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EUROPEAN ORGANISATION FOR NUCLEAR RESEARCH (CERN)

Submitted to: Nature Physics CERN-EP-2020-016

23rd April 2020

Observation of electroweak production of two jets

and a Z-boson pair with the ATLAS detector at the

LHC

The ATLAS Collaboration

Electroweak symmetry breaking explains the origin of the masses of elementary particles via their interactions with the Higgs field. Besides the measurements of the Higgs boson properties, the study of the scattering of massive vector bosons (with spin one) at the Large Hadron Collider allows to probe the nature of electroweak symmetry breaking with an unprecedented sensitivity. Among all processes related to vector-boson scattering, the electroweak production of two jets and a Z -boson pair is a rare and important one. This article reports on the first observation of this process using proton–proton collision data corresponding to an integrated luminosity of 139 f b−1recorded at a centre-of-mass energy of 13 TeV by the ATLAS detector. Two different final states originating from the decays of the Z -boson pair, one containing four charged leptons and the other containing two charged leptons and two neutrinos, are considered. The hypothesis of no electroweak production is rejected with a statistical significance of 5.5 σ, and the measured cross-section for electroweak production is consistent with the Standard Model prediction. In addition, cross-sections for inclusive production of a Z -boson pair and two jets are reported for the two final states.

© 2020 CERN for the benefit of the ATLAS Collaboration.

Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.

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1 Introduction

Electroweak symmetry breaking (EWSB) plays a central role in the Standard Model (SM) of particle physics, as it explains the origin of elementary particle masses via the interactions of each particle with the Higgs field. Following the discovery of the Higgs boson [1,2], the scrutiny of EWSB has become a primary focus of research at the Large Hadron Collider (LHC). In addition to direct measurements of the Higgs boson’s properties, the scattering of two massive vector bosons (VBS) offers another key avenue to probe the EWSB mechanism [3–5]. As a result of the delicate configuration of quantum field interactions for the SM VBS processes [3], the presence of the Higgs boson is predicted to exactly cancel out the otherwise diverging VBS amplitudes at high energies and prevent unitarity violation at the TeV scale. However, many possible extensions to the SM, such as Supersymmetry [6], Little Higgs [7], or Composite Higgs [8] models, offer alternative EWSB mechanisms that would manifest as deviations from the SM VBS production cross-sections at high energies. The study of the high-energy behaviour of VBS is therefore crucial in the attempt to quantify the exact nature of EWSB. Moreover, VBS offers a sensitive means to search for new phenomena related to anomalies in the weak-boson self-interactions [9], which are precisely predicted by the gauge theory in the SM.

The LHC provides an unprecedented opportunity to study the VBS process in proton–proton (pp) collisions, due to the high collision energies and large luminosity. At the LHC, VBS occurs when two vector bosons (V ) are radiated from the initial-state quarks in the colliding protons, and then scatter into another pair of vector bosons in the final state. The detector signature of VBS includes the decay products of the pair of outgoing bosons and a pair of hadronic jets ( j), which originate from the deflection of the initial-state quarks that radiated the weak bosons. The most promising channel to measure VBS is the purely electroweak (EW) production of VV j j (EW VV j j) in pp collisions, in which the contributions from the non-VBS processes (such as triboson production) could be sufficiently suppressed with a proper choice of kinematic selections. Thus far, the EW W±W±j j and W Z j j processes have been observed using LHC Run 2 data [10–12], and no significant deviations from the SM predictions have been found. The CMS Collaboration has searched for EW Z Z j j production using 36.1 fb−1of 13 TeV pp collision data, which was too small a sample to claim evidence [13] of this rarest EW VV j j process. Despite the small rate, EW Z Z j j production is of significant interest, due to the low background and the unique feature of a fully reconstructed final state when both of the Z bosons decay into charged leptons. The complete reconstruction of the final-state bosons provides maximal information in which the properties of the VBS process that are sensitive to EWSB can be probed. Furthermore, of all the measurements to date, VBS Z Z production is uniquely sensitive to the possible anomalous interaction between four Z bosons. This is forbidden at tree-level in the SM and the study of EW Z Z j j production is therefore a direct test of an important prediction of the electroweak theory. Finally, precision measurements of high-mass VBS Z Z production also allow an almost model-independent measurement of the Higgs boson width. The Higgs width is precisely predicted by the SM and is sensitive to new phenomena in the Higgs sector. However, the current methods to extract the Higgs width (using the gluon–gluon fusion production mechanism) are known to fail for certain types of new phenomena and the use of the VBS production mechanism was proposed in order to alleviate this problem [14].

This article reports the first observation of EW Z Z j j production using the complete set of 13 TeV pp collision data recorded by the ATLAS experiment during the LHC Run 2, as well as a measurement of the cross-sections of the inclusive (EW and non-EW) Z Z j j processes. The search is performed in two final states where both Z bosons decay leptonically: in final states with either four charged leptons and two jets (```` j j), or two charged leptons, two neutrinos and two jets (``νν j j). The definition of the signal

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region is optimised to suppress the reducible backgrounds coming from processes with different final states. Multivariate discriminants (MDs) are used to further separate the EW signal from the remaining backgrounds, including both the reducible ones and the irreducible non-EW Z Z j j process, which contains two strong interactions at the lowest order in perturbation theory and is referred to as QCD VV j j production. Figure1depicts the typical diagrams for both the EW VBS and QCD Z Z j j processes. These MDs exploit the characteristics of VBS production, such as a large separation in rapidity between the two jets (∆y( j j)) as well as a significant invariant mass of the jet pair (mj j). The production of Z Z j j in which one or both Z bosons decay into electrons or muons via τ-leptons is considered as signal, but it makes a negligible contribution to the selected event sample.

W/Z H W/Z q q0 Z Z q q0 Z H Z q q0 Z Z q q0 W W q q0 Z Z q q0 W W W q q0 Z Z q q0 q ¯ q Z Z g g q g Z Z g q g g Z Z ¯ q q g g Z Z g g H g g Z Z g g

Figure 1: Typical diagrams for the production of Z Z j j, including the relevant EW VBS diagrams (first row) and QCD diagrams (second row).

2 Experimental apparatus

The ATLAS experiment [15–17] at the LHC uses a multipurpose particle detector with a forward–backward symmetric cylindrical geometry and a near 4π coverage in solid angle. 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. Cylindrical 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). The angular distance between two physics objects is measured in units of ∆R ≡

p

(∆η)2+ (∆φ)2. The ATLAS

detector consists of an inner tracking detector (ID) surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field, electromagnetic (EM) and hadron calorimeters, and a muon spectrometer (MS). The ID covers the pseudorapidity range |η| < 2.5. It consists of silicon pixel, silicon microstrip, and transition radiation tracking detectors. Lead/liquid-argon (LAr) sampling calorimeters provide EM energy measurements with high granularity. A steel/scintillator-tile hadron calorimeter covers the central pseudorapidity range (|η| < 1.7). The endcap and forward regions are instrumented with LAr calorimeters for EM and hadronic energy measurements up to |η| = 4.9. The MS surrounds the calorimeters and is based on three large air-core toroidal superconducting magnets with eight coils each. The field integral

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of the toroids ranges between 2.0 and 6.0 Tm across most of the detector. The MS includes a system of precision tracking chambers and fast detectors for triggering. A two-level trigger system [18] is used to select events for offline analysis. The first-level trigger is implemented in hardware and uses a subset of the detector information. This is followed by the software-based high-level trigger, which reduces the event selection rate to about 1 kHz.

3 Data and simulation

The data for this analysis were recorded using single-lepton and multi-lepton triggers, corresponding to an integrated luminosity of 139 fb−1. The overall trigger efficiency for the inclusive Z Z j j events selected for this analysis ranges from 95% to 99%.

The EW Z Z j j production was modelled using the MadGraph5_aMC@NLO 2.6.1 event generator [19] with matrix elements (ME) calculated at leading order (LO) in perturbative QCD (pQCD) and with the NNPDF2.3LO [20] parton distribution functions (PDF). The QCD Z Z j j production was modelled using Sherpa 2.2.2 [21] with the NNPDF3.0NNLO [22] PDF, where events with up to one (three) outgoing partons were generated at NLO (LO) in pQCD. The production of Z Z j j from the gluon–gluon initial state with a four-fermion loop or with the exchange of a Higgs boson was generated separately. This process, referred to as the gg Z Z j j process, was modelled using Sherpa 2.2.2 and gg2VV [23] in the ```` j j and ``νν j j channels, respectively, and normalised to a calculation accurate to NLO in perturbative QCD. The leptonic decays of Z bosons are included in the simulation. Interference between EW and QCD Z Z j j was modelled with MadGraph5_aMC@NLO 2.6.1 calculated at LO and is treated as systematic on the predicted EW process. The effect is far smaller than the statistical uncertainty from data.

The production of WW j j and W Z j j with the subsequent leptonic decays of vector bosons were modelled with Sherpa 2.2.2. Diboson processes with the subsequent semileptonic decays were modelled using Powheg-Box v2 [24]. Triboson production was modelled using Sherpa 2.2.2. For top-quark pair production, Powheg-Box v2 was used. The production of single top quarks was simulated using Powheg-Box v1 [25–27]. The production of t ¯t in association with vector bosons (ttV ) was modelled with MadGraph5_aMC@NLO 2.3.3 for ttW , with Sherpa 2.2.1 and MadGraph5_aMC@NLO 2.3.3 for tt Z, and with MadGraph5_aMC@NLO 2.2.2 for ttWW. The Z + jets processes were modelled using Sherpa 2.2.1.

The above theoretical calculations are accurate to a given order in perturbation theory for partonic final states. To correctly model the hadronic final state that interacts with the detector, parton showering, hadronisation and underlying-event algorithms were applied to the partonic final states predicted from each calculation. Those were modelled with Pythia 8.186 [28] using the NNPDF2.3 [20] PDF and the A14 set of tuned parameters [29] for all the samples except for the ones from Sherpa, where those were simulated within the Sherpa program.

All samples were passed through a detailed simulation of the ATLAS detector [30] based on Geant4 [31], to produce predictions that can be directly compared with the data. Furthermore, simulated inelastic pp collisions were overlaid to model additional pp collisions in the same and neighbouring bunch crossings (pile-up). Simulated events were reweighted to match the pile-up conditions in the data. All simulated events were processed using the same reconstruction algorithms as used in data.

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4 Event selection

The selection of the ```` j j and ``νν j j events relies on multiple physics objects, including electrons, muons, and jets. The signal region (SR) is defined with a set of selection criteria, which were optimised to preferentially select the EW Z Z j j events.

Events are first required to have a collision vertex associated with at least two tracks each with transverse momentum (pT) > 0.5 GeV. The vertex with the highest sum of p2Tof the associated tracks is referred to as

the primary vertex.

Muons are identified by tracks reconstructed in the MS and are matched to tracks reconstructed in the ID. In the region 2.5 < |η| < 2.7, muons can also be identified by tracks from the MS alone, and these are called stand-alone muons. Identified muons are required to have pT > 7 GeV. In the MS gap region

(|η| < 0.1) muons are identified by an ID track with pT > 15 GeV associated with a compatible calorimeter

energy deposit, and are called calorimeter-tagged muons. Muons are required to have |η| < 2.7 (2.5) and satisfy the ‘loose’ (‘medium’) identification criterion [32] in the ```` j j (``νν j j) channel. Electrons are reconstructed from energy deposits in the electromagnetic calorimeter matched to a track in the ID. Candidate electrons must satisfy the ‘loose’ (‘medium’) identification criterion [33] in the ```` j j (``νν j j) channel, and have pT > 7 GeV and |η| < 2.47. All electrons and muons must be isolated and satisfy the

‘FixedCutLoose’ and ‘loose’ isolation criteria [32,33] in the ```` j j and ``νν j j channels, respectively. Furthermore, electrons (muons) are required to have associated tracks satisfying |d0/σd0| < 5 (3) and

|z0× sin θ| < 0.5 mm, where d0is the transverse impact parameter relative to the beam line, σd0 is its

uncertainty, and z0is the longitudinal impact parameter relative to the primary vertex.

Jets are reconstructed from clusters of calorimeter energy deposits using the anti-kt algorithm [34,35] with radius parameter R = 0.4. The jet energy scale is calibrated using simulation and further corrected with in situ methods [36]. A jet-vertex tagger [37] is applied to jets with pT < 60 GeV and |η| < 2.4 to

preferentially suppress jets that originated from pile-up. In addition, jets containing b-hadrons (b-jets) are identified using a multivariate b-tagging algorithm [38]. The chosen b-tagging algorithm has an efficiency of 85% for b-jets and a rejection factor of 33 against light-flavour jets.

An overlap-removal procedure detailed in Ref. [39] is applied to the selected leptons and jets in the ``νν j j channel, to avoid ambiguities in the event selection and in the energy measurement of the physics objects. A similar approach is adopted in the ```` j j channel, except that leptons are given a higher priority to be kept when overlapping with jets, to enhance the selection efficiency.

The neutrinos in the ``νν j j final state do not interact with the ATLAS detector and cannot be reconstructed. Their presence is identified using the missing transverse momentum vector (E®Tmiss), which is computed as the negative of the vector sum of transverse momenta of all the leptons and jets, as well as the tracks originating from the primary vertex but not associated with any of the leptons or jets [40]. The statistical significance of ETmiss(ETmiss-significance) is calculated using resolution information of physics objects used in the ETmissreconstruction [41].

In the ```` j j channel, quadruplets of leptons are formed by selecting two opposite-sign, same-flavour (OSSF) lepton pairs, where the leptons are required to be separated from each other by ∆R > 0.2. At most one muon is allowed to be a stand-alone or calorimeter-tagged muon, and the three leading leptons must have pT > 20, 20 and 10 GeV, respectively. All the `+`

pairs are required to have an invariant mass (m`+`) greater than 10 GeV, to reject events from low-mass resonances. If multiple quadruplets are found,

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mass, |m`+`−− mZ|+ |m`0+`0−− mZ|, is selected. The dilepton masses are required to be within the range

66–116 GeV.

In the ``νν j j channel, candidate events are required to have one OSSF lepton pair with m`+`− in the range

from 80 to 100 GeV, and the leading (sub-leading) lepton must have pT > 30 (20) GeV. Events with

b-tagged jets or additional leptons (pT > 7 GeV and satisfying the ‘loose’ requirement) are rejected to reduce

the background contributions from t ¯t and W Z events. Events are required to have an ETmiss-significance greater than 12 to suppress the background from Z + jets processes.

In both channels, the two jets with the highest pTand satisfying a negative product of jet rapidities (yj1× yj2)

are selected. In the ```` j j channel the jets are required to have pT > 30 (40) GeV in the |η| < 2.4

(2.4 < |η| < 4.5) region, while in the ``νν j j channel the leading (sub-leading) selected jet is required to have pT> 60 (40) GeV. Finally, to further suppress background contributions, mj jis required to be greater

than 300 (400) GeV in the ```` j j (``νν j j) channel, and ∆y( j j) is required to be greater than two. The harsher jet requirement in the ``νν j j channel is optimised to suppress the more significant contamination from reducible backgrounds.

After selection, the resulting observed and expected yields are listed in Table1, where in total 127 (82) data events are selected in the ```` j j (``νν j j) channel. The expected event yields from each process are summed together and the interference effects between the EW and QCD processes are taken as an additional uncertainty in the EW Z Z j j predictions. Several control regions (CRs), defined with dedicated selections optimised to enhance the fractions of background events, are defined to constrain the contributions from the various background processes. The kinematic distributions from both channels, including the mj j

spectra in the ```` j j SR, QCD Z Z j j CR and ``νν j j SR, as well as the invariant mass of the four-lepton system (mZ Z) in the ```` j j SR, are presented in Figure2. The background estimates, dedicated CRs and various sources of experimental and theoretical uncertainties are discussed in the following two sections. The number of events in data is found to be consistent with the SM prediction including the EW Z Z j j contribution.

Table 1: Observed data and expected event yields in 139 fb−1of data in the ```` j j and ``νν j j signal regions. All the minor backgrounds are summed together as ‘Others’. Uncertainties in the predictions include both the statistical and systematic components. Process ```` j j ``νν j j EW Z Z j j 20.6 ± 2.5 12.3 ± 0.7 QCD Z Z j j 77 ± 25 17.2 ± 3.5 QCD gg Z Z j j 13.1 ± 4.4 3.5 ± 1.1 Non-resonant-`` – 21.4 ± 4.8 W Z 22.8 ± 1.1 Others 3.2 ± 2.1 1.2 ± 0.9 Total 114 ± 26 78.4 ± 6.2 Data 127 82

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0 100 200 300 400 500 600 700 800 [GeV] jj m 0.5 0.75 1 1.25 1.5 Data / Pred. 0 5 10 15 20 25 30 35 40 Events / 40 GeV ATLAS -1 = 13 TeV, 139 fb s ℓℓℓ ℓjj QCD Control Region Data ZZ(EW) ZZ(QCD) ggZZ Others Uncertainty (a) 500 1000 1500 2000 2500 [GeV] jj m 0.5 0.75 1 1.25 1.5 Data / Pred. 0 10 20 30 40 50 60 Events / 200 GeV ATLAS -1 = 13 TeV, 139 fb s ℓℓℓ ℓjj Signal Region Data ZZ(EW) ZZ(QCD) ggZZ Others Uncertainty (b) 500 1000 1500 2000 2500 [GeV] jj m 0.5 0.75 1 1.25 1.5 Data / Pred. 0 5 10 15 20 25 30 35 40 Events / 200 GeV ATLAS -1 = 13 TeV, 139 fb s ℓℓννjj Signal Region Data ZZ(EW) ZZ(QCD) ggZZ WZ NonRes Others Uncertainty (c) 200 300 400 500 600 700 800 [GeV] ZZ m 0.5 0.75 1 1.25 1.5 Data / Pred. 0 5 10 15 20 25 30 35 40 Events / 30 GeV ATLAS -1 = 13 TeV, 139 fb s ℓℓℓ ℓjj Signal Region Data ZZ(EW) ZZ(QCD) ggZZ Others Uncertainty (d)

Figure 2: Observed and expected mj j distributions in the (a) ```` j j QCD CR and the (b) ```` j j and (c) ``νν j j signal regions, as well as the mZ Z distribution in the (d) ```` j j signal region. The error bands include the expected experimental and theoretical uncertainties. The contributions from the QCD and EW production of Z Z j j events are scaled by 0.96 and 1.35, respectively, which correspond to the observed normalisation factors in the statistical fit to the combined channel (Table2). All the minor backgrounds are summed together as ‘Others’. The last bin includes the overflow events. The open arrows represent the out-of-range markers.

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5 Background estimation

The backgrounds arise from two kinds of processes, one with final-state particles that are the same as those in the signal process, and the other one where one or more lepton candidates are misidentified in data. In the ```` j j channel, the largest background arises from the QCD Z Z j j process, which has an identical final state to the EW Z Z j j process. The kinematic properties of the QCD Z Z j j background are estimated using the simulated events described in Section3. However, the simulation is normalised to data in a dedicated EW-suppressed control region, defined by reversing either the mj jor the ∆y( j j) selection criteria. Furthermore, the modelling of the kinematic properties of the QCD Z Z j j simulation is validated in an additional EW-suppressed CR, which is defined by requiring the centrality to be larger than 0.5 for at least one of the selected Z bosons. The centrality is a variable that estimates the position of a Z -boson with respect to the rapidity span of the two outgoing hadronic jets [42]. Good agreement between data and simulation is found for most kinematic distributions. The impact on the signal extraction of a potential mismodelling of the mj jdistribution in the QCD Z Z j j simulation (seen in previous analyses [43–45]) is explicitly tested, by reweighting the QCD Z Z j j simulation in the SR using an mj j-based correction factor that is defined as the ratio of data to simulation in the EW-suppressed CR at high centrality. The signal extracted using the reweighted and nominal QCD Z Z j j simulations are found to be in agreement when considering the statistical uncertainty on the mj j-based correction itself.

Small background contributions from Z + jets, top-quark and W Z j j processes may contain misidentified leptons and are estimated using a method similar to that described in Ref. [46], where the lepton misidentification is measured in data regions with enhanced contributions from Z + jets and top-quark processes. Minor background contributions from triboson and ttV production are estimated from simulation. All of those backgrounds collectively yield an estimated contribution of about 3% to the selected data sample in the ```` j j channel.

In the ``νν j j channel, the normalisation and kinematic properties of QCD Z Z j j processes are modelled from simulation due to a large contamination from other processes, which are considered in dedicated CRs. The W Z j j background, with one lepton produced outside of the detector acceptance, is estimated using a data CR defined by requiring three selected leptons and a looser event selection, following the methodology explained in Ref. [47]. The simulation is found to overestimate the W Z j j contribution by 15% in this CR, and therefore the W Z j j yield in the SR is scaled by 0.85. The W Z j j distribution of the MD in the SR is evaluated from simulation, with the contributions from EW W Z j j processes scaled by 1.77, corresponding to the difference between data and simulation observed in a previous analysis, in a similar phase space [11], where the overall normalisation factor is found to be consistent with the one derived in this article. The WW j j and t ¯t processes are referred to as the non-resonant-`` backgrounds, since they contain a lepton pair not originating from a Z or γ∗boson. The non-resonant-`` background is estimated using a CR defined in data by applying the same selection as in the SR with the exception that an eµ pair is required, following the methodology explained in Ref. [47]. The MD distribution in the SR for the non-resonant-`` process is estimated from simulation.

The Z + jets background is largely suppressed, and the yield is evaluated by extrapolating the low Emiss

T -significance region distribution in data to the high E miss

T -significance region using an exponential

function, while the MD distribution in the SR is modelled by simulation. Small background contributions from triboson and ttV production are modelled with simulation. All of those backgrounds collectively yield an estimated contribution of about 1% to the selected data sample in the ``νν j j channel.

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6 Experimental and theoretical uncertainties

Systematic uncertainties associated with the prediction of each signal and background process are estimated. These uncertainties are either experimental or theoretical in nature, due to imperfect modelling of the detector in the simulation or the underlying physics of each process.

The major experimental uncertainties originate from the luminosity uncertainty, the energy measurements of leptons and jets, and the lepton reconstruction and selection efficiencies. Smaller experimental uncertainties are also considered, such as those due to the trigger selection efficiency, the calibration of the ETmisssoft-term, the pile-up correction, and the b-jet identification efficiency. Overall, the total experimental uncertainty in the predicted yields is about 10% (5%) in the ```` j j (``νν j j) channel, dominated by the jet and lepton calibration. The uncertainty in the combined 2015–2018 integrated luminosity is 1.7% [48], obtained using the LUCID-2 detector [49] for the primary luminosity measurements.

In addition, the uncertainties in the predicted yields from non-Z Z j j backgrounds are dominated by the statistical uncertainties from data in the dedicated CRs, which are about 15% for the overall backgrounds. The W Z j j shape uncertainty originates from experimental and theoretical uncertainties as well as from the uncertainty in the quoted EW W Z j j cross-section measurement. The non-resonant-`` shape uncertainty is estimated by comparing the MD distributions from data and simulation. In addition, an uncertainty is assigned to the QCD Z Z j j processes by comparing the MD distributions in low and high pile-up conditions, to account for a potential mismodelling of pile-up in simulation. The differences in the predicted yields in different MD regions are below 10% except in the last bin in the QCD Z Z j j CR where it reaches 50% due to the statistical uncertainty of the simulated events.

The theoretical uncertainties of the EW and QCD Z Z j j processes include the uncertainties from PDFs, QCD scales, αS, parton showering and hadronisation. The PDF uncertainty is estimated following

the PDF4LHC [50] procedure. The effect of the QCD scale uncertainty is estimated by varying the renormalisation and factorisation scales following the procedure described in Ref. [51]. The parton showering and hadronisation uncertainty is estimated by comparing the nominal Pythia 8 parton showering with the alternative Herwig 7 [52,53] algorithm. The effect of the αSuncertainty is estimated by varying

the αSvalue by ±0.001. The total theoretical uncertainty in the reconstructed event yields for the EW

(QCD) Z Z j j process is estimated to be about 10% (30%). The interference effect between the EW and QCD processes is checked with MadGraph5_aMC@NLO 2.6.1, and found to make a relative contribution (to the EW signal) varying from 10% to 2% in the different MD regions, much smaller than the statistical uncertainty from data. This effect is taken as an uncertainty in the EW Z Z j j predictions. An additional uncertainty in the modelling of the QCD Z Z j j process is considered by comparing the predicted MD shapes from Sherpa to MadGraph5_aMC@NLO 2.6.1 at particle level in the case where two partons are explicitly required at LO in the ME calculation. The differences in the predicted yields in different MD regions range from −30% to +20%.

7 Observation of electroweak Z Z j j

To separate the EW Z Z j j processes from their backgrounds, MDs based on the Gradient Boosted Decision Tree algorithm [54] are trained with simulated events using the TMVA framework [55]. In each channel, a single MD is trained in the SR, which uses event kinematic information sensitive to the characteristics of the EW signal. The resulting MDs provide an optimal separation of the EW Z Z j j signal and the

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backgrounds, where signal-like (background-like) events are featured in the high (low) MD region. In the ```` j j channel, twelve input variables are used: mj j, ∆y( j j), pTof the leading and sub-leading jets (p

j1 T

and pTj2), yj1× yj2, pTof the Z boson reconstructed from the charged-lepton pair with the mass closer to the

Z-boson mass, rapidity of both Z bosons (yZ1and yZ2), pT and mass of the four-lepton system, pTof the

third lepton, pTof the Z Z j j system divided by the scalar pTsum of Z bosons and two jets (ST). Thirteen

input variables are utilised in the ``νν j j channel: mj j, ∆y( j j), yj1× yj2, pTj2, ETmiss, ETmiss-significance, ST, pseudorapidity and azimuthal angle differences between two charged leptons (∆η, ∆φ), ∆R, invariant mass of the charged-lepton pair, and pTof leading and sub-leading leptons. The jet-related information

provides the greatest sensitivity in the ```` j j channel, while both the jet-related and the dilepton-related variables are important in the ``νν j j channel.

In the ```` j j channel the MD distributions in both the QCD Z Z j j CR (Figure3(a)) and the SR (Figure3(b)) are used in the statistical fit, while only the MD distribution in the SR (Figure3(c)) is fitted in the ``νν j j channel. The binning of MD distributions in the SRs is chosen to maximise the sensitivity of detecting EW Z Z j j events. In the ```` j j channel, the normalisation of QCD Z Z j j production (µ```` j jQCD ) is varied simultaneously in the fit in the SR and QCD CR. The ratio of measured fiducial cross-section to the SM prediction for EW Z Z j j production (µEW) is taken as the parameter of interest.

To examine the compatibility of the data and the signal-plus-background hypothesis, a test statistic is defined using the profile likelihood ratio method [56]. The statistical tests are performed in both the individual ```` j j and ``νν j j channels, and in the combined channel. The experimental systematic uncertainties are considered as correlated in all the bins and regions whenever applicable. The theoretical uncertainties for Z Z j j production are treated as uncorrelated between the ```` j j and ``νν j j channels, due to the different fiducial volume definitions. The QCD scale uncertainty for QCD Z Z j j production can be assessed in various ways in terms of correlations between different fitted regions and is conservatively treated as uncorrelated between the SR and the QCD CR in the ```` j j channel. Furthermore, the generator modelling uncertainty for QCD Z Z j j production is treated as uncorrelated between the low and high MD regions. The results are shown in Table2. From the combined channel, the observed µEWis 1.35 ± 0.34, while

µ```` j j

QCD is determined to be 0.96 ± 0.22. The statistical component accounts for 88% of the total uncertainty

in µEW. The probability that the background can randomly fluctuate to produce a measured likelihood ratio

at least as signal-like as the excess observed in the data is 1.9 × 10−8, leading to the observation of EW Z Z j j production. Correspondingly, with a normalised Gaussian distribution, the background-only hypothesis is rejected at 5.5 σ (4.3 σ) from the data (expectation). The EW Z Z j j cross-section in the combined fiducial volume, formed by combining the respective fiducial regions in the ```` j j and ``νν j j channels, is found to be 0.82 ± 0.21 fb, calculated as µEWmultiplied by the SM prediction of 0.61 ± 0.03 fb.

Table 2: Observed µEWand µ ```` j j

QCD , as well as the observed and expected significance of EW Z Z j j processes

from the individual ```` j j and ``νν j j channels, and the combined fits. The full set of statistical and systematic uncertainties is included.

µEW µ```` j j

QCD Significance Obs. (Exp.)

```` j j 1.5 ± 0.4 0.95 ± 0.22 5.5 (3.9) σ

``νν j j 0.7 ± 0.7 – 1.2 (1.8) σ

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1 − −0.8−0.6 −0.4−0.2 0 0.2 0.4 0.6 0.8 1 MD 0.5 0.75 1 1.25 1.5 Data / Pred. 0 10 20 30 40 50 60 70

Events / Bin ATLAS

-1 = 13 TeV, 139 fb s ℓℓℓ ℓjj QCD Control Region Data ZZ(EW) ZZ(QCD) ggZZ Others Uncertainty (a) 1 − −0.8−0.6 −0.4−0.2 0 0.2 0.4 0.6 0.8 1 MD 0.5 0.75 1 1.25 1.5 Data / Pred. 0 2 4 6 8 10 12 14 16 18 20 22

Events / 0.125 ATLASs = 13 TeV, 139 fb-1

ℓℓℓ ℓjj Signal Region Data ZZ(EW) ZZ(QCD) ggZZ Others Uncertainty (b) 1 − −0.8−0.6 −0.4−0.2 0 0.2 0.4 0.6 0.8 1 MD 0.5 0.75 1 1.25 1.5 Data / Pred. 0 5 10 15 20 25 30 35 Events / Bin ATLAS -1 = 13 TeV, 139 fb s ℓℓννjj Signal Region Data ZZ(EW) Others ZZ(QCD) WZ NonRes ggZZ Uncertainty (c)

Figure 3: Observed and expected multivariate discriminant distributions after the statistical fit in the (a) ```` j j QCD CR, and in the (b) ```` j j and (c) ``νν j j signal regions. The error bands include the experimental and theoretical uncertainties, as well as the uncertainties in µEWand µ

```` j j

QCD . All the minor backgrounds are summed together as

‘Others’. The statistical uncertainties of the data are shown as error bars. The open arrows represent the out-of-range markers.

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8 Measurement of fiducial cross-sections

In addition to the observation of the EW Z Z j j process, the cross-sections for the production of inclusive Z Z j j are also measured in the ```` j j and ``νν j j channels. This measurement, corrected for detector inefficiency and resolution without any further theoretical interpretation, provides the most model-independent results. The cross-sections are measured following the formula σ = (Ndata− Nbkg)/(L × C),

where Ndataand Nbkgrefer to the number of events in data and the expected number of background events

from non-Z Z j j processes respectively, L refers to the integrated luminosity, and C is the correction factor to extrapolate the QCD and EW Z Z j j events from detector level to the fiducial volume, calculated as the ratio of the number of Z Z j j events passing the detector-level event selection to the number of events selected in the fiducial volume.

The definitions of the fiducial volumes closely follow the detector-level selections, using ‘particle-level’ electrons, muons, ETmissand jets, which are reconstructed in simulation from stable final-state particles, prior to their interactions with the detector, following the procedure described in Ref. [51]. In the ```` j j channel, the dilepton mass requirement is relaxed (relative to the detector-level selection) to the wider range 60–120 GeV to ensure compatibility with the previous CMS publication [13]. In the ``νν j j channel, both the electrons and muons are selected in the |η| < 2.5 region to simplify the charged-lepton selections. In addition, no requirement is placed on the ETmiss-significance due to the complexity of defining this variable at particle level; however, the particle-level ETmiss is required to be greater than 130 GeV. All the other kinematic selection requirements have the same definition as the detector-level ones.

The C-factors are found to be (69.9 ± 3.1)% in the ```` j j channel, and (21.6 ± 1.2)% in the ``νν j j channel, where the errors reflect the total uncertainties. The smaller C-factor in the ``νν j j channel is due to the large event migration effect in events passing the ETmissselection requirement at particle level that have a small ETmiss-significance at detector level. The measured and predicted fiducial cross-sections are presented in Table3. Uncertainties from different sources are presented explicitly. The data statistical uncertainty dominates, while the experimental uncertainties related to jet measurements and the background estimates are the major systematic uncertainties in the ```` j j and ``νν j j channels, respectively. The measurements of 1.27 ± 0.14 fb for the ```` j j channel and 1.22 ± 0.35 fb for the ``νν j j channel are compatible with the SM predictions. The measurement precision in the ```` j j channel is better than the accuracy of the theoretical prediction.

Table 3: Measured and predicted fiducial cross-sections in both the ```` j j and ``νν j j channels for the inclusive Z Z j j processes. Uncertainties due to different sources are presented explicitly, including the one from the statistical uncertainty of the data and simulated samples (stat), the one from the theoretical predictions (theo), the experimental ones due to the lepton and jet calibrations (exp), the ones from background estimates (bkg), and the one from the luminosity (lumi).

Measured fiducial σ [fb] Predicted fiducial σ [fb]

```` j j 1.27 ± 0.12(stat) ± 0.02(theo) ± 0.07(exp) ± 0.01(bkg) ± 0.03(lumi) 1.14 ± 0.04(stat) ± 0.20(theo) ``νν j j 1.22 ± 0.30(stat) ± 0.04(theo) ± 0.06(exp) ± 0.16(bkg) ± 0.03(lumi) 1.07 ± 0.01(stat) ± 0.12(theo)

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9 Conclusion

The rare electroweak production of Z Z j j events is observed using 139 fb−1of √

s = 13 TeV proton–proton collision data collected with the ATLAS detector. The events are identified within a large hadron-collision background, owing to an optimised analysis strategy as well as the excellent performance of the LHC and the ATLAS detector. The measurement of the cross-section for electroweak boson scattering producing a pair of Z bosons is consistent with Standard Model predictions. This result is a milestone in studies of electroweak VV j j production at the LHC, and an important contribution to understanding the nature of electroweak symmetry breaking in the Standard Model.

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Acknowledgements

We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.

We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRT, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russia Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, Compute Canada and CRC, Canada; ERC, ERDF, Horizon 2020, Marie Skłodowska-Curie Actions and COST, European Union; Investissements d’Avenir Labex, Investissements d’Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya and PROMETEO Programme Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), 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. [57].

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A. Bitadze101, C. Bittrich48, K. Bjørke134, T. Blazek28a, I. Bloch46, C. Blocker26, A. Blue57, U. Blumenschein93, G.J. Bobbink120, V.S. Bobrovnikov122b,122a, S.S. Bocchetta97, A. Bocci49, D. Boerner46, D. Bogavac14, A.G. Bogdanchikov122b,122a, C. Bohm45a, V. Boisvert94, P. Bokan53,172, T. Bold84a, A.E. Bolz61b, M. Bomben136, M. Bona93, J.S. Bonilla132, M. Boonekamp145, C.D. Booth94, H.M. Borecka-Bielska91, L.S. Borgna95, A. Borisov123, G. Borissov90, J. Bortfeldt36, D. Bortoletto135, D. Boscherini23b, M. Bosman14, J.D. Bossio Sola104, K. Bouaouda35a, J. Boudreau139,

E.V. Bouhova-Thacker90, D. Boumediene38, S.K. Boutle57, A. Boveia127, J. Boyd36, D. Boye33c,al, I.R. Boyko80, A.J. Bozson94, J. Bracinik21, N. Brahimi102, G. Brandt182, O. Brandt32, F. Braren46, B. Brau103, J.E. Brau132, W.D. Breaden Madden57, K. Brendlinger46, L. Brenner46, R. Brenner172, S. Bressler180, B. Brickwedde100, D.L. Briglin21, D. Britton57, D. Britzger115, I. Brock24, R. Brock107, G. Brooijmans39, W.K. Brooks147d, E. Brost29, J.H Broughton21, P.A. Bruckman de Renstrom85,

D. Bruncko28b, A. Bruni23b, G. Bruni23b, L.S. Bruni120, S. Bruno74a,74b, M. Bruschi23b, N. Bruscino73a,73b, P. Bryant37, L. Bryngemark97, T. Buanes17, Q. Buat36, P. Buchholz151, A.G. Buckley57, I.A. Budagov80, M.K. Bugge134, F. Bührer52, O. Bulekov112, T.J. Burch121, S. Burdin91, C.D. Burgard120, A.M. Burger130, B. Burghgrave8, J.T.P. Burr46, C.D. Burton11, J.C. Burzynski103, V. Büscher100, E. Buschmann53, P.J. Bussey57, J.M. Butler25, C.M. Buttar57, J.M. Butterworth95, P. Butti36, W. Buttinger36,

C.J. Buxo Vazquez107, A. Buzatu158, A.R. Buzykaev122b,122a, G. Cabras23b,23a, S. Cabrera Urbán174, D. Caforio56, H. Cai173, V.M.M. Cairo153, O. Cakir4a, N. Calace36, P. Calafiura18, A. Calandri102, G. Calderini136, P. Calfayan66, G. Callea57, L.P. Caloba81b, A. Caltabiano74a,74b, S. Calvente Lopez99, D. Calvet38, S. Calvet38, T.P. Calvet155, M. Calvetti72a,72b, R. Camacho Toro136, S. Camarda36, D. Camarero Munoz99, P. Camarri74a,74b, D. Cameron134, C. Camincher36, S. Campana36,

M. Campanelli95, A. Camplani40, A. Campoverde151, V. Canale70a,70b, A. Canesse104, M. Cano Bret60c, J. Cantero130, T. Cao161, Y. Cao173, M.D.M. Capeans Garrido36, M. Capua41b,41a, R. Cardarelli74a, F. Cardillo149, G. Carducci41b,41a, I. Carli143, T. Carli36, G. Carlino70a, B.T. Carlson139,

E.M. Carlson176,168a, L. Carminati69a,69b, R.M.D. Carney153, S. Caron119, E. Carquin147d, S. Carrá46, J.W.S. Carter167, M.P. Casado14,e, A.F. Casha167, R. Castelijn120, F.L. Castillo174, L. Castillo Garcia14, V. Castillo Gimenez174, N.F. Castro140a,140e, A. Catinaccio36, J.R. Catmore134, A. Cattai36, V. Cavaliere29, E. Cavallaro14, M. Cavalli-Sforza14, V. Cavasinni72a,72b, E. Celebi12b, L. Cerda Alberich174, K. Cerny131, A.S. Cerqueira81a, A. Cerri156, L. Cerrito74a,74b, F. Cerutti18, A. Cervelli23b,23a, S.A. Cetin12b, Z. Chadi35a, D. Chakraborty121, J. Chan181, W.S. Chan120, W.Y. Chan91, J.D. Chapman32, B. Chargeishvili159b, D.G. Charlton21, T.P. Charman93, C.C. Chau34, S. Che127, S. Chekanov6, S.V. Chekulaev168a, G.A. Chelkov80, B. Chen79, C. Chen60a, C.H. Chen79, H. Chen29, J. Chen60a, J. Chen39, J. Chen26, S. Chen137, S.J. Chen15c, X. Chen15b, Y-H. Chen46, H.C. Cheng63a, H.J. Cheng15a, A. Cheplakov80, E. Cheremushkina123, R. Cherkaoui El Moursli35e, E. Cheu7, K. Cheung64, T.J.A. Chevalérias145, L. Chevalier145, V. Chiarella51, G. Chiarelli72a, G. Chiodini68a, A.S. Chisholm21, A. Chitan27b, I. Chiu163, Y.H. Chiu176, M.V. Chizhov80, K. Choi11, A.R. Chomont73a,73b, S. Chouridou162, Y.S. Chow120,

M.C. Chu63a, X. Chu15a,15d, J. Chudoba141, J.J. Chwastowski85, L. Chytka131, D. Cieri115, K.M. Ciesla85, D. Cinca47, V. Cindro92, I.A. Cioară27b, A. Ciocio18, F. Cirotto70a,70b, Z.H. Citron180,j, M. Citterio69a, D.A. Ciubotaru27b, B.M. Ciungu167, A. Clark54, M.R. Clark39, P.J. Clark50, C. Clement45a,45b, Y. Coadou102, M. Cobal67a,67c, A. Coccaro55b, J. Cochran79, R. Coelho Lopes De Sa103, H. Cohen161, A.E.C. Coimbra36, B. Cole39, A.P. Colijn120, J. Collot58, P. Conde Muiño140a,140h, S.H. Connell33c, I.A. Connelly57, S. Constantinescu27b, F. Conventi70a,ap, A.M. Cooper-Sarkar135, F. Cormier175, K.J.R. Cormier167, L.D. Corpe95, M. Corradi73a,73b, E.E. Corrigan97, F. Corriveau104,ad,

A. Cortes-Gonzalez36, M.J. Costa174, F. Costanza5, D. Costanzo149, G. Cowan94, J.W. Cowley32, J. Crane101, K. Cranmer125, S.J. Crawley57, R.A. Creager137, S. Crépé-Renaudin58, F. Crescioli136, M. Cristinziani24, V. Croft170, G. Crosetti41b,41a, A. Cueto5, T. Cuhadar Donszelmann149,

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M.J. Da Cunha Sargedas De Sousa60b, J.V. Da Fonseca Pinto81b, C. Da Via101, W. Dabrowski84a, F. Dachs36, T. Dado28a, S. Dahbi33e, T. Dai106, C. Dallapiccola103, M. Dam40, G. D’amen29,

V. D’Amico75a,75b, J. Damp100, J.R. Dandoy137, M.F. Daneri30, N.S. Dann101, M. Danninger152, V. Dao36, G. Darbo55b, O. Dartsi5, A. Dattagupta132, T. Daubney46, S. D’Auria69a,69b, C. David168b, T. Davidek143, D.R. Davis49, I. Dawson149, K. De8, R. De Asmundis70a, M. De Beurs120, S. De Castro23b,23a,

S. De Cecco73a,73b, N. De Groot119, P. de Jong120, H. De la Torre107, A. De Maria15c, D. De Pedis73a, A. De Salvo73a, U. De Sanctis74a,74b, M. De Santis74a,74b, A. De Santo156, K. De Vasconcelos Corga102, J.B. De Vivie De Regie65, C. Debenedetti146, D.V. Dedovich80, A.M. Deiana42, J. Del Peso99,

Y. Delabat Diaz46, D. Delgove65, F. Deliot145,q, C.M. Delitzsch7, M. Della Pietra70a,70b, D. Della Volpe54, A. Dell’Acqua36, L. Dell’Asta74a,74b, M. Delmastro5, C. Delporte65, P.A. Delsart58, D.A. DeMarco167, S. Demers183, M. Demichev80, G. Demontigny110, S.P. Denisov123, L. D’Eramo136, D. Derendarz85, J.E. Derkaoui35d, F. Derue136, P. Dervan91, K. Desch24, C. Deterre46, K. Dette167, C. Deutsch24, M.R. Devesa30, P.O. Deviveiros36, F.A. Di Bello73a,73b, A. Di Ciaccio74a,74b, L. Di Ciaccio5,

W.K. Di Clemente137, C. Di Donato70a,70b, A. Di Girolamo36, G. Di Gregorio72a,72b, B. Di Micco75a,75b, R. Di Nardo75a,75b, K.F. Di Petrillo59, R. Di Sipio167, C. Diaconu102, F.A. Dias40, T. Dias Do Vale140a, M.A. Diaz147a, J. Dickinson18, E.B. Diehl106, J. Dietrich19, S. Díez Cornell46, A. Dimitrievska18,

W. Ding15b, J. Dingfelder24, F. Dittus36, F. Djama102, T. Djobava159b, J.I. Djuvsland17, M.A.B. Do Vale81c, M. Dobre27b, D. Dodsworth26, C. Doglioni97, J. Dolejsi143, Z. Dolezal143, M. Donadelli81d, B. Dong60c, J. Donini38, A. D’onofrio15c, M. D’Onofrio91, J. Dopke144, A. Doria70a, M.T. Dova89, A.T. Doyle57, E. Drechsler152, E. Dreyer152, T. Dreyer53, A.S. Drobac170, D. Du60b, Y. Duan60b, F. Dubinin111, M. Dubovsky28a, A. Dubreuil54, E. Duchovni180, G. Duckeck114, A. Ducourthial136, O.A. Ducu110, D. Duda115, A. Dudarev36, A.C. Dudder100, E.M. Duffield18, L. Duflot65, M. Dührssen36, C. Dülsen182, M. Dumancic180, A.E. Dumitriu27b, A.K. Duncan57, M. Dunford61a, A. Duperrin102, H. Duran Yildiz4a, M. Düren56, A. Durglishvili159b, D. Duschinger48, B. Dutta46, D. Duvnjak1, G.I. Dyckes137, M. Dyndal36, S. Dysch101, B.S. Dziedzic85, K.M. Ecker115, M.G. Eggleston49, T. Eifert8, G. Eigen17, K. Einsweiler18, T. Ekelof172, H. El Jarrari35e, R. El Kosseifi102, V. Ellajosyula172, M. Ellert172, F. Ellinghaus182,

A.A. Elliot93, N. Ellis36, J. Elmsheuser29, M. Elsing36, D. Emeliyanov144, A. Emerman39, Y. Enari163, M.B. Epland49, J. Erdmann47, A. Ereditato20, P.A. Erland85, M. Errenst36, M. Escalier65, C. Escobar174, O. Estrada Pastor174, E. Etzion161, H. Evans66, M.O. Evans156, A. Ezhilov138, F. Fabbri57, L. Fabbri23b,23a, V. Fabiani119, G. Facini178, R.M. Faisca Rodrigues Pereira140a, R.M. Fakhrutdinov123, S. Falciano73a, P.J. Falke5, S. Falke5, J. Faltova143, Y. Fang15a, Y. Fang15a, G. Fanourakis44, M. Fanti69a,69b,

M. Faraj67a,67c,s, A. Farbin8, A. Farilla75a, E.M. Farina71a,71b, T. Farooque107, S.M. Farrington50, P. Farthouat36, F. Fassi35e, P. Fassnacht36, D. Fassouliotis9, M. Faucci Giannelli50, W.J. Fawcett32, L. Fayard65, O.L. Fedin138,o, W. Fedorko175, A. Fehr20, M. Feickert173, L. Feligioni102, A. Fell149, C. Feng60b, M. Feng49, M.J. Fenton171, A.B. Fenyuk123, S.W. Ferguson43, J. Ferrando46, A. Ferrante173, A. Ferrari172, P. Ferrari120, R. Ferrari71a, D.E. Ferreira de Lima61b, A. Ferrer174, D. Ferrere54,

C. Ferretti106, F. Fiedler100, A. Filipčič92, F. Filthaut119, K.D. Finelli25, M.C.N. Fiolhais140a,140c,a, L. Fiorini174, F. Fischer114, W.C. Fisher107, I. Fleck151, P. Fleischmann106, T. Flick182, B.M. Flierl114, L. Flores137, L.R. Flores Castillo63a, F.M. Follega76a,76b, N. Fomin17, J.H. Foo167, G.T. Forcolin76a,76b, A. Formica145, F.A. Förster14, A.C. Forti101, A.G. Foster21, M.G. Foti135, D. Fournier65, H. Fox90, P. Francavilla72a,72b, S. Francescato73a,73b, M. Franchini23b,23a, S. Franchino61a, D. Francis36, L. Franconi20, M. Franklin59, A.N. Fray93, P.M. Freeman21, B. Freund110, W.S. Freund81b, E.M. Freundlich47, D.C. Frizzell129, D. Froidevaux36, J.A. Frost135, C. Fukunaga164,

E. Fullana Torregrosa174, T. Fusayasu116, J. Fuster174, A. Gabrielli23b,23a, A. Gabrielli18, S. Gadatsch54, P. Gadow115, G. Gagliardi55b,55a, L.G. Gagnon110, B. Galhardo140a, G.E. Gallardo135, E.J. Gallas135, B.J. Gallop144, G. Galster40, R. Gamboa Goni93, K.K. Gan127, S. Ganguly180, J. Gao60a, Y. Gao50, Y.S. Gao31,l, C. García174, J.E. García Navarro174, J.A. García Pascual15a, C. Garcia-Argos52,

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M. Garcia-Sciveres18, R.W. Gardner37, N. Garelli153, S. Gargiulo52, C.A. Garner167, V. Garonne134, S.J. Gasiorowski148, P. Gaspar81b, A. Gaudiello55b,55a, G. Gaudio71a, I.L. Gavrilenko111, A. Gavrilyuk124, C. Gay175, G. Gaycken46, E.N. Gazis10, A.A. Geanta27b, C.M. Gee146, C.N.P. Gee144, J. Geisen97, M. Geisen100, C. Gemme55b, M.H. Genest58, C. Geng106, S. Gentile73a,73b, S. George94, T. Geralis44, L.O. Gerlach53, P. Gessinger-Befurt100, G. Gessner47, S. Ghasemi151, M. Ghasemi Bostanabad176, M. Ghneimat151, A. Ghosh65, A. Ghosh78, B. Giacobbe23b, S. Giagu73a,73b, N. Giangiacomi23b,23a, P. Giannetti72a, A. Giannini70a,70b, G. Giannini14, S.M. Gibson94, M. Gignac146, D. Gillberg34,

G. Gilles182, D.M. Gingrich3,ao, M.P. Giordani67a,67c, P.F. Giraud145, G. Giugliarelli67a,67c, D. Giugni69a, F. Giuli74a,74b, S. Gkaitatzis162, I. Gkialas9,g, E.L. Gkougkousis14, P. Gkountoumis10, L.K. Gladilin113, C. Glasman99, J. Glatzer14, P.C.F. Glaysher46, A. Glazov46, G.R. Gledhill132, I. Gnesi41b,

M. Goblirsch-Kolb26, D. Godin110, S. Goldfarb105, T. Golling54, D. Golubkov123, A. Gomes140a,140b, R. Goncalves Gama53, R. Gonçalo140a, G. Gonella132, L. Gonella21, A. Gongadze80, F. Gonnella21, J.L. Gonski39, S. González de la Hoz174, S. Gonzalez Fernandez14, S. Gonzalez-Sevilla54,

G.R. Gonzalvo Rodriguez174, L. Goossens36, N.A. Gorasia21, P.A. Gorbounov124, H.A. Gordon29, B. Gorini36, E. Gorini68a,68b, A. Gorišek92, A.T. Goshaw49, M.I. Gostkin80, C.A. Gottardo119, M. Gouighri35b, A.G. Goussiou148, N. Govender33c, C. Goy5, E. Gozani160, I. Grabowska-Bold84a, E.C. Graham91, J. Gramling171, E. Gramstad134, S. Grancagnolo19, M. Grandi156, V. Gratchev138, P.M. Gravila27f, F.G. Gravili68a,68b, C. Gray57, H.M. Gray18, C. Grefe24, K. Gregersen97, I.M. Gregor46, P. Grenier153, K. Grevtsov46, C. Grieco14, N.A. Grieser129, A.A. Grillo146, K. Grimm31,k, S. Grinstein14,y, J.-F. Grivaz65, S. Groh100, E. Gross180, J. Grosse-Knetter53, Z.J. Grout95, C. Grud106, A. Grummer118, L. Guan106, W. Guan181, C. Gubbels175, J. Guenther36, A. Guerguichon65, J.G.R. Guerrero Rojas174, F. Guescini115, D. Guest171, R. Gugel52, T. Guillemin5, S. Guindon36, U. Gul57, J. Guo60c, W. Guo106, Y. Guo60a, Z. Guo102, R. Gupta46, S. Gurbuz12c, G. Gustavino129, M. Guth52, P. Gutierrez129,

C. Gutschow95, C. Guyot145, C. Gwenlan135, C.B. Gwilliam91, A. Haas125, C. Haber18, H.K. Hadavand8, A. Hadef60a, M. Haleem177, J. Haley130, G. Halladjian107, G.D. Hallewell102, K. Hamacher182,

P. Hamal131, K. Hamano176, H. Hamdaoui35e, M. Hamer24, G.N. Hamity50, K. Han60a,x, L. Han60a, S. Han15a, Y.F. Han167, K. Hanagaki82,v, M. Hance146, D.M. Handl114, B. Haney137, R. Hankache136, E. Hansen97, J.B. Hansen40, J.D. Hansen40, M.C. Hansen24, P.H. Hansen40, E.C. Hanson101, K. Hara169, T. Harenberg182, S. Harkusha108, P.F. Harrison178, N.M. Hartmann114, Y. Hasegawa150, A. Hasib50, S. Hassani145, S. Haug20, R. Hauser107, L.B. Havener39, M. Havranek142, C.M. Hawkes21,

R.J. Hawkings36, D. Hayden107, C. Hayes106, R.L. Hayes175, C.P. Hays135, J.M. Hays93, H.S. Hayward91, S.J. Haywood144, F. He60a, M.P. Heath50, V. Hedberg97, S. Heer24, K.K. Heidegger52, W.D. Heidorn79, J. Heilman34, S. Heim46, T. Heim18, B. Heinemann46,am, J.J. Heinrich132, L. Heinrich36, J. Hejbal141, L. Helary61b, A. Held125, S. Hellesund134, C.M. Helling146, S. Hellman45a,45b, C. Helsens36,

R.C.W. Henderson90, Y. Heng181, L. Henkelmann61a, S. Henkelmann175, A.M. Henriques Correia36, H. Herde26, V. Herget177, Y. Hernández Jiménez33e, H. Herr100, M.G. Herrmann114, T. Herrmann48, G. Herten52, R. Hertenberger114, L. Hervas36, T.C. Herwig137, G.G. Hesketh95, N.P. Hessey168a, A. Higashida163, S. Higashino82, E. Higón-Rodriguez174, K. Hildebrand37, J.C. Hill32, K.K. Hill29, K.H. Hiller46, S.J. Hillier21, M. Hils48, I. Hinchliffe18, F. Hinterkeuser24, M. Hirose133, S. Hirose52, D. Hirschbuehl182, B. Hiti92, O. Hladik141, D.R. Hlaluku33e, J. Hobbs155, N. Hod180, M.C. Hodgkinson149, A. Hoecker36, D. Hohn52, D. Hohov65, T. Holm24, T.R. Holmes37, M. Holzbock114, L.B.A.H. Hommels32, S. Honda169, T.M. Hong139, J.C. Honig52, A. Hönle115, B.H. Hooberman173, W.H. Hopkins6, Y. Horii117, P. Horn48, L.A. Horyn37, S. Hou158, A. Hoummada35a, J. Howarth101, J. Hoya89, M. Hrabovsky131, J. Hrdinka77, I. Hristova19, J. Hrivnac65, A. Hrynevich109, T. Hryn’ova5, P.J. Hsu64, S.-C. Hsu148, Q. Hu29, S. Hu60c, Y.F. Hu15a,15d, D.P. Huang95, Y. Huang60a, Y. Huang15a, Z. Hubacek142, F. Hubaut102,

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I. Ibragimov151, L. Iconomidou-Fayard65, P. Iengo36, R. Ignazzi40, O. Igonkina120,aa,*, R. Iguchi163, T. Iizawa54, Y. Ikegami82, M. Ikeno82, D. Iliadis162, N. Ilic119,167,ad, F. Iltzsche48, G. Introzzi71a,71b, M. Iodice75a, K. Iordanidou168a, V. Ippolito73a,73b, M.F. Isacson172, M. Ishino163, W. Islam130, C. Issever19,46, S. Istin160, F. Ito169, J.M. Iturbe Ponce63a, R. Iuppa76a,76b, A. Ivina180, H. Iwasaki82, J.M. Izen43, V. Izzo70a, P. Jacka141, P. Jackson1, R.M. Jacobs24, B.P. Jaeger152, V. Jain2, G. Jäkel182, K.B. Jakobi100, K. Jakobs52, T. Jakoubek141, J. Jamieson57, K.W. Janas84a, R. Jansky54, M. Janus53, P.A. Janus84a, G. Jarlskog97, N. Javadov80,ae, T. Javůrek36, M. Javurkova103, F. Jeanneau145, L. Jeanty132, J. Jejelava159a, A. Jelinskas178, P. Jenni52,b, N. Jeong46, S. Jézéquel5, H. Ji181, J. Jia155, H. Jiang79, Y. Jiang60a, Z. Jiang153,p, S. Jiggins52, F.A. Jimenez Morales38, J. Jimenez Pena115, S. Jin15c, A. Jinaru27b, O. Jinnouchi165, H. Jivan33e, P. Johansson149, K.A. Johns7, C.A. Johnson66, R.W.L. Jones90, S.D. Jones156, S. Jones7, T.J. Jones91, J. Jongmanns61a, P.M. Jorge140a, J. Jovicevic36, X. Ju18, J.J. Junggeburth115, A. Juste Rozas14,y, A. Kaczmarska85, M. Kado73a,73b, H. Kagan127, M. Kagan153, A. Kahn39, C. Kahra100, T. Kaji179, E. Kajomovitz160, C.W. Kalderon29, A. Kaluza100, A. Kamenshchikov123, M. Kaneda163, N.J. Kang146, S. Kang79, L. Kanjir92, Y. Kano117, J. Kanzaki82, L.S. Kaplan181, D. Kar33e, K. Karava135, M.J. Kareem168b, S.N. Karpov80, Z.M. Karpova80, V. Kartvelishvili90, A.N. Karyukhin123,

A. Kastanas45a,45b, C. Kato60d,60c, J. Katzy46, K. Kawade150, K. Kawagoe88, T. Kawaguchi117, T. Kawamoto145, G. Kawamura53, E.F. Kay176, V.F. Kazanin122b,122a, R. Keeler176, R. Kehoe42,

J.S. Keller34, E. Kellermann97, D. Kelsey156, J.J. Kempster21, J. Kendrick21, K.E. Kennedy39, O. Kepka141, S. Kersten182, B.P. Kerševan92, S. Ketabchi Haghighat167, M. Khader173, F. Khalil-Zada13,

M. Khandoga145, A. Khanov130, A.G. Kharlamov122b,122a, T. Kharlamova122b,122a, E.E. Khoda175, A. Khodinov166, T.J. Khoo54, E. Khramov80, J. Khubua159b, S. Kido83, M. Kiehn54, C.R. Kilby94, E. Kim165, Y.K. Kim37, N. Kimura95, O.M. Kind19, B.T. King91,*, D. Kirchmeier48, J. Kirk144,

A.E. Kiryunin115, T. Kishimoto163, D.P. Kisliuk167, V. Kitali46, O. Kivernyk5, T. Klapdor-Kleingrothaus52, M. Klassen61a, C. Klein32, M.H. Klein106, M. Klein91, U. Klein91, K. Kleinknecht100, P. Klimek121, A. Klimentov29, T. Klingl24, T. Klioutchnikova36, F.F. Klitzner114, P. Kluit120, S. Kluth115, E. Kneringer77, E.B.F.G. Knoops102, A. Knue52, D. Kobayashi88, T. Kobayashi163, M. Kobel48, M. Kocian153,

T. Kodama163, P. Kodys143, P.T. Koenig24, T. Koffas34, N.M. Köhler36, M. Kolb145, I. Koletsou5,

T. Komarek131, T. Kondo82, K. Köneke52, A.X.Y. Kong1, A.C. König119, T. Kono126, V. Konstantinides95, N. Konstantinidis95, B. Konya97, R. Kopeliansky66, S. Koperny84a, K. Korcyl85, K. Kordas162,

G. Koren161, A. Korn95, I. Korolkov14, E.V. Korolkova149, N. Korotkova113, O. Kortner115, S. Kortner115, T. Kosek143, V.V. Kostyukhin149,166, A. Kotsokechagia65, A. Kotwal49, A. Koulouris10,

A. Kourkoumeli-Charalampidi71a,71b, C. Kourkoumelis9, E. Kourlitis149, V. Kouskoura29, A.B. Kowalewska85, R. Kowalewski176, W. Kozanecki101, A.S. Kozhin123, V.A. Kramarenko113, G. Kramberger92, D. Krasnopevtsev60a, M.W. Krasny136, A. Krasznahorkay36, D. Krauss115, J.A. Kremer84a, J. Kretzschmar91, P. Krieger167, F. Krieter114, A. Krishnan61b, K. Krizka18,

K. Kroeninger47, H. Kroha115, J. Kroll141, J. Kroll137, K.S. Krowpman107, U. Kruchonak80, H. Krüger24, N. Krumnack79, M.C. Kruse49, J.A. Krzysiak85, T. Kubota105, O. Kuchinskaia166, S. Kuday4b,

J.T. Kuechler46, S. Kuehn36, A. Kugel61a, T. Kuhl46, V. Kukhtin80, R. Kukla102, Y. Kulchitsky108,ag, S. Kuleshov147d, Y.P. Kulinich173, M. Kuna58, T. Kunigo86, A. Kupco141, T. Kupfer47, O. Kuprash52, H. Kurashige83, L.L. Kurchaninov168a, Y.A. Kurochkin108, A. Kurova112, M.G. Kurth15a,15d,

E.S. Kuwertz36, M. Kuze165, A.K. Kvam148, J. Kvita131, T. Kwan104, L. La Rotonda41b,41a,

F. La Ruffa41b,41a, C. Lacasta174, F. Lacava73a,73b, D.P.J. Lack101, H. Lacker19, D. Lacour136, E. Ladygin80, R. Lafaye5, B. Laforge136, T. Lagouri147b, S. Lai53, I.K. Lakomiec84a, S. Lammers66, W. Lampl7,

C. Lampoudis162, E. Lançon29, U. Landgraf52, M.P.J. Landon93, M.C. Lanfermann54, V.S. Lang46, J.C. Lange53, R.J. Langenberg103, A.J. Lankford171, F. Lanni29, K. Lantzsch24, A. Lanza71a,

A. Lapertosa55b,55a, S. Laplace136, J.F. Laporte145, T. Lari69a, F. Lasagni Manghi23b,23a, M. Lassnig36, T.S. Lau63a, A. Laudrain65, A. Laurier34, M. Lavorgna70a,70b, S.D. Lawlor94, M. Lazzaroni69a,69b, B. Le105,

Figure

Figure 1 depicts the typical diagrams for both the EW VBS and QCD Z Z j j processes. These MDs exploit the characteristics of VBS production, such as a large separation in rapidity between the two jets ( ∆ y( j j) ) as well as a significant invariant mass
Figure 2: Observed and expected m j j distributions in the (a) ```` j j QCD CR and the (b) ```` j j and (c) ``νν j j signal regions, as well as the m Z Z distribution in the (d) ```` j j signal region
Table 2: Observed µ EW and µ ```` j j
Figure 3: Observed and expected multivariate discriminant distributions after the statistical fit in the (a) ```` j j QCD CR, and in the (b) ```` j j and (c) ``νν j j signal regions

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