Measurement of the $WZ\rightarrow \ell\nu\ell\ell$ cross section and limits on anomalous triple gauge couplings in $p\bar{p}$ collisions at $\sqrt{s}$ = 1.96 TeV

We present a new measurement of the $WZ\rightarrow \ell\nu\ell\ell$ ($\ell = e,\mu$) cross section and limits on anomalous triple gauge couplings. Using 4.1 fb$^{-1}$ of integrated luminosity of $p\bar{p}$ collisions at $\sqrt{s} = 1.96$ TeV, we observe 34 $WZ$ candidate events with an estimated background of $6.0 \pm 0.4$ events. We measure the $WZ$ production cross section to be $3.90^{+1.06}_{-0.90}$ pb, in good agreement with the standard model prediction. We find no evidence for anomalous $WWZ$ couplings and set 95% C.L. limits on the coupling parameters, $-0.075<\lambda_{Z}<0.093$ and $-0.027<\Delta\kappa_{Z}<0.080$, in the HISZ parameterization for a $\Lambda = 2$ TeV form factor scale. These are the best limits to date obtained from the direct measurement of the $WWZ$ vertex.

ory.Therefore, any significant deviation from the SM predictions yields information on the nature of a more fundamental theory.Production of W Z pairs is the least studied diboson process within the SM, as it is a charged final state and can only be produced at hadron colliders.A detailed study of this process probes the electroweak sector of the SM.In addition, searches for new phenomena in the production of heavy gauge boson pairs are interesting, as many extensions of the SM predict [1][2][3][4] additional heavy gauge bosons that can decay into a W Z boson pairs.
In the SM, W Z boson pairs are produced at leading order (LO) via t-, u-, and s-channels.These channels inter-fere and maintain unitarity at high energies.In the case of the t-and u-channels, the W and Z bosons are radiated from initial state quarks, while the s-channel production occurs via the W W Z triple gauge boson vertex, which is a consequence of the non-Abelian nature of the SM.There are 14 free parameters describing the generalized Lagrangian for the W W V interaction [5,6], where V is either a Z boson or a photon.Assuming gauge invariance and conservation of the C, P , and CP symmetries, only six remain.Their notation and SM values are λ V = 0, κ V = g V 1 = 1 for the W W V vertex, while the deviations from the SM values are noted as ∆κ V , ∆g V  1 , and λ V .The U (1) electromagnetic gauge invariance implies ∆g γ 1 = 0.In this Letter, we describe the W W Z vertex in threedimensional (3D) phase space of coupling parameters, ∆κ Z , ∆g Z  1 , and λ Z .We also consider the HISZ parameterization [7] that implies ∆κ Z = ∆g Z 1 (cos 2 θ W −sin 2 θ W ). Thus, the W W Z vertex can be described by ∆κ Z and λ Z only.
If the coupling parameters have non-SM values, new physics is required to prevent gauge boson production from violating unitarity at high energies.The high energy behavior is controlled by introducing a dipole form factor scale, Λ, in the description of the couplings, α(ŝ) → α 0 /(1 + ŝ/Λ 2 ) 2 , where ŝ is the square of the partonic center-of-mass energy and α 0 is the coupling value in the low energy approximation.
The W Z production cross section was previously measured to be σ(pp → W Z) = 5.0 +1.8 −1.6 pb [8] and σ(pp → W Z) = 2.7 +1.7 −1.3 pb [9], by the CDF and D0 collaborations, respectively, using ∼1 fb −1 of integrated luminosity.Combined limits on the gauge couplings from the CERN LEP collider were obtained [10] by the indirect measurement of the W W Z coupling in the e + e − → W + W − process.The only direct measurement of W W Z couplings was performed at the Tevatron.Using 1 fb −1 of integrated luminosity, 95% C.L. limits on anomalous W W Z couplings were derived [9] by the D0 experiment: −0.17 < λ Z < 0.21, −0.14 < ∆g Z 1 < 0.34 for the HISZ relation and −0.12 < ∆κ Z = ∆g Z 1 < 0.29, using Λ = 2 TeV.The CDF experiment used data equivalent to 350 pb −1 of integrated luminosity that resulted in 95% C.L. limits on anomalous W W Z couplings [11]: −0.28 < λ Z < 0.28 and −0.50 < ∆κ Z < 0.43 assuming equal coupling relation between W W Z and W W γ couplings and Λ = 1.5 TeV.
In this Letter, we present a new measurement of the W Z production cross section and set 95% C.L. limits on the deviation from the SM predictions of triple gauge couplings (λ Z , ∆κ Z , ∆g Z 1 ) using data equivalent to 4.1 fb −1 of integrated luminosity of pp collisions at √ s = 1.96TeV at the Tevatron collected by the D0 detector.This supersedes the previous D0 measurement.We consider only the leptonic decays of the W and Z bosons into final states with electrons, muons, and with missing transverse energy (E / T ) [12] due to the neutrino from the W boson decay.
The detailed description of the D0 detector can be found elsewhere [13], while here we present a brief overview of the main sub-systems of the detector.The inner most part is a central tracking system surrounded by a 2 T superconducting solenoidal magnet.The two components of the central tracking system, a silicon microstrip tracker and a central fiber tracker, are used to reconstruct interaction vertexes and provide the measurement of the momentum of charged particles.The tracking system and a magnet are followed by the calorimetry system that consists of central (CC) and endcap (EC) electromagnetic and hadronic uranium-liquid argon sampling calorimeters, and an intercryostat detector (ICD).A central calorimeter and two endcap calorimeters cover the pseudorapidity ranges |η| < 1.1 and 1.5 < |η| < 4.2, respectively, while the ICD provides coverage for 1.1 < |η| < 1.4.The calorimeter measures energy of hadrons, electrons, and photons.Outside of the D0 calorimeter lies a muon system which consists of layers of drift tubes and scintillation counters and a 1.8 T toroidal magnet.
An electron candidate is identified as a cluster of energy in the CC, EC, or ICD that is matched to a track reconstructed in the D0 central tracker.Due to different coverage of the tracker, we select EC electrons within 1.5 < |η| < 2.5 and CC electrons within |η| < 1.1.The cluster in the CC or EC must be isolated and have a shower shape consistent with that of an electron.In the intercryostat region (ICR), 1.1 < |η| < 1.5, we cluster energy found in the CC, ICD, or EC detectors.These ICR electrons are required to pass a neural network discriminant that uses the cluster's shower shape and associated track information.A muon candidate is reconstructed as segments within the muon system that are matched to a track reconstructed in the central tracker.The muon candidate track must be isolated from activity in the tracker and the calorimeter.
The Monte Carlo (MC) samples of W Z signal and ZZ background are produced using the pythia [14] generator.The production of the W and Z bosons in association with jets (W +jets, Z+jets), collectively referred to as V +jets, and t t processes are generated using alpgen [15] interfaced with pythia for showering and hadronization.All MC samples are passed through the geant [16] simulation of the D0 detector.The simulated samples are further corrected to describe the luminosity dependence of the trigger and reconstruction efficiencies in data, as well as the beam spot position.All MC samples are normalized to the luminosity in data using nextto-leading order (NLO) calculations of the cross sections and are subject to the same selection criteria as that applied to data.
We consider four independent decay signatures: eee + E / T , eeµ + E / T , µµe + E / T , and µµµ + E / T .Electron reconstructed in the ICR must be selected as one of the electrons from the Z boson decay.We require the events to Channel A × ǫ (%) eee 1.35 ± 0.15 eeµ 1.57 ± 0.12 µµe 1.07 ± 0.11 µµµ 1.34 ± 0.13 have at least three lepton candidates with p T > 15 GeV that originate from the same vertex and separated from each other by at least ∆R = (∆φ) 2 + (∆η) 2 > 0.5.
The event must also have a significant E / T to account for the unobserved neutrino.We require E / T to be above 20 GeV.Events are selected using triggers based on electrons and muons.Since there are multiple high p T leptons from the decay of the heavy gauge bosons the trigger efficiency is measured to be 98% ± 2% for all signatures.
In the W Z candidate selection, we first identify the leptons from the Z boson decay.We consider all pairs of electrons or muons, additionally requiring opposite electrical charge in the cases of muon pairs or electron pairs including an ICR electron.The pair that has an invariant mass closest to and consistent with the Z boson nominal mass is selected as coming from the Z boson decay.If such pair is not found the event is rejected.The lepton from the W boson decay is selected as the one with the highest transverse momentum from the remaining unassigned muons and CC or EC electrons in the event.This assignment is studied in the simulation and found to be 100% correct for eeµ and µµe channels.It is found to be correct in about 92% and 89% of cases for eee and µµµ signatures, respectively.The effects of misassignment on the product of acceptance and efficiency of the selection criteria, A × ǫ, are estimated in the signal simulation.Values of A × ǫ measured using the assignment method described above differ from those obtained using MC generator-level information by less than one per cent.Therefore, the systematic uncertainty on A × ǫ due to the misassignment is neglected in this analysis.
In order to reduce the background contamination, the thresholds in the selection criteria are further optimized for each W Z decay mode by maximizing S/ √ S + B. Here, S is the expected number of W Z signal events and B is the total number of background events.The simulation is used to estimate S as well as to measure A × ǫ for each decay signature.The kinematic selection criteria are applied to measure the acceptance in simulations, while the lepton identification efficiencies are measured in data.The results are summarized in Table I.
The major background is from processes with a Z boson and an additional object misidentified as the lepton from the W boson decay.Such processes are Z+jets, ZZ, and Zγ.A small background contribution is expected from processes without Z boson, such as W +jets and t t processes.
The ZZ and t t backgrounds are estimated from the simulation, while the V +jets, with V being either a Z or W bosons, and Zγ backgrounds are estimated using data-driven methods.
One or more jets in the V +jets process can be misidentified as a lepton from the W or Z boson decays.To estimate this contribution, we define a false lepton category for electrons and muons.A false electron is required to have most of its energy deposited in the electromagnetic calorimeter and satisfy electron calorimeter isolation criteria, while having a shower shape inconsistent with that of an electron.A muon candidate is categorized as false if it fails the isolation criteria.These requirements ensure that the false lepton is either a misidentified jet or a lepton from the semi-leptonic decay of heavy flavor quarks.Using a multijet data sample, we measure the ratio of misidentified leptons passing two different selection criteria, false lepton and signal lepton, as a function of p T and η for electrons and muons, respectively.We then select a sample of Z boson decays with an additional false lepton candidate for each final state signature.The contribution from the V +jets background is estimated by scaling the number of events in this sample by the corresponding p T -or η-dependent misidentification ratio.Initial or final state radiation in Zγ events can mimic the signal process if the photon either converts into e + e − pair or when a central track is wrongly matched to a photon.As a result, the Zγ process is a background to two out of the four final state signatures with W → eν decays.To estimate the contribution from this background, we measure the rate at which a photon is misidentified as an electron.This is estimated using a data sample of Z → µµ events with a final state radiation photon, since it offers an almost background-free source of photons due to the invariant mass, M (µµγ), constraint to the Z boson mass.The muon decay of the Z boson is chosen to avoid an ambiguity when assigning the electromagnetic shower to the final state photon candidate.The misidentification rate is measured as a function of the p T of the electromagnetic shower.The Zγ contribution is estimated by multiplying the p T -dependent misidentification rate by the photon p T distribution in the Zγ NLO MC simulation [17].
The selection yields 34 W Z candidate events with an estimated 23.3 ± 1.5 signal, and 6.0 ± 0.6 background events.The number of observed candidate events as well as the expected numbers of signal and background events for each signature are summarized in Table II candidate is calculated as follows where E ℓ T and φ ℓ are transverse energy and azimuthal angle, respectively, of the electron or muon selected as the W boson decay product and φ E / T is the azimuthal angle of the missing transverse momentum.The distribution of the W boson candidates is given in Fig. 2.
Several sources of systematic uncertainty are considered.The systematic uncertainties on the lepton identification efficiencies are 5%, 4%, and 6% for CC/EC electrons, muons, and ICR electrons, respectively.The systematic uncertainty assigned to the PDF choice is 5%.A systematic uncertainty of 5% is assigned on A × ǫ due to modeling of the kinematics of the W Z system.In addition, we assign 7% [18] and 10% [19] systematic uncer-tainty to the estimated t t and ZZ backgrounds, respectively, due to the uncertainty on their theoretical cross sections.The major sources of systematic uncertainty on the estimated V +jets contribution are the E / T requirement and the statistics in the multijet sample used to measure the lepton misidentification ratios.These effects are estimated independently for each signature and found to be between 20-30%.The systematic uncertainty on the Zγ background is estimated to be 40% and 58% for the eee and µµe channels, respectively.
A likelihood method [20] is used to combine the four measurements, taking into account the correlations among the systematic uncertainties on the expected signal and the estimated background contributions.The cross section is σ(W Z) = 3.90 +1.01 −0.85 (stat + syst) ± 0.31 (lumi) pb.The uncertainties are dominated by the statistics of the number of observed candidates.The luminosity uncertainty includes 6.1% relative uncertainty [21] due to the luminosity measurement and the normalization uncertainty of the background contributions estimated from MC simulation.
The presence of anomalous W W Z couplings would lead to both an increase in the cross section and a change in the p T spectrum of the W and Z bosons.We use the Z boson p T distribution to set limits on the coupling parameters using a form factor scale Λ = 2 TeV.The Z boson p T spectra from data, the SM, and two anomalous coupling predictions are shown in Fig. 3.The difference is most pronounced in the last bin, which includes also the events above 150 GeV.A three-dimensional grid of values of anomalous couplings ∆κ Z , ∆g Z  1 , and λ Z is produced.For each point of the grid we generate W Z production using mcfm [ 4. In each case the third coupling is restricted to the SM value.For the HISZ parameterization the results are presented as limits on two coupling parameters: ∆κ Z and λ Z .The corresponding two-dimensional 95% C.L. limit contour is shown on Fig. 5.The onedimensional limits on the coupling parameters obtained without any coupling relation and with HISZ parameterization are summarized in Table III.In summary, we have presented a measurement of the W Z production cross section using 4.1 fb −1 of integrated luminosity of D0 data.We observe 34 events with 23.3 ± 1.5 expected signal events and 6.0 ± 0.6 estimated background events.We measure the W Z cross section to be 3.90 +1.06  −0.90 pb, which is in agreement with the SM NLO prediction of 3.25 ± 0.19 pb [19].This is the most precise measurement to date of the W Z cross section.We find no evidence for anomalous W W Z couplings and set 95% C.L. limits of −0.075 < λ Z < 0.093  and −0.027 < ∆κ Z < 0.080 for the HISZ parametrization using Λ = 2 TeV.These are the most stringent limits on W W Z couplings obtained from the study of direct W Z production.

FIG. 1 :FIG. 2 :
FIG. 1: (Color online) Invariant mass distribution of selected Z candidates in data (black points), with W Z signal (open histogram) and total background (dark histogram) overlaid.

FIG. 3 :
FIG. 3: (Color online) The Z boson pT spectrum from data (points), total background (dark histogram), the SM W Z single + total background (open histogram), and two anomalous coupling models (dashed and dotted histograms).The last bin includes overflows.

FIG. 5 :
FIG.5:(Color online) Two-dimensional 95% C.L limit contours for the HISZ parameterization.The point corresponds to the minimum of the likelihood surface.The vertical and horizontal lines represent the separately calculated onedimensional limits.

TABLE I :
Acceptance multiplied by efficiency, A × ǫ, of the full selection criteria for each decay signature.A×ǫ values are calculated with respect to the fully leptonic W Z decay simulation.The uncertainties are both statistical and systematic.

TABLE II :
Number of observed events, expected number of signal events, and expected number of background events for each final state signature with total (statistical and systematic) uncertainties.andobtain normalized to luminosity p T spectrum of the Z boson.This spectrum combined with that from the estimated background is compared with the measured Z boson p T spectrum in data.The likelihood of the match is calculated with the assumption of Poisson statistics for the signal and Gaussian uncertainties for the background.The two-dimensional 95% C.L. limit contours in three planes, (∆κ Z , λ Z ), (∆g Z 1 , λ Z ), and (∆g Z 1 , ∆κ Z ), are shown in Fig.

TABLE III :
One-dimensional 95% C.L. limits on anomalous coupling parameters obtained from varying one of the couplings while fixing the remaining couplings to the SM values (top three results).The last two results correspond to onedimensional 95% C.L. limits on anomalous coupling parameters for the HISZ parameterization.A form factor scale of Λ = 2 TeV is used.