Main

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 boson1,2, 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 mechanism3,4,5. As a result of the delicate configuration of quantum field interactions for the SM VBS processes3, 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. Any significant deviation from the predicted high-energy behaviour of VBS would point to new phenomena in the EWSB sector which are motivated by many plausible extensions to the SM6,7,8. Moreover, VBS offers a sensitive means to search for anomalies in the weak-boson self-interactions9,10,11, 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 owing 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 VVjj (EW VVjj) 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±jj and WZjj processes have been observed using LHC Run 2 data12,13,14,15, and no significant deviations from the SM predictions have been found. The Compact Muon Solenoid Collaboration has searched for EW ZZjj production using 137 fb−1 of 13 TeV pp collision data with an observed significance of 4.0 s.d.16. Despite the small rate, EW ZZjj production is of great interest owing 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 ZZ 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 ZZjj production is therefore a direct test of an important prediction of the EW theory. Finally, precision measurements of high-mass VBS ZZ 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 to alleviate this problem17.

This article reports observation of EW ZZjj production at the LHC, as well as a measurement of the cross-sections of the inclusive (EW and non-EW) ZZjj processes. The set of 13 TeV pp collision data recorded by the ATLAS experiment during LHC Run 2 is used. 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 (ℓℓℓℓjj), or two charged leptons, two neutrinos and two jets (ℓℓννjj). The definition of the signal region (SR) is optimized 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 ZZjj process, which contains two strong interactions at the lowest order in perturbation theory and is referred to as quantum chromodynamics (QCD) VVjj production. Figure 1 depicts the typical diagrams for both the EW VBS and QCD ZZjj processes. These MDs exploit the characteristics of VBS production, such as a large separation in rapidity between the two jets (Δy(jj)) as well as a large invariant mass of the jet pair (mjj). The production of ZZjj 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.

Fig. 1: Typical Feynman diagrams for the production of ZZjj.
figure 1

a–d, The relevant EW VBS diagrams for the s-channel (a) and the t-channel production (b) through a Higgs boson, the weak-boson self-interaction process (c) and the production through exchange of a W boson (d). e–i, The relevant QCD diagrams for the tree-level production with different quark and gluon initial states (e–g), the box diagram without a Higgs boson (h) and the triangle diagram through a Higgs boson (i). Straight lines represent quarks (q, \(q^{\prime}\)), spiral lines represent gluon (g), wavy lines represent W and Z bosons and the dashed lines represent the Higgs boson.

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Experimental apparatus

The ATLAS experiment18,19,20 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 in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the interaction point 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 \(\eta =-\ln \tan (\theta /2)\). The angular distance between two physics objects is measured in units of \({{\Delta }}R\equiv \sqrt{{({{\Delta }}\eta )}^{2}+{({{\Delta }}\phi )}^{2}}\). The ATLAS detector consists of an inner tracking detector surrounded by a thin superconducting solenoid providing a 2 T 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) sampling calorimeters provide electromagnetic 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 electromagnetic and hadronic energy measurements up to ∣η∣ = 4.9. The muon spectrometer covers the pseudorapidity range ∣η∣ < 2.7 and is based on three large air-core toroidal superconducting magnets with eight coils each. The field integral of the toroids ranges between 2.0 and 6.0 T m across most of the detector. The muon spectrometer includes a system of precision tracking chambers and fast detectors for triggering. A two-level trigger system21 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.

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 ZZjj events selected for this analysis ranges from 95% to 99% for the inclusive sample of all final states considered.

The EW ZZjj production was modelled using the Powheg-Box v2 event generator22 with matrix elements (ME) calculated at next to leading order (NLO) in perturbative QCD (pQCD) and with the NNPDF3.0LO23 parton distribution functions (PDF). The contributions from triboson and VH processes in ℓℓℓℓjj and ℓℓννjj channels were estimated using the MadGraph5_aMC@NLO 2.6.1 event generator24 with ME calculated at leading order (LO) in pQCD with the NNPDF3.0LO PDF. Reweighting factors were calculated as a function of mjj from the MadGraph5_aMC@NLO events and applied to the POWHEG-V2 events. The effect is found to be below a few per cent level. The QCD ZZjj production was modelled using Sherpa 2.2.2 (ref. 25) with the NNPDF3.0NNLO23 PDF. The events with up to one outgoing parton were generated at NLO in pQCD, while those with two or three partons were modelled with LO accuracy. The production of ZZjj 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 ggZZjj process, was modelled using Sherpa 2.2.2 with the NNPDF3.0NNLO PDF and gg2VV26 with the CT10NNLO27 PDF in the ℓℓℓℓjj and ℓℓννjj channels, respectively, and normalized to a calculation accurate to NLO in pQCD. The leptonic decays of Z bosons are included in the simulation. Interference between EW and QCD ZZjj 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 WWjj and WZjj 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 (ref. 28). Triboson production not in the ℓℓℓℓjj or ℓℓννjj channels 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 (refs. 29,30,31). The production of \(t\overline{t}\) 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 ttZ 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, hadronization and underlying event algorithms were applied to the partonic final states predicted from each calculation. Those were modelled with Pythia 8.18632 using the NNPDF2.3LO33 PDF and the A14 set of tuned parameters34 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 detector35 based on Geant436, 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)37. 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.

Event selection

The selection of the ℓℓℓℓjj and ℓℓννjj events relies on multiple physics objects, including electrons, muons and jets. The SR is defined with a set of selection criteria which were optimized to preferentially select the EW ZZjj events.

Events are first required to have a collision vertex associated with at least two tracks each with transverse momentum (pT) of >0.5 GeV. The vertex with the highest sum of \({p}_{{{{\rm{T}}}}}^{2}\) of the associated tracks is referred to as the primary vertex.

Muons are identified by tracks reconstructed in the muon spectrometer and are matched to tracks reconstructed in the inner detector (ID). In the region 2.5 < ∣η∣ < 2.7, muons can also be identified by tracks from the muon spectrometer alone, and these are called stand-alone muons. Identified muons are required to have pT > 7 GeV. In the gap region (∣η∣ < 0.1) in the muon spectrometer, muons are identified by a track from the inner tracking detector 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 and satisfy the ‘loose’ identification criterion38 in the ℓℓℓℓjj channel, while they must satisfy ∣η∣ < 2.5 and the ‘medium’ identification in the ℓℓννjj channel. Electrons are reconstructed from energy deposits in the electromagnetic calorimeter matched to a track in the ID. Candidate electrons must have pT > 7 GeV and ∣η∣ < 2.47, and satisfy the ‘loose’ and ‘medium’ identification criteria39 in the ℓℓℓℓjj and ℓℓννjj channels, respectively. All electrons and muons must be isolated and satisfy the ‘FixedCutLoose’ and ‘loose’ isolation criteria38,39 in the ℓℓℓℓjj and ℓℓννjj channels, respectively. Furthermore, electrons (muons) are required to have associated tracks satisfying \(| {d}_{0}/{\sigma }_{{d}_{0}}| < 5\,(3)\) and \(| {z}_{0}\times \sin \theta | < 0.5\) mm, where d0 is the transverse impact parameter relative to the beam line, \({\sigma }_{{d}_{0}}\) is its uncertainty and z0 is the longitudinal impact parameter relative to the primary vertex.

Jets are reconstructed from clusters of calorimeter energy deposits using the anti-kt algorithm40,41 with radius parameter R = 0.4. The jet energy scale is calibrated using simulation and further corrected with in situ methods42. A jet vertex tagger43 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 algorithm44. 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. 45 is applied to the selected leptons and jets in the ℓℓννjj channel, to avoid ambiguities in the event selection and in the energy measurement of the physics objects. A similar approach is adopted in the ℓℓℓℓjj 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 ℓℓννjj final state do not interact with the ATLAS detector and cannot be reconstructed. Their presence is identified using the missing transverse momentum vector (\({\overrightarrow{E}}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\)), 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 jets46. The statistical significance of \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\) (\({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\)-significance) is calculated using resolution information of physics objects used in the \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\) reconstruction47.

In the ℓℓℓℓjj channel, quadruplets of leptons are formed by selecting two opposite-sign, same-flavour lepton pairs, where the leptons are required to be separated from each other by ΔR > 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 ℓ+ℓ− pairs are required to have an invariant mass (\({m}_{{\ell }^{+}{\ell }^{-}}\)) greater than 10 GeV, to reject events from low-mass resonances. If multiple quadruplets are found, the one that minimizes the sum of the differences between the dilepton masses and the nominal Z-boson mass, \(| {m}_{{\ell }^{+}{\ell }^{-}}-{m}_{Z}| +| {m}_{{\ell }^{^{\prime} +}{\ell }^{^{\prime} -}}-{m}_{Z}|\), is selected. The dilepton masses are required to be within the range 66–116 GeV.

In the ℓℓννjj channel, candidate events are required to have one opposite-sign, same-flavour lepton pair with \({m}_{{\ell }^{+}{\ell }^{-}}\) in the range from 80 to 100 GeV, and the leading (sub-leading) lepton must have pT > 30 GeV (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 \(t\overline{t}\) and WZ events. Events are required to have an \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\)-significance greater than 12 to suppress the background from Z + jets processes.

In both channels, the two jets with the highest pT and satisfying a negative product of jet rapidities (\({y}_{{j}_{1}}\times {y}_{{j}_{2}}\)) are selected. In the ℓℓℓℓjj channel, the jets are required to have pT > 30 GeV (40 GeV) in the ∣η∣ < 2.4 (2.4 < ∣η∣ < 4.5) region, while in the ℓℓννjj channel the leading (sub-leading) selected jet is required to have pT > 60 GeV (40 GeV). Finally, to further suppress background contributions, Δy(jj) is required to be greater than 2, and mjj is required to be greater than 300 and 400 GeV in the ℓℓℓℓjj and ℓℓννjj channels, respectively. The harsher jet requirement in the ℓℓννjj channel is optimized to suppress the larger contamination from reducible backgrounds.

After selection, the resulting observed and expected yields are listed in Table 1, where in total 127 and 82 data events are selected in the ℓℓℓℓjj and ℓℓννjj channels, respectively. Several control regions (CRs), defined with dedicated selections optimized 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 mjj spectra in the ℓℓℓℓjj SR, QCD ZZjj CR and ℓℓννjj SR, as well as the invariant mass of the four-lepton system (mZZ) in the ℓℓℓℓjj SR, are presented in Fig. 2. The background estimates, dedicated CRs and various sources of experimental and theoretical uncertainties are discussed in the following two sections.

Table 1 Observed data and expected event yields in 139 fb−1 of data in the ℓℓℓℓjj and ℓℓννjj SRs. All the minor backgrounds are summed together as ‘Others’, and the WWjj and \(t\overline{t}\) processes are referred to as the non-resonant-ℓℓ backgrounds. Uncertainties in the predictions include both the statistical and systematic components on the predicted yields before fit
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Fig. 2: Observed and expected distributions.
figure 2

a−d, The mjj distributions in the ℓℓℓℓjj QCD CR (a) and the ℓℓℓℓjj (b) and ℓℓννjj SRs (c), as well as the mZZ distribution in the ℓℓℓℓjj SR (d). The error bands represent the s.d. and include the expected experimental and theoretical systematic uncertainties. The contributions from the QCD and EW production of ZZjj events are scaled by 0.99 and 0.92, respectively, which correspond to the observed normalization factors in the statistical fit to the combined channel (Table 2). ZZ (EW), ZZ (QCD) and ggZZ represent contributions from EW, non-gg QCD and gg QCD ZZjj processes, respectively. WZ represents contribution from WZjj process. All the minor backgrounds are summed together as ‘Others’, and the WWjj and \(t\overline{t}\) processes are referred to as ‘NonRes’. The last bin includes the overflow events. The statistical uncertainties of the data are shown as error bars. The open arrows represent the out-of-range markers. The horizontal bin width is indicated on the vertical axis legend.

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The number of events in data is found to be consistent with the SM prediction including the EW ZZjj contribution.

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 another where one or more lepton candidates are misidentified in data.

In the ℓℓℓℓjj channel, the largest background arises from the QCD ZZjj process, which has an identical final state to the EW ZZjj process. The kinematic properties of the QCD ZZjj background are estimated using the simulated events described in the data and simulation section. However, the simulation is normalized to data in a dedicated EW-suppressed control region, defined by reversing either the mjj or the Δy(jj) selection criteria. Furthermore, the modelling of the kinematic properties of the QCD ZZjj simulation is validated in an additional EW-suppressed validation region, 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 jets48. The EW ZZjj contribution is less than 4% in the additional EW-suppressed validation region. More than 70% of the QCD ZZjj events in the mjj > 300 GeV region is not overlapping with the events in the additional EW-suppressed validation region. Good agreement between data and simulation is found for most kinematic distributions. The impact on the signal extraction of a potential mis-modelling of the mjj distribution in the QCD ZZjj simulation (seen in previous analyses49,50,51) is explicitly tested, by reweighting the QCD ZZjj simulation in the SR using an mjj-dependent correction factor that is defined as the ratio of data to simulation in the EW-suppressed validation region at high centrality. The signal extracted using the reweighted and nominal QCD ZZjj simulations is found to be in agreement when considering the statistical uncertainty on the mjj-dependent correction itself.

Small background contributions from Z + jets, top-quark and WZjj processes may contain misidentified leptons and are estimated using a method similar to that described in ref. 52, 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 ℓℓℓℓjj channel.

In the ℓℓννjj channel, the normalization and kinematic properties of QCD ZZjj processes are modelled from simulation due to a large contamination from other processes, which are considered in dedicated CRs. The WZjj 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. 53. The simulation is found to overestimate the WZjj contribution by 23% in this CR, and therefore the WZjj yield in the SR is scaled by 0.81. The WZjj distribution of the MD in the SR is evaluated from simulation, with the contributions from EW WZjj processes scaled by 1.77, corresponding to the difference between data and simulation observed in a previous analysis, in a similar phase space13, where the overall normalization factor is found to be consistent with the one derived in this article. The WWjj and \(t\overline{t}\) processes are referred to as the non-resonant-ℓℓ backgrounds, since they contain a lepton pair not originating from a Z or γ* boson. The non-resonant-ℓℓ 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. 53. The MD distribution in the SR for the non-resonant-ℓℓ process is estimated from simulation.

The Z + jets background is largely suppressed, and the yield is evaluated by extrapolating the low \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\)-significance region distribution in data to the high \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\)-significance region using an exponential function, while the MD distribution in the SR is modelled by simulation. Uncertainties are assigned to account for variations in the fitting functions as well as differences between estimated and simulated yields and distributions. 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 ℓℓννjj channel.

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 \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\) soft-term, the pile-up correction and the b-jet identification efficiency. Overall, the total experimental uncertainty in the predicted yields is about 10% and 5% in the ℓℓℓℓjj and ℓℓννjj channels, respectively. The dominant uncertainties originate from jet and lepton calibration. The uncertainty in the combined 2015–2018 integrated luminosity is 1.7% (ref. 54), obtained using the LUminosity Cherenkov Integrating Detector-2 detector55 for the primary luminosity measurements.

In addition, the uncertainties in the predicted yields from non-ZZjj backgrounds are dominated by the statistical uncertainties from data in the dedicated CRs, which are about 15% for the overall backgrounds. The WZjj shape uncertainty originates from experimental and theoretical uncertainties as well as from the uncertainty in the quoted EW WZjj cross-section measurement. The non-resonant-ℓℓ shape uncertainty is estimated by comparing the MD distributions from data and simulation. In addition, an uncertainty is assigned to the QCD ZZjj processes by comparing the MD distributions in low and high pile-up conditions, to account for a potential mis-modelling of pile-up in simulation. This uncertainty is only considered for the QCD ZZjj background, given its dominant impact in this analysis and the non-negligible probability for QCD ZZjj events to contain a pile-up jet. The differences in the predicted yields in different MD regions are below 10%, except in the last bin in the QCD ZZjj CR where it reaches 50% due to the statistical uncertainty of the simulated events.

The theoretical uncertainties of the EW and QCD ZZjj processes include the uncertainties from PDFs, QCD scales, strong coupling constant (αS), parton showering and hadronization. Those are estimated with the MadGraph5_aMC@NLO 2.6.1 for EW ZZjj and Sherpa 2.2.2 for QCD ZZjj processes. The PDF uncertainty is estimated following the PDF4LHC56 procedure. The effect of the QCD scale uncertainty is estimated by varying the renormalization and factorization scales following the procedure described in ref. 57. The parton showering and hadronization uncertainty is estimated by comparing the nominal Pythia 8 parton showering with the alternative Herwig 758,59 algorithm. The effect of the αS uncertainty is estimated by varying the αS value by ±0.001. The total theoretical uncertainties in the reconstructed event yields for the EW and QCD ZZjj process are estimated to be about 10% and 30%, respectively. Those uncertainties have been checked to confirm that the nuisance parameters associated with them are not over-constrained with the current dataset. Therefore, it is inferred that this analysis is not sensitive to theoretical uncertainties beyond the LO. The interference effect between the EW and QCD processes is studied using MadGraph5_aMC@NLO 2.6.1 interfaced to Pythia 8.186 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 ZZjj predictions. An additional uncertainty in the modelling of the QCD ZZjj 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%.

Observation of EW Z Z j j

To separate the EW ZZjj processes from their backgrounds, MDs based on the gradient boosted decision tree algorithm60 are trained with simulated events using the Toolkit for Multivariate Data Analysis framework61. 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 ZZjj signal and the backgrounds, where signal-like and background-like events are featured in the high- and low-MD regions, respectively. In the ℓℓℓℓjj channel, 12 input variables are used: mjj, Δy(jj), pT of the leading and sub-leading jets (\({p}_{{{{\rm{T}}}}}^{j1}\) and \({p}_{{{{\rm{T}}}}}^{j2}\)), yj1 × yj2, pT of the Z boson reconstructed from the charged-lepton pair with the mass closer to the Z-boson mass, rapidity of both Z bosons (yZ1 and yZ2), pT and mass of the four-lepton system, pT of the third lepton, pT of the ZZjj system divided by the scalar pT sum of Z bosons and two jets (ST). Thirteen input variables are utilized in the ℓℓννjj channel: mjj, Δy(jj), yj1 × yj2, \({p}_{{{{\rm{T}}}}}^{j2}\), \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\), \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\)-significance, ST, pseudorapidity and azimuthal angle differences between two charged leptons (Δη, Δϕ), ΔR, invariant mass of the charged-lepton pair and pT of leading and sub-leading leptons. The jet-related information provides the greatest sensitivity in the ℓℓℓℓjj channel, while both the jet-related and the dilepton-related variables are important in the ℓℓννjj channel.

In the ℓℓℓℓjj channel, the MD distributions in both the QCD ZZjj CR and the SR are used in the statistical fit, while only the MD distribution in the SR is fitted in the ℓℓννjj channel. The binning of MD distributions in the SRs (Fig. 3) is chosen to maximize the sensitivity of detecting EW ZZjj events. In the ℓℓℓℓjj channel, the normalization of QCD ZZjj production (\({\mu }_{{{{\rm{QCD}}}}}^{\ell \ell \ell \ell jj}\)) is varied simultaneously in the fit in the SR and QCD CR. The ratio of measured fiducial cross-section (with the fiducial region detailed in Section 8) to the SM prediction for EW ZZjj production (μEW) is taken as the parameter of interest.

Fig. 3: Observed and expected MD distributions.
figure 3

a–c, Distributions after the statistical fit in the ℓℓℓℓjj QCD CR (a), and in the ℓℓℓℓjj (b) and ℓℓννjj SRs (c). The error bands represent the s.d. and include the experimental and theoretical systematic uncertainties, as well as the uncertainties in μEW and \({\mu }_{{{{\rm{QCD}}}}}^{\ell \ell \ell \ell jj}\). ZZ (EW), ZZ (QCD) and ggZZ represent contributions from EW, non-gg QCD and gg QCD ZZjj processes, respectively. WZ represents contribution from WZjj process. All the minor backgrounds are summed together as ‘Others’, and the WWjj and \(t\overline{t}\) processes are referred to as ‘NonRes’. The statistical uncertainties of the data are shown as error bars. The open arrows represent the out-of-range markers. The horizontal bin width is indicated on the vertical axis legend.

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To examine the compatibility of the data and the signal-plus-background hypothesis, a test statistic is defined using the profile likelihood ratio method62. The statistical tests are performed in both the individual ℓℓℓℓjj and ℓℓννjj 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 ZZjj production are treated as uncorrelated between the ℓℓℓℓjj and ℓℓννjj channels, due to the different fiducial volume definitions. The QCD scale uncertainty for QCD ZZjj 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 ℓℓℓℓjj channel. Furthermore, the generator modelling uncertainty for QCD ZZjj production is treated as uncorrelated between the low- and high-MD regions.

The results are presented in Table 2. From the combined channels, the observed μEW is 0.92 ± 0.24, while \({\mu }_{{{{\rm{QCD}}}}}^{\ell \ell \ell \ell jj}\) is determined to be 0.99 ± 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 1.6 × 10−8, leading to the observation of EW ZZjj production. Correspondingly, with a normalized Gaussian distribution, the background-only hypothesis is rejected at 5.7σ (5.9σ) from the data (expectation). The EW ZZjj cross-section in the combined fiducial volume, formed by combining the respective fiducial regions in the ℓℓℓℓjj and ℓℓννjj channels, is found to be 0.70 ± 0.18 fb, calculated as μEW multiplied by the SM prediction of 0.76 ± 0.04 fb.

Table 2 Significance of EW ZZjj processes. Observed μEW and \({\mu }_{{{{\rm{QCD}}}}}^{\ell \ell \ell \ell jj}\), as well as the observed and expected significance of EW ZZjj processes from the individual ℓℓℓℓjj and ℓℓννjj channels, and the combined fits. The full set of statistical and systematic uncertainties is included
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Measurement of fiducial cross-sections

In addition to the observation of the EW ZZjj process, the cross-sections for the production of inclusive ZZjj are also measured in the ℓℓℓℓjj and ℓℓννjj 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 Ndata and Nbkg refer to the number of events in data and the expected number of background events from non-ZZjj processes, respectively, L refers to the integrated luminosity and C is the correction factor to extrapolate the QCD and EW ZZjj events from detector level to the fiducial volume, calculated as the ratio of the number of ZZjj 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, \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\) and jets, which are reconstructed in simulation from stable final-state particles, before their interactions with the detector, following the procedure described in ref. 57. In the ℓℓℓℓjj channel, the dilepton mass requirement is relaxed (relative to the detector-level selection) to the wider range of 60–120 GeV to ensure compatibility with the previous Compact Muon Solenoid publication63. In the ℓℓννjj 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 \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\)-significance due to the complexity of defining this variable at particle level; however, the particle-level \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\) 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 ℓℓℓℓjj channel and (22.4 ± 1.2)% in the ℓℓννjj channel, where the errors reflect the total uncertainties. The smaller C factor in the ℓℓννjj channel is due to the large event migration effect in events passing the \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\) selection requirement at particle level that have a small \({E}_{{{{\rm{T}}}}}^{{{{\rm{miss}}}}}\)-significance at detector level. The measured and predicted fiducial cross-sections are presented in Table 3. 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 ℓℓℓℓjj and ℓℓννjj channels, respectively. The measurements of 1.27 ± 0.14 fb for the ℓℓℓℓjj channel and 1.13 ± 0.32 fb for the ℓℓννjj channel are compatible with the SM predictions. The measurement precision in the ℓℓℓℓjj channel is better than the accuracy of the theoretical prediction.

Table 3 Measured and predicted fiducial cross-sections. Cross-sections are presented in both the ℓℓℓℓjj and ℓℓννjj channels for the inclusive ZZjj 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)
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Outlook

The rare EW production of ZZjj events is observed using 139 fb−1 of \(\sqrt{s}\) = 13 TeV proton–proton collision data collected with the ATLAS detector. The measurement of this rarest EW VVjj process is an important milestone in the study of EW physics at the LHC. This result also marks an important step towards understanding the nature of EW symmetry breaking, as it completes the observation of all major channels and confirms the consistency of the experimental results with the mechanism predicted by the SM. This result marks the start of a new era in precision studies of rare processes in the EW sector and in searches for new phenomena that can be investigated with higher precision and in higher energy regimes with future larger datasets.

Methods

Auxiliary material

Additional auxiliary figures can be found at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2017-19/.