Measurement of the pp to ZZ production cross section and constraints on anomalous triple gauge couplings in four-lepton final states at sqrt(s) = 8 TeV

A measurement of inclusive ZZ production cross section and constraints on anomalous triple gauge couplings in proton-proton collisions at sqrt(s) = 8 TeV are presented. A data sample, corresponding to an integrated luminosity of 19.6 inverse femtobarns was collected with the CMS experiment at the LHC. The measurements are performed in the leptonic decay modes ZZ to lll'l', where l = e, mu and l' = e, mu, tau. The measured total cross section, sigma(pp to ZZ) = 7.7 +/- 0.5 (stat.) +0.5-0.4 (syst.) +/- 0.4 (theo.) +/- 0.2 (lum.) pb for both Z bosons produced in the mass range 60<m[Z]<120 GeV, is consistent with standard model predictions. Differential cross sections are measured and well described by the theoretical predictions. The invariant mass distribution of the four-lepton system is used to set limits on anomalous ZZZ and ZZ gamma couplings at the 95% confidence level: -0.004<f[4,Z]<0.004, -0.004<f[5,Z]<0.004, -0.005<f[4,gamma]<0.005, and -0.005<f[5,gamma]<0.005.


Introduction
The study of diboson production in proton-proton collisions provides an important test of the non-Abelian structure of the standard model (SM) Lagrangian. In the SM, ZZ production proceeds mainly through quark-antiquark tand u-channel scattering diagrams. At higher order in QCD gluon-gluon fusion also contributes via box diagrams with quark loops. There are no SM contributions to ZZ production from triple boson vertices, since ZZZ and ZZγ couplings are not present at tree level. Anomalous triple gauge couplings (ATGC) ZZZ and ZZγ are introduced using an effective Lagrangian following Ref. [1]. In this parametrization, two ZZZ and two ZZγ couplings are allowed by electromagnetic gauge invariance and Lorentz invariance for on-shell Z bosons and are parametrized by two CP-violating ( f V 4 ) and two CP-conserving ( f V 5 ) parameters, where V = (Z, γ). Nonzero ATGC values could be induced by new physics models such as supersymmetry [2].
In this paper, which is based on the full 2012 data set and corresponds to an integrated luminosity of 19.6 fb −1 , results are presented for the ZZ inclusive and differential production cross sections as well as limits for the ZZZ and ZZγ ATGCs.

The CMS detector and simulation
The CMS detector is described in detail elsewhere [8]; the key components for this analysis are summarized here. The CMS experiment uses a right-handed coordinate system, with the origin at the nominal interaction point, the x axis pointing to the center of the LHC ring, the y axis pointing up (perpendicular to the plane of the LHC ring), and the z axis along the counterclockwise-beam direction. The polar angle θ is measured from the positive z axis and the azimuthal angle φ is measured in the x-y plane. The magnitude of the transverse momentum is p T = √ p 2 x + p 2 y . A superconducting solenoid is located in the central region of the CMS detector, providing an axial magnetic field of 3.8 T parallel to the beam direction. The silicon pixel and strip tracker, the crystal electromagnetic calorimeter (ECAL), and the brass and scintillator hadron calorimeter are located within the solenoid and cover the absolute pseudorapidity range |η| < 3.0, where pseudorapidity is defined as η = − ln[tan (θ/2)]. The ECAL barrel region (EB) covers |η| < 1.479 and two endcap regions (EE) cover 1.479 < |η| < 3.0. A quartz-fiber Cherenkov calorimeter extends the coverage up to |η| < 5.0. Muons are measured in gas ionization detectors embedded in the steel flux-return yoke outside the solenoid. The first level of the CMS trigger system, composed of custom hardware processors, is designed

Event reconstruction
A complete reconstruction of the individual particles emerging from each collision event is obtained via a particle-flow (PF) technique [22,23], which uses the information from all CMS subdetectors to identify and reconstruct individual particles in the collision event. The particles are classified into mutually exclusive categories: charged hadrons, neutral hadrons, photons, muons, and electrons.
Electrons are reconstructed within the geometrical acceptance, |η e | < 2.5, and for transverse momentum p e T > 7 GeV. The reconstruction combines the information from clusters of energy deposits in the ECAL and the trajectory in the inner tracker [24]. Particle trajectories in the tracker volume are reconstructed using a modeling of the electron energy loss and fitted with a Gaussian sum filter [25]. The contribution of the ECAL energy deposits to the electron transverse momentum measurement and its uncertainty are determined via a multivariate regression approach. Electron identification relies on a multivariate technique that combines observables sensitive to the amount of bremsstrahlung along the electron trajectory, the geometrical and momentum matching between the electron trajectory and associated clusters, as well as shower shape observables.
Muons are reconstructed within |η µ | < 2.4 and for p µ T > 5 GeV [26]. The reconstruction combines information from both the silicon tracker and the muon detectors. The PF muons are selected from among the reconstructed muon track candidates by applying minimal requirements on the track components in the muon system and matching with minimum ionizing particle energy deposits in the calorimeters.
For τ leptons, two principal decay modes are distinguished: a leptonic mode, τ , with a final state including either an electron or a muon, and a hadronic mode, τ h , with a final state including hadrons. The PF particles are used to reconstruct τ h with the "hadron-plus-strip" algorithm [27], which optimizes the reconstruction and identification of specific τ h decay modes.
The π 0 components of the τ h decays are first reconstructed and then combined with charged hadrons to reconstruct the τ h decay modes. Cases where τ h includes three charged hadrons are also included. The missing transverse energy that is associated with neutrinos from τ decays is ignored in the reconstruction. The τ h candidates in this analysis are required to have |η τ h | < 2.3 and p τ h T > 20 GeV. The isolation of individual electrons or muons is measured relative to their transverse momentum p T , by summing over the transverse momenta of charged hadrons and neutral particles in a cone with ∆R = √ (∆η) 2 + (∆φ) 2 < 0.4 around the lepton direction at the interaction vertex: The ∑ p charged T is the scalar sum of the transverse momenta of charged hadrons originating from the primary vertex. The primary vertex is chosen as the vertex with the highest sum of p 2 T of its constituent tracks. The ∑ p neutral T and ∑ p γ T are the scalar sums of the transverse momenta for neutral hadrons and photons, respectively. The average transverse-momentum flow density ρ is calculated in each event using a "jet area" [28], where ρ is defined as the median of the p jet T /A jet distribution for all pileup jets in the event, each of area A jet . The effective area A eff is the geometric area of the isolation cone times an η-dependent correction factor that accounts for the residual dependence of the isolation on pileup. Electrons and muons are considered isolated if R Iso < 0.4. Allowing τ leptons in the final state increases the background contamination, therefore tighter isolation requirements are imposed for electrons and muons in ZZ → ττ decays: R Iso < 0.25 for Z → τ + τ − , and R e Iso < 0.1 for Z → τ e τ h , and R µ Iso < 0.15 for τ µ τ h .
The isolation of the τ h is calculated as the scalar sum of the transverse momenta of the charged hadrons and neutral particles in a cone of ∆R < 0.5 around the τ h direction reconstructed at the interaction vertex. The τ h isolation includes a correction for pileup effects, which is based on the scalar sum of transverse momenta of charged particles not associated with the primary vertex in a cone of ∆R < 0.8 about the τ h candidate direction (p PU T ). The isolation variable is defined as: where the scale factor of f = 0.0729, which is used in estimating the contribution to the isolation sum from neutral hadrons and photons, accounts for the difference in the cone sizes. Two standard working points are defined based on the value of the isolation sum corrected for the pileup contribution: I PF < 1 (8) GeV for final states including one (two) τ h candidates.
The electron and muon pairs from Z-boson decays are required to originate from the primary vertex. This is ensured by demanding that the significance of the three-dimensional impact parameter relative to the event vertex, SIP 3D , satisfies SIP 3D = | IP σ IP | < 4 for each lepton. The IP is the distance of closest approach of the lepton track to the primary vertex and σ IP is its associated uncertainty.
The efficiencies for the product of reconstruction, identification, and isolation of primary electrons or muons are measured in data using a "tag-and-probe" technique [29] applied to an inclusive sample of Z events. The measurements are performed in bins of p T and |η |. The efficiency for selecting electrons in the ECAL barrel(endcaps) is about 70%(60%) for 7 < p e T < 10 GeV, 85%(77%) at p e T 10 GeV, and 95%(89%) for p e T ≥ 20 GeV. It is about 85% in the transition region between the ECAL barrel and endcaps (1.44 < |η| < 1.57), averaging over the whole p T range. The muons are reconstructed and identified with an efficiency greater than ∼98% in the full |η µ | < 2.4 range. The τ h reconstruction efficiency is approximately 50% [27].

Event selection
Final-state radiation (FSR) may affect the measured four-momentum of the leptons if it is not properly included in the reconstruction. For electrons, a significant portion of the FSR photons is included in the reconstructed energy because of the size of the electromagnetic clusters, but for muons additional treatment of the FSR photons is important. All photons reconstructed within |η µ | < 2.4 are considered as possible FSR candidates if they have a transverse momentum p γ T > 2(4) GeV and are found within ∆R < 0.07(0.07 < ∆R < 0.5) from the closest selected lepton candidate and are isolated. The photon isolation observable R γ Iso is the sum, divided by p γ T , of the transverse momenta of charged hadrons, neutral hadrons, and photons in a cone of ∆R < 0.3 around the candidate photon direction. Isolated photons must satisfy R γ Iso < 1. The recovered FSR photon is included in the lepton four-momentum and the lepton isolation is then recalculated without it.
The performance of the FSR selection algorithm has been determined using simulated samples, and the rate is verified with the Z and ZZ events in data. The photons within the acceptance for the FSR selection are reconstructed with an efficiency of about 50% and with a mean purity of 80%. The FSR photons are recovered in 0.5(5)% of inclusive Z events with electron (muon) pairs.

Event selection
Potential ZZ events are first selected by the trigger system, which requires the presence of a pair of electrons or muons, or a triplet of electrons. Triggers requiring an electron and a muon are also used. For the double-lepton triggers, the highest p T and second highest p T leptons are required to exceed 17 and 8 GeV, respectively, while for the triple-electron trigger the thresholds are 15, 8, and 5 GeV. The trigger efficiency for ZZ events within the acceptance of this analysis is greater than 98%.
In selected ZZ events, the Z candidate with the mass closest to the Z-boson mass is denoted Z 1 and the other one, Z 2 . The selection is designed to give mutually exclusive sets of signal candidates first selecting ZZ decays to 4e, 4µ, and 2e2µ, in the following denoted ; these events are not considered in ZZ → ττ channel. The leptons are identified and isolated as described in Section 3. The significance of the impact parameter with respect to the primary vertex is required to be SIP 3D < 4. When building the Z candidates, the FSR photons are kept if |m γ − m Z | < |m − m Z | and m γ < 100 GeV. In the following, the presence of the photons in the kinematics is implicit. The leptons constituting a Z candidate are required to be the same flavor and to have opposite charges ( + − ). The pair is retained if it satisfies 60 < m Z < 120 GeV. If more than one Z 2 candidate satisfies all criteria, the ambiguity is resolved by choosing the pair of leptons with the highest scalar sum of p T . Among the four selected leptons forming the Z 1 and the Z 2 , at least one should have p T > 20 GeV and another one should have p T > 10 GeV. These p T thresholds ensure that the selected events have leptons with p T values on the high-efficiency plateau for the trigger.
For the ττ final state, events are required to have one Z 1 → + − candidate with p T > 20 GeV for one of the leptons and p T > 10 GeV for the other lepton, and a Z 2 → τ + τ − , with τ decaying into e, µ, or τ h . The leptons from the τ decays are required to have p T > 10 GeV. The τ h candidates are required to have p τ h T > 20 GeV. The FSR recovery is not applied to the ττ final states, since it does not improve the mass reconstruction. The invariant mass of the reconstructed Z 1 is required to satisfy 60 < m < 120 GeV, and that of the Z 2 to satisfy m min < m ττ < 90 GeV, where m min = 20 GeV for Z 2 → τ e τ µ final states and 30 GeV for all others.

Background estimate
The lepton identification and isolation requirements described in Section 3 significantly suppress all background contributions, and the remnant portion of them arise mainly from the Z and WZ production in association with jets, as well as tt. In all these cases, a jet or a nonisolated lepton is misidentified as an isolated e, µ, τ h , τ e , or τ µ . To estimate the expected number of background events in the signal region, control data samples are defined for each lepton flavor combination . The e and τ e , and µ and τ µ are considered as different flavors, since they originate from different particles.
The control data samples for the background estimate are obtained by selecting events containing Z 1 , which passes all selection requirements, and two additional lepton candidates . The additional lepton pair must have opposite charge and matching flavor (e ± e ∓ , µ ± µ ∓ , τ ± τ ∓ ). Control data samples enriched with Z+X events, where X stands for bb, cc, gluon, or light quark jets, are obtained by requiring that both additional leptons pass only relaxed identification criteria and are not required to be isolated. By requiring one of the additional leptons to pass the full selection requirements, one obtains data samples enriched with WZ events and significant number of tt events. The expected number of background events in the signal region for each flavor pair is obtained by scaling the number of observed Z 1 + events by the lepton misidentification probability and combining the results for Z+X and WZ, tt control regions together. The procedure is identical for all lepton flavors.
The misidentification probability, i.e., the probability for a lepton candidate that passes the relaxed requirements to pass the full selection, is measured separately for each flavor from a sample of Z 1 + candidate events with a relaxed identification and no isolation requirements on the candidate . The misidentification probability for each lepton flavor is defined as the ratio of the number of leptons that pass the final isolation and identification requirements to the total number of leptons in the sample. It is measured in bins of lepton p T and η. The contamination from WZ events, which may lead to an overestimate of the misidentification probability because of the presence of genuine isolated leptons, is suppressed by requiring that the measured missing transverse energy is less than 25 GeV.
The estimated background contributions to the signal region are summarized in Table 1. The procedure excludes a possible double counting of events and contains corrections for small contributions of prompt leptons, which may enter the control data sample. The predicted background rate has a small effect on the ZZ cross section measurement in the channels, but is comparable to the signal size for the case of ττ.

Systematic uncertainties
The systematic uncertainties for trigger efficiency (1.5%) are evaluated from data. The uncertainties on the event yield associated with lepton identification and isolation are 1-2% for muons and electrons, and 6-7% for τ h . The uncertainty in the LHC integrated luminosity of the data sample is 2.6% [30].
Theoretical uncertainties in the ZZ → acceptance are evaluated using MCFM and by varying the renormalization and factorization scales, up and down, by a factor of two with respect to the default values µ R = µ F = m Z . The variations in the acceptance are 0.1% (NLO qq → ZZ) and 0.4% (gg → ZZ), and can be neglected. Uncertainties related to the choice of the PDF and the strong coupling constant α s are evaluated following the PDF4LHC [31] prescription and using CT10, MSTW08, and NNPDF [32] PDF sets and found to be 4% (NLO qq → ZZ) and 5% (gg → ZZ).
The uncertainties in Z+jets, WZ+jets, and tt yields reflect the uncertainties in the measured values of the misidentification rates and the limited statistics of the control regions in the data, and vary between 20 and 70%.
The uncertainty in the unfolding procedure discussed in Section 7 arises from differences between SHERPA and POWHEG for the unfolding factors (2-3%), from scale and PDF uncertainties (4-5%), and from experimental uncertainties (4-5%).

The ZZ cross section measurement
The measured and expected event yields for all decay channels are summarized in Table 1. The reconstructed four-lepton invariant mass distributions for the 4e, 4µ, 2e2µ, and summed ττ decay channels are shown in Fig. 1 and compared with the SM expectations. The shape of the background is taken from data. The reconstructed four-lepton invariant mass distribution for the combined 4e, 4µ, and 2e2µ channels is shown in Fig. 2(upper left).  The measured yields are used to evaluate the total ZZ production cross section. The signal acceptance is evaluated from simulation and corrected for each individual lepton flavor in bins of p T and η using factors obtained with the "tag-and-probe" technique. The requirements on p T and η for the particles in the final state reduce the full possible phase space of the ZZ → 4 measurement by a factor of 0.56-0.59 for the 4e, 4µ, and 2e2µ and by a factor of 0.18-0.21 for the ττ final states, with respect to all events generated in the mass window 60 < m Z 1 , m Z 2 < 120 GeV. The branching fraction for Z → is (3.3658 ± 0.0023)% for each lepton flavor [33].
To include all final states in the cross section calculation, a simultaneous fit to the number of observed events in all decay channels is performed. The likelihood is written as a combination of individual channel likelihoods for the signal and background hypotheses, with statistical  The correlation between the reconstructed Z 1 and Z 2 masses for the (lower left) combined 4e, 4µ, and 2e2µ final states and (lower right) for ττ final states. Points represent the data, the shaded histograms labeled ZZ represent the POWHEG +GG2ZZ+PYTHIA predictions for ZZ signal, the histograms labeled WZ/Z+jets show background, which is estimated from data, as described in the text. and systematical uncertainties used as nuisance parameters in the fit. Each τ-lepton decay mode, listed in Table 1, is treated as a separate channel. Table 2 lists the total cross section obtained from each individual decay mode as well as the total cross section based on the combination of all channels. Table 2: The total ZZ production cross section as measured in each decay channel and for the combination of all channels.

Decay channel
Total cross section, pb The measured cross sections can be compared to the theoretical value of 7.7 ± 0.6 pb calculated with MCFM 6.0 at NLO qq → ZZ and LO gg → ZZ with the MSTW2008 PDF and renormalization and factorization scales set to µ R = µ F = m Z .
The measurement of the differential cross sections is an important part of this analysis, since it provides detailed information about ZZ kinematics. Three decay channels, 4e, 4µ, and 2e2µ, are combined, since their kinematic distributions are the same; the ττ channel is not included. The observed yields are unfolded using the method described in Ref. [34].
The differential distributions normalized to the fiducial cross sections are presented in Figs. 3 and 4 for the combination of the 4e, 4µ, and 2e2µ decay channels. The fiducial cross section definition includes p T and |η | selections on each lepton, and the 60-120 GeV mass requirement. Figure 3 shows the differential cross sections in bins of p T for: (upper left) the highest-p T lepton in the event, (upper right) the Z 1 , and (lower left) the ZZ system. Figure 3(lower left) shows the normalized dσ/dm ZZ distribution. The data are corrected for background contributions and compared with the theoretical predictions from POWHEG and MCFM. The bottom part of each plot shows the ratio of the measured to the predicted values. Figure 4 shows the angular correlations between Z bosons, which are in good agreement with the MC simulations. Some difference between POWHEG and MCFM calculations appears at very low p T of the ZZ system and for azimuthal separation of the Z bosons close to π. This region is better modeled by POWHEG interfaced with the PYTHIA parton shower program.

Limits on anomalous triple gauge couplings
The presence of ATGCs would be manifested as an increased yield of events at high four-lepton masses. Figure 5 presents the distribution of the four-lepton reconstructed mass, which is used to set the limits, for the combined 4e, 4µ, and 2e2µ channels. The shaded histogram represents the results of the POWHEG simulation for the ZZ signal, and the dashed line, which agrees well with it, is the prediction of SHERPA for f Z 4 = 0 normalized to the MCFM cross section. The dotted line indicates the SHERPA predictions for a specific ATGC value ( f Z 4 = 0.015) with all the other anomalous couplings set to zero.  Figure (lower right) shows the normalized dσ/dm ZZ distribution. Points represent the data, and the shaded histograms labeled ZZ represent the POWHEG +GG2ZZ+PYTHIA predictions for ZZ signal, while the solid curves correspond to results of the MCFM calculations. The bottom part of each subfigure represents the ratio of the measured cross section to the expected one from POWHEG +GG2ZZ+PYTHIA (black crosses with solid symbols) and MCFM (red crosses). The shaded areas on all the plots represent the full uncertainties calculated as the quadrature sum of the statistical and systematic uncertainties, whereas the crosses represent the statistical uncertainties only.  Figure 4: Differential cross section normalized to the fiducial cross section for the combined 4e, 4µ, and 2e2µ decay channels as a function of (left) azimuthal separation of the two Z bosons and (right) ∆R between the Z-bosons. Points represent the data, and the shaded histograms labeled ZZ represent the POWHEG +GG2ZZ+PYTHIA predictions for ZZ signal, while the solid curves correspond to results of the MCFM calculations. The bottom part of each subfigure represents the ratio of the measured cross section to the expected one from POWHEG +GG2ZZ+PYTHIA (black crosses with solid symbols) and MCFM (red crosses). The shaded areas on all the plots represent the full uncertainties calculated as the quadrature sum of the statistical and systematic uncertainties, whereas the crosses represent the statistical uncertainties only. from a comparison of the data to a grid of ATGC models in the ( f Z 4 , f γ 4 ) and ( f Z 5 , f γ 5 ) parameter planes. Expected signal values are interpolated between the 2D grid points using a seconddegree polynomial, since the cross section for signal depends quadratically on the coupling parameters. A profile likelihood method [33] is used to derive the limits. Systematic uncertainties are taken into account by varying the number of expected signal and background events within their uncertainties. No form factor is used when deriving the limits so that the results do not depend on any assumed energy scale characterizing new physics. The constraints on anomalous couplings are displayed in Fig. 6. The curves indicate 68% and 95% confidence levels, and the solid dot shows where the likelihood reaches its maximum. Coupling values outside the contours are excluded at the corresponding confidence levels. The limits are dominated by statistical uncertainties.
One-dimensional 95% CL limits for the f Z,γ 4 and f Z,γ 5 anomalous coupling parameters are: In the one-dimensional fits, all of the ATGC parameters except the one under study are set to zero. These values extend previous CMS results on vector boson self-interactions [3] and improve on the previous limits by factors of three to four, they are presented in Fig. 6 as horizontal and vertical lines.

Summary
Measurements have been presented of inclusive ZZ production cross section in proton-proton collisions at 8 TeV in the ZZ → decay mode, with = e, µ and = e, µ, τ. The data  Figure 5: Distribution of the four-lepton reconstructed mass for the combined 4e, 4µ, and 2e2µ channels. Points represent the data, the shaded histogram labeled ZZ represents the POWHEG +GG2ZZ+PYTHIA predictions for ZZ signal, the histograms labeled WZ/Z+jets shows background, which is estimated from data, as described in the text. The dashed and dotted histograms indicate the results of the SHERPA simulation for the SM ( f Z 4 = 0) and in the presence of an ATGC ( f Z 4 = 0.015) with all the other anomalous couplings set to zero. The last bin includes all entries with masses above 1000 GeV. sample corresponds to an integrated luminosity of 19.6 fb −1 . The measured total cross section σ(pp → ZZ) = 7.7 ± 0.5 (stat.) +0.5 −0.4 (syst.) ± 0.4 (th.) ± 0.2 (lum.) pb and the differential cross sections agree well with the SM predictions. Improved limits on anomalous ZZZ and ZZγ triple gauge couplings are established, significantly restricting their possible allowed ranges.