aa r X i v : . [ h e p - e x ] O c t th International Conference on High Energy Physics, Philadelphia, 2008
Electroweak Cross-sections and Widths
A. Robson (on behalf of the CDF and D0 Collaborations)
Glasgow University, Glasgow G12 8QQ, UK
The status of W and Z cross-section and width measurements from the CDF and D0 experiments is reviewed. Recentresults that are discussed: the cross-section for Z production times the branching ratio to tau pairs, the rapidity andtransverse momentum distributions of Z production in the electron channel, and the direct measurements of the Wwidth and the Z invisible width; the latter from an analysis of events with large missing transverse energy and one ormore energetic jets.
1. W AND Z PHYSICS AT THE TEVATRON
Already early in Run 2 of the Tevatron, using less than 100 pb − of data, total inclusive W and Z cross-sectionmeasurements were essentially systematically limited [1]. From the theoretical side, W and Z cross-sections arewell-known, fully differentially to NNLO. From an experimental point of view, the Tevatron W and Z boson datasetsprovide a pure sample of high- p T electrons and muons. Now with more than thirty times the statistics of those earlymeasurements, the W and Z datasets provide a powerful tool for lepton reconstruction, identification and triggermeasurements. But at a fundamental level, total inclusive W and Z cross-section measurements are benchmarks forall high- p T physics analyses.A tower of physics measurements is built on the selection of W and Z events. W and Z plus photon measurementsand heavy diboson WW, WZ and ZZ measurements probe triple gauge couplings; and the precision of top-quarkcross-sections continues to improve. Each of these measurements needs to demonstrate consistent determinationsof inclusive W and Z cross-sections as a test of the implementation of selections, efficiencies, good run lists andluminosity computations. Observations of the rarer processes can be seen as stations on the way to a heavy Higgsboson, decaying to a pair of W bosons [2].However dedicated measurements on single W and Z events also continue. Their focus now is on the morechallenging tau decay modes, and on using the large datasets to make differential cross-section measurements inorder to look for discrepancies with higher-order calculations and to test the edges of phase space, and to makehigh-precision measurements of Standard Model parameters such as masses and widths.
2. Z → τ τ Tau leptons are more complex objects to reconstruct than electrons or muons, and measurement techniques continueto improve. At D0, τ identification starts from calorimeter clusters, reconstructed in a cone of ∆ R < .
5, that havetheir energy concentrated in an inner cone of ∆
R < .
3. The tracks within the inner cone are required to beconsistent with a tau, such that m tracks < . τ energy corrections have significantly reduced uncertainties.D0 selects Z → τ µ τ h from an inclusive muon trigger. Both the muon and tau have p T >
15 GeV, and in additionthere is a minimum requirement on the scalar sum- p T of the tau tracks. The leptons have opposite charge.A data-driven estimate of the QCD background, which is mostly bb, is obtained from same-charge events, andcorrected for the expected rate of same-charge events from a QCD-enhanced dataset. Electroweak backgrounds are14 th International Conference on High Energy Physics, Philadelphia, 2008
Visible Mass [GeV] E ve n t s / G e V Visible Mass [GeV] E ve n t s / G e V OS Data - τ + τ → * γ Z/ tOther EW+t ν l → W *SS Data imj f -1 DØ, 1 fb
Figure 1: (left) The ‘visible mass’, m vis = p ( P µ + P τ + P T ) , for Z → τ µ τ h candidates. (right) The Z rapidity distribution. obtained from simulation, and the W plus jets background is corrected for the component already accounted for inthe same-charge events. The background uncertainties are much reduced compared to previous D0 measurements.The resulting selection is shown in Figure 1. 1511 events are observed, of which around 20% are background. Across-section is extracted: σ (pp → Z) · Br (Z → τ τ ) = 240 ± ± ±
3. Z RAPIDITY
In Z boson production, the rapidity y = ln E + p z E − p z is closely related to the momentum fractions x of the interactingpartons: at leading order the relation is x , = m √ s e ± y . Measuring the Z boson rapidity is therefore a direct probe ofthe PDFs of the interacting partons.Furthermore, at CDF, Z bosons can be reconstructed over the entire kinematic range in the electron channel, usingthe forward calorimeters. This gives access to events at very low x , where PDFs are relatively uncertain.Events are selected in three topologies, according to whether the electrons are reconstructed in the central orforward parts of the detector.Backgrounds are estimated in a data-driven way, by forming signal and background templates of the electronisolation distribution, and extrapolating the non-isolated tail into the low isolation signal region.The acceptance as a function of rapidity is taken from simulation, and the rapidity dependences of the electronidentification efficiencies are determined.The measured rapidity distribution is shown in Figure 1. Whereas previous versions of this measurement havebeen entirely statistically dominated, the current large dataset results in systematic uncertainties comparable withthe statistical uncertainties in some regions of rapidity. Comparison is made with an NNLO calculation and NNLOPDFs, and with an NLO calculation and several NLO PDFs. Although at present the measurement does not clearlyfavour one set over another, with even more statistics there could be some scope for constraining PDFs.
4. Z TRANSVERSE MOMENTUM
Measuring the p T of the Z tests QCD predictions for initial state gluon radiation. Whereas the high end of the p T spectrum (above ∼
30 GeV/ c ) is dominated by single hard emissions and perturbative QCD is reliable, the lowend of the spectrum is dominated by multiple soft gluon radiation, which must be calculated by resummation ormodelled by a non-perturbative parton shower monte carlo. The Resbos event generator implements NLO QCDand the CSS resummation formalism, using the BNLY form-factor and parameters determined by global fits to DISand fixed-target data. This is a particularly interesting time to be probing this model, as recent global fits have24 th International Conference on High Energy Physics, Philadelphia, 2008suggested the presence of an extra contribution to the form-factor at small x . This would imply a broadening of theZ p T at high rapidities ( | y Z | >
2) at the Tevatron, and a significant effect on centrally-produced W and Z bosons atthe LHC. D0 has looked for evidence of this effect [4].In 1 fb − , around 64000 Z events are reconstructed in the electron channel, of which around 5000 have | y Z | > m ee . A regularized unfolding technique isused to recontruct the underlying p T distribution. The low end of the Z p T distribution for all rapidities is comparedto the Resbos prediction, and found to be in good agreement. The Z p T for events that have | y Z | > Resbos predictions both with and without the extra small- x form-factor, as shown in Figure 2. Without thesmall- x form-factor the fit is found to be χ /dof=11.1/11, whereas with the extra term the fit is χ /dof=31.9/11.This measurement therefore disfavours the small- x broadening.It is interesting to note that when the complete Z p T spectrum is examined, a NNLO calculation reproduces theshape well, but requires rescaling by 25% to match the normalisation.
5. W WIDTH
The width of the W boson is predicted very precisely in the Standard Model, and so its accurate measurement isa powerful check of the consistency of the Standard Model. CDF has measured Γ W using 350 pb − of data [5].Experimentally, transverse quantities are accessible at the Tevatron; for example the transverse mass m T = q p ℓ T p ν T (1 − cos φ ℓν ). Events can have m T > m W either as a result of the intrinsic W width, or as a result ofdetector smearing. The Gaussian effects of detector smearing are found to fall faster than the intrinsic Breit-Wignerlineshape, so the procedure for measuring the width is to use the region m T <
90 GeV/ c for normalisation, and tofit templates to the high m T region.Events to construct the templates are taken from a leading-order monte carlo, matched with Resbos for QCDinitial state radiation and with a calculation from Berends and Kleiss for QED final state radiation. A fast simulationmodels electron conversion and showering, muon energy loss, and includes a parametric model of the energy in thedetectors not associated with the high- p T electron or muon (the ‘recoil energy’), which originates from QCD, theunderlying event and bremstrahlung. The final uncertainty on Γ W from the recoil modeling is ∆Γ = 54 MeV and∆Γ = 49 MeV in the electron and muon channels respectively. The modeling of the tracking scale and resolution andthe calorimeter energy scale and resolution are checked on Z → µµ and Z → ee events respectively; and also on theJ/ ψ . Uncertainties from the tracking scale and resolution are ∆Γ = 17; 26 MeV (e; µ ) and from the calorimeter scaleand resolution ∆Γ = 21; 31 MeV (e; µ ). Backgrounds are dominated by QCD multijet events in the electron channeland by Z → µµ and decays in flight in the muon channel (∆Γ = 32; 33 MeV (e; µ )).The fit in the muon channel is shown in Figure 2. The fits are excellent and the W width is found to be:Γ W = 2032 ± , (1)which is the world’s most precise single direct measurement. It is consistent with the Standard Model prediction(Γ W = 2093 ± indirectW = 2092 ±
42 MeV) [1].
6. Z INVISIBLE WIDTH
The invisible width of the Z is measured very precisely indirectly from LEP: Γ Z (invis) = 500 . ± . Z (invis) = 503 ±
16 MeV. An analagousmeasurement from CDF in 1 fb − [7], using events with a single jet and large missing E T , is completely uncorrelated.Single-jet events are selected from a missing E T trigger. Independently, σ (Z + 1 jet) · Br (Z → ℓℓ ) is measuredfrom high- p T lepton triggers. The ratio of invisible and visible widths can be written as the ratio of cross-sections:Γ invisZ Γ ℓℓ Z = σ (Z + 1 jet) · Br (Z → invis) σ (Z + 1 jet) · Br (Z → ℓℓ ) = N obs − N bck κ · σ (Z + 1 jet) · Br (Z → ℓℓ ) · L , (2)34 th International Conference on High Energy Physics, Philadelphia, 2008 (GeV/c) T * q γ Z/ - ( G e V / c ) T / dq σ d × σ / -1 (b) )(GeV) νµ ( T M
50 100 150 200 E ve n t s / G e V
10 67) MeV ± = (1948 W Γ /dof [fit range] = 17/21 χ /dof [full range] = 21/29 χ data νµ → W MC + bckgd νµ → W bckgd ) -1 CDF Run II ( 350 pb
Figure 2: (left) The Z p T distribution for high-rapidity events. (right) The transverse mass fit in the muon channel. where κ is a correction to take into account the different acceptance of the ‘+1 jet’ selection in Z → νν events comparedto Z → ℓℓ events.The visible lepton cross-section is measured to be σ (Z + 1 jet) · Br (Z → ℓℓ ) = 0 . ± .
024 pb. This leads to anextracted value Γ invZ = 466 ±
42 MeV, where the electroweak backgrounds, QCD backgrounds and visible lepton cross-section make approximately equal contributions to the uncertainty. This can also be interpreted as a measurementof the number of neutrino species, N ν = 2 . ± .
7. CONCLUSIONS
W and Z cross-section measurements underpin the Tevatron high- p T physics programme. Dedicated measurementscontinue, harnessing the high statistics datasets: improving tau identification; testing higher-order calculations andPDFs and probing QCD; and making precision measurements of Standard Model parameters. Acknowledgments
The author thanks the UK Science and Technology Facilities Council for financial support.
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