency. Producing ‘unfolded’ particle-level measurements, which are corrected fortheseeffectsandcandirectlybecomparedwiththeprediction of a MC event generator, in event topologies associated withsearchresults is anovelwaytoaddress this whilstsimultaneously extending the programme of precision SM measurements at the LHC. The ATLAS experiment [7] has previously reported differential measurements of t¯ tand Z+jets production in regions related to a search for leptoquarks in dilepton+dijetevents[8].Thispaperpresentsthefirsteffortto measure WW production cross-sections in topologies associated with SUSY searches. Inclusiveandfiducial WW productioncross-sectionshave been measured in proton–proton (pp) collisions at √s= 7TeV[9,10], 8 TeV [11–13] and 13 TeV [14–17]atthe LHC, as well as in e+e−collisions at LEP [18] and in p¯pcollisions at the Tevatron [19–21]. This analysis complements existing ATLAS measurements of WW production at 13 TeV in 0-jet events [15] and in ≥1-jet events [16] by measuring differential cross-sections in a fiducial region kinematically close to the WW control region used in a previous search for electroweak production of supersymmetric charginos or sleptons [22]. That search targeted electroweak production of SUSY particles decaying into final states with two leptons (electrons or muons) and missing transverse momentum using 139 fb−1of pp collisions at 13 TeV collected during Run 2 of the LHC and is referred to hereafter as the ‘EWK 2+0-jets search’. In that search, WW production was the main background process and the associated theoretical uncertainties were among the dominant systematic uncertainties in the search regions. The present measurement targets event topologies with higher values of the dilepton invariant mass, meμ, and the magnitude of the missing transversemomentum, Emiss T,thanwereusedinpreviousmeasurements, and can thus be used to provide additional constraints on BSM physics, and probe the expected SM backgrounds for future searches. 0123456789().: V,-vol 123 718 Page 2 of 29 Eur. Phys. J. C (2023) 83:718 The WW →e±νμ∓νdecay channel is studied in events with no identified jets with a transverse momentum pT> 20 GeV and pseudorapidity |η|<2.4,1and with Emiss T between 60 and 80 GeV. Missing transverse momentum is calculated so as to represent the momentum imbalance in the plane transverse to the colliding beams. High values of Emiss Tcan be produced when weakly interacting neutral particles escape the detector unseen, and Emiss Tis thus an important variable in many BSM searches. This analysis also imposes requirements on the dilepton invariant mass that are more stringent than those in the 36 fb−1WW+0jet measurement [15]. The dominant background process is top-quark production (t¯ tand single-top Wt), which is estimated using the same data-driven method as was used in the EWK 2+0-jets search. The measurements are performed in a fiducial phase space close to the geometric and kinematic acceptance of the experimental analysis. Differential crosssection measurements are performed for six variables, which are the same as those considered in the 36 fb−1WW+0-jet measurement [15]: •The rapidity of the dilepton system, |yeμ|. •The azimuthal separation between the two leptons, |φeμ|. •The angular variable cos θ∗=|tanh(y(eμ)/2)|, which is longitudinally boost invariant and sensitive to the spin structure of the produced dileptons [23], and where y(eμ) is the difference between the electron and muon rapidities. •The transverse momentum of the leading lepton, plead  T. •The invariant mass of the dilepton system, meμ. •The transverse momentum of the dilepton system, peμ T. In this paper, |yeμ|,|φeμ|and cos θ∗are referred to collectively as ‘angular’ variables, as they probe angular correlations and are sensitive to the spin structure of the WW production system, and plead  T,meμand peμ Tare referred to collectively as ‘scale’ variables, as they characterise the energy scale of the process. The rest of this paper is structured as follows. First, Sect.2 describes the ATLAS detector and then Sect.3presents the analysis that is performed to measure the fiducial and differential cross-sections. This includes the data and MC samples used, the reconstructed-object definitions and event selections used to define the detector-level signal regions, and the SM background estimation, as well as the systematic uncer1ATLAS 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 upward. Cylindrical coordinates (r,φ) are used in the transverse plane, φbeing the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angle θas η=−ln tan(θ/2). tainties considered and the unfolding techniques used to correct detector-level information back to particle level. Finally, the results are reported in Sect.4, and Sect.5presents the conclusions. 2 ATLAS detector The ATLAS experiment at the LHC is a multipurpose particle detector with a forward–backward symmetric cylindrical geometry and a near 4πcoverage in solid angle. It consists of an inner tracking detector surrounded by a thin superconducting solenoid providing a 2T axial magnetic field, electromagnetic and hadron calorimeters, and a muon spectrometer. The inner tracking detector covers the pseudorapidity range |η|<2.5. It consists of silicon pixel, silicon microstrip, and transition radiation tracking detectors. Lead/liquid-argon(LAr)samplingcalorimetersprovideelectromagnetic (EM) energy measurements with high granularity.A steel/scintillator-tilehadroncalorimetercovers thecentral pseudorapidity range (|η|<1.7). The endcap and forwardregionsareinstrumentedwithLArcalorimetersforboth the EM and hadronic energy measurements up to |η|=4.9. The muon spectrometer surrounds the calorimeters and is based on three large superconducting air-core toroidal magnets with eight coils each. The field integral of the toroids ranges between 2.0 and 6.0T across most of the detector. The muon spectrometer includes a system of precision tracking chambers and fast detectors for triggering. A two-level trigger system is used to select events. The first-level trigger is implemented in hardware and uses a subset of the detector information to accept events at a rate below 100kHz. This is followed by a software-based trigger that reduces the accepted event rate to 1kHz on average depending on the data-taking conditions. An extensive software suite [24]is used 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 Analysis 3.1 Data and simulated event samples This analysis uses pp collision data at a centre-of-mass energy of √s=13 TeV collected by the ATLAS detector during the second data-taking run of the LHC, which took place between 2015 and 2018. After applying standard dataquality requirements for LHC and detector operations [25], this dataset corresponds to a total integrated luminosity of 139fb−1withanuncertaintyof1.7%[26],obtainedusingthe LUCID-2 sub-detector [27] for the primary luminosity measurements. Candidate events were selected by a trigger that 123 Eur. Phys. J. C (2023) 83:718 Page 3 of 29 718 requiredatleastoneelectron–muonpair[28,29].The triggerlevel thresholds for the pTof the leptons were 17 GeV for the electron and 14 GeV for the muon. The thresholds applied in the lepton offline selection ensured that trigger efficiencies are constant in the relevant phase space. Simulated MC event samples are used for the SM background estimates and to correct the signal distributions for detector effects. These were processed through a full simulation of the ATLAS detector [30] based on Geant4 [31] and reconstructed with the same algorithms as those used for the data. The generation of the simulated event samples includes the effect of multiple pp interactions per bunch crossing (pile-up), as well as changes in detector response because of interactions in bunch crossings before or after the onecontainingthe hardinteraction.Differencesbetweendata and simulation in the lepton reconstruction efficiency, energy scale, energy resolution and trigger efficiency [32,33], and in the b-tagging efficiency [34], are treated through correction factors that are derived from data and applied as weights to the simulated events. The MC samples are also reweighted so that the distribution of the average number of interactions per bunch crossing reproduces the observed distribution in the data. Simulated WW signal samples were produced by summing q¯qand gg-initiated samples. The q¯q-initiated WW signal was simulated at next-to-leading-order (NLO) accuracy in QCD using the Powheg Box v2 [35–37] generator interfaced to Pythia 8.186 [38] for the modelling of the parton shower, hadronisation, and underlying event, with parameter values set according to the AZNLO tune [39]. The CT10nlo parton distribution function (PDF) set [40] was used for the hard-scattering processes, whereas the CTEQ6L1 PDF set [41] was used for the parton shower [42]. The events were normalised to the cross-section calculated to next-to-next-to-leading order (NNLO) in QCD [43]. Loop-induced gg →WW →νν events were simulated at LO with up to one additional parton emission using Sherpa 2.2.2, with virtual QCD corrections provided by the Open Loops library [42,44–46]. The gg →WW process wasnormalised to its inclusiveNLO QCD cross-section [47]. An alternative sample of q¯q→WW events was simulated using Sherpa 2.2.2 [42,48] with matrix elements at NLO accuracy in QCD for up to one additional parton emission and at LO accuracy for up to three additional parton emissions. For the Sherpa q¯qand gg-initiated samples the NNPDF3.0nnlo set of PDFs was used [49], along with the dedicated set of tuned parton-shower parameters developed by the Sherpa authors. No alternative simulation is considered for the gg →WW process, which contributes only a small fraction of the signal. Table 1summarises the generators used for the SM backgrounds along with the relevant PDF sets, the set of tuned parameters used to configure the hadronisation and underlyTable 1 Simulated background event samples with the corresponding matrix element and parton shower (PS) generators, cross-section order in αsused to normalise the event yield, underlying-event tune and the generator PDF sets used. Where used, the label ‘V’ refers to a Wor Zboson Physics process Generator Parton shower Normalisation Tune PDF (generator) PDF (PS) t¯ tPowheg Box v2 [36,37,53,54]Pythia 8.230 [55] NNLO+NNLL [56]A14[57] NNPDF3.0nlo [49] NNPDF2.3lo [58] Single top (Wt)Powheg Box v2 [36,37,59]Pythia 8.230 NLO+NNLL [60,61] A14 NNPDF3.0nlo [49] NNPDF2.3lo VZ =WZ,ZZ Powheg Box v2 [36,37,62,63]Pythia 8.210 NLO [42,62,63] AZNLO [39]CT10nlo [40] CTEQ6L1 [64] ‘Others’: Higgs Powheg Box v2 [35–37]Pythia 8.212 [55] NNNLO+NNLL [65–71] AZNLO [39] PDF4LHC15nnlo [72] CTEQ6L1 VVV Sherpa 2.2.2 [42,48,73]Sherpa 2.2.2 NLO [42,48]Sherpa default [42] NNPDF3.0nnlo [49] NNPDF3.0nnlo t¯ t+HMadGraph5_aMC@NLO [74]Pythia 8.230 [55]NLO[65] A14 NNPDF3.0nlo NNPDF2.3lo t¯ t+VMadGraph5_aMC@NLO Pythia 8.210 [55]NLO[74,75] A14 NNPDF3.0nlo NNPDF2.3lo t¯ t+WW MadGraph5_aMC@NLO Pythia 8.186 [38]NLO[74] A14 NNPDF2.3lo NNPDF2.3lo tZ,t¯ tt¯ t,t¯ tt MadGraph5_aMC@NLO Pythia 8.230 NLO [74] A14 NNPDF3.0nlo NNPDF2.3lo Z/γ (→)+jets Sherpa 2.2.1 [48,73,76]Sherpa 2.2.1 NNLO [77]Sherpa default [76] NNPDF3.0nnlo NNPDF3.0nnlo 123 718 Page 4 of 29 Eur. Phys. J. C (2023) 83:718 ing event, and the cross-section order in αsused to normalise the event yields for these samples. This study uses the same simulated samples and groupings for the SM background processes as the EWK 2+0-jets search [22]. The ‘Others’ categorygroupstogetherprocessesthatproducesmallornegligible contributions to the signal regions of the search, and includes Drell–Yan, t¯ t+Vand Higgs boson production. Further information about the simulations of t¯ t, single-top (Wt), multiboson and boson-plus-jet processes can also be found in the relevant public ATLAS notes [42,50–52]. 3.2 Event reconstruction and selection Events are required to have at least one reconstructed vertex with at least two associated tracks with pT>400 MeV. When more than one vertex is reconstructed, the one with the highest p2 Tof associated tracks is taken to be the primary vertex. All final-state objects (electrons, muons and jets in this study) are required to satisfy ‘baseline’ criteria to ensure they are well-reconstructed and originate from the primary vertex, and additional ‘signal’ criteria are applied to define the objects used in the measurement. Baseline electrons are required to have pT>10 GeV, pseudorapidity |η|<2.47 and a longitudinal impact parameter z0, relative to the primary vertex, satisfying |z0sin θ|<0.5 mm; baseline muons must fulfill the same criteria except |η|<2.6. Electrons must satisfy a Loose likelihood-based identification requirement [32], while muons must satisfy the Medium identification requirements defined in Ref. [33]. Signal electrons are required to satisfy a Tight identification requirement [32] and the track associated with the signal electron is required to have |d0|/σ(d0)<5, where d0is the transverse impact parameter relative to the primary vertex and σ(d0)is its uncertainty, whilst for signal muons the associated track must have |d0|/σ(d0)<3. The signal-lepton isolation criteriausedintheEWK2+0-jets search [22] are also applied in this study. Hadronic jets are reconstructed from energy deposits in topological clusters of calorimeter cells [78,79] using the anti-ktalgorithm [80], as implemented in the FastJet package [81], with a radius parameter R=0.4. They are then calibrated by the application of a jet energy scale derived from 13 TeV data and simulation [82]. To reduce the effects of pile-up, for jets with |η|<2.5 and pT<120 GeV a significant fraction of the tracks associated with each jet must have an origin compatible with the primary vertex, as defined by the jet vertex tagger [83]. For jets with |η|>2.5 and pT<60 GeV, similar pile-up suppression is achieved through the forward jet vertex tagger [84]. Finally, events are rejected if they contain a jet that does not satisfy the jetquality requirements [85,86]; this removes events impacted by detector noise or non-collision backgrounds. Jets containing b-hadrons (‘b-jets’) are identified by the MV2c10 boosted decision tree algorithm [34], using quantities such astheimpactparametersofassociatedtracksalongwithwellreconstructed secondary vertices. A selection that provides 85% efficiency for tagging b-jets in simulated t¯ tevents is used in this study. Only jet candidates with pT>20 GeV and |η|<2.4 are considered,2althoughall jets with |η|<4.9are included in the calculation of missing transverse momentum and in the procedure to remove reconstruction ambiguities that could lead to double counting of baseline objects. This procedure is applied as follows: •jet candidates within R=(y)2+(φ)2=0.2of an electron candidate are removed; •jetswithfewerthan threetracks thatlie withinR=0.4 of a muon candidate are removed; •electrons and muons within R=0.4 of the remaining jets are discarded, to reject leptons from the decay of bor c-hadrons; •electron candidates are rejected if they are found to share an inner-detector track with a muon. The measurements are performed in events with exactly one signal electron and one signal muon with opposite electric charge and each satisfying pT>25 GeV, and a veto on additional baseline leptons and hadronic jets. The multiplicities of non-b-tagged jets and b-tagged jets are considered separately in the background estimation for this study: events with exactly one b-tagged jet with a veto on additional nonb-tagged jets are used to estimate and validate the top-quark background. Requirements are also placed on the missing transverse momentum (pmiss T), which has magnitude Emiss T. This is defined as the negative vector sum of the transverse momentaofall identified physicsobjects (electrons, photons, muons and jets), plus an additional ‘soft term’ to include lowmomentum tracks associated with the primary vertex but not with these physics objects. The Emiss Tvalue is adjusted for the calibration of the selected physics objects [87]. To access a region of phase space similar to the WW control region in the EWK 2+0-jets search, additional requirements are placed on the following variables in this study: •The invariant mass of the dilepton system, meμ> 100 GeV. •Themagnitudeofthemissingtransversemomentumvector, Emiss T∈[60,80]GeV. •The‘stransversemass’variable,mT2 ∈[60,80]GeV[88, 89], with mT2 defined as: mT2(pT,1,pT,2,pmiss T)=min qT,1+qT,2=pmiss T max[mT(pT,1,qT,1), mT(pT,2,qT,2)], 2Hadronic τ-lepton decay products are treated as jets. 123 Eur. Phys. J. C (2023) 83:718 Page 5 of 29 718 Table 2 Summary of the selection criteria used for the signal region in this study. The same selections are used at detector level and particle level Selection requirement Criteria Lepton flavour e±μ∓ Lepton pT>25 GeV Lepton |η|<2.47(e±),<2.6(μ∓) Lepton veto No additional electrons with pT>10 GeV, |η|<2.47 No additional muons with pT>10 GeV, |η|<2.6 meμ>100 GeV Jet veto No jets with pT>20 GeV, |η|<2.4 mT2 ∈[60,80] GeV Emiss T∈[60,80] GeV where mTis the transverse mass defined as mT= 2×|pT,a|×|pT,b|×(1−cos(φ)), and φ is the azimuthal angle between the particles with transverse momenta pT,aand pT,b. The vectors pT,1and pT,2are the transverse momenta of the two leptons, and qT,1 and qT,2satisfy pmiss T=qT,1+qT,2.ThemT2 variable was designed to be sensitive to the mass scales of pair-produced heavy particles that each decay semiinvisibly. The minimisation is performed over all the possible decompositions of pmiss Tinto two hypothetical invisible particles with momenta qT,1and qT,2.Fort¯ tor WW decays, assuming an ideal detector with perfect momentum resolution, mT2(pT,1,pT,2,pmiss T)has a kinematic endpoint at the mass of the Wboson [89]. The signal regions of the EWK 2+0-jets search required higher values, mT2 >100 GeV. In the EWK 2+0-jets search, the top-quark contamination in events with a jet veto was observed to increase with mT2 in the region mT2 ∈[60,100]GeV. To maximise WW purity, the control region required mT2 ∈[60,65]GeV and Emiss T∈[60,100]GeV with validation of the estimate being performed in events with mT2 ∈[65,100]GeV and Emiss T>60 GeV. Since mT2 is sensitive to the angular separation of the lepton pair, the mT2 range is widened for the analysis described in this paper to provide a broader phase space for measuring angular distributions. Since Emiss Tand mT2 are correlated, the Emiss Trange is tightened to reduce the top-quarkcontamination.Thesechangesincreasethenumber of events in the region used to perform the differential crosssection measurements without reducing the WW purity. The previously used requirement on the ‘object-based Emiss Tsignificance’ [90] is removed to simplify the definition of the fiducial region at particle level.3The definition of the signal region used for this measurement is summarised in Table 2. The same selections are used at particle level when defining the fiducial region used for the fiducial and differential cross-section calculations, as discussed in Sect.3.4. Figure 1shows detector-level comparisons between the data and the SM processes for the six variables that are unfolded to particle level in this study. 3.3 Background estimation The estimation of the SM backgrounds in this study uses the same techniques as those used in the EWK 2+0-jets search [22]. For the search, the SM backgrounds were classified into irreducible backgrounds from processes producing prompt leptons and reducible backgrounds containing one or more fake/non-prompt (FNP) leptons. The main irreducible backgrounds were SM diboson (WW,WZ,ZZ)and topquark (t¯ tand Wt) production, which were estimated from simulated events and normalised using a simultaneous likelihood fit to data in dedicated control regions (CRs). The yields and shapes of kinematic distributions of the relevant backgroundswere thenvalidatedina setofvalidationregions (VRs). Three CRs were used: CR-WW, targeting WW production; CR-VZ, targeting WZ and ZZ production, which were normalised by using a single parameter in the likelihood fit to the data; and CR-top, targeting t¯ tand single-topquark production, which were also normalised by using a single parameter in the likelihood fit to the data. Both CRVZ and CR-top require high mT2, and high values of Emiss T and its significance. CR-VZ uses same-flavour (dielectron and dimuon) events with a jet veto and requires the dilepton invariant mass to be consistent with an on-shell Zboson. CR-top requires one electron and one muon, one b-tagged jet with a veto on additional non-b-tagged jets. The remaining background from FNP leptons was estimated from data using the matrix method [91]. In this study, WW is the target signal process, with the remaining processes being backgrounds that are subtracted from the data prior to calculating the fiducial and differential cross-sections. The statistical interpretation for the search was performed using the HistFitter framework [92]. The likelihood for the ‘background-only’ fit used to constrain the background normalisation factors was a product of Poisson probability density functions describing the observed number of events in 3The ‘object-based Emiss Tsignificance’ helps to separate events with true Emiss T(arising from weakly interacting particles) from those where it is consistent with particle mismeasurement, resolution effects or identification inefficiencies. On an event-by-event basis, given the full event composition, the Emiss Tsignificance evaluates the p-value that the observed Emiss Tis consistent with the null hypothesis of zero real Emiss T, as further detailed in Ref. [90]. 123 718 Page 6 of 29 Eur. Phys. J. C (2023) 83:718 Fig. 1 Signal region detector-level distributions of |yeμ|(top left), |φeμ|(top right), cos θ∗(middle left), plead  T(middle right), meμ (bottom left), and peμ T(bottom right). Data are indicated by black markers along with the distribution for the WW signal and background SM processes. The last bin of each scale-variable distribution contains overflow events. The lower panels show the ratio of data to the total SM background prediction. The uncertainty bands shown include statistical and systematic uncertainties, excluding theory uncertainties in the WW signal. ‘FNP leptons’ refers to the background from fake/non-prompt leptons, calculated using the data-driven matrix method each CR and Gaussian distributions that constrain the nuisance parameters associated with the systematic uncertainties. Poisson distributions were used for MC statistical uncertainties. Further details of the likelihood fit can be found in the EWK 2+0-jets search paper [22]. After the fit, the normalisation factors returned for the WW,t¯ tand single-topquark, and WZ/ZZprocesses were 1.25±0.11, 0.82±0.06 and 1.18 ±0.05 respectively (where the errors include both statistical and systematic uncertainties), which for diboson processes were applied to MC samples scaled to NLO QCD cross-sections (the NNLO QCD cross-sections were not used in the original search paper because the samples were normalised to the data in the control regions). Good agreement, within about one standard deviation, was observed for the yields and kinematic distributions in all VRs when applying these normalisation factors and their corresponding uncertainties. The deviation of the WW normalisation factor from unity by more than 1σsuggests there is tension between the 123 Eur. Phys. J. C (2023) 83:718 Page 7 of 29 718 Fig. 2 Detector-level distributions of |yeμ|(top left), |φeμ|(top right), cos θ∗ (middle left), plead  T(middle right), meμ(bottom left), and peμ T(bottom right) in the top validation region. Data are indicated by black markers along with the distribution for the WW signal and background SM processes. The last bin of each scale-variable distribution contains overflow events. The lower panels show the ratio of data to the total SM background prediction. The uncertainty bands shown include statistical and systematic uncertainties, excluding theory uncertainties in the WW signal. ‘FNP leptons’ refers to the background from fake/non-prompt leptons, calculated using the data-driven matrix method SM and data in the parameter space probed by the search, and this is tested in the present study. In this study, the normalisation factors from the EWK 2+0-jets search are applied directly to the VZ (WZ/ZZ) and top (t¯ t,Wt)backgrounds that are subtracted from the data when performing the cross-section measurements described in Sect.3.4. The uncertainties in the normalisation factors are propagated through the calculation as discussed in Sect.3.5. The correlations and constraints that the likelihood fit imposes on the nuisance parameters describing the systematic uncertainties are not applied in this study; the systematic uncertainties are instead assumed to take their nominal values as discussed in Sect.3.5. This approach is designed to be conservative, but it has negligible impact on the results because no significant constraints were observed in the EWK 2+0-jets search. To validate the use of the original top normalisation factor from the EWK 2+0-jets search in the adjusted phase space of this study, an additional val123 718 Page 8 of 29 Eur. Phys. J. C (2023) 83:718 idation exercise is performed to check the modelling of the top-quark background in a region with the same selection as in Table 2but requiring exactly one b-tagged jet. Good agreement is observed across all six distributions considered for differential cross-section measurements, as shown in Fig.2. 3.4 Fiducial cross-section determination The differential cross-sections are measured in the fiducial phase space of the WW →e±νμ∓νdecay channel using particle-level implementations of the selection criteria defined in Table 2. The particle-level quantities associated with simulated events are calculated using the SimpleAnalysis [93] framework. The signal particle-level distributions produced by SimpleAnalysis have been validated against the Rivet [94] toolkit that enables further reinterpretation of SM measurements and validation of MC generators. The Rivet routine for this measurement is available on HepData [95]. Electrons and muons are required to originate from the hard interaction and not from hadron decays. Electrons and muons from leptonically decaying τ-leptons are included in the fiducial region. The momenta of photons that are emitted in a cone of size R=0.1 around the lepton direction and do not originate from hadron decays are added to form ‘dressed’ leptons. Particle-level jets are reconstructed using the anti-ktalgorithm [80] with radius parameter R=0.4fromvisiblestablefinal-stateparticles,excluding promptdressedleptons.Theparticle-levelmissingtransverse momentum is defined as the vectorial sum of the momenta of invisible particles in the event. For SM processes this is the sum of the neutrino momenta. The fiducial cross-section is calculated as: σWW =Nobs −Nbkg C·L, where Nobs is the observed number of data events in the fiducial region, Nbkg is the predicted number of background events, Lthe integrated luminosity, and Cis a correction factor to account for limited acceptances and detector inefficiencies. It is calculated using MC simulation as the number of simulated signal events passing the detector-level event selectiondividedbythenumberofeventsinthefiducialphase space. In this study, C=0.55 ±0.08 is applied, where the uncertainty comes from statistical, experimental and theoretical sources, as described in Sect.3.5. The differential cross-sections are calculated using the iterative Bayesian unfolding (IBU) technique [96,97]as implemented in the RooUnfold package [98]. This unfolding technique corrects the detector-level distributions of data (with the non-WW backgrounds subtracted) for bin-to-bin migrations due to the event reconstruction. It also applies fiducial corrections (corresponding to events that are reconstructed in the signal region but originate outside the fiducial region at particle level) and reconstruction efficiency corrections (due to events that lie inside the fiducial region at particle level but do not enter the signal region due to detector inefficiencies). The bins chosen for the differential measurements were optimised for a desired level of statistical uncertainty and to reduce the migration of events between particlelevel and detector-level bins. The number of iterations used in IBU is also optimised by considering the bias due to the assumed true distribution and the resulting statistical uncertainty of the measurement, with too many iterations generatinghighstatisticaluncertaintiesandtoofewiterationsbiasing the measurements towards the MC prediction. In this study, two iterations are chosen for cosθ∗and |φeμ|, three iterations are used for meμand plead  T, and four iterations are used for |yeμ|and peμ T. In addition to the bias tests (discussed in Sect.3.5) to measure any systematic effects due to the use of the signal WW MC sample in the unfolding procedure, several signal injection tests were performed using SUSY models for chargino-pair production that were on the edge of the exclusion sensitivity in the EWK 2+0-jets search. These are important checks of the validity of using these measurements to calculate constraints on BSM physics. Detector-level distributions of WW plus injected BSM signal were input to the unfolding calculation to test whether the particle-level WW plusBSM distributioncouldberecovered. Theunfoldingcalculation matched the expected WW plus BSM distributions for a range of SUSY models displaying different kinematics because of their different SUSY particle masses. The results of the BSM injection tests are available on HepData [95]. 3.5 Systematic uncertainties Systematic uncertainties in the WW differential crosssections measured in this study arise from experimental sources(whichimpactthesubtractednon-WWbackgrounds, and the calculation used to correct the signal for detector effects), uncertainties in the modelling of the top-quark background (which includes theoretical uncertainties, and uncertainties associated with the data-driven background estimate), and signal modelling. Statistical uncertainties associated with the MC samples used for the signal and background processes, and with the observed data distributions, also impact the unfolded distributions. The sources of experimental uncertainty considered in the EWK 2+0-jets search [22] are also considered in this study. The dominant experimental uncertainties are due to the calibration of the jet energy scale and resolution [79,82]. Additional uncertainties that arise from the lepton reconstruction efficiency, lepton energy scale and lepton energy resolution, and differences between the trigger efficiencies in data and simulation are grouped into the lepton uncertainties category. There are also uncertainties in the scale factors applied 123 Eur. Phys. J. C (2023) 83:718 Page 9 of 29 718 to the simulated samples to account for differences between data and simulation in the b-jet identification efficiency, and an uncertainty in pmiss Tassociated with the soft-term resolution and scale [87]. Finally, an uncertainty is assigned to the reweighting procedure (pile-up reweighting) applied to simulated events to match the distribution of the number of interactions per bunch crossing observed in data. Several sources of uncertainty in the modelling of t¯ t and Wt events are accounted for by varying the normalisation and shape of the subtracted backgrounds. For t¯ t production, uncertainties in the parton shower simulation are estimated from differences between samples generated with Powheg Box interfaced to either Pythia 8.186 or Herwig 7.04 [99,100]. Uncertainties in the modelling of initialand final-state radiation are estimated by comparing the nominal sample with two alternative samples generated with Powheg Box interfaced to Pythia 8.186 but with the radiation settings varied [101]. Finally, an additional uncertainty associated with the choice of event generator is estimated by comparing the nominal samples with samples generated with MadGraph5_aMC@NLO interfaced to Pythia 8.186 [102]. For single-top-quark production, an uncertainty is assigned to the treatment of the interference between the Wt and t¯ tsamples. This is done by comparing the nominal sample generated using the diagram removal method with a sample generated using the diagram subtraction method [101]. Of the systematic uncertainties considered in the EWK 2+0-jets search, uncertainties in the data-driven estimate of FNP leptons and theoretical uncertainties in the diboson WZ/ZZ backgrounds are not applied in this study because these processes contribute little to the subtracted backgrounds.Additionalsystematicuncertaintiesareapplied to the unfolding to account for the uncertainty in the normalisation of the top-quark and VZ backgrounds, although the VZ normalisation uncertainties are observed to be negligible. The luminosity uncertainty (1.7%) is applied to the subtracted backgrounds that are not estimated using data-driven techniques. Tests were performed to estimate the bias introduced by using information from the nominal signal MC sample in the unfolding procedure. This includes a datadriven test, whereby MC simulated WW signal events are reweighted at generator level to obtain better agreement between the detector-level signal and the backgroundsubtracted data. The nominal unfolding procedure is then applied to the reweighted detector-level signal distributions to check whether the reweighted particle-level distributions can be reproduced. The impact of theoretical uncertainties in the signal modelling is evaluated by using the detector-level signal distributions with the alternative Sherpa qq →WW signal sample introduced in Sect.3.1 as input to the nominal unfolding procedure, and comparing the result with the alternative particle-level signal distribution. In all tests the expected particle-level distributions were accurately recovered so no additional uncertainties were assigned to the unfolding procedure. Finally, statistical uncertainties from the data are calculated using pseudo-experiments that vary the data distributions according to their Poisson uncertainties in each bin, which are then passed through the unfolding calculation. Statistical uncertainties associated with the simulated MC samples are evaluated using a similar technique. 4 Results The measured fiducial cross-section for WW →e±νμ∓ν production in the phase space defined in Table 2is: σ(WW →e±νμ∓ν) =19.2±0.3(stat)±2.5(syst)±0.4(lumi)fb =19.2±2.6(total)fb. Table 3shows the relative impact of the categories of systematic uncertainties discussed in Sect.3.5 on the measured fiducial cross-section. The largest contribution is from the experimental jet uncertainty, which contributes a 12% uncertainty to the measured fiducial cross-section. The jet uncertainties are higher than in the previous ATLAS 13 TeV WW+0-jet measurement [15] and this can be attributed to the lower pT threshold used to define the jet veto. The measured value is compatible with the nominal predictions of 17.8 fb and 17.1 fb from Powheg Box v2 +Pythia 8.186 and Sherpa 2.2.2, respectively, where both are combined with Sherpa 2.2.2+Open Loops (LO+PS)for the gg-initiatedstates.Theratioofthemeasured cross-section to the nominal Powheg Box v2 +Pythia 8.186 prediction is 1.08. To compare this ratio with the Table 3 Breakdown of the relative uncertainties per category and the total uncertainty on the fiducial cross-section measurement Uncertainty source Uncertainty [%] Jets 11.7 Top modelling 4.8 Data statistics 3.1 Lepton modelling 1.9 Luminosity 1.7 Pile-up reweighting 1.2 Emiss Tmodelling 1.1 MC statistical uncertainties 0.5 Total systematic uncertainty 13.0 Total uncertainty 13.4 123 718 Page 16 of 29 Eur. Phys. J. C (2023) 83:718 C. Appelt18 , N. Aranzabal36 , V. Araujo Ferraz81a , C. Arcangeletti53 , A.T.H.Arce 51 , E. Arena91 , J.-F. Arguin107 , S. Argyropoulos54 , J.-H. Arling48 , A. J. Armbruster36 , O. Arnaez154 , H. 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Barends33a , T. Barillari109 , M.-S. Barisits36 ,J.Barkeloo 122 , T. Barklow142 , R. M. Barnett17a , P. Baron121 , D. A. Baron Moreno100 , A. Baroncelli62a , G. Barone29 , A. J. Barr125 , L. Barranco Navarro47a,47b , F. Barreiro98 , J. Barreiro Guimarães da Costa14a , U. Barron150 , M. G. Barros Teixeira129a ,S.Barsov 37 , F. Bartels63a , R. Bartoldus142 ,A.E.Barton 90 ,P.Bartos 28a , A. Basalaev48 , A. Basan99 , M. Baselga49 , I. Bashta76a,76b , A. Bassalat66,z,M.J.Basso 154 ,C.R.Basson 100 , R. L. Bates59 , S. Batlamous35e, J.R.Batley 32 , B. Batool140 , M. Battaglia135 , M. Bauce74a,74b , P. Bauer24 , A. Bayirli21a , J. B. Beacham51 , T. Beau126 , P. H. Beauchemin157 , F. Becherer54 , P. Bechtle24 , H. P. Beck19,p, K. Becker165 , C. Becot48 , A. J. Beddall21d , V. A. Bednyakov38 ,C.P.Bee 144 , L. J. Beemster15, T. A. Beermann36 , M. Begalli81b , M. Begel29 , A. Behera144 , J. K. Behr48 , C.BeiraoDaCruzESilva 36 , J. F. Beirer36,55 , F. Beisiegel24 ,M.Belfkir 115b , G. Bella150 , L. 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Bryngemark142 , T. Buanes16 , Q. Buat137 , P. Buchholz140 , A. G. Buckley59 , I. A. Budagov38,*, M. K. Bugge124 , O. Bulekov37 , B. A. Bullard61 , S. Burdin91 , C. D. Burgard48 , A. M. Burger40 , B. Burghgrave8, J.T.P.Burr 32 ,C.D.Burton 11 , J. C. Burzynski141 , E. L. Busch41 , V. Büscher99 , P. J. Bussey59 , J. M. Butler25 , C. M. Buttar59 , J. M. Butterworth95 , W. Buttinger133 , C. J. Buxo Vazquez106, A. R. Buzykaev37 , G. Cabras23b , S. Cabrera Urbán161 , D. Caforio58 , H. Cai128 ,Y.Cai 14a,14d , V.M.M.Cairo 36 , O. Cakir3a , N. Calace36 , P. Calafiura17a , G. Calderini126 , P. Calfayan67 , G. Callea59 , L. P. Caloba81b,D.Calvet 40 ,S.Calvet 40 ,T.P.Calvet 101 , M. Calvetti73a,73b , R. Camacho Toro126 , S. Camarda36 , D. Camarero Munoz98 , P. Camarri75a,75b , M. T. Camerlingo76a,76b , D. Cameron124 , C. Camincher163 , M. Campanelli95 , A. Camplani42 , V. Canale71a,71b , A. Canesse103 , M. Cano Bret79 , J. Cantero161 ,Y.Cao 160 , F. Capocasa26 , M. Capua43a,43b , A. Carbone70a,70b , R. Cardarelli75a , J. C. J. Cardenas8, F. Cardillo161 ,T.Carli 36 , G. Carlino71a , B. T. Carlson128,r, E. M. Carlson155a,163 , L. Carminati70a,70b , M. Carnesale74a,74b , S. Caron112 , E. Carquin136f ,S.Carrá 70a,70b , G. Carratta23a,23b ,J.W.S.Carter 154 , T.M.Carter 52 , M. P. Casado13,h, A. F. Casha154, E. G. Castiglia170 , F. L. Castillo63a , L. Castillo Garcia13 , V. Castillo Gimenez161 ,N.F.Castro 129a,129e , A. Catinaccio36 , 123 Eur. Phys. J. C (2023) 83:718 Page 17 of 29 718 J. R. Catmore124 , V. Cavaliere29 , N. Cavalli23a,23b , V. Cavasinni73a,73b , E. Celebi21a ,F.Celli 125 , M. S. Centonze69a,69b ,K.Cerny 121 , A. S. Cerqueira81a ,A.Cerri 145 , L. Cerrito75a,75b , F. Cerutti17a , A. Cervelli23b , S. A. Cetin21d , Z. Chadi35a , D. Chakraborty114 , M. Chala129f , J. Chan168 , W. S. Chan113 , W. Y. Chan152 , J. D. Chapman32 , B. Chargeishvili148b , D. G. Charlton20 , T. P. Charman93 , M. Chatterjee19 , S. Chekanov6, S. V. Chekulaev155a , G. A. 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Coelho Barrue129a , R. Coelho Lopes De Sa102 , S. Coelli70a , H. Cohen150 , A.E.C.Coimbra 70a,70b ,B.Cole 41 ,J.Collot 60 , P. Conde Muiño129a,129g , S. H. Connell33c , I. A. Connelly59 , E.I.Conroy 125 , F. Conventi71a,ad , H. G. Cooke20 , A. M. Cooper-Sarkar125 , F. Cormier162 , L. D. Corpe36 , M. Corradi74a,74b , E.E.Corrigan 97 , F. Corriveau103,v, A. Cortes-Gonzalez18 , M.J.Costa 161 , F. Costanza4, D. Costanzo138 , B.M.Cote 118 , G. Cowan94 , J.W.Cowley 32 , K. Cranmer116 , S. Crépé-Renaudin60 , F. Crescioli126 , M. Cristinziani140 , M. Cristoforetti77a,77b,c,V.Croft 157 , G. Crosetti43a,43b , A. Cueto36 , T. Cuhadar Donszelmann158 , H. Cui14a,14d ,Z.Cui 7, A. R. Cukierman142 , W. R. Cunningham59 , F. Curcio43a,43b , P. Czodrowski36 , M. M. Czurylo63b , M. J. Da Cunha Sargedas De Sousa62a , J. V. Da Fonseca Pinto81b ,C.DaVia 100 , W. Dabrowski84a , T. Dado49 , S. Dahbi33g ,T.Dai 105 , C. Dallapiccola102 ,M.Dam 42 ,G.D’amen 29 , V. D’Amico76a,76b ,J.Damp 99 , J. R. Dandoy127 , M. 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Zinsser63b , M. Ziolkowski140 ,L.Živkovi´c15 , A. Zoccoli23a,23b , K. Zoch56 , T. G. Zorbas138 ,O.Zormpa 46 ,W.Zou 41 , L. Zwalinski36 1Department of Physics, University of Adelaide, Adelaide, Australia 2Department of Physics, University of Alberta, Edmonton, AB, Canada 3(a)Department of Physics, Ankara University, Ankara, Türkiye; (b)Division of Physics, TOBB University of Economics and Technology, Ankara, Türkiye 4LAPP, Univ. Savoie Mont Blanc, CNRS/IN2P3, Annecy, France 5APC, Université Paris Cité, CNRS/IN2P3, Paris, France 6High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA 7Department of Physics, University of Arizona, Tucson, AZ, USA 8Department of Physics, University of Texas at Arlington, Arlington, TX, USA 9Physics 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 (a)Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China; (b)Physics Department, Tsinghua University, Beijing, China; (c)Department of Physics, Nanjing University, Nanjing, China; (d)University of Chinese Academy of Science (UCAS), Beijing, China 15 Institute of Physics, University of Belgrade, Belgrade, Serbia 16 Department for Physics and Technology, University of Bergen, Bergen, Norway 17 (a)Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA; (b)University of California, Berkeley, CA, USA 18 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany 19 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland 20 School of Physics and Astronomy, University of Birmingham, Birmingham, UK 21 (a)Department of Physics, Bogazici University, Istanbul, Türkiye; (b)Department of Physics Engineering, Gaziantep University, Gaziantep, Türkiye; (c)Department of Physics, Istanbul University, Istanbul, Türkiye; (d)Istinye University, Sariyer, Istanbul, Türkiye 22 (a)Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia; (b)Departamento de Física, Universidad Nacional de Colombia, Bogotá, Colombia 23 (a)Dipartimento di Fisica e Astronomia A. Righi, Università di Bologna, Bologna, Italy; (b)INFN Sezione di Bologna, Bologna, Italy 24 Physikalisches Institut, Universität Bonn, Bonn, Germany 25 Department of Physics, Boston University, Boston, MA, USA 26 Department of Physics, Brandeis University, Waltham, MA, USA 27 (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, 123 Eur. Phys. J. C (2023) 83:718 Page 25 of 29 718 Romania; (d)Physics Department, National Institute for Research and Development of Isotopic and Molecular Technologies, Cluj-Napoca, Romania; (e)University Politehnica Bucharest, Bucharest, Romania; (f)West University in Timisoara, Timisoara, Romania 28 (a)Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic; (b)Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 29 Physics Department, Brookhaven National Laboratory, Upton, NY, USA 30 Departamento de Física, y CONICET, Facultad de Ciencias Exactas y Naturales, Instituto de Física de Buenos Aires (IFIBA), Universidad de Buenos Aires, Buenos Aires, Argentina 31 California State University, Long Beach, CA, USA 32 Cavendish Laboratory, University of Cambridge, Cambridge, UK 33 (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, Quezon City, Philippines; (e)Department of Physics, University of South Africa, Pretoria, South Africa; (f)University of Zululand, KwaDlangezwa, Richards Bay, South Africa; (g)School of Physics, University of the Witwatersrand, Johannesburg, South Africa 34 Department of Physics, Carleton University, Ottawa, ON, Canada 35 (a)Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies-Université Hassan II, 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 36 CERN, Geneva, Switzerland 37 Affiliated with an Institute Covered by a Cooperation Agreement with CERN, Geneva, Switzerland 38 Affiliated with an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland 39 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA 40 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France 41 Nevis Laboratory, Columbia University, Irvington, NY, USA 42 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 43 (a)Dipartimento di Fisica, Università della Calabria, Rende, Italy; (b)INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Frascati, Italy 44 Physics Department, Southern Methodist University, Dallas, TX, USA 45 Physics Department, University of Texas at Dallas, Richardson, TX, USA 46 National Centre for Scientific Research “Demokritos”, Agia Paraskevi, Greece 47 (a)Department of Physics, Stockholm University, Stockholm, Sweden; (b)Oskar Klein Centre, Stockholm, Sweden 48 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany 49 Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany 50 Institut für Kernund Teilchenphysik, Technische Universität Dresden, Dresden, Germany 51 Department of Physics, Duke University, Durham, NC, USA 52 SUPA-School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK 53 INFN e Laboratori Nazionali di Frascati, Frascati, Italy 54 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany 55 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 56 Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland 57 (a)Dipartimento di Fisica, Università di Genova, Genoa, Italy; (b)INFN Sezione di Genova, Genoa, Italy 58 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 59 SUPA-School of Physics and Astronomy, University of Glasgow, Glasgow, UK 60 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France 61 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA 62 (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)Key Laboratory for Particle 123