Measurement of the W+W- production in pp collisions at √s = 7 TeV with the ATLAS detector and limits on anomalous WWZ and WWγ couplings

This paper presents a measurement of the W þ W (cid:1) production cross section in pp collisions at ﬃﬃﬃ s p ¼ 7 TeV . The leptonic decay channels are analyzed using data corresponding to an integrated luminosity of 4 : 6 fb (cid:1) 1 collected with the ATLAS detector at the Large Hadron Collider. The W þ W (cid:1) production cross section (cid:1) ð pp ! W þ W (cid:1) þ X Þ is measured to be 51 : 9 (cid:2) 2 : 0 ð stat Þ (cid:2) 3 : 9 ð syst Þ (cid:2) 2 : 0 ð lumi Þ pb , compatible with the Standard Model prediction of 44 : 7 þ 2 : 1 (cid:1) 1 : 9 pb . A measurement of the normalized ﬁducial cross section as a function of the leading lepton transverse momentum is also presented. The reconstructed transverse momentum distribution of the leading lepton is used to extract limits on anomalous WWZ and WW(cid:2) couplings.

Measurement of W þ W À production in pp collisions at ffiffi ffi s p ¼ 7 TeV with the ATLAS detector and limits on anomalous WWZ and WW couplings G. Aad et al. * (ATLAS Collaboration) (Received 10 October 2012;published 3 June 2013) This paper presents a measurement of the W þ W À production cross section in pp collisions at ffiffi ffi s p ¼ 7 TeV. The leptonic decay channels are analyzed using data corresponding to an integrated luminosity of 4:6 fb À1 collected with the ATLAS detector at the Large Hadron Collider. The W þ W À production cross section ðpp ! W þ W À þ XÞ is measured to be 51:9 AE 2:0ðstatÞ AE 3:9ðsystÞ AE 2:0ðlumiÞ pb, compatible with the Standard Model prediction of 44:7 þ2:1 À1:9 pb. A measurement of the normalized fiducial cross section as a function of the leading lepton transverse momentum is also presented. The reconstructed transverse momentum distribution of the leading lepton is used to extract limits on anomalous WWZ and WW couplings. DOI: 10.1103/PhysRevD.87.112001 PACS numbers: 14.70.Fm, 12.60.Cn, 13.85.Fb, 13.38.Be

I. INTRODUCTION
Measurements of vector boson pair production at particle colliders provide important tests of the electroweak sector of the Standard Model (SM). Deviations of the production cross section or of kinematic distributions from their SM predictions could arise from anomalous triple gauge boson interactions [1] or from new particles decaying into vector bosons [2]. Vector boson pair production at the Large Hadron Collider (LHC) [3] also represents an important source of background to Higgs boson production [4] and to searches for physics beyond the SM. This paper describes a measurement of the W þ W À (hereafter WW) inclusive and differential production cross sections and limits on anomalous WWZ and WW triple gauge couplings (TGCs) in purely leptonic decay channels WW ! '' 0 0 with ', ' 0 ¼ e, . WW ! ' and WW ! processes with leptons decaying into electrons or muons with additional neutrinos are also included. Three final states are considered based on the lepton flavor, namely, ee, , and e. Leading-order (LO) Feynman diagrams for WW production at the LHC include s-channel production with either a Z boson or a virtual photon as the mediating particle or u-and t-channel quark exchange. The s-and t-channel diagrams are shown in Fig. 1. Gluongluon fusion processes involving box diagrams contribute about 3% to the total cross section. The SM cross section for WW production in pp collisions at ffiffi ffi s p ¼ 7 TeV is predicted at next-to-leading order (NLO) to be 44:7 þ2:1 À1:9 pb. The calculation of the total cross section is performed using MCFM [5] with the CT10 [6] parton distribution functions (PDFs). An uncertainty of þ4:8% À4:2% is evaluated based on the variation of renormalization ( R ) and factorization ( F ) scales by a factor of two ( þ3:6% À2:5% ) and CT10 PDF uncertainties derived from the eigenvector error sets as described in Ref. [7] ( þ3:1% À3:4% ) added in quadrature. The contribution from SM Higgs production [4] with the Higgs boson decaying into a pair of W bosons (H ! WW) depends on the mass of the Higgs boson (m H ). For m H ¼ 126 GeV, the SM WW production cross section would be increased by 3%. Contributions from vector boson fusion (VBF) and double parton scattering (DPS) [8] processes are found to be less than 0.1%. The processes involving the SM Higgs boson, VBF and DPS are not included neither in the WW cross-section predictions, nor in deriving the corrected measured cross sections. Events containing two W bosons from top-quark pair production and single top-quark production are explicitly excluded from the signal definition, and are treated as background contributions.
The s-channel diagram contains the WWZ and WW couplings. The SM predicts that these couplings are g WWZ ¼ Àe cot W and g WW ¼ Àe, where e is related to the fine-structure constant ð¼ e 2 =4Þ and W is the FIG. 1 (color online). SM LO Feynman diagrams for WW production through the q " q initial state at the LHC for (a) the s channel and (b) the t-channel. The s-channel diagram contains the WWZ and WW TGC vertices. weak mixing angle. Detailed studies of WW production allow one to test the non-Abelian structure of the SM electroweak theory and probe anomalous WWZ and WW TGCs, which may be sensitive to low-energy manifestations of new physics at a higher mass scale. WW production and anomalous WWZ and WW TGCs have been previously studied by the LEP [9] and Tevatron [10] experiments, and were also recently studied by the LHC experiments [11][12][13]. The data set used in this paper corresponds to an integrated luminosity of 4:6 fb À1 [14] collected with the ATLAS detector at the LHC, and the results presented supersede the previous ATLAS measurements [12].
This paper is organized as follows. Section II describes the overall analysis strategy. Section III describes the ATLAS detector. Section IV summarizes the Monte Carlo (MC) simulation used for the signal and background modeling. Section V details the reconstruction of final-state objects and event selection criteria. Sections VI and VII describe the WW signal and background estimation. Results are presented in Sec. VIII for inclusive and fiducial cross sections; in Sec. IX for the normalized differential fiducial cross section as a function of the transverse momentum (p T ) [15] of the lepton with higher p T (denoted by the ''leading lepton''); and in Sec. X for limits on anomalous WWZ and WW TGCs. Conclusions are drawn in Sec. XI.

II. ANALYSIS STRATEGY
Candidate WW events are selected with two oppositesign charged leptons (electrons or muons) and large missing transverse momentum (E miss T ), a signature referred to as '' '' 0 þ E miss T '' in this paper. The cross section is measured in a fiducial phase space and also in the total phase space. The fiducial phase space is defined in Sec. IV and is chosen to be close to the phase space defined by the offline selection criteria. The fiducial cross section fid WW for the pp ! WW þ X ! '' 0 0 þ X process is calculated according to the equation where N data and N bkg are the number of observed data events and estimated background events, respectively. C WW is defined as the ratio of the number of events satisfying all offline selection criteria to the number of events produced in the fiducial phase space and is estimated from simulation. L is the integrated luminosity of the data sample. The total cross section WW for the pp ! WW þ X process is calculated for each channel using the equation where A WW represents the kinematic and geometric acceptance from the total phase space to the fiducial phase space, and BR is the branching ratio for both W bosons decaying into e or (including decays through leptons with additional neutrinos). The combined total cross section from the three channels is determined by minimizing a negative log-likelihood function as described in Sec. VIII. To obtain the normalized differential WW cross section in the fiducial phase space (1= fid WW Â d fid WW =dp T ), the reconstructed leading lepton p T distribution is corrected for detector effects after the subtraction of background contamination. The measured leading lepton p T spectrum is also used to extract anomalous WWZ and WW TGCs.

III. THE ATLAS DETECTOR
The ATLAS detector [16] is a multipurpose particle physics detector with approximately forward-backward symmetric cylindrical geometry. The inner detector (ID) system is immersed in a 2 T axial magnetic field and provides tracking information for charged particles in the pseudorapidity range jj < 2:5. It consists of a silicon pixel detector, a silicon microstrip detector, and a transition radiation tracker.
The calorimeter system covers the pseudorapidity range jj < 4:9. The highly segmented electromagnetic calorimeter consists of lead absorbers with liquid-argon (LAr) as active material and covers the pseudorapidity range jj < 3:2. In the region jj < 1:8, a presampler detector using a thin layer of LAr is used to correct for the energy lost by electrons and photons upstream of the calorimeter. The electron energy resolution is about 2%-4% at p T ¼ 45 GeV. The hadronic tile calorimeter is a steel/scintillating-tile detector and is situated directly outside the envelope of the electromagnetic calorimeter. The two endcap hadronic calorimeters have LAr as the active material and copper absorbers. The calorimeter coverage is extended to jj ¼ 4:9 by a forward calorimeter with LAr as active material and copper and tungsten as absorber material. The jet energy resolution is about 15% The muon spectrometer measures the deflection of muons in the large superconducting air-core toroid magnets. It covers the pseudorapidity range jj < 2:7 and is instrumented with separate trigger and high-precision tracking chambers. A precision measurement of the track coordinates in the principal bending direction of the magnetic field is provided by drift tubes in the pseudorapidity range jj < 2:0. At large pseudorapidities, cathode strip chambers with higher granularity are used in the innermost plane over 2:0 < jj < 2:7. The muon trigger system, which covers the pseudorapidity range jj < 2:4, consists of resistive plate chambers in the barrel (jj < 1:05) and thin gap chambers in the endcap regions (1:05 < jj < 2:4). The muon momentum resolution is about 2%-3% at p T ¼ 45 GeV.
A three-level trigger system is used to select events for offline analysis. The level-1 trigger is implemented in hardware and uses a subset of detector information to reduce the event rate to a design value of at most 75 kHz. This is followed by two software-based trigger levels, level-2 and the event filter, which together reduce the event rate to about 400 Hz which is recorded for analysis.

IV. MONTE CARLO SIMULATION
Signal WW events are modeled using MC-simulated samples, while contributions from various SM background physics processes are estimated using a combination of MC samples and control samples from data. MC events are generated at ffiffi ffi s p ¼ 7 TeV and processed through the full detector simulation [17] based on GEANT4 [18]. The simulation includes the modeling of additional pp interactions in the same and neighboring bunch crossings.
The simulation of the WW signal production is based on samples of q " q ! WW and gg ! WW events generated with MC@NLO [19] and GG2WW [20], respectively. Initial parton momenta are modeled with the CT10 PDFs. The parton showering and hadronization, and the underlying event are modeled with HERWIG [21] and JIMMY [22].
The SM background processes, which are described in Sec. VII, are simulated using ALPGEN [23] for the W þ jets, Drell-Yan Z= Ã þ jets and W processes, MC@NLO for the t " t process, MADGRAPH [24] for the W Ã process, ACERMC [25] for the single top-quark process, and HERWIG for WZ and ZZ processes. The TAUOLA [26] and PHOTOS [27] programs are used to model the decay of leptons and QED final-state radiation of photons, respectively. The MC predictions are normalized to the data sample based on the integrated luminosity and cross sections of the physics processes. Higher-order corrections, if available, are applied. The cross section is calculated to next-to-next-toleading-order (NNLO) accuracy for W and Z= Ã [28], NLO plus next-to-next-to-leading-log order for t " t [29], and NLO for WZ and ZZ processes [5].
To improve the agreement between data and simulation, lepton selection efficiencies are measured in both data and simulation, and correction factors are applied to the simulation to account for differences with respect to data. Furthermore, the simulation is tuned to reproduce the calorimeter energy and the muon momentum scale and resolution observed in data.

V. OBJECTS AND EVENT SELECTION
The data analyzed were selected online by a singlelepton (e or ) trigger with a threshold on the transverse energy in the electron case and on the transverse momentum in the muon case. Different thresholds (18 GeV for muons and 20 GeV or 22 GeV for electrons) were applied for different running periods. After applying data quality requirements, the total integrated luminosity is 4:6 fb À1 with an uncertainty of 3.9% for all three channels ee, , and e [14].
Because of the presence of multiple pp collisions in a single bunch crossing, each event can have multiple vertices reconstructed. The primary vertex of the hard collision is defined as the vertex with the highest P p 2 T of associated ID tracks. To reduce contamination due to cosmic rays, the primary vertex must have at least three associated tracks with p T > 0:4 GeV.
Electrons are reconstructed from a combination of an electromagnetic cluster in the calorimeter and a track in the ID, and are required to have p T > 20 GeV and lie within the range jj < 2:47, excluding the transition region between the barrel and endcap calorimeters (1:37 < jj < 1:52). The electron p T is calculated using the energy measured in the electromagnetic calorimeter and the track direction measured by the ID. Candidate electrons must satisfy the tight quality definition [30] reoptimized for 2011 data-taking conditions, which is based on the calorimeter shower shape, track quality, and track matching with the calorimeter cluster.
Muon candidates must be reconstructed in the ID and the muon spectrometer, and the combined track is required to have p T > 20 GeV and jj < 2:4. Good quality reconstruction is ensured by requiring minimum numbers of silicon microstrip and pixel hits associated with the track [31].
To ensure candidate electrons and muons originate from the primary interaction vertex, they are also required to have a longitudinal impact parameter (jz 0 j) smaller than 1 mm and a transverse impact parameter (jd 0 j) divided by its resolution ( d 0 ) smaller than ten for electrons and three for muons. These requirements reduce contamination from heavy-flavor quark decays and cosmic rays.
To suppress the contribution from hadronic jets which are misidentified as leptons, electron and muon candidates are required to be isolated in both the ID and the calorimeter. The sum of transverse energies of all clusters around the lepton but not associated with the lepton within a cone of size ÁR ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi ðÁÞ 2 þ ðÁÞ 2 p ¼ 0:3 is required to be less than 14% of the lepton transverse momentum. Corrections to the sum of transverse energies of all clusters around the lepton are applied to account for the energy deposition inside the isolation cone due to electron energy leakage or muon energy deposition and additional pp collisions. The sum of the p T of all tracks with p T > 1 GeV that originate from the primary vertex and are within a cone of size ÁR ¼ 0:3 around the lepton track is required to be less than 13% (15%) of the electron (muon) p T .
Jets are reconstructed from topological clusters of energy in the calorimeter using the anti-k t algorithm [32] with radius parameter R ¼ 0:4. Topological clustering extends up to jj ¼ 4:9, and clusters are seeded by calorimeter cell deposits having energy exceeding 4 standard deviations of the cell noise level. Jet energies are calibrated D 87, 112001 (2013) using p T -and -dependent correction factors based on the simulation, and validated by collision data studies [33]. Jets are classified as originating from b-quarks by using an algorithm that combines information about the impact parameter significance of tracks in a jet which has a topology of semileptonic b-or c-hadron decays [34]. The efficiency of the b-tagging algorithm is 85% for b-jets in t " t events, with an average light jet rejection factor of 10.
Since electrons are also reconstructed as jets, if a reconstructed jet and an electron satisfying the criteria mentioned above lie within ÁR ¼ 0:3 of each other, the jet is discarded. Electrons and muons are required to be separated from each other by ÁR > 0:1. Since muons can radiate photons which can convert to electron-positron pairs, if a muon and an electron lie within ÁR ¼ 0:1 of each other, the electron is discarded.
The measurement of the missing transverse momentum two-dimensional vectorẼ miss T and its magnitude E miss T is based on the measurement of the energy collected by the electromagnetic and hadronic calorimeters, and muon tracks reconstructed by the ID and the muon spectrometer. Calorimeter cells associated with reconstructed jets with p T > 20 GeV are calibrated at the hadronic energy scale, whereas calorimeter cells not associated with any object are calibrated at the electromagnetic energy scale.
Events with exactly two oppositely charged leptons passing the lepton selection criteria above are selected. At least one of the two leptons is required to be geometrically matched to a lepton reconstructed by the trigger algorithm. In order to ensure that the lepton trigger efficiency reaches its plateau region and does not depend on the p T of the lepton, the matching lepton is required to have p T > 25 GeV. The leading lepton p T requirement also helps to reduce the W þ jets background contribution.
Events satisfying the above requirements are dominated by the contribution from the Drell-Yan process. To reject this background contribution, different requirements on the dilepton invariant mass m '' 0 and a modified missing transverse energy, E miss T;Rel , are applied to each final state. The E miss T;Rel variable is defined as where Á is the difference in the azimuthal angle between theẼ miss T and the nearest lepton or jet. The E miss T;Rel variable is designed to reject events where the apparent E miss T arises from a mismeasurement of lepton momentum or jet energy. The selection criteria applied to m '' 0 and E miss T;Rel are m '' 0 > 15, 15, 10 GeV, jm '' 0 À m Z j > 15, 15, 0 GeV, and Comparison between data and simulation for the dilepton invariant mass distribution before the m '' 0 cut for the (a) ee, (b) , and (c) e channels, respectively. The contributions from various physics processes are estimated using MC simulation and normalized to the cross sections as described in Sec. IV. With the application of the m '' 0 and E miss T;Rel selection criteria, the remaining background events come mainly from t " t and single top-quark processes. To reject this background contribution, events are vetoed if there is at least one jet candidate with p T > 25 GeV and jj < 4:5 (this selection criterion is denoted by the term ''jet veto'' in this paper). To further reduce the Drell-Yan contribution, the transverse momentum of the dilepton system, p T ð'' 0 Þ, is required to be greater than 30 GeV for all three channels.  show comparisons between data and simulation for the m '' 0 , E miss T;Rel , jet multiplicity, and p T ð'' 0 Þ distributions before the successive cuts are applied to the ee, , and e channels, respectively. The contributions from various physics processes are estimated using MC simulation and normalized to the cross sections as described in Sec. IV. These plots indicate the discrimination power of these variables to reduce the dominant t " t, W þ jets, and Drell-Yan backgrounds and improve the signal-to-background ratio. Discrepancies between data and SM predictions based on pure MC estimates for some plots indicate the need for data-driven background estimates as are used for the WW signal extraction.

VI. WW SIGNAL ACCEPTANCE
The fractions of simulated WW signal events remaining after each step of the event selection are summarized in Table I. The fractions for direct WW decays into electrons or muons are shown separately from processes involving leptons (WW ! ' and WW ! processes with leptons decaying into electrons or muons). The acceptance for the channel is higher than the ee channel since the identification efficiency for muons is higher than that for FIG. 4 (color online). Comparison between data and simulation for the jet multiplicity distribution of jets with p T > 25 GeV before jet veto requirement for the (a) ee, (b) , and (c) e channels, respectively. The contributions from various physics processes are estimated using MC simulation and normalized to the cross sections as described in Sec. IV. The error band on each plot includes both statistical and systematic uncertainties on the signal and background estimations. Systematic uncertainties on the signal estimation are described in Sec. VI. Systematic uncertainties on background estimations include uncertainties on lepton, jet, and E miss T reconstruction and identification, as well as uncertainties on theoretical production cross sections for these processes. FIG. 5 (color online). Comparison between data and simulation for the dilepton p T distribution before the p T ð'' 0 Þ cut for the (a) ee, (b) , and (c) e channels, respectively. The contributions from various physics processes are estimated using MC simulation and normalized to the cross sections as described in Sec. IV. The error band on each plot includes both statistical and systematic uncertainties on the signal and background estimations. Systematic uncertainties on the signal estimation are described in Sec. VI. Systematic uncertainties on background estimations include uncertainties on lepton, jet, and E miss T reconstruction and identification, as well as uncertainties on theoretical production cross sections for these processes. D 87, 112001 (2013) electrons. The acceptance for the e channel is the highest one due to looser selection requirements applied to m '' 0 and E miss T;Rel . In order to minimize the theoretical uncertainty due to the extrapolation from the measured phase space to the total phase space for the cross-section measurement, a fiducial phase space is defined at the generator level by selection criteria similar to those used offline. Generatorlevel jets are reconstructed by running the anti-k t algorithm with radius parameter R ¼ 0:4 on all final-state particles generated with the MC@NLO and GG2WW event generators after parton showering and hadronization. The fiducial phase space is defined with the following criteria: lepton p T > 20 GeV, muon pseudorapidity jj < 2:4, electron pseudorapidity jj < 1:37 or 1:52 < jj < 2:47, no generator-level jets with p T > 25 GeV, rapidity jyj < 4:5, and separated from an electron by ÁR > 0:3. The leading lepton p T is required to be above 25 GeV and p '' 0 T > 30 GeV. The events are further required to have m '' 0 > 15, 15, 10 GeV, jm '' 0 À m Z j > 15, 15, 0 GeV, and p þ " T;Rel > 45, 45, 25 GeV for the ee, , and e channels, respectively. The p þ " T;Rel variable is defined similarly to E miss T;Rel , where theẼ miss T is replaced by the vector sum of thep T of the two generator-level neutrinos. To reduce the dependence on QED radiation, the electron and muon p T include contributions from photons within ÁR ¼ 0:1 of the lepton direction.
With this definition of the fiducial phase space, the overall acceptance times efficiency can be separated into two factors A WW and C WW , where A WW represents the extrapolation from the fiducial phase space to the total phase space, while C WW represents detector effects such as lepton trigger and identification efficiencies, with a small contribution from differences in generated and measured phase spaces due to detector resolution.
Corrections to the simulation of lepton identification efficiencies and resolutions are discussed in Sec. IV. A correction to the modeling of the jet veto efficiency (the fraction of events with zero reconstructed jets) is determined as the ratio of data to MC jet veto efficiencies for the Z= Ã ! '' process. This ratio is applied to WW MC [35] as where P WW pred is the corrected jet veto efficiency for pp ! WW, P MC WW is the MC estimate of this efficiency, and P data is the efficiency determined using Z= Ã ! '' events selected with two leptons satisfying the lepton selection criteria and jm '' À m Z j < 15 GeV in data (MC). By applying this correction, experimental uncertainties associated with the jet veto efficiency are significantly reduced, in particular, the uncertainty on the jet energy scale. The dominant uncertainty is due to the theoretical prediction of the differences in jet energy spectra between the WW and Z= Ã processes, which are both modeled with MC@NLOþHERWIG for this correction.
For the factor C WW (A WW ), the dominant uncertainty is the theoretical uncertainty on P MC Z= Ã (P MC WW ). The theoretical uncertainty from missing higher-order corrections is evaluated by varying renormalization and factorization scales up and down by a factor of 2 for both the inclusive (! 0) and exclusive (! 1) jet cross sections and adding these two uncertainties in quadrature [36]. Uncertainties associated with the parton shower and hadronization models are evaluated by comparing the PYTHIA [37] and HERWIG models, interfaced to the MC generating the process of interest. Uncertainties due to PDFs are computed using the CT10 error eigenvectors, and using the difference between the central CT10 and MSTW2008NLO [38] PDF sets. Including uncertainties from the jet energy scale (JES) and jet energy resolution (JER), P WW pred is estimated to be 0:624 AE 0:012, 0:625 AE 0:010, and 0:633 AE 0:010 for the ee, , and e channels, respectively.
Additional theoretical uncertainties on A WW are evaluated using the same procedures as for the jet veto efficiency. Additional uncertainties on C WW are calculated using uncertainties on the lepton trigger, reconstruction and isolation efficiencies, as well as energy scale and resolution uncertainties on the reconstruction of lepton, jet, soft clustered energy in the calorimeter, and energy deposits from additional pp collisions. The uncertainty on the single-lepton trigger efficiency is less than 0.5% [39]. Electron and muon reconstruction and identification efficiency uncertainties are less than 2.0% and 0.4%, respectively [40]. The lepton isolation efficiency is determined with an uncertainty of 0.3% and 0.2% for electrons and muons, respectively. The simulation is corrected for the differences with respect to the data in lepton energy scale and resolution. The uncertainty is less than 1.0% and 0.1% on the energy scale and less than 0.6% and 5.0% on the resolution, for electrons and muons, respectively [30]. Uncertainties on the JES range from 2.5% to 8%, varying with jet p T and [41]. Uncertainties on the JER range from 9%-17% for jet p T ' 30 GeV to about 5%-9% for jets with p T > 180 GeV depending on jet [41]. The uncertainties on the lepton energy scale and resolution, JES and JER, are propagated to the E miss T , which also receives contributions from energy deposits due to additional pp collisions in the same or close by bunch crossings, and from energy deposits not associated with any reconstructed object [42].
All systematic uncertainties described above are propagated to the calculations of A WW , C WW , and A WW Â C WW . The overall systematic uncertainty on A WW is 5.7% for all three channels. The contributions from all systematic sources for A WW are listed in Table II. The overall systematic uncertainty on C WW is 4.2%, 3.1%, and 3.2% for the ee, , and e channels, respectively. The contributions from all systematic sources for C WW are listed in Table III.
The product of A WW Â C WW is defined as the ratio of events satisfying all offline selection criteria to the number of events produced in the total phase space. The systematic uncertainty on A WW Â C WW is 4.9%, 4.0%, and 4.1% for the ee, , and e channels. Owing to the presence of correlations between A and C, these uncertainties are smaller than those obtained by adding in quadrature the uncertainties from the PDFs, F , R , and parton shower model. As a result, the uncertainty on A WW Â C WW is used for the calculation of the total cross-section uncertainty in each individual channel. Table IV summarizes the central value and also the statistical and systematic uncertainties on A WW , C WW , and A WW Â C WW for all three channels.

VII. BACKGROUND ESTIMATION
SM processes producing the '' 0 þ E miss T signature with no reconstructed jets in the final state are top-quark production, when additional jets in the final state are not reconstructed or identified (denoted by ''top-quark background''); W production in association with jets (denoted by ''W þ jets background'') when one jet is reconstructed as a lepton; Z= Ã production in association with jets (denoted by ''Drell-Yan background'') when apparent E miss T is generated from the mismeasurement of the p T of the two leptons from Z= Ã boson decay; WZ and ZZ processes when only two leptons are reconstructed in the final state; and the W process when the photon converts into electrons. The contribution from QCD multijet production when two jets are reconstructed as leptons is found to be negligible.

A. Background contribution from SM non-WW diboson production processes
The expected background contributions from SM non-WW diboson processes (WZ, ZZ, and W) are  D 87, 112001 (2013) estimated using simulation. The total number of selected non-WW diboson background events corresponding to 4:6 fb À1 is estimated to be 13 AE 1ðstatÞ AE 2ðsystÞ, 21 AE 1ðstatÞ AE 2ðsystÞ, and 44 AE 2ðstatÞ AE 6ðsystÞ for the ee, , and e channels, respectively. The systematic uncertainties arise mainly from theoretical uncertainties on the non-WW diboson production cross sections and uncertainties on the lepton, jet, and E miss T modeling in the simulation.

B. Background contribution from SM top-quark production processes
Background contributions from top-quark production processes are suppressed by the jet veto requirement. However, top-quark events containing no reconstructed jets with p T > 25 GeV and jj < 4:5 could still mimic the signature of WW candidates. The top-quark background contribution is estimated using a data-driven method.
An extended signal region (ESR) is defined after the E miss T;Rel cut but before applying the jet veto and p T ð'' 0 Þ criteria. In addition, a control region (CR) is defined as a subset of the ESR, which contains events having at least one b-tagged jet with p T > 20 GeV. The jet multiplicity distribution for top-quark events in the ESR, T ESR data , is estimated from the jet multiplicity distribution in the CR, T CR data . In a first step, the non-top-quark background distribution T CR MC;nt in the CR is estimated with simulation, scaled by a normalization factor f 0 n , and then subtracted from the measured T CR data distribution. Subsequently, the resulting distribution is extrapolated bin-by-bin from the CR to the ESR via the MC prediction of the ratio T ESR MC;i =T CR MC;i for each jet multiplicity bin i. The method can be summarized by the following equation for each jet multiplicity bin: where each symbol T represents a full jet multiplicity distribution. The normalization scale factor f 0 n for the non-top-quark background contributions in the CR is determined from events in the ESR by fitting the jet multiplicity distribution observed in data with the templates constructed from the data in the CR for top-quark contributions and from simulation for non-top-quark contributions. The value of f 0 n is found to be 1:07 AE 0:03. In a final step, the number of top-quark background events in the signal region is estimated using the number of topquark events in the ESR observed in data scaled by the ratio of top-quark events in the signal region to the number in the ESR in the MC simulation for the zero-jet bin.
The number of top-quark background events in the signal region is estimated to be 22 AE 12ðstatÞ AE 3ðsystÞ, 32 AE 14ðstatÞ AE 5ðsystÞ, and 87 AE 23ðstatÞ AE 13ðsystÞ for the ee, , and e channels, respectively. The statistical uncertainty is mainly due to the limited number of data events observed in the CR. The systematic uncertainties are dominated by the b-tagging uncertainty.
An alternative data-driven method is used to cross-check the top-quark background estimation. To reduce the associated uncertainties on the jet veto probability, a data-based correction is derived from a top-quark dominated sample based on the WW selection but with the requirement of at least one b-jet with p T > 25 GeV [12]. In this sample, the ratio P 1 of events with one jet to the total number of events is sensitive to the modeling of the jet energy spectrum in top-quark events. A multiplicative correction based on the ratio P data 1 =P MC 1 is applied to reduce the uncertainties resulting from the jet veto requirement. The results from the two data-driven methods are found to be consistent with each other within their uncertainties.

C. Background contribution from W þ jets production process
The W þ jets process can produce the '' 0 þ E miss T signature when one jet is reconstructed as a charged lepton. Since the probability for a jet to be identified as a lepton may not be accurately modeled in the MC simulation, a data-driven method is employed to estimate this contribution. A leptonlike jet is defined as a jet that passes all lepton selection criteria but fails the lepton isolation requirement in the muon case, and fails at least one of the isolation or tight quality requirements in the electron case. The ratio f ' is then calculated as the ratio of jets satisfying the full lepton identification criteria to the number of leptonlike jets. A jet-enriched data sample is selected containing one lepton that passes all lepton selection criteria and a leptonlike jet. The number of events in this sample is then scaled by the ratio f ' to obtain the expected number of W þ jets events in the signal region. The ratio f ' is measured as a function of the jet p T and from a jet-enriched sample for electrons and muons separately. The number of W þ jets background events in the signal regions is estimated to be 21 AE 1ðstatÞ AE 11ðsystÞ, 7 AE 1ðstatÞ AE 3ðsystÞ, and 70 AE 2ðstatÞ AE 31ðsystÞ for the ee, , and e channels, respectively. The dominant source of systematic uncertainties stems from the f ' measurement. The same method is applied to a W þ jets-enriched sample selected with the requirement of two same-sign leptons to validate the W þ jets estimation method. Consistent results are obtained for the number of observed and predicted events in this control region.
An alternative method is used to check the W þ jets estimation in the signal region. This method defines leptons with two different sets of quality criteria, one with the standard lepton selection criteria (called tight lepton here) and the other one with less restrictive lepton identification criteria (called loose lepton here). For loose muons, the isolation requirement is dropped. For loose electrons, the medium electron identification criteria as defined in Ref. [30] are used and the isolation requirement is also dropped. Events with two loose leptons are assigned to one of four categories depending on whether both leptons, only the leading lepton, only the trailing lepton, or neither of the two leptons, satisfy the tight lepton identification criteria. The corresponding numbers of events are denoted by N TT , N TL , N LT , and N LL . The sample composition can be solved from a linear system of equations: ðN TT ; N TL ; N LT ; N LL Þ T ¼ EðN '' 0 ; N 'j ; N j' 0 ; N jj Þ T ; (6) where N '' 0 is the number of events with two prompt leptons, N 'j (N j' 0 ) is the number of events where only the leading (trailing) lepton is a prompt lepton, and N jj is the number of events where neither of the two leptons are prompt leptons. The 4 Â 4 matrix E contains the probabilities for a loose quality lepton to pass the tight quality selection for both prompt leptons and jets. These probabilities are estimated by applying the loose and tight selections to Z= Ã ! '' events and to a sample of dijet events, respectively. To take into account the lepton p T dependence of these two probabilities, the matrix equation is inverted for each event, giving four weights, corresponding to these four combinations. These weights are then summed over all events in the signal region with loose lepton requirements to yield the estimated total number of background events from W þ jets and dijet processes. The results from the two data-driven methods are found to be consistent with each other within their uncertainties.

D. Background contribution from Drell-Yan production process
The Drell-Yan background is one of the dominant background contributions in the ee and channels. Its contribution is suppressed by the requirements on m '' 0 , E miss T;Rel , and p T ð'' 0 Þ. A control region dominated by the Drell-Yan process is defined by applying the same set of selection cuts as used for the signal region and reversing the p T ð'' 0 Þ cut. The Drell-Yan background in the signal region is estimated from the number of events observed in this control region, after subtracting other background contributions using MC expectations, scaled by the ratio of the number of MC Z þ jets events in the signal region to the number in the control region. The number of Drell-Yan background events in the signal region is estimated to be 12 AE 3ðstatÞ AE 3ðsystÞ, 34 AE 6ðstatÞ AE 10ðsystÞ, and 5 AE 2ðstatÞ AE 1ðsystÞ events in the ee, , and e channels, respectively. As a crosscheck, the results obtained above are compared to the predictions from simulation. Good agreement between the two estimates is found. Table V shows the number of events selected in data and the estimated background contributions with statistical and systematic uncertainties for the three individual channels and the combined channel. The expected numbers of WW signal events for the individual and the combined channels are also shown. In total 1325 '' 0 þ E miss T candidates are observed in data with 824 AE 4ðstatÞ AE 69ðsystÞ signal events expected from the WW process and 369 AE 31ðstatÞ AE 53ðsystÞ background events expected from non-WW processes. The WW processes mediated by a SM Higgs boson with a mass of 126 GeV would contribute an additional 3, 7, and 16 events in the ee, , and e channels, respectively. Figure 6 shows the comparison between data and predictions for the leading lepton p T , azimuthal angle difference between the two leptons, p T and the transverse mass m T of the '' 0 þ E miss

VIII. INCLUSIVE AND FIDUCIAL CROSS-SECTION RESULTS
T being the transverse momentum vectors of the two leptons. The shapes of the Drell-Yan and top-quark distributions are taken from simulation and are scaled according to the data-driven estimates of the respective background.   The W þ jets background contribution is based on the data-driven method as described in Sec. VII C, and the non-WW diboson background contributions are estimated using simulation. The fiducial and total cross sections for the WW process for the three individual decay channels are calculated using Eqs. (1) and (2), respectively. The results are shown in Table VI together with the SM predictions. Reasonable agreement is found between the measured cross sections and the theoretical predictions. For the total cross-section measurement, the relative statistical uncertainty is 12%, 8%, and 5% for the ee, , and e channels, respectively, and the overall relative systematic uncertainty is 18%, 10%, and 8%, respectively. TABLE VI. The measured fiducial and total cross sections for the three channels separately and also the total cross section for the combined channels, compared with theoretical predictions. The fiducial cross sections include the branching ratio for both W bosons decaying into e or (including decays through leptons with additional neutrinos). For the measured cross sections, the first uncertainty is statistical, the second is systematic without luminosity uncertainty, and the third is the luminosity uncertainty. The combined total cross section from the three decay channels is determined by minimizing the negative loglikelihood function: where i ¼ 1, 2, 3 runs over the three channels, i s and i b represent the expected WW signal and estimated background for the ith channel, and N i obs represents the number of observed data events. The expected WW signal is computed as i WW and C i WW are the corresponding A WW and C WW in the ith channel.
The combined total cross section is WW ¼ 51:9 AE 2:0ðstatÞ AE 3:9ðsystÞ AE 2:0ðlumiÞ pb and is also shown in Table VI. The statistical uncertainty is 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. Systematic uncertainties include all sources except luminosity and are taken into account by convolving the Poisson probability distributions for signal and background with the corresponding Gaussian distributions. Correlations between the signal and background uncertainties due to common sources of systematic uncertainties are taken into account in the definition of the likelihood.

IX. NORMALIZED DIFFERENTIAL FIDUCIAL CROSS SECTION
The measured leading lepton p T distribution is unfolded to remove all experimental effects due to detector acceptance, resolution, and lepton reconstruction efficiencies. The unfolded distribution provides a differential crosssection measurement in the fiducial phase space and allows a comparison with different theoretical models. A Bayesian unfolding technique [43] with three iterative steps is used in this analysis.
In unfolding of binned data, effects of the experimental acceptance and resolution are expressed in a response matrix, whose elements are the probability of an event in the ith bin at the generator level being reconstructed in the jth measured bin. The lepton p T bins are chosen to be wider than the detector resolution to minimize migration effects and to maintain a sufficient number of events in each bin. The bin purity is found to be above 80%, implying small bin-to-bin migration effects.
The measured leading lepton p T distribution in data is then corrected using a regularized inversion of the response matrix. Finally, the distribution is corrected for efficiency and acceptance calculated from simulation. Figure 7 shows the normalized fiducial cross sections (1= fid WW Â d fid WW =dp T ) extracted in bins of the leading lepton p T together with the SM predictions. The combined fiducial cross section fid WW is defined as the sum of the fiducial cross sections in each decay channel. The corresponding numerical values and the correlation matrix are shown in Table VII. The overall uncertainty is about 5% for leading lepton p T < 80 GeV and increases to 40% for leading lepton p T > 140 GeV. The dominant source of uncertainty on the normalized differential cross section is statistical and is determined from MC ensembles. Two thousand pseudoexperimental spectra are generated by fluctuating the content of each bin according to a Poisson distribution with a mean that is equal to the bin content. The unfolding procedure is applied to each pseudoexperiment, and the root mean square of the results is taken as the statistical uncertainty. Systematic uncertainties on the normalized differential cross section mainly arise from uncertainties which directly impact the shape of the leading lepton p T spectrum, i.e. the lepton energy scale and resolution, identification and isolation efficiencies, jet and E miss T modeling, and background estimations. The systematic uncertainties are evaluated by varying the response matrix for each uncertainty, and combining the resulting changes in the unfolded spectrum. Uncertainties on the expected background shapes and contributions are treated in a similar way. The performance of the unfolding procedure was verified by comparing the true and unfolded spectrum generated using pseudoexperiments. The unfolded results are stable with different numbers of iterations used and different input distributions.

X. ANOMALOUS WWZ AND WW COUPLINGS
The reconstructed leading lepton p T distribution is used to set limits on anomalous WWZ and WW TGCs. The Lorentz invariant Lagrangian describing the WWZ and WW interactions [44] has 14 independent coupling parameters. Assuming electromagnetic gauge invariance and C and P conservations, the number of independent parameters reduces to five: g Z 1 , Z , , Z , and . In the SM, the coupling parameters have the following values: Deviations of these coupling parameters from their SM values Ág Z 1 ð g Z 1 À 1Þ, Á Z ð Z À 1Þ, Á ð À 1Þ, Z , and , all equal to zero in the SM, would result in an increase of the production cross section and alter kinematic distributions, especially for large values of the leading lepton p T . Since unitarity restricts the WWZ and WW couplings to their SM values at asymptotically high energies, each of the couplings is usually modified by ðŝÞ ¼ 0 =ð1 þŝ=Ã 2 Þ 2 , where corresponds to one of the five couplings, 0 is the value of the anomalous coupling at low energy,ŝ is the square of the invariant mass of the WW system, and Ã is the mass scale at which new physics affecting anomalous couplings would be introduced.
Limits on these couplings can be obtained under the assumption that the WWZ and WW couplings are equal (denoted by the ''equal couplings scenario'') (Á Z ¼ Á , Z ¼ , and g Z 1 ¼ 1). Two other different sets of parameters are also considered. One, motivated by SUð2Þ Â Uð1Þ gauge invariance, was used by the LEP collaborations (denoted by the ''LEP scenario'') [45] and assumes Á ¼ ðcos 2 W =sin 2 W ÞðÁg Z 1 À Á Z Þ and Z ¼ . The other one (denoted by the ''HISZ scenario'') [46] assumes Ág Z 1 ¼ Á Z =ðcos 2 W À sin 2 W Þ, Á ¼ 2Á Z cos 2 W =ðcos 2 W Àsin 2 W Þ, and Z ¼ . Because of the constraints mentioned above, the number of independent parameters is only two for the equal couplings scenario and the HISZ scenario, and three for the LEP scenario. Limits are also set assuming no relationships among these five parameters.
A reweighting method is applied to SM WW events generated with MC@NLO and processed through the full detector simulation to obtain the leading lepton p T distribution with anomalous couplings. The reweighting method uses an event weight to predict the rate with which a given event would be generated if anomalous couplings were present. The event weight is the ratio of the squared matrix elements with and without anomalous couplings i.e., jMj 2 =jMj 2 SM , where jMj 2 is the matrix element squared in the presence of anomalous couplings and jMj 2 SM is the matrix element squared in the SM. The event generator BHO [47] is used for the calculation of the two matrix elements. Generator-level comparisons of WW production between MC@NLO and BHO with all anomalous couplings set to zero are performed and consistent results are obtained. Samples with different sets of anomalous couplings are generated and the ratio of the leading lepton p T distribution to the SM prediction is parametrized as a function of the input anomalous coupling parameters. This function is then used to interpolate the leading lepton p T distribution for any given anomalous couplings. To verify the reweighting method, the event weights for a given set of anomalous couplings are calculated and applied to events generated with BHO assuming no anomalous couplings. The reweighted distributions are compared to those predicted by the BHO generator, and good agreement is observed for the inclusive cross section and for the kinematic distributions as shown in Fig. 8(a). Figure 8(b) compares the reconstructed leading lepton p T spectrum in data with that from the sum of expected signal and background contributions. The predicted leading lepton p T distributions for three different anomalous TGC values are also shown. Events at high values of the leading lepton p T distribution are sensitive to anomalous TGCs. Limits on anomalous TGCs are obtained by forming a likelihood test incorporating the observed number of candidate events, the expected signal as a function of anomalous TGCs, and the estimated number of background events in each p T bin. The systematic uncertainties are included in the likelihood function as nuisance parameters with correlations taken into account. The 95% TABLE VII. Normalized fiducial cross section together with the overall uncertainty in bins of the leading lepton p T . The weighted bin center is calculated as the cross-section-weighted average of the leading lepton p T in each bin derived from MC@NLO and GG2WW. The correlation coefficients between different leading lepton p T bins are also shown. Only half of the symmetric correlation matrix is presented.
Leading lepton p T [GeV] [25,40]  confidence level (C.L.) intervals on anomalous TGC parameters include all values of anomalous TGC parameters for which the negative log-likelihood functions increase by no more than 1.92 (2.99) units above the minimum for the one (two)-dimensional case. Table VIII shows expected and observed 95% C.L. limits on anomalous WWZ and WW couplings for three scenarios (LEP, HISZ, and equal couplings) with two scales, Ã ¼ 6 TeV and Ã ¼ 1. The Ã ¼ 6 TeV scale is chosen as it is the rounded largest value that still preserves unitarity for all extracted anomalous TGC limits of this analysis. Table IX shows the results assuming no relationships between the five couplings. Figure 9 shows the two-dimensional 95% C.L. contour limits of Á Z vs Z , Á Z vs Ág Z 1 , Á vs Ág Z 1 , and Z vs Ág Z 1 for the LEP scenario. Except for the anomalous coupling parameter(s) under study, all other parameters are set to their SM values.
Limits in the LEP scenario are compared with limits obtained from the CMS [13], CDF [10], D0 [10], and LEP [9] experiments in Fig. 10. Because of higher energy and higher WW production cross section at the LHC, the limits The leading lepton p T spectrum from the SM prediction, compared with a prediction using BHO and by reweighting the SM prediction assuming the LEP scenario with Á Z ¼ 0:1, Z ¼ 0, Ág Z 1 ¼ À0:1, and Ã ¼ 1. (b) The reconstructed leading lepton p T spectrum in data and sum of MC signal and background for the SM prediction and for three different anomalous TGC predictions. The shaded band corresponds to the total statistical and systematic uncertainties. The rightmost bin shows the sum of all events with leading lepton p T above 180 GeV.  obtained in this paper are better than the Tevatron results and approach the precision of the combined limits from the LEP experiments.

XI. CONCLUSION
The WW production cross section in pp collisions at ffiffi ffi s p ¼ 7 TeV is measured using 4:6 fb À1 of data collected with the ATLAS detector at the LHC. The measurement is conducted using the WW ! '' 0 0 (', ' 0 ¼ e, ) channels including decays through leptons with additional neutrinos. In total 1325 candidates are selected with an estimated background of 369 AE 61 events for the three decay channels into ee, , and e final states. The combined production cross section ðpp ! WW þ XÞ is 51:9 AE 2:0ðstatÞ AE 3:9ðsystÞ AE 2:0ðlumiÞ pb, compatible with the SM NLO prediction of 44:7 þ2:1 À1:9 pb. The overall statistical and systematic uncertainty is 9% and an improvement of 30% has been achieved compared with the previous ATLAS measurement [12]. The results presented supersede the previous results obtained with 1 fb À1 of data. Cross sections are also measured in a fiducial phase space. The leading lepton p T distribution is unfolded to obtain the normalized differential fiducial cross section in the chosen fiducial phase space. Reasonable agreement is observed between the measured distribution and theoretical predictions using MC@NLO. Anomalous WWZ and WW couplings are probed using the reconstructed leading lepton p T distribution of the selected WW events. With the assumption that WWZ and WW couplings are equal, 95% C.L. limits are set on Á Z and Z in the intervals ½À0:061; 0:093 and ½À0:062; 0:065, respectively, for a scale of Ã ¼ 6 TeV. Limits on these anomalous couplings are also reported for three other scenarios and two scales Ã ¼ 6 TeV and Ã ¼ 1. The limits on The Á Z result in the LEP scenario from CMS was obtained using the Á limit in the HISZ scenario [13] and inserting it in the LEP scenario assuming Ág Z 1 ¼ 0.