The measurement of angular distributions of the decay leptons in di-boson final states allows to reconstruct the spin density element rho_00 in processes where ZZ and WZ final states are produced via quark anti-quark annihilation in proton-proton collisions at the LHC. This note presents the expected sensitivity of such measurement with the ATLAS experiment, using electrons and muons as final state leptons, based on an integrated luminosity of 100 inverse femtobarns. Besides the statistical accuracy on the fraction of longitudinally polarized Z or W boson, various contributions to the systematic uncertainty, have been studied

Bella, G

The measurement of angular distributions of the decay leptons in di- boson final states allows to reconstruct the spin density element rho_00 in processes where ZZ resp. WZ final states are produced via quark anti-quark annhilation in proton-proton collisions at the LHC. This contribution presents the expected sensitivity of such a measurement with the ATLAS experiments, using electrons and muons as final state leptons, based on an integrated luminosity of 100 fb^-1. Besides the statistical accuracy on the fraction of longitudinally polarized Z bosons (resp. W and Z bosons), various contributions, both experimental and theoretical ones, to the systematic uncertainty have been studied

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Prospects of measuring ZZ and WZ polarization with ATLAS

ATL-PHYS-PROC-2009-12506October2009PROSPECTS OF MEASURING ZZ AND WZ POLARIZATION WITHATLASG. Bella 1 †On behalf of the ATLAS Collaboration(1) Raymond and Beverly Sackler School of Physics and AstronomyTel Aviv University† E-mail: Gideon.Bella@cern.chAbstractThe measurement of angular distributions of the decay leptons in di-boson finalstates allows the reconstruction of the spin density matrix element ρ00 in processeswhere ZZ and WZ final states are produced via quark anti-quark annihilation inproton-proton collisions at the LHC. This note presents the expected sensitivityof such measurements with the ATLAS experiment, using electrons and muons asfinal state leptons, based on an integrated luminosity of 100 fb−1. Besides thestatistical accuracy on the fractions of longitudinally polarized Z or W bosons,various contributions to the systematic uncertainty have been studied.The W gauge boson is mainly produced singly in qq¯ annihilation at hadron-hadroncolliders. The same is true for the Z gauge boson, which has also been produced inelectron-positron annihilations at LEP. In these processes, the gauge boson has alwaystransverse polarization due to the helicity conservation in the annihilation process. How-ever, some fraction of longitudinal polarization is allowed and expected in the StandardModel (SM) when the annihilation process yields two gauge bosons. Longitudinally po-larized W bosons have been observed for the first time at LEP [1], in W+W− production,and later also at the Tevatron [2] in top-quark decays. The longitudinal polarization de-gree of freedom for the W and the Z bosons is a direct result of the Higgs mechanism, andit would be a valuable test of the SM to measure the fraction of longitudinally producedbosons in di-boson events at hadron colliders and compare with theory. Any deviationfrom the SM predictions would be evidence for new physics. Furthermore, di-boson eventscan be produced as decay products of the Higgs boson, and their polarization state mightbe of help in the determination of the Higgs spin [3] and its separation from the di-bosoncontinuum.This note describes feasibility studies using Monte Carlo (MC) events of the ZZ [4]and WZ [5] production channels at LHC, to be measured by the ATLAS detector [6].LHC is a proton-proton collider at CERN which is expected to start operation at theend of 2009, and eventually will reach a center-of-mass (c.m.s) energy of 14 TeV. Thisenergy value was assumed in our study with an integrated luminosity of 100 fb−1, which isthe expected luminosity value, before a possible upgrade of the machine into Super LHC(SLHC), expected to achieve a luminosity increase by an order of magnitude. Backgroundconsiderations lead us to use only the leptonic decays, W → `ν and Z → `+`−, where` = e, µ.1Electron energy is measured at ATLAS by the liquid argon electromagnetic calorimeterwith a resolution of 1.2% for electron energy around 100 GeV [7]. The electron directionis obtained from the inner detector consisting of pixel detectors, silicon strip layers anda straw-tube transition radiation detector which also assists electron identification. Theelectromagnetic calorimeter is inside the hadron calorimeter, which is surrounded by themuon spectrometer measuring the muon momenta with a resolution of (4 - 5)% for muonswith transverse momentum, pT , below 150 GeV [7]. The pseudo-rapidity range for trig-gering and measuring electrons and muons is |η| < 2.5. The calorimeters cover a largerrange, up to |η| = 5. This hermetic coverage allows a precise measurement of the missingtransverse energy, ET , which is used to identify the neutrino from the W decay and obtainits transverse momentum.Monte Carlo event samples have been generated using Pythia [9] for the ZZ andMC@NLO [9] for the WZ channel. These events have been passed through the full ATLASdetector simulation and then through the ATLAS reconstruction program to be usedalso for real data events. Similar event samples have been used also for the expectedbackground processes (see below).ZZ candidates are required to have two lepton anti-lepton pairs, each pair with invari-ant mass within 12 GeV of the Z mass. All leptons are required to have |η| < 2.5. Two ofthe leptons must satisfy pT > 20 GeV and the other two must have pT > 7 GeV. Followingthese cuts, 2194 events are left in our 100 fb−1 pseudo-data sample. Background sourcesconsidered were tt¯ and Zbb¯ events, and the total background level was found to be lessthan 1% and was neglected.The WZ channel is more difficult to separate from background and more stringentcuts are needed. WZ candidates are required to have three leptons with pT > 25 GeVand |η| < 2.5. Out of these three leptons, there must be one lepton anti-lepton pair withinvariant mass within 12 GeV of the Z mass. In addition the event must have missingET above 25 GeV, and the transverse mass constructed from the missing ET and thethird lepton must be between 50 and 90 GeV. The angle in the transverse plane betweenthe missing ET vector and the third lepton must exceed 40o. Finally, to further suppressbackground from tt¯ events, no more than one jet is allowed in the event, and its transversemomentum should not exceed 30 GeV. In our 100 fb−1 pseudo-data sample, 2873 WZcandidates are left after these cuts with a background level of 1%, where the backgroundsources considered were tt¯, W+W−, ZZ, Z+jet and Zγ events. This background wasneglected in the further analysis.The kinematic observable which is sensitive to the gauge boson polarization is theboson decay angle, θ∗`, which is the angle between the lepton (anti-lepton) produced inthe W−, Z (W+) decay in the rest-frame of the boson with respect to the boson momentumin the di-boson rest-frame. Its distribution is given by,1σdσd cos θ∗`= ρ−−38(1 + cos θ∗`)2 + ρ++38(1− cos θ∗`)2 + ρ0034sin2 θ∗`,for the W boson, and by,1σdσd cos θ∗`= ρ−−38(1 + 2A cos θ∗`+ cos2 θ∗`) + ρ++38(1− 2A cos θ∗`+ cos2 θ∗`) + ρ0034sin2 θ∗`,for the Z boson. Here, A = 2v`a`/(v2`+ a2`), where v` (a`) is the vector (axial-vector)coupling of the Z boson to leptons. The spin density matrix elements, ρ−−, ρ++ and2ρ00 correspond to transverse left-handed, transverse right-handed and longitudinal polar-ization of the boson. They satisfy ρ−− + ρ++ + ρ00 = 1 and each one of them can beinterpreted as the fraction of bosons produced in the corresponding polarization state.−100 −50 0 50 100 Arbitrary scale050100150200 GeV s√∆ Mean −2.276 GeV RMS 33.43 GeV ATLAS Preliminary−1.5 −1 −0.5 0 0.5 1 1.5 Arbitrary scale0100200300400500600*lθ cos∆ Mean 0.007938  RMS 0.2955  ATLAS Preliminary(a) (b)Figure 1: Resolution for WZ events in (a)√sˆ, (b) cos θ∗`For ZZ events, it is ratherstraightforward to obtain θ∗`fromthe measured kinematic observ-ables of the four leptons. Forthe WZ events, the longitudi-nal momentum of the neutrino,pν`, is not measured, but it canbe calculated if the neutrinoand the the corresponding lep-ton are constrained to the Wmass. A quadratic equation isobtained yielding two solutionsfor pν`. The value taken for pν`isa weighted average of the two solutions, where the weights are the corresponding SM cross-section values [8]. The resulting resolutions in the di-boson invariant mass,√sˆ, and incos θ∗`are shown in Fig. 1.Since the gauge boson polarization is expected to depend on√sˆ, the analysis is doneseparately for 4 (3) bins in√sˆ, for the ZZ (WZ) channels. In addition, there is a separationbetween the W+Z and W−Z channels. To correct for detector and analysis effects, theMC events are further divided into 10 bins in cos θ∗`. For each bin i, the ratio between thenumber of events at the generator level and the number after the detector and selection isthe correction factor, Ci, which accounts for both overall efficiency and resolution effects.For the ZZ channel, we extract ρ00 using the event-by-event “projection operator”method,ρ00 =1Nevents∑eventsCi · Λ00(cos θ∗` )where Ci corresponds to the (√sˆ, cos θ∗`) bin containing the event and Λ00 is the projec-tion operator for the longitudinal polarization state, given by, Λ00 = 2 − 5 cos2 θ∗` , andcalculated for the measured cos θ∗`of that particular event.This projection operator method could not be used for the WZ channels, since someof the bins in the MC distribution after the detector were sparse, yielding very large,uncertain and sometimes even infinite correction factors. Therefore, an event-by-eventmaximum likelihood method was adopted, where the inverse correction factors are used,and they multiply the theoretical cos θ∗`distribution for each event.The systematic effect from the uncertainty in the Parton Distribution Functions (PDF)was studied in the ZZ channel by using different sets of PDFs (CTEQ, MRST, EHLQ2),and in the WZ channels by using the 40 CTEQ6M [9] error sets. Another source ofsystematic errors considered is MC statistics. For the WZ channels, the dominatingsystematic effect comes from the replacement of the SM cross-section values used forthe weighted average of the two solutions for pν`by theoretical cross-section values [8]calculated with anomalous couplings within the Tevatron limits. The overall systematicerrors are typically (20 - 50)% of the statistical ones.300.10.20.30.40.5100 200 300 400 500 √s   GeVρ00 ATLASPreliminaryZ00.10.20.30.40.5200 300 400 500√sreco  GeVρ00W- ATLAS Preliminary00.10.20.30.40.5200 300 400 500√sreco  GeVρ00ZATLASPreliminary00.10.20.30.40.5200 300 400 500√sreco  GeVρ00W+ATLASPreliminary√(a) (b)Figure 2: Longitudinal polarization fraction, ρ00, as functionof the di-boson mass,√sˆ, obtained from our 100 fb−1 pseudo-data samples, for (a) Z in ZZ events, (b) W− (left), Z (right),W+ (bottom)Fig. 2 shows the resultsof the longitudinal polar-ization fraction, ρ00, for thedifferent channels as func-tion of√sˆ. The curvescorrespond to the theoret-ically expected ρ00(√sˆ), asobtained from large statis-tics, generator level MCsamples.In summary, it has beenshown in this note thatthe measurement of the Zand W polarizations in ZZand WZ events is feasiblewith an integrated lumi-nosity of 100 fb−1, whichwill be available only afterseveral years of successfulLHC running. The errors are dominated by statistics, and more accurate results areexpected with the higher luminosities expected in SLHC.I would like to thank the organizers of this workshop for the opportunity to presentthis work, and for the good organization and the nice atmosphere in the workshop. Thiswork was partially supported by the Israel Science Foundation (grant No. 183/07).References[1] OPAL Collaboration, G. Abbiendi et al., Eur. Phys. J.C8 (1999) 191.[2] CDF Collaboration, T. Affolder et al., Phys. Rev. Lett. 84 (2000) 216.[3] S. Rosati, on behalf of the ATLAS and CMS collaborations, contribution to thisworkshop.[4] E. Brodet, “Prospects of measuring ZZ polarization in the ATLAS detector”, ATL-PHYS-PUB-2008-002.[5] ATLAS Collaboration, “Measuring WZ longitudinal polarization with the ATLASdetector”, ATL-PHYS-PUB-2009-078.[6] ATLAS Collaboration, G. Aad et al., JINST 3 (2008) S08003.[7] ATLAS Collaboration, “Expected performance of the ATLAS experiment, detector,trigger and physics”, CERN-OPEN-2008-020, arXiv:0901.0512v4 [hep-ex].[8] G. Bella, “Weighting di-boson Monte Carlo events in hadron colliders”,arXiv:0803.3307v1 [hep-ph].[9] See references in the Introduction chapter of [7].4

Prospects of Measuring ZZ and WZ Polarization with ATLAS

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