Measurement of the ZZ production cross section and Z → ` + ` − ` ′ + ` ′ − branching fraction in pp collisions at √ s = 13 TeV

Four-lepton production in proton-proton collisions, pp → (Z/γ∗) (Z/γ∗) → `+`−`′+`′−, where `, `′ = e or μ, is studied at a center-of-mass energy of 13 TeV with the CMS detector at the LHC. The data sample corresponds to an integrated luminosity of 2.6 fb−1. The ZZ production cross section, σ(pp → ZZ) = 14.6+1.9 −1.8 (stat) +0.5 −0.3 (syst) ± 0.2 (theo) ± 0.4 (lumi) pb, is measured for events with two opposite-sign, same-flavor lepton pairs produced in the mass region 60 < m`+`− , m`′+`′− < 120 GeV. The Z boson branching fraction to four leptons is measured to be B(Z → `+`−`′+`′−) = 4.9+0.8 −0.7 (stat) +0.3 −0.2 (syst) +0.2 −0.1 (theo)± 0.1 (lumi)× 10−6 for the four-lepton invariant mass in the range 80 < m`+`−`′+`′− < 100 GeV and dilepton mass m`+`− > 4 GeV for all opposite-sign, same-flavor lepton pairs. The results are in agreement with standard model predictions. Published in Physics Letters B as doi:10.1016/j.physletb.2016.10.054. c © 2016 CERN for the benefit of the CMS Collaboration. CC-BY-3.0 license ∗See Appendix A for the list of collaboration members ar X iv :1 60 7. 08 83 4v 2 [ he pex ] 9 N ov 2 01 6

tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), which provide coverage in pseudorapidity |η| < 1.479 in a barrel and 1.479 < |η| < 3.0 in two endcap regions. Forward calorimeters extend the coverage provided by the barrel and endcap detectors to |η| < 5.0. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid in the range |η| < 2.4, with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive plate chambers.
Electron momenta are estimated by combining energy measurements in the ECAL with momentum measurements in the tracker. The momentum resolution for electrons with transverse momentum p T ≈ 45 GeV from Z → e + e − decays ranges from 1.7% for nonshowering electrons in the barrel region to 4.5% for showering electrons in the endcaps [12]. Matching muons to tracks measured in the silicon tracker results in a p T resolution for muons with 20 < p T < 100 GeV of 1.3-2.0% in the barrel and better than 6% in the endcaps. The p T resolution in the barrel is better than 10% for muons with p T up to 1 TeV [13].

Signal and background simulation
Signal events are generated with powheg 2.0 [14][15][16] at nextto-leading-order (NLO) in QCD for quark-antiquark processes and leading-order (LO) for quark-gluon processes. This includes ZZ, Zγ * , Z, and γ * γ * production with a constraint of m + − > 4 GeV applied between all pairs of oppositely charged leptons at the generator level to avoid infrared divergences. The gg → ZZ process is simulated at LO with mcfm v7.0 [17]. These samples are scaled to correspond to cross sections calculated at NNLO for qq → ZZ [1] (scaling K factor 1.1) and at NLO for gg → ZZ [18] (K factor 1.7).
The gg → ZZ process is calculated to O α 5 s , where α s is the strong coupling constant, while the other contributing processes are calculated to O α 4 s ; this higher-order correction is included because the effect is known to be large [18].
A sample of Higgs boson events is produced in the gluon-gluon fusion process with powheg 2.0 in the NLO QCD approximation. The Higgs boson decay is modeled with jhugen 3.1.8 [19][20][21]. The qq → WZ process is generated with powheg 2.0.
The pythia v8.175 [22][23][24] package is used for parton showering, hadronization, and the underlying event simulation, with parameters set by the CUETP8M1 tune [25]. The NNPDF3.0 [26] set is used as the default set of parton distribution functions (PDFs). For all simulated event samples, the PDFs are calculated to the same order in QCD as the process in the sample.
The detector response is simulated using a detailed description of the CMS detector implemented with the Geant4 package [27]. The event reconstruction is performed with the same algorithms used for data. The simulated samples include additional interactions per bunch crossing, referred to as "pileup." The simulated events are weighted so that the pileup distribution matches the data, with an average of about 11 interactions per bunch crossing.

Event reconstruction
All long-lived particles in each collision event -electrons, muons, photons, and charged and neutral hadrons -are identified and reconstructed with the CMS particle-flow (PF) algorithm [28,29] from a combination of the signals from all subdetectors. Reconstructed electrons [12] and muons [13] are candidates for inclusion in four-lepton final states if they have p e T > 7 GeV and |η e | < 2.5 or p μ T > 5 GeV and |η μ | < 2.4. These are designated "signal leptons." Signal leptons are also required to originate from the event vertex, defined as the proton-proton interaction vertex whose associated charged particles have the highest sum of p 2 T . The distance of closest approach between each lepton track and the event vertex is required to be less than 0.5 cm in the plane transverse to the beam axis, and less than 1 cm in the direction along the beam axis. Furthermore, the significance of the three-dimensional impact parameter relative to the event vertex, SIP 3D , is required to satisfy SIP 3D ≡ |IP/σ IP | < 4 for each lepton, where IP is the distance of closest approach of each lepton track to the event vertex and σ IP is its associated uncertainty. Signal leptons are required to be isolated from other particles in the event. The relative isolation is defined as where the sums run over the charged and neutral hadrons, and photons, in a cone defined by R ≡ ( η) 2 + ( φ) 2 < 0.3 around the lepton trajectory, where φ is the azimuthal angle in radians.
To minimize the contribution of charged particles from pileup to the isolation calculation, charged hadrons are included only if they originate from the event vertex. The contribution of neutral particles from pileup is p PU T . For electrons, p PU T is evaluated with the "jet area" method described in Ref. [30]; for muons, it is taken to be half the sum of the p T of all charged particles in the cone originating from pileup vertices. The factor one-half accounts for the expected ratio of charged to neutral particle energy in hadronic Emission of final-state radiation (FSR) photons by the signal leptons may degrade the performance of the isolation requirements and Z boson mass reconstruction. These photons are omitted from the isolation determination for signal leptons and are implicitly included in dilepton kinematic calculations. Photons are FSR candidates if p γ T > 2 GeV, |η γ | < 2.4, their relative isolation (defined as in Eq. (1) with p PU T = 0) is less than 1.8, and R ( , γ ) < 0.5 with respect to the nearest signal lepton. To avoid double counting of bremmstrahlung photons that are already included in electron reconstruction, photons are not FSR candidates if there is any signal electron within R (γ , e) < 0.15 or within | φ (γ , e)| < 2 and | η (γ , e)| < 0.05. Because FSR photons have a higher average energy than photons from pileup and are expected to be mostly collinear with the emitting lepton, a photon candidate In simulated ZZ → + − + − events, the efficiency to select generated FSR photons is around 55%, and roughly 85% of selected photons are matched to FSR photons. At least one FSR photon is identified in approximately 2%, 5%, and 8% of simulated events in the 4e, 2e2μ, and 4μ channels, respectively. In data events with two on-shell Z bosons, no FSR photons are selected in the 4e decay channel, while at least one FSR photon is selected in three and five events in the 2e2μ and 4μ decay channels, respectively.
The lepton reconstruction, identification, and isolation efficiencies are measured with a tag-and-probe technique [31]  The muons are reconstructed and identified with efficiencies above ∼98% within |η μ | < 2.4.

Event selection
The primary triggers for this analysis require the presence of a pair of loosely isolated leptons of the same or different flavors.
The highest p T lepton must have p T > 17 GeV, and the subleading lepton must have p e T > 12 GeV if it is an electron or p it is a muon. The dielectron and dimuon triggers require that the tracks corresponding to the leptons originate from within 2 mm of each other in the plane transverse to the beam axis. Triggers requiring a triplet of lower-p T leptons with no isolation criterion, or a single high-p T electron without an isolation requirement, are also used. An event is used if it passes any trigger regardless of the decay channel. The total trigger efficiency for events within the acceptance of this analysis is greater than 98%.
A signal event must contain at least two Z/γ * candidates, each formed from an oppositely charged pair of isolated signal electrons or muons. Among the four leptons, the highest p T lepton must have p T > 20 GeV, and the second-highest p T lepton must have Within each event, all permutations of leptons giving a valid pair of Z/γ * candidates are considered separately. Within each + − + − candidate, the dilepton candidate with an invariant mass closest to 91.2 GeV, taken as the nominal Z boson mass, is denoted Z 1 and is required to have a mass greater than 40 GeV. The other dilepton candidate is denoted Z 2 . Both m Z 1 and m Z 2 are required to be less than 120 GeV. All pairs of oppositely charged leptons in the candidate are required to have m > 4 GeV regardless of flavor.
If multiple + − + − candidates within an event pass all selections, the passing candidate with m Z 1 closest to the nominal Z boson mass is chosen. In the rare case of further ambiguity, which may arise in events with five or more signal leptons, the Z 2 candidate that maximizes the scalar p T sum of the four leptons is chosen.
Additional requirements are applied to select events for measurements of specific processes. The → ZZ cross section is measured using events where both m Z 1 and m Z 2 are greater than 60 GeV. The Z → + − + − branching fraction is measured using events with 80 < m + − + − < 100 GeV, a range chosen to retain most of the decays in the resonance while removing most other processes with four-lepton final states.

Background estimate
The major background contributions arise from Z boson and WZ diboson production in association with jets and from tt production. In all these cases, particles from jet fragmentation satisfy both lepton identification and isolation criteria, and are thus misidentified as signal leptons.
The probability for such objects to be selected is measured from a sample of Z + candidate events, where Z is a pair of oppositely charged, same-flavor leptons that pass all analysis requirements and satisfy |m + − − m Z | < 10 GeV, where m Z is the nominal Z boson mass. Each event in this sample must have exactly one additional object candidate that passes relaxed identification requirements with no isolation requirements applied. The misidentification probability for each lepton flavor is defined as a ratio of the number of candidates that pass the final isolation and identification requirements to the total number in the sample, measured in bins of lepton candidate p T and η. The number of Z + candidate events is corrected for contamination from WZ production, or ZZ production in which one lepton is not reconstructed. These events Table 1 The contributions of each source of signal systematic uncertainty in the cross section measurements. The integrated luminosity uncertainty and the PDF and scale uncertainties are considered separately. All other uncertainties are added in quadrature into a single systematic uncertainty. Uncertainties that vary by decay channel are listed as a range. , the projection onto the plane transverse to the beams of the negative vector sum of the momenta of all reconstructed particles in the event. Addition- candidate and the missing transverse momentum vector is required to be less than 30 GeV. The residual contribution of WZ and ZZ events, which may be up to a few percent of the events with candidate passing all selection criteria, is estimated from simulation and subtracted.
To account for all sources of background events, two control samples are used to estimate the number of background events in the signal regions. Both are defined to contain events with a dilepton candidate satisfying all requirements (Z 1 ) and two additional lepton candidates + − . In one control sample, enriched in WZ events, one candidate is required to satisfy the full identification and isolation criteria and the other must fail the full criteria and instead satisfy only relaxed ones; in the other, enriched in Z+jets events, both candidates must satisfy the relaxed criteria, but fail the full criteria. The additional leptons must have opposite charge and the same flavor (e ± e ∓ , μ ± μ ∓ ). From this set of events, the expected number of background events in the signal region is obtained by scaling the number of observed Z 1 + + − events by the misidentification probability for each lepton failing the selection. Low-mass dileptons may be sufficiently collinear that their isolation cones overlap, and their misidentification probabilities are therefore correlated. To mitigate the effect of these correlations, only the control sample in which both additional leptons fail the full selection is used if R + , − < 0.6. The background contributions to the signal regions of Z → + − + − and ZZ → + − + − are summarized in Section 8.

Systematic uncertainties
Systematic uncertainties are summarized in Table 1. In both data and simulated event samples, trigger efficiencies are evaluated with a tag-and-probe technique. The ratio between data and simulation is applied to simulated events, and the size of the resulting change in expected yield is taken as the uncertainty for the determination of the trigger efficiency. This uncertainty is around 2% of the final estimated yield. For Z → e + e − e + e − events, the uncertainty increases to 4%.
The lepton identification and isolation efficiencies in simulation are corrected with scaling factors derived with a tag-and-probe method and applied as a function of lepton p T and η. To estimate the uncertainties associated with the tag-and-probe technique, the total yield is recomputed with the scaling factors varied up and down by the tag-and-probe fit uncertainties. The uncertainties associated with the identification efficiency in the ZZ → + − + − (Z → + − + − ) signal regions are found to be 0.9% (6%) in the 4e final state, 0.7% (4%) in the 2e2μ final state, and 0.4% (2%) in the 4μ final state. The corresponding uncertainties associated with the isolation efficiency are 1.1% (6%) in the 4e final state, 0.7% (3%) in the 2e2μ final state, and 0.3% (1%) in the 4μ final state.
These uncertainties are higher for Z → + − + − events because the leptons generally have lower p T , and the samples used in the tag-and-probe method have fewer events and more contamination from nonprompt leptons in this low-p T region.
Uncertainties due to the effect of factorization (μ F ) and renormalization (μ R ) scale choice on the Z Z → + − + − acceptance are evaluated with powheg and mcfm by varying the scales up and down by a factor of two with respect to the default values μ F = μ R = m ZZ . These variations are much smaller than 1% and are neglected. Parametric uncertainties (PDF+α s ) are evaluated using the CT10 [32] and NNPDF3.0 sets and are found to be less than 1%. The largest difference between predictions from powheg and mcfm with different scales and PDF sets, 1.5%, is considered to be the theoretical uncertainty in the acceptance calculation. An additional theoretical uncertainty arises from scaling the powheg qq → ZZ simulated sample from its NLO cross section to the NNLO prediction, and the mcfm gg → ZZ samples from their LO cross sections to the NLO predictions. The change in the acceptance corresponding to this scaling procedure is found to be 1.1%. All theoretical uncertainties are added in quadrature. The largest uncertainty in the estimated background yield arises from differences in sample composition between the Z + control sample used to calculate the lepton misidentification probability and the Z + + − control sample. A further uncertainty arises from the limited number of events in the Z + sample. A systematic uncertainty of 40% of the estimated background yield is applied to cover both effects. The size of this uncertainty varies by channel, but is less than 1% of the total expected yield. The uncertainty in the integrated luminosity of the data sample is 2.7% [33].

Cross section measurements
The distributions of the four-lepton mass and the masses of the Z 1 and Z 2 candidates are shown in Fig. 1. The SM predictions include nonresonant ZZ predictions normalized using the NNLO cross section, production of the SM Higgs boson with mass 125 GeV [34], and resonant Z → + − + − production. The background estimated from data is also shown. The reconstructed invariant mass of the Z 1 candidates, and a scatter plot showing the correlation between m Z 2 and m Z 1 in data events, are shown in Fig. 2. In the scatter plot, clusters of events corresponding to ZZ → + − + − , Zγ * → + − + − , and Z → + − + − production can be seen.
The four-lepton invariant mass distribution below 110 GeV is shown in Fig. 3 (top). Fig. 3 (bottom) shows m Z 2 plotted against m Z 1 for events with m + − + − between 80 and 100 GeV, and the observed and expected event yields in this mass region are given in Table 2.
The reconstructed four-lepton invariant mass is shown in Fig. 4  (top) for events with two on-shell Z bosons. Fig. 4 (bottom) shows the invariant mass distribution for all Z candidates in these events. The corresponding observed and expected yields are given in Table 3. The observed yields are used to evaluate the pp → Z → + − + − and pp → ZZ → + − + − production cross sections from a combined fit to the number of observed events in all the final states. The likelihood is a combination of individual channel likelihoods for the signal and background hypotheses with the statistical and systematic uncertainties in the form of scaling nuisance parameters. The ratio of the measured cross section to the SM cross section given by this fit including all channels is scaled by the cross section used in the simulation to find the measured fiducial cross section.
The definitions for the fiducial phase spaces for the Z → + − + − and ZZ → + − + − cross section measurements are given in Table 4.
The branching fraction for the Z → + − + − decay, B(Z → + − + − ), is measured by comparing the cross section given by Eq. (2) with the Z → + − cross section, and is computed as Table 2 The observed and expected yields of four-lepton events in the mass region 80 < m + − + − < 100 GeV and estimated yields of background events evaluated from data, shown for each final state and summed in the total expected yield. The first uncertainty is statistical, the second one is systematic.
The total ZZ cross section is shown in Fig. 5 as a function of the proton-proton center-of-mass energy. Results from the CMS [2][3][4] and ATLAS [5][6][7] experiments are compared to predictions from matrix and mcfm with the NNPDF3.0 PDF sets and fixed scales μ F = μ R = m Z . The matrix prediction uses PDFs calculated at NNLO, while the mcfm prediction uses NLO PDFs. The uncertainties are statistical (inner bars) and statistical and systematic added in quadrature (outer bars). The band around the matrix predictions reflects scale uncertainties, while the band around the mcfm predictions reflects both scale and PDF uncertainties. The theoretical predictions and all CMS measurements are performed in the dilepton mass range 60-120 GeV. All ATLAS measurements are in the mass window 66-116 GeV. The smaller mass window is estimated to cause a 1.6% reduction in the measured cross section.

Summary
Results have been presented for a study of four-lepton final states in proton-proton collisions at √ s = 13 TeV with the CMS detector at the LHC. The pp → ZZ cross section has been measured to be σ (pp → ZZ) = 14.6 +1.9 Table 3 The observed and expected yields of ZZ events, and estimated yields of background events evaluated from data, shown for each final state and summed in the total expected yield. The first uncertainty is statistical, the second one is systematic. T > 5 GeV, |η | < 2.5, m + − > 4 GeV (any opposite-sign same-flavor pair)

Acknowledgements
We thank Massimiliano Grazzini and his collaborators for providing the NNLO cross section calculations. We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the comput-