Measurement of WZ production in proton-proton collisions at sqrt(s) = 7 TeV with the ATLAS detector

A study of WZ production in proton-proton collisions at sqrt(s) = 7 TeV is presented using data corresponding to an integrated luminosity of 4.6 fb^-1 collected with the ATLAS detector at the Large Hadron Collider in 2011. In total, 317 candidates, with a background expectation of 68+/-10 events, are observed in double-leptonic decay final states with electrons, muons and missing transverse momentum. The total cross-section is determined to be sigma_WZ(tot) = 19.0+1.4/-1.3(stat.)+/-0.9(syst.)+/-0.4(lumi.) pb, consistent with the Standard Model expectation of 17.6+1.1/-1.0 pb. Limits on anomalous triple gauge boson couplings are derived using the transverse momentum spectrum of Z bosons in the selected events. The cross section is also presented as a function of Z boson transverse momentum and diboson invariant mass.


Introduction
The underlying structure of electroweak interactions in the Standard Model (SM) is the non-abelian SU (2) L × U (1) Y gauge group. This model has been very successful in describing measurements to date. Properties of electroweak gauge bosons such as their masses and couplings to fermions have been precisely measured at LEP, the Tevatron and SLD [1]. However, triple gauge boson couplings (TGCs) predicted by this theory have not yet been determined with a similar precision.
In the SM, the TGC vertex is completely determined by the electroweak gauge structure and so a precise measurement of this vertex, for example through the analysis of diboson production at the Large Hadron Collider (LHC), tests the gauge symmetry and probes for possible new phenomena involving gauge bosons. Anomalous TGCs, deviating from gauge constraints, 1 The SM tree-level Feynman diagrams for W ± Z production through the s-, t-, and u-channel exchanges in qq ′ interactions at hadron colliders.
may enhance the W ± Z production cross-section at high diboson invariant masses. The cross-section can also be enhanced by the production of new particles decaying into W ± Z pairs, such as those predicted in supersymmetric models with an extended Higgs sector and models with extra vector bosons [2]. At the LHC, W ± Z diboson production arises predominantly from quark-antiquark initial states at leading order (LO) and quark-gluon initial states at next-toleading order (NLO) [3]. Figure 1 shows the LO Feynman diagrams for W ± Z production from qq ′ initial states. Only the s-channel diagram has a TGC vertex and is hence the only channel to contribute to potential anomalous coupling behaviour of gauge bosons.
In proton-proton (pp) collisions at a centre-of-mass energy √ s = 7 TeV, the SM cross-section for W ± Z production is predicted at NLO to be 17.6 +1.1 −1.0 pb. This has been computed for 66 < m ℓℓ < 116 GeV, where m ℓℓ is the invariant mass of the dilepton system from the Z boson decay, using MCFM [4] with the CT10 [5] parton distribution functions (PDFs). The uncertainty on the prediction comes from the PDF uncertainties, eval-uated using the CT10 eigenvector sets, and the QCD renormalization and factorization scales, which are varied simultaneously up or down by a factor of two with respect to the nominal value of (m W + m Z )/2. This paper presents measurements of the W ± Z production cross-section with the ATLAS detector in pp collisions at √ s = 7 TeV. The analysis considers four channels of double-leptonic decays W ± Z→ ℓ ± νℓ + ℓ − involving electrons and muons, i.e. e ± e + e − , µ ± e + e − , e ± µ + µ − and µ ± µ + µ − , plus large missing transverse momentum. The results are based on an integrated luminosity of 4.64±0.08 fb −1 collected in 2011, and supersede the earlier ATLAS results based on a subsample of these data [6].
The paper is organized as follows: Section 2 briefly describes the ATLAS detector and the data sample, including the simulated signal and background samples used in this analysis. Section 3 details the definition and reconstruction of physically observable objects such as particles and jets, and the event selection criteria. Section 4 presents the signal acceptance, and Section 5 the background estimation. Section 6 presents the measured W ± Z production cross-section, constraints on the anomalous TGCs, and the fiducial cross-section as a function of the Z boson transverse momentum and the W ± Z diboson invariant mass.

The ATLAS Detector and Data Sample
The ATLAS detector [7] is a multi-purpose particle physics detector operating at one of the beam interaction points of the LHC. 1 The innermost part of the detector is a precision tracking system covering the pseudorapidity range |η| < 2.5. It consists of silicon pixels, silicon strips, and straw-tube chambers operating in a 2 T axial magnetic field supplied by a superconducting solenoid. Outside the solenoid are highly segmented electromagnetic and hadronic calorimeters covering |η| < 4.9.
The outermost subsystem is a large muon spectrometer covering |η| < 2.7, which reconstructs muon tracks and measures their momenta using the azimuthal magnetic field produced by three sets of air-core superconducting toroids. This analysis primarily uses the inner detector and the electromagnetic calorimeter to recon-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 z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). struct electrons, the inner detector and the muon spectrometer to reconstruct muons, and the electromagnetic and hadronic calorimeters to reconstruct the missing momentum transverse to the beam line, E miss T . The E miss T is corrected to account for muons reconstructed by the inner detector and the muon spectrometer.
W ± Z candidate events with multi-lepton final states are selected with single-muon or single-electron triggers. During the 2011 data-taking, the transverse momentum (p T ) threshold for the single-muon trigger was 18 GeV. The p T threshold for the single-electron trigger was initially 20 GeV, and was raised to 22 GeV in the latter part of 2011 to cope with increasing instantaneous luminosity. For the W ± Z events that pass all selection criteria, the trigger efficiency is in the range of (96-99)% depending on the final state being considered.

Simulated Event Samples
Simulated event samples are used to estimate both the signal selection efficiency and some of the background contributions. The response of the ATLAS detector is simulated [8] using Geant4 [9].
The production of W ± Z pairs and subsequent decays are modelled with the MC@NLO [10,11] event generator, which incorporates NLO QCD matrix elements into the parton shower by interfacing to the Herwig [12] program. The CT10 [5] PDF set is used. The underlying event is modelled with the Jimmy [13] program.
Background processes for W ± Z signal detection are jets produced in association with W ± or Z bosons, 3 in 2011. The average number of interactions per bunch crossing, µ , increased throughout 2011 with the instantaneous luminosity, and reached a maximum of 17. Particles produced in multiple interactions, either coincident with the event of interest or in neighbouring bunch crossings, are referred to as 'pile-up' and are included in the simulation. The number of extra interactions in simulated events is adjusted according to the measured µ distribution in each data-taking period.

Event Reconstruction and Selection
The following event selection criteria are applied to the events collected with the single-electron or single-muon trigger described in Section 2. A primary vertex reconstructed from at least three well-reconstructed chargedparticle tracks, each with p T > 400 MeV, is required in order to remove non-collision background and ensure good object reconstruction. If an event contains more than one primary vertex, the vertex with the largest total p 2 T of the associated tracks is selected.

Object Reconstruction and Selection
Events are selected in the W ± Z→ ℓ ± νℓ + ℓ − channel, where the ℓ are either e or µ. The physical objects selected are electrons, muons, and neutrinos that manifest themselves as E miss T . Contamination from jets, mainly due to semileptonic decays of hadrons or due to misidentification of hadrons as leptons, is suppressed by requiring the electrons and muons to be isolated from other reconstructed objects.
Muon candidates are identified by matching tracks reconstructed in the muon spectrometer to tracks reconstructed in the inner detector. The momentum of the combined muon track is calculated from the momenta of the two tracks corrected for the energy loss in the calorimeter. To identify muons that traverse fewer than two of the three layers of the muon spectrometer, inner detector tracks that match at least one track segment in the muon spectrometer are also included. Such muons are referred to as tagged muons to distinguish them from the combined muons. The transverse momentum of the muon must be greater than 15 GeV and the pseudorapidity |η| < 2.5, using the full range of the inner detector. The muon momentum in simulated events is smeared to account for a small difference in resolution between data and simulation. At the closest approach to the primary vertex, the ratio of the transverse impact parameter d 0 to its uncertainty (the d 0 significance) must be smaller than three, and the longitudinal impact parameter |z 0 | must be less than 1 mm. These requirements reduce contamination from heavy flavour decays. Isolated muons are selected with a requirement that the scalar sum of the p T of the tracks within ∆R = 0.3 of the muon, where ∆R ≡ (∆η) 2 + (∆φ) 2 , must be less than 15% of the muon p T . Electron candidates are formed by matching clusters found in the electromagnetic calorimeter to tracks reconstructed in the inner detector [26]. The transverse energy E T , calculated from the cluster energy and the track direction, must be greater than 15 GeV. The pseudorapidity of the cluster must be in the ranges |η| < 1.37 or 1.52 < |η| < 2.47 to ensure good containment of the electromagnetic shower in the calorimeters. The lateral and transverse shapes of the cluster must be consistent with those of an electromagnetic shower. The d 0 significance must be smaller than 10, and |z 0 | must be less than 1 mm. To ensure isolation, the total calorimeter E T in a cone of ∆R = 0.3 around the electron candidate, not including the E T of the candidate itself, must be less than 14% of the electron E T , and the scalar sum of the p T of the tracks within ∆R = 0.3 of the electron must be less than 13% of the electron p T . The calorimeter response is corrected for the additional energy deposited by pile-up. The electron energy in simulated events is smeared to account for a small difference in resolution between data and simulation. If an electron candidate and a muon candidate are found within ∆R = 0.1 of each other, the electron candidate is removed. This mainly removes final-state radiation, where a photon was misidentified as an electron, and also jets from pile-up that were misidentified as electrons.
The missing transverse momentum E miss T is estimated from reconstructed electrons with |η| < 2.47, muons with |η| < 2.7, jets with |η| < 4.9, as well as clusters of energy in the calorimeter not included in reconstructed objects with |η| < 4.5 [27]. The clusters are calibrated to the electromagnetic or the hadronic energy scale according to cluster topology. The expected energy deposit of the muon in the calorimeter is subtracted. Jets are reconstructed with the anti-k t jet-finding algorithm [28] with radius parameter R = 0.4, and are calibrated and corrected for detector effects using simulation, which has been tuned and validated with data. Events that contain jets, with p T > 20 GeV and |η| < 4.9, which are poorly reconstructed as determined using calorimeter signal timing and shower shape information, are rejected to improve E miss T resolution. 4

Signal Event Selection
Events with two leptons of the same flavour and opposite charge with an invariant mass m ℓℓ within 10 GeV of the Z boson mass are selected. This reduces much of the background from multi-jet, top-quark, and W + W − production. Figure 2(a) shows the m ℓℓ distribution of the Z candidate in events that pass the complete event selection criteria described in this section, except for the m ℓℓ requirement.
Events are then required to have at least three reconstructed leptons originating from the same primary vertex, two leptons from a Z boson decay and one additional lepton attributed to the decay of a W ± boson. To reduce background from Z + jets, the third lepton is required to pass more stringent identification criteria than required for the leptons attributed to the Z boson. The additional criteria imposed on electrons are: a more stringent quality requirement for the matched track, a requirement on the ratio of the energy measured in the calorimeter to the momentum of the matched track, and a requirement that transition radiation is detected if the candidate traversed the straw-tube chambers. Muons attributed to the W ± boson decay are required to be reconstructed as combined, and not tagged, muons.  The transverse mass of the W ± boson is calculated as where p ℓ T is the transverse momentum of the third lepton and ∆φ is the azimuthal angle between the third lepton and the E miss T . Figure 2(d) shows the M W T distribution of the events that reach this stage of the selection. The observed M W T distribution appears to have a narrower peak than predicted by the simulation. The events with 70 < M W T < 80 GeV have been scrutinized for signs of experimental problems, and no issues were found. The limited resolution of the E miss T measurement makes it unlikely that the observed excess is a narrow peak.
M W T is required to be greater than 20 GeV. The E miss T and M W T requirements suppress most of the remaining background from Z + jets and other diboson production.
In order to ensure that the trigger efficiency is well determined, at least one of the muons (electrons) from the W ± Z candidate is required to have p T > 20 (25)   , and (d) are the candidate events remaining before the cut on the variable displayed. The stacked histograms are expectations from simulation for W Z, ZZ, and Z+γ. For Z+jets and tt, the expected shape is taken from simulation but the normalization is taken from the data-driven estimates. The rightmost bins include overflows. Table 1 Expected number of signal W ± Z→ ℓ ± νℓ + ℓ − events after each stage of selection. The first nine rows are computed with a simulated W ± Z sample scaled to 4.6 fb −1 . Efficiency corrections refer to application of correction factors that account for the differences in the trigger and reconstruction efficiencies between the real and simulated data. The last row shows the additional contribution from W ± Z → τ + X. GeV and to be geometrically matched to a muon (electron) reconstructed by the trigger algorithm. These p T thresholds are sufficiently large compared with the trigger p T thresholds to guarantee that the efficiency is not dependent on the p T of the lepton.

Signal Acceptance
The numbers of simulated W ± Z events after each stage of the event selection, scaled to 4.6 fb −1 , are listed in Table 1. The "Efficiency corrections" row shows the predictions corrected for the differences in the trigger and reconstruction efficiencies between the measured and simulated data. The acceptance increases with the number of muons in the final state because the reconstruction efficiency for muons is higher than for electrons. The additional contribution from W ± Z → τ +X, where the τ decays into an electron or a muon, is shown in the last row of Table 1. Table 2 summarizes the systematic uncertainties on the expected signal yields. For electrons and muons, the reconstruction efficiencies, p T scale and resolution, and efficiencies for the isolation and impact-parameter requirements are studied using samples of W ± , Z, and J/ψ decays. Differences observed between data and simulated samples are accounted for, and the uncertainties in the correction factors are used to evaluate the systematic uncertainties.
The uncertainties related to E miss T come mainly from the calibration of cluster and jet energies. The effects of event pile-up are evaluated from the distribution of total transverse energy as a function of µ .
Single-muon and single-electron trigger efficiencies are studied in samples of Z → ℓℓ events. Their effects on the W ± Z measurement are small because the presence of three leptons provides redundancy for triggering. The uncertainty in acceptance due to theoretical modelling in the event generator is estimated by comparing MC@NLO with another NLO generator, POWHEG BOX [29]. Uncertainties due to the PDFs are computed using the CT10 eigenvectors and the difference between the CT10 and MSTW 2008 [30] PDF sets. Uncertainties related to the factorization scale µ F and renormalization scale µ R are estimated by setting µ F = µ R and varying this value up and down by a factor of two.

Background Estimation
The major sources of background are summarized in Table 3. Data-driven methods are used to estimate the background from Z +jets and tt production. Simulation is used for the remaining background sources, including ZZ, tt + W/Z, and Z + γ production. Background from other sources, such as heavy-flavour multi-jet events, is strongly suppressed by the requirement of three leptons with small d 0 , and is negligible. For studies of anomalous TGC (Section 6.2) and of normalized fiducial crosssections (Section 6.3), the background is estimated separately in bins of the transverse momentum p Z T of the Z boson and the invariant mass m WZ of the W ± Z pair.
For background events with three true leptons from vector boson decays, the simulation models the acceptance and efficiency of the selection criteria reliably. The main background in this category is ZZ production, in which both Z bosons decay leptonically. The background distributions and acceptances are determined directly from simulation for this process, and the theoretical cross-section is used for normalization. The total contribution of the ZZ background is 21.0 ± 0.7 events, where the error is dominated by the uncertainty on the theoretical cross-section.
Weak boson radiation associated with tt production can also produce three or more leptons and thus constitutes a significant background despite its small production cross-section. The total contribution of the tt+W/Z background is 4.7±0.2 events. Z +γ events can pass the selection criteria if the photon is misidentified as an electron. The contribution from this background is estimated from simulation to be 3.7 ± 1.1 events.

Z + Jets Background
Production of a Z boson associated with jets is the largest source of background in this measurement. For a Z + jets event to pass the event selection criteria, an isolated lepton must be reconstructed from one of the jets. The extra lepton is usually attributed to the W ± boson.
A lepton-like jet is defined as a jet that passes a few basic lepton selection criteria but not necessarily the full set of selection (for e) or isolation (for both e and µ) requirements. An event containing a Z boson and a lepton-like jet is a background event if the lepton-like jet passes all lepton selection criteria. Those that fail the lepton quality or isolation requirements constitute a control sample. To ensure that the control sample is as similar to the signal as possible, all other event selection criteria, including E miss T > 25 GeV, are applied. In order to estimate the Z + jets background from this control sample, the probability f of a lepton-like jet passing all lepton selection criteria is estimated in another control sample: events containing a Z boson and a lepton-like jet with E miss T < 25 GeV. This sample is dominated by Z +jets events, and f can thus be directly measured. The contributions from other processes are subtracted using simulation. Simulation is also used to estimate the fraction of the Z+jets background in which a lepton-like jet is attributed to the Z boson. 14.5 ± 2.9 11.5 ± 2.5 21.0 ± 3.5 21.0 ± 5.6 From the combination of the two control samples, the total Z + jets background is estimated to be 31.9 ± 9.2 events. The largest source of uncertainty is the extrapolation from the E miss T < 25 GeV sample to the E miss T > 25 GeV sample, which was studied in simulation and in dijet data. Also included are the statistical uncertainties of the control samples and the uncertainties on the theoretical cross-sections of the processes subtracted from the control samples.

tt Background
A large part of the top-quark background is eliminated by the impact-parameter and isolation requirements on the leptons, both of which reject lepton candidates originating in jets. The rejection factors, however, cannot be reliably derived from simulation, and therefore datadriven corrections are applied to the simulated tt events to estimate them.
In this analysis, tt events are the only significant source of background that does not contain a Z boson. A control sample enriched in tt background events is defined by changing the charge combination of the dilepton pair from opposite sign to same sign. All other selection criteria are unchanged. Kinematic distributions of simulated tt events are similar in shape and normalization for same-charge and opposite-charge selections. The data-to-simulation ratio of the event yield in the same-sign sample is 2.2 ± 1.0. This ratio is used to scale the tt background predicted in simulation. Using this procedure, the total contribution from the tt background is estimated to be 6.8 ± 3.2 events.

Results
The numbers of expected and observed events after applying all selection criteria are shown in Table 4. In total, 317 W ± Z candidates are observed in data with 231 ± 8 signal (including final states with τ leptons) and 68 ± 10 background events expected. There are 206 W + Z and 111 W − Z candidates, consistent with the expectations of 186 ± 11 and 110 ± 6, respectively. Invariant mass m WZ of the W ± Z pair. The shaded bands indicate the total statistical and systematic uncertainties of the prediction. For Z+jets and tt, the expected shape is taken from simulation but the normalization is taken from the data-driven estimates. The rightmost bins include overflow. Figure 3 shows the distributions of the transverse momentum p Z T of the Z boson and the invariant mass m WZ of the W ± Z pair in selected events. To reconstruct m WZ , the momenta of the three leptons are combined with E miss T , and a W ± boson mass constraint is used to solve for the z component p ν z of the neutrino momentum. This generally leaves a two-fold ambiguity which is resolved by choosing the solution with the smaller |p ν z |. In 27% of the candidate events, the measured transverse mass is larger than the nominal W ± mass, and no real solutions exist for p ν z . The most likely cause is that the measured E miss T is larger than the actual neutrino p T . In this case, the best estimate is obtained by choosing the real part of the complex solutions, essentially reducing the magnitude of E miss T until a physical solution appears. The data distributions are compared with the expected SM signal and background. The shapes of the Z + jets and tt distributions are taken from simulation and scaled according to the data-driven estimates.

Cross-Section Measurement
Two cross-sections are extracted from the number of observed events. One is the fiducial W ± Z→ ℓ ± νℓ + ℓ − cross-section in a region of final-state phase space defined by the event selection criteria, the other is the total W ± Z production cross-section. To extract the total cross-section, theoretical predictions must be used to extrapolate the measured event yield through the experimentally inaccessible part of the phase space, introducing additional theoretical uncertainties. The fiducial cross-section is free from such extrapolation, and is therefore less sensitive to theoretical uncertainties than the total cross-section.
In order to combine the different channels, a common phase space region is defined in which a fiducial cross-section is extracted. The common phase space is defined as p µ,e T > 15 GeV for the leptons from the decay of the Z bosons, p µ,e T > 20 GeV for the leptons from the decay of the W ± bosons, |η µ,e | < 2.5, p ν T > 25 GeV, |m ℓℓ − m Z | < 10 GeV, and M W T > 20 GeV, to approximate the event selection. In simulated events, the momenta of photons that are within ∆R = 0.1 of one of the three leptons are added to the lepton momentum. In addition, a separation of ∆R > 0.3 between the two leptons of all possible pairings of the three leptons is required. This requirement emulates the isolation criteria applied to the leptons, which tend to reduce the signal acceptance for events with very large Z boson momenta. The definition of the fiducial phase space is identical to that used in Ref. [6] except for the requirement of ∆R > 0.3 between the leptons.
For a given channel W ± Z→ ℓ ± νℓ + ℓ − , where ℓ is either e or µ, the fiducial cross-section is calculated from where N obs and N bkg denote the number of observed and background events respectively, Ldt is the integrated luminosity, and C WZ is the ratio of the number of accepted signal events to the number of generated events in the fiducial phase space. Corrections are applied to C WZ to account for measured differences in trigger and reconstruction efficiencies between simulated and data samples and for the extrapolation to the fiducial phase space. The contribution from τ lepton decays, approximately 4%, is removed from the fiducial cross-section definition by the term in parentheses, where N MC τ is the number of accepted simulated W ± Z events in which at least one of the bosons decays into τ , and N MC sig is the number of accepted simulated W ± Z events with decays into any lepton. Since the fiducial 8 phase space is defined by the kinematics of the finalstate leptons, the calculated cross-section implicitly includes the leptonic branching fractions of the W ± and Z bosons.
The total cross-section is defined in the dilepton invariant mass range of 66 < m ℓℓ < 116 GeV for Z → ℓℓ. It is computed as: where B W and B Z are the W and Z leptonic branching fractions, respectively, and A WZ is the ratio of the number of events within the fiducial phase space to the number of events within 66 < m ℓℓ < 116 GeV. The ratio A WZ calculated using MC@NLO equals 0.330, 0.332, 0.333, and 0.338 for the eee, µee, eµµ, and µµµ channels, respectively. The differences are due to the FSR photons emitted outside the ∆R = 0.1 cone around the electrons.
Cross-section measurements are extracted using a maximum-likelihood method to combine the four channels. The likelihood function is defined as where Pois(N i obs , N i s + N i b ) is the Poisson probability of observing N i obs events in channel i when N i s signal and N i b background events are expected. The nuisance parameters x affect N i s and N i b as where S i k and B i k are the relative systematic uncertainties on the signal and background, respectively, due to the k-th source of systematic uncertainty.
To find the most probable value of σ (fiducial or total) the negative log-likelihood function (from Equation 4) is minimized simultaneously over σ and all the nuisance parameters x k . The final results for the combined fiducial and total cross-sections are σ fid WZ = 92 +7 −6 (stat.) ± 4(syst.) ± 2(lumi.) fb, σ tot WZ = 19.0 +1.4 −1.3 (stat.) ± 0.9(syst.) ± 0.4(lumi.) pb. The fiducial cross-section σ fid WZ is the sum of the four channels. Cross-sections extracted separately for the four channels agree within their uncertainties. The uncertainties are estimated by taking the difference between the cross-section at the minimum of the negative log-likelihood function and the cross-section where the negative log-likelihood is 0.5 units above the minimum Table 5 Systematic uncertainties, in %, on the fiducial and total cross-sections. The background uncertainties are split into data-driven estimates (Z + jets and tt) and estimates from simulation (all other processes). in the direction of the fit parameter σ. The likelihood is maximized over the nuisance parameters for each σ.
The systematic uncertainties include all sources except luminosity. Correlations between the signal and background uncertainties owing to common sources of systematics are taken into account in the definition of the likelihood. Table 5 summarizes the systematic uncertainties on the cross-sections from different sources. The largest single source of systematic uncertainty is the data-driven estimate of the background contributions, dominated by that for Z + jets production (±3.8%).

Anomalous Triple Gauge Couplings
General expressions for the effective Lagrangian for the W W Z vertex can be found in Refs. [31,32]. Retaining only terms that separately conserve charge conjugation C and parity P , the Lagrangian reduces to where g W W Z = −e cot θ W , e is the elementary charge, θ W is the weak mixing angle, W µ and Z µ are the W and Z boson wave functions, X µν ≡ ∂ µ X ν − ∂ ν X µ for X = W or Z, and g Z 1 , κ Z , and λ Z are dimensionless coupling constants. The SM predicts g Z 1 = 1, κ Z = 1, and λ Z = 0. This analysis sets limits on possible deviations of these parameters from their SM values, i.e. on ∆g Z 1 ≡ g Z 1 − 1, ∆κ Z ≡ κ Z − 1, and λ Z , known as the anomalous TGC parameters. The W ± Z production cross-section is a bilinear function of these anomalous TGCs.
To avoid tree-level unitarity violation, the anomalous couplings must vanish asŝ, the four-momentum squared of the W ± Z system, approaches infinity. To achieve this, an arbitrary form factor may be introduced [32]. Here the dipole form factor adopted is where α stands for ∆g Z 1 , ∆κ Z , or λ Z , α 0 is the value of the anomalous coupling at low energy, and Λ is the cut-off scale, the scale at which new physics enters. The results are reported both with and without this form factor.
Since an enhancement in the cross-section due to an anomalous coupling would grow withŝ, measurement sensitivity to anomalous TGCs is enhanced by binning the data in a kinematic variable related toŝ. The transverse momentum p Z T of the Z boson provides a natural choice for such binning as it is strongly correlated withŝ and can be directly reconstructed from the measured lepton momenta with good precision. The data are therefore divided into six bins in p Z T of width 30 GeV followed by a wide bin that includes 180-2000 GeV.
MC@NLO [11] is used to generate W ± Z events with non-SM TGC. The generator computes, for each event, a set of weights that can be used to reweight the full sample to any chosen set of anomalous couplings. This functionality is used to express the predicted signal yields in each bin of p Z T as a function of the anomalous couplings. Figure 4 shows the p Z T distribution of the selected events together with the SM prediction. Also shown for illustration are predictions with nonzero anomalous couplings without form factor: each coupling is increased to the expected 99% confidence-level upper limit while keeping the other two couplings at the SM value. For this plot the 99%, rather than 95%, confidence-level upper limits are used to accentuate differences in shape. As expected, the largest deviations from the SM are in the last bin of p Z T , while the deviations in the lower-p Z T bins depend on which coupling is varied.
Frequentist confidence intervals are obtained on the anomalous couplings by forming a profile likelihood test incorporating the observed number of candidate events in each p Z T bin, the expected signal as a function of the anomalous couplings and the estimated number of background events [33]. The systematic uncertainties are included in the likelihood function as nuisance parameters with correlated Gaussian constraints. A point in the anomalous TGC space is accepted (rejected) at the 95% confidence level if less (more) than 95% of randomly generated pseudo-experiments exhibit a value of the profile likelihood ratio larger than that observed in data. Table 6 summarizes the observed 95% confidence intervals on the anomalous couplings ∆g Z 1 , ∆κ Z , and λ Z , with the cut-off scale Λ = 2 TeV and without the form factor. The limits on each anomalous TGC parameter are obtained with the other two anomalous TGC parameters set to zero. The expected intervals in Table 6 are medians of the 95% confidence-level upper and lower limits obtained in pseudo-experiments that assume the SM coupling. The widths of the expected and observed confidence intervals are dominated by statistical uncertainty. Figure 5 compares the observed limits with the Tevatron results [34,35].
The 95% confidence regions are shown as contours on the (∆g Z 1 , ∆κ Z ), (∆g Z 1 , λ Z ), and (∆κ Z , λ Z ) planes in Figure 6. In each plot the remaining parameter is set to the SM value. The limits were derived with no form factor.

Normalized Fiducial Cross-Sections
The effective Lagrangian adopted in the TGC analysis in Section 6.2 allows us to probe non-SM physics with little model dependence. An alternative approach is to measure kinematic distributions, such as the p Z T spectrum, that could be compared with model-dependent   [34], and D0 [35]. Integrated luminosity, centre-of-mass energy and cut-off Λ for each experiment are shown. theoretical predictions. For this purpose, it is necessary to convert the measured distributions to the underlying true distributions by unfolding the effects of the experimental acceptance and resolution. The iterative Bayesian unfolding proposed by D'Agostini [36] is applied here. An implementation of this technique has previously been used by ATLAS to unfold the p T spectrum of inclusively produced W ± bosons [37].
In the unfolding of binned data, effects of the experimental acceptance and resolution are expressed in a response matrix, each element of which is the probability of an event in the i-th true bin being reconstructed in the j-th measured bin. In iterative Bayesian unfolding, the response matrix is combined with the measured spectrum to form a likelihood, which is then multiplied by a prior distribution to produce the posterior probability of the true spectrum. The SM prediction is used as the initial prior, and once the posterior probability is obtained, it is used as the prior for the next iteration after smoothing. The spectrum becomes insensitive to the initial prior after a few iterations. The number of iterations is adjusted to control the degree of regularization [36]. The differences between successive iterations can be used to estimate the stability of the unfolding method.
To achieve stable unfolding, that is, without excessive sensitivity to statistical fluctuations in data or to details of the unfolding technique, the measured quantity must be a good approximation to the underlying true quantity: the response matrix must be close to diagonal. The p Z T distribution used in the TGC analysis is a natural choice that has good resolution and sensitivity to possible new physics. The fractions of W ± Z events that migrate between two p Z T bins are 2-7%. In addition to p Z T , the distribution of the diboson invariant mass m WZ is also measured. The resolution of the reconstructed m WZ is limited by the E miss T resolution. To avoid large bin-to-bin migration and achieve stable unfolding, three m WZ bins are used: 170-270 GeV, 270-405 GeV, and 405-2500 GeV. With this binning, the fractions of events that migrate between two m WZ bins are 13-17%. Figure 7 shows the fiducial cross-sections extracted in bins of p Z T and m WZ , normalized by the sum of all bins. Comparison with the SM prediction shows good agreement. The corresponding numerical values are presented in Tables 7 and 8 for p Z T and m WZ , respectively. The dominant source of uncertainties on the normalized cross-sections is statistical. The statistical uncertainties are determined by a Monte Carlo method. Two thousand pseudo-experimental spectra are generated by fluctuating the content of each bin according to a Poisson distribution. The unfolding procedure is applied to each pseudo-experiment, and the r.m.s. of the results is taken as the statistical uncertainty. The systematic uncertainties are evaluated by varying the response matrix   for each source of the uncertainty, and combining the resulting changes in the unfolded spectrum. Because of the normalization, the results are affected only by the uncertainties that depend on p Z T or m WZ . The stability of the unfolding procedure is tested in two ways: firstly by comparing the unfolded spectra after two and after three iterations, and secondly by checking that the true variable distribution is correctly reproduced from a simulated sample generated with non-zero anomalous couplings.

Conclusion
Measurements of W ± Z production in proton-proton collisions at √ s = 7 TeV have been presented using a data sample with an integrated luminosity of 4.6 fb −1 , collected with the ATLAS detector at the LHC. The candidate W ± Z events were selected in the fully leptonic final states with electrons, muons, and large missing transverse momentum. In total, 317 candidates were observed with a background expectation of 68 ± 10 events. The fiducial and total cross-sections are determined to be σ fid WZ = 92 +7 −6 (stat.) ± 4(syst.) ± 2(lumi.) fb, and σ tot WZ = 19.0 +1.4 −1.3 (stat.) ± 0.9(syst.) ± 0.4(lumi.) pb, respectively, where the fiducial cross-section is defined by p µ,e T > 15 GeV for the leptons from the decay of the Z bosons, p µ,e T > 20 GeV for the leptons from the decay of the W ± bosons, |η µ,e | < 2.5, p ν T > 25 GeV, |m ℓℓ − m Z | < 10 GeV, M W T > 20 GeV, and ∆R > 0.3 between the two leptons of all possible pairings of the three leptons. These results are significantly more precise than the earlier ATLAS measurement [6] which this paper supersedes. The total cross-section is consistent with the SM expectation of 17.6 +1. without a form factor. The limits are again more stringent than the earlier ATLAS measurement. Normalized fiducial cross-sections have also been presented in bins of p Z T and m WZ , and are in good agreement with SM predictions.