Measurement of $ZZ$ production cross-sections in the four-lepton final state in $pp$ collisions at $\sqrt{s}=13.6$ TeV with the ATLAS experiment

This paper reports cross-section measurements of $ZZ$ production in $pp$ collisions at $\sqrt{s}=13.6$ TeV at the Large Hadron Collider. The data were collected by the ATLAS detector in 2022, and correspond to an integrated luminosity of 29 fb$^-1$. Events in the $ZZ\rightarrow4\ell$ ($\ell = e$, $\mu$) final states are selected and used to measure the inclusive and differential cross-sections in a fiducial region defined close to the analysis selections. The inclusive cross-section is further extrapolated to the total phase space with a requirement of 66 $<m_Z<$ 116 GeV for both $Z$ bosons, yielding $16.8 \pm 1.1$ pb. The results are well described by the Standard Model predictions.


Introduction
The study of the production of pairs of massive electroweak gauge bosons ('dibosons') has an important place in the physics programme at the Large Hadron Collider (LHC).Among all the contributing Feynman diagrams, those containing triple-gauge-boson couplings (TGCs) or involving the Higgs boson are particularly interesting, due to their direct connections with two fundamental features of the Standard Model (SM) electroweak (EW) theory, namely the non-Abelian gauge group structure and spontaneous EW symmetry breaking.Moreover, diboson production is a key process used to directly search for new phenomena beyond the SM (BSM).The diboson studies can be traced back to experiments at LEP [1] and Tevatron [2,3]; the LHC extends the precision measurements to unprecedented energy scales, owing to the high centre-of-mass energy and the large integrated luminosity.
The production of two on-shell  bosons is the rarest diboson process, but still attractive because of the high signal-to-background ratio for the fully leptonic decay channels.The   process is a key channel to search for anomalous neutral TGCs (aTGCs) [4] and to study off-shell production of the Higgs boson [5].Various measurements of   production have been performed by the ATLAS and CMS collaborations using data taken at √  = 5.02, 7, 8, and 13 TeV [6][7][8][9][10][11][12][13][14][15].Two complementary final states originating from the decays of the  boson pair are utilised in those measurements, one with four charged leptons (  → 4ℓ), and the other with two charged leptons and two neutrinos (  → 2ℓ2), where ℓ refers to  or .The smallest relative error in the measured inclusive cross-section was achieved with 13 TeV data, and is 5% [14] and 7% [15] for the   → 4ℓ and   → 2ℓ2 channels, respectively.Differential measurements have been performed on kinematic variables sensitive to aTGCs and off-shell Higgs boson production.These measurements also cast light on calculations of higher-order quantum chromodynamics (QCD) and EW corrections.Two key variables commonly considered for the   → 4ℓ channels are the invariant mass and the transverse momentum of the four-lepton system,  4ℓ and  4ℓ T , respectively, that are studied here.This paper reports a first measurement of   production in   collisions at √  = 13.6 TeV, which extends the test of the SM for this rare process to a new   centre-of-mass energy.The   → 4ℓ channel, where ℓ can be an electron or a muon, is utilised in this measurement, and a signal region is defined by selecting four high- T , isolated leptons, with a fiducial region defined close to the detector-level selections.The cross-section for   → 4ℓ production is measured in the fiducial region, and extrapolated to the total   production cross-section satisfying 66 <   < 116 GeV.Finally, the differential measurements are presented.

The ATLAS detector
The ATLAS detector [16,17] at the LHC is a multipurpose particle detector with a forward-backward symmetric cylindrical geometry and a near 4 coverage in solid angle. 1 It 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 of || < 2.5.It consists of silicon pixel, silicon microstrip, and transition radiation tracking detectors.Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic (EM) energy measurements with 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the -axis along the beam pipe.The -axis points from the IP to the centre of the LHC ring, and the -axis points upwards.Polar coordinates (, ) are used in the transverse plane,  being the azimuthal angle around the -axis.The pseudorapidity is defined in terms of the polar angle  as  = − ln tan(/2).Angular distance is measured in units of Δ ≡ √︁ (Δ) 2 + (Δ) 2 .
high granularity.A steel/scintillator-tile hadron calorimeter covers the central pseudorapidity range of || < 1.7.The endcap and forward regions are instrumented with LAr calorimeters for both the EM and hadronic energy measurements up to || = 4.9.The muon spectrometer surrounds the calorimeters and is based on three large superconducting air-core toroidal magnets with eight coils each.The field integral of the toroids ranges between 2.0 and 6.0 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 system is used to select events.The first-level trigger is implemented in hardware and uses a subset of the detector information to accept events at a rate below 100 kHz.This is followed by a software-based trigger that reduces the accepted event rate to 3 kHz on average, depending on the data-taking conditions.An extensive software suite [18] is used in data simulation, in the reconstruction and analysis of real and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment.

Data and simulation
This measurement uses the   collision data recorded by the ATLAS detector in 2022, the first year of the Run 3 data taking period.The data sample corresponds to an integrated luminosity of 29 fb −1 , with an uncertainty of 2.2% [19].The mean number of interactions per bunch crossing, known as pile-up, averaged over all colliding bunch pairs is about 40.Events are required to have fired at least one single-lepton trigger [20,21].For the main triggers, the transverse momentum ( T ) thresholds are 26 and 24 GeV for electrons and muons, respectively.The combined trigger efficiency is above 99% for events satisfying the signal selections given in Section 4.
Simulated data samples from Monte Carlo (MC) generators are used to estimate detector effects, and to provide theoretical predictions for comparison with the measured results.The MC samples employed are summarised in the following.The next-to-next-to-leading-order (NNLO) parton distribution function (PDF) set of NNPDF3.0 [22] was used in the matrix-element (ME) calculation for all processes.The dominant contribution to   production, the  q-initiated process ( q →  ), was generated with Sherpa 2.2.12 [23][24][25], with ME calculation accuracy at next-to-leading order (NLO) in the strong coupling   for final states with up to one additional parton, and at leading-order (LO) accuracy for up to three additional partons.The ME calculations utilised OpenLoops [25] for the virtual QCD corrections, and were merged with the Sherpa parton shower (PS) using the ME+PS@NLO prescription [26].The  q →   contribution also includes  →   production processes.Sherpa 2.2.12 provides higherorder NLO EW corrections as alternative internal weights [27].The predicted cross-section in the fiducial region for this measurement, defined in Section 4, is reduced by 12% when adopting the alternative weights, which then lies below other theoretical predictions [28,29] by approximately 10%.Therefore the NLO EW weights are not used to estimate detector effects, and are only shown when comparing the measured data with predictions.
The loop-induced gluon-initiated signal ( →  ) was simulated with Sherpa 2.2.12 at LO precision with up to one extra parton, with the same PS modelling as described above.The  →   sample includes the box-diagram  →   process and the off-shell Higgs production with  * →   decays.The predicted cross-section of  →   is scaled by a -factor of 1.7 to account approximately for the higher-order QCD corrections.The -factor was calculated for massless quark loops [30,31] in the heavy top-quark approximation [32].A relative uncertainty of 60% was assessed from QCD scale variations [33].
These three sets of processes with the subsequent   → 4ℓ decays provide the signal in this measurement.
Figure 1 shows representative Feynman diagrams for the respective contributions to   production.
Additional samples were generated to estimate the background contribution in the selected phase space.Irreducible backgrounds arise from  t and tri-boson () production, where  = , , both modelled with Sherpa 2.2.12, requiring at least four charged leptons in the final state.Backgrounds with non-prompt leptons (Section 5) arise primarily from  boson production with associated jets (+jets), production of   and  t.Production of +jets was simulated using Sherpa 2.2.12 with up to two partons at NLO and four partons at LO in   .The   process was simulated using Sherpa 2.2.12, with a similar configuration as for the  q →   signal.Events from  t production were generated with Powheg Box v2 +Pythia 8.3 at NLO in   .
A full simulation of detector effects using Geant4 [41,42] was applied to all these samples, along with dedicated calibrations and corrections to physics objects to match the performance of real data.

Object and phase space definitions
To account for the performance of the ATLAS detector and the   → 4ℓ final-state signature, the candidate events must satisfy requirements on data-taking quality, triggers (Section 3), physics objects and reconstructed boson candidates, to improve the signal purity by suppressing the backgrounds.The data quality requirements are imposed to reject running periods in which detector subsystems were not operating robustly.All candidate events have at least one primary vertex [43] with at least two associated inner tracking detector tracks.The object and event selections, which are described below, are similar to those defined for previous ATLAS measurements [14,44].
Electrons are reconstructed from energy deposited in the electromagnetic calorimeter matched to tracks in the inner tracking detector.Electrons are required to have  T > 7 GeV and || < 2.47.Candidates within the transition region between barrel and endcap calorimeters (1.37 < || < 1.52) are excluded.In addition, to distinguish real, isolated electrons from other objects, 'LooseAndBLayer' likelihood identification and 'Loose' isolation selections [45,46], both optimised for Run 3 analysis conditions, must be satisfied.
Muons are reconstructed [47] primarily by matching the tracks in the muon spectrometer and inner tracker.Because of the limited geometrical coverage of the muon spectrometer at the centre of the detector (|| < 0.1), a fully reconstructed inner detector track is also matched to a muon spectrometer track segment or a calorimeter energy deposition (calorimeter-tagged muons) for muon identification.Muon candidates are required to have  T > 5 GeV and || < 2.5.The  T threshold is increased to 15 GeV for calorimeter-tagged muons.Candidates are required to further satisfy the 'Loose' identification and 'PflowLoose' isolation [47,48] quality requirements.
To select lepton candidates originating from the primary vertex, a requirement is placed on the longitudinal impact parameter,  0 , multiplied by the sine of the track polar angle  with | 0 × sin | < 0.5 mm.A requirement is also placed on the significance of the transverse impact parameter  0 with | 0 |/  0 < 5(3) for electrons (muons).
Events with at least two individual pairs of same-flavour-opposite-charge (SFOC) leptons are selected.The two highest- T leptons are required to have  T > 27 GeV and 10 GeV, respectively.Any SFOC pair must have an invariant mass greater than 5 GeV, removing low-mass resonance contributions.Any lepton in the final state must be separated from other leptons with the requirement of Δ(ℓ  , ℓ  ) > 0.05.In each event with at least four leptons, the quadruplet of leptons is formed from two separate SFOC pairs.The SFOC pair with mass closest to the  mass [49] is called the leading pair (ℓℓ, 1).Then the subleading pair (ℓℓ, 2) is formed from the remaining leptons, with mass next closest to the  mass.In addition, the two SFOC lepton pairs are required to satisfy 66 <  ℓℓ,1 ,  ℓℓ,2 < 116 GeV.The invariant mass of the four leptons in the two pairs is required to be  4ℓ > 180 GeV, motivated to select only on-shell   events.Candidate events selected with these criteria enter into the signal region (SR) for this measurement.
The fiducial phase space is defined with a set of criteria very close to that of the detector-level SR criteria.This strategy helps to reduce the amount of phase-space extrapolation in the fiducial measurements and therefore reduces the theoretical uncertainties of the results.The criteria are applied to 'particle-level' physics objects, which are reconstructed from stable final-state particles, before their interactions with the detector.For electrons, QED final-state radiation is partly recovered by adding to the lepton four-momentum the four-momenta of surrounding photons not originating from hadrons within an angular distance Δ < 0.1 (dressed leptons), while the bare leptons defined after QED radiation are considered for muons.The different choices are to best mimic the corresponding object reconstruction at the detector level.
The total lepton phase space is defined for both individual SFOC pairs having 66 <  ℓℓ < 116 GeV, and any SFOC lepton pair in the decay final state must satisfy the requirement of    > 5 GeV, where   and    are calculated with the leptons defined at Born level, i.e. before any QED final-state radiation.Table 1 summarises the total and fiducial phase-space definitions.The cross-section in the total phase space is calculated by correcting for the branching fraction for   → 4ℓ decays, thus maintaining the invariant mass selections on  and   systems.

Background estimation
The background contamination in the SR is expected to be less than 5% of the total yield with the majority being from reducible backgrounds.The irreducible backgrounds consist almost entirely of  t and triboson production.They are evaluated using MC simulation, as discussed in Section 3. The uncertainties in these backgrounds, experimental and theoretical, are discussed in Section 6.The final states with -leptons from  decays contribute at the per-mille level and are neglected.A prompt lepton refers to a final-state lepton that does not originate from the decay of a hadron or -lepton.
Events with two or three prompt leptons can satisfy the SR criteria, if associated non-prompt leptons, jets or photons are mis-identified as signal leptons (fake leptons), leading to a reducible fake background.Most reducible background arises from fake leptons in +jets and  t events.Fake contributions from events with fewer than two prompt leptons are negligible and neglected.
Modelling of such background using purely MC predictions is unreliable and therefore a fake-factor (FF) technique that estimates the background with real data is used.The FF is calculated in a region dominated by single  production, with events that always have a selected SFOC lepton pair, with an invariant mass satisfying 66 <  ℓℓ < 116 GeV.The signal trigger and data-quality selections are applied.Any extra lepton in this region is considered to be fake after subtracting other prompt contributions from   and   production estimated from simulation.The FF is then calculated as the ratio of the number of leptons satisfying the standard lepton selection to the number satisfying the same selection except failing to meet the isolation or transverse impact parameter requirements (fake-enriched selection).A 'Loose' likelihood identification [46] is additionally required in the fake-enriched selection for electrons, to suppress the overwhelming photon contributions.The fake factors are obtained in bins of  T and , separately for electrons and muons.
An application region is defined using all the SR criteria, except that one or two leptons are required to satisfy the fake-enriched selection instead of the standard lepton selection.The number of reducible background events in the SR is calculated by applying the FFs to fake-enriched events in the application region, after subtracting the contribution from   production, following the methodology described in Ref. [14].The inclusive yield is reported in Table 2 and the relative uncertainty is assessed to be 30%, as discussed in Section 6.
The shape of the reducible background is obtained by applying the FF method in each kinematic bin and it is subject to large statistical uncertainties due to the limited sample size in data in the application region.To reduce these statistical fluctuations, a smoothing procedure based on a variable-span smoothing technique [50] is utilised.The smoothed fake distribution and uncertainty are estimated with 50 000 MC sets generated using random values taken from a Gaussian distribution for each bin before smoothing.
Then the smoothing is performed on all the sets.The mean value and standard deviation of the sets in each bin are taken as the nominal value and uncertainty of the smoothed fake background.In addition, to evaluate the uncertainty from the choice of smoothing technique, Lowess smoothing [51] is used as an alternative.The smoothing procedure significantly reduces the bin-by-bin fluctuations and improves the background predictions for the differential cross-section measurements.

Systematic uncertainties
The systematic uncertainties can be categorised into experimental and theoretical uncertainties.The uncertainties in the overall cross-section measurements from the sources listed in Table 3 are given there.
Experimental uncertainties address the imprecision in luminosity determination and modelling of detector effects.In addition, a MC statistical uncertainty arises from the limited size of the simulated samples.
The integrated luminosity impacts both the signal and background expected yields.The uncertainty is 2.2% [19].The pile-up modelling uncertainty is assessed by varying by ±4% the value of the visible inelastic cross-section that reweights the pile-up distribution in the simulation to that observed in the data [52].
Uncertainties in the lepton-energy calibration, and in the efficiency of lepton reconstruction, identification, isolation and trigger, influence the expected yields and distributions, and also the migration matrices and acceptance and correction factors in the cross-section measurements, defined below.The estimates are based on studies of the detector performance using Run 2 and Run 3 data [45, 47, 53].
Several sources of uncertainty affect the estimate of the reducible backgrounds, coming from the limited number of data events in the application region, the uncertainty in the subtracted prompt-lepton contributions in that region, and additional uncertainties in the FF estimates [14].The contribution from the production of  and  t processes to the SR is relatively small, and constant relative uncertainties of 10% and 15% are assigned to them, respectively, to account for the total systematic uncertainty covering experimental and theoretical sources.
The theoretical uncertainties in modelling the  q →   process are considered for sources including PDF sets, higher-order QCD corrections and parton shower models.The PDF uncertainty is estimated by using 100 eigenvector variations of the NNPDF3.0set, as suggested in Ref. [22].In addition, the nominal prediction is compared with another prediction employing an alternative PDF set, the NLO CT18 [54], to evaluate the uncertainty due to the choice of PDF set.The higher-order QCD uncertainties are evaluated by varying the default choice of renormalisation and factorisation scales independently by factors of two, removing combinations where the variations differ by a factor of four.The largest deviations are taken as the uncertainty.The impact of parton shower uncertainties are calculated following the recommendation of the Sherpa [26] authors.
For the  →   process, a conservative QCD correction uncertainty of 60% is assigned [30,33], thus the other sources of theoretical uncertainties are not added, as they are assumed to be small compared to the QCD uncertainty.For the EW  →   + 2  process, a constant theoretical uncertainty of 20% is assigned [55].

Results
The observed data yield and the estimated signal and background contributions in the SR are listed in Table 2, while Figure 2 gives the detector-level distributions for  4ℓ and  4ℓ T .Good agreement is found between the observations and predictions.Using these samples, the measurements of the inclusive and differential cross-sections are presented in this section.T in the signal region.Data are compared with the predictions with all uncertainties included.The lower panels show the ratios of the data to the predictions.

Measurement of inclusive cross-sections
The inclusive cross-section in the fiducial region is calculated as: where  obs and  bkg denote the data yield and the expected background contribution in the SR, respectively.The integrated luminosity of 29 fb −1 is denoted by , while    is the correction factor to account for reconstruction inefficiencies and resolution effects.
The    factor is computed as the ratio of the number of simulated detector-level signal events passing the SR criteria to the number of particle-level events satisfying the fiducial selection.The value of    is determined to be 0.555 ± 0.022, where the uncertainty includes all sources discussed, and is dominated by the uncertainties from electron identification and muon isolation.The theoretical uncertainties have little impact on    compared to that on the overall normalisation, as they cancel out in the ratio.The fiducial cross-section is measured to be: fid = 36.7 ± 1.6(stat) ± 1.5(syst) ± 0.8(lumi) fb.
The measurement precision is 6.3%, with a breakdown into categories shown in Table 3.The statistical uncertainty of the data is at the same level as the total systematic uncertainty.As described in Section 6, the theoretical uncertainty consists of uncertainties from the PDF sets, QCD corrections and parton showering of the signal processes.The uncertainty due to the background estimate contains all sources of uncertainties in the evaluation of reducible and irreducible backgrounds.The fiducial cross-section is extrapolated to the total phase space, by dividing it by the acceptance factor (   ) and the branching fraction for   → 4ℓ decays with ℓ = , .The    factor is the ratio of the cross-section in the fiducial region to that in the total lepton phase space, calculated from theoretical predictions at particle level.In this measurement, the    factor is determined by the MATRIX programme [29].MATRIX predicts the cross-section for   → 4ℓ processes at fixed order, with next-to-next-to-leading-order QCD and NLO EW accuracy for the  q →   process, and with NLO QCD accuracy for the  →   process.The NNPDF3.0 PDF set is utilised in the MATRIX calculation.The relative PDF uncertainty from Sherpa is applied to the MATRIX prediction because MATRIX does not support the calculation of PDF variations.The value of    is 0.482 ± 0.003, with the uncertainty coming from the PDF set and the QCD scale.The value of    is alternatively derived from the signal samples; a good agreement is found with that from MATRIX.The total cross-section is: The relative uncertainty is 6.5%.
The measured inclusive cross-sections in the fiducial and total phase spaces are presented in Table 4, and compared with predictions.The prediction from MC simulation includes  q →  ,  →  , and EW  →   + 2  processes, with the accuracy described in Section 3. The uncertainty in the predicted cross-section from MC simulation includes the theoretical uncertainty sources described in Section 6, and is dominated by the QCD-correction error from the -factor for  →  .The MATRIX prediction includes the QCD scale variation, and the PDF uncertainty from Sherpa.The measured cross-sections are well described by the predictions.

Measurement of differential cross-sections
The differential cross-section is measured by subtracting the expected background from observed data events in each bin of the studied observable in the fiducial phase space, and unfolding to correct for the detector effects, including efficiency, resolution and acceptance.Moreover, events falling outside the fiducial region might still satisfy the detector-level selection criteria because of resolution effects; the corresponding fraction are subtracted in this measurement.All these effects can be accounted for with a response matrix, the element    of which is defined as the probability that an event in particle-level bin  is reconstructed at detector-level in bin .The diagonal elements denote the fraction of events in a detector-level bin that originate from the same bin at particle-level, which defines the unfolding purity.
The unfolding is performed by calculating the response matrix using the signal samples, and applying it to the distribution of the measured observable at detector-level.To reduce the statistical uncertainty while constraining the regularisation bias, an iterative unfolding method based on Bayes' theorem [56], with the particle-level distribution from MC as a prior, is used.The number of iterations for the Bayesian unfolding is chosen to be two for both  4ℓ and  4ℓ T .The nominal response matrix, corrections and priors are all derived from simulation.The unfolding purity is globally greater than 80%.
The statistical uncertainty in the unfolded distributions is estimated with 1000 MC sets generated from the observed distributions (pseudodata), using Poisson random values for each bin.The root mean square of the deviation of the resulting unfolded spectrum of the pseudodata sets, from the actual unfolded data, is considered as the statistical uncertainty in each bin.The uncertainty due to any inherent bias in the unfolding method and the residual mis-modelling in simulation is evaluated with a procedure described in Ref. [57].The simulations are reweighted by a polynomial function to match the observed data when unfolded with the nominal response matrix.After unfolding, the differences between the reweighted MC distribution and the measured data distribution define the unfolding bias uncertainty in each bin, which remains globally below 1%, owing to the high resolution of the measured observable.The experimental and theoretical uncertainties discussed in Section 6 are estimated separately for signal and background.For the signal process, each uncertainty variation leads to a modification of the response matrix and therefore results in a difference in the unfolded distribution.The background uncertainties impact the data subtraction before unfolding.
Figure 3 presents the measured differential cross-sections for  4ℓ and  4ℓ T .The unfolded distributions are compared with the SM predictions, accounting for production of  q →  ,  →  , and EW  →   + 2 .The EW  →   + 2  contribution is included in the  q →   category in the figure .The results agree well within the total statistical and systematic uncertainty in most of the bins.For the  4ℓ distribution, the two predictions, both with and without EW corrections, describe the data adequately, while for the  4ℓ T distribution, Sherpa gives a better description of the low- 4ℓ T region, due to its merging and matching of multiple partons in the predictions.The impact of the NLO EW correction is generally not large compared to the precision of the measurements, but for MATRIX the description with the correction included is slightly better than without.In the case of Sherpa, the predictions without NLO EW corrections are slightly better than those including them, correlated with the reduced cross-section estimate discussed in Section 3. T bins.The error bars on the measurement points give the total uncertainty and the hatched band gives the systematic uncertainty.The upwards arrows in the ratio panels indicate that the cross-section of the corresponding prediction is more than 1.5 times the data in that bin.In all predictions, EW  →   + 2  is modelled by Powheg Box v2.Sherpa models  q →   at NLO QCD and LO EW accuracy, and provides NLO EW corrections as alternative internal weights.The Sherpa  q →   predictions using nominal and alternative weights are shown respectively as 'qqNLO' and 'qq[NLO × NLO EW]'.The  →   process predicted by Sherpa is at LO QCD accuracy, and scaled to NLO QCD using a -factor of 1.7.The error bands on the Sherpa predictions show the theoretical uncertainties in the signal process, where QCD, PDF and parton shower uncertainties are considered.MATRIX calculates  q →   at NNLO QCD, and at up to NLO EW accuracy.MATRIX calculates  →   at NLO QCD accuracy.Only the QCD scale uncertainty is considered in the MATRIX predictions.The lower panels show the ratios of the SM predictions to the measured data.

Conclusion
This paper presents cross-section measurements of   production in the 4ℓ final state, based on 29 fb −1 of data collected by the ATLAS detector at the LHC in   collisions at √  = 13.6 TeV.The inclusive crosssections within both a fiducial and the total phase-space regions are measured.Differential measurements of  4ℓ and  4ℓ T are also presented.The results are well described by the predictions, both from state-of-the-art MC simulation and from fixed-order calculations with accuracy up to NNLO QCD + NLO EW.These results are the first step in the programme of diboson production measurements at the new centre-of-mass energy of 13.6 TeV.[13] CMS Collaboration, Measurement of the   production cross section and  → ℓ + ℓ − ℓ ′+ ℓ ′− branching fraction in   collisions at

Figure 2 :
Figure 2: Kinematic distributions for (a)  4ℓ and (b)  4ℓT in the signal region.Data are compared with the predictions with all uncertainties included.The lower panels show the ratios of the data to the predictions.

Figure 3 :
Figure 3: The measured differential cross-sections (filled points) are compared with the predictions, in each of the (a)  4ℓ and (b)  4ℓT bins.The error bars on the measurement points give the total uncertainty and the hatched band gives the systematic uncertainty.The upwards arrows in the ratio panels indicate that the cross-section of the corresponding prediction is more than 1.5 times the data in that bin.In all predictions, EW  →   + 2  is modelled by Powheg Box v2.Sherpa models  q →   at NLO QCD and LO EW accuracy, and provides NLO EW corrections as alternative internal weights.The Sherpa  q →   predictions using nominal and alternative weights are shown respectively as 'qqNLO' and 'qq[NLO × NLO EW]'.The  →   process predicted by Sherpa is at LO QCD accuracy, and scaled to NLO QCD using a -factor of 1.7.The error bands on the Sherpa predictions show the theoretical uncertainties in the signal process, where QCD, PDF and parton shower uncertainties are considered.MATRIX calculates  q →   at NNLO QCD, and at up to NLO EW accuracy.MATRIX calculates  →   at NLO QCD accuracy.Only the QCD scale uncertainty is considered in the MATRIX predictions.The lower panels show the ratios of the SM predictions to the measured data.

Table 2 :
Observed and predicted detector level yields in the signal region, corresponding to the integrated luminosity of 29 fb −1 .All systematic uncertainties described in Section 6 are included.

Table 3 :
Breakdown of relative uncertainty in the measured fiducial cross-section  fid .

Table 4 :
The measured inclusive cross-sections compared with the predictions from MC simulation and from the MATRIX calculation at fixed order.Both the fiducial and total phase space results are included.In all predictions, EW  →   + 2  is modelled by Powheg Box v2.