In 1997 each LEP experiment collected approximately $55 {pb}^{-1}$ of data at
a center-of-mass energy of 183 GeV. These data yield a sample of candidate
$e^+e^- \to W^+W^-$ events from which the mass of the W boson, M_W, is
measured. The preliminary LEP combined result, including data taken at $\roots
= 161$ and 172 GeV and assuming the Standard Model relation between the W decay
width and mass, is $M_W = 80.38 \pm 0.07 (exp) \pm 0.03 (CR/BE) \pm 0.02
(E_{bm})$ GeV, where the uncertainties correspond to experimental,
colour-reconnection/Bose-Einstein, and LEP beam energy respectively.Comment: 7 pages, 1 figure. Proceedings for talk 1-12 given at the DPF99
  Conference in Los Angeles, Californi

Glenzinski, D.

English

arXiv

In 1997 each LEP experiment collected approximately $55 {pb}^{-1}$ of data at a center-of-mass energy of 183 GeV. These data yield a sample of candidate $e^+e^- \to W^+W^-$ events from which the mass of the W boson, M_W, is measured. The preliminary LEP combined result, including data taken at $\roots = 161$ and 172 GeV and assuming the Standard Model relation between the W decay width and mass, is $M_W = 80.38 \pm 0.07 (exp) \pm 0.03 (CR/BE) \pm 0.02 (E_{bm})$ GeV, where the uncertainties correspond to experimental, colour-reconnection/Bose-Einstein, and LEP beam energy respectively

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arXiv:hep-ex/9902020v2  16 Feb 1999Measurement of the W Mass from LEP2D. GlenzinskiEnrico Fermi Institute, University of Chicago(with the LEP Collaborations)Talk 1-12 given at the DPF99 Conference, Los Angeles, California.In 1997 each LEP experiment collected approximately 55pb−1 of data at a center-of-mass energyof 183 GeV. These data yield a sample of candidate e+e− → W+W− events from which the massof the W boson, MW, is measured. The preliminary LEP combined result, including data taken at√s = 161 and 172 GeV and assuming the Standard Model relation between the W decay widthand mass, is MW = 80.38 ± 0.07(exp) ± 0.03(CR/BE) ± 0.02(Ebm) GeV, where the uncertaintiescorrespond to experimental, colour-reconnection/Bose-Einstein, and LEP beam energy respectively.I. INTRODUCTIONThe success of the Standard Model (SM) over the last two decades should not obscure the importance of thoroughlyinvestigating the weak interaction. It is interesting to consider that 15 years ago, when neutrino scattering experimentshad measured sin2 θW = 0.217± 0.014, the following SM constraints were available [1]:MW(indirect) = 83.0± 2.8 GeV (1)MZ0(indirect) = 93.8± 2.3 GeV (2)Tree level deviations could be accommodated in those errors! Today we have measured [2] sin2 θW to 0.0002, MZ0 to0.002 GeV, and MW to 0.07 GeV — the success of the SM is so thorough that it can only be wrong at the quantumloop level, and even then, beyond leading order. Despite this rousing success, it is still necessary to test the SM byconfronting experimental observations with theoretical predictions as any deviations might point to new physics. Asa fundamental parameter of the SM, the mass of the W boson, MW, is of particular importance.Aside from being an important test of the SM in its own right, the direct measurement of MW can be used toset constraints on the mass of the Higgs boson, MH, by comparison with theoretical predictions involving radiativecorrections sensitive to MH. The constraints imposed using MW are complimentary to the constraints imposed by theasymmetry (AbFB, AℓFB, ALR,...) and width (Rℓ, Rb, Rc,...) measurements. For example, the very precise asymmetrymeasurements presently yield the tightest constraints on MH, but are very sensitive to the uncertainty in the hadroniccontribution to the photon vacuum polarisation, Πγγhad. In contrast, the constraint afforded by a direct measureof MW is comparably tight but with a much smaller sensitivity to Πγγhad, and is presently dominated by statisticaluncertainties [3].A. WW Production at LEPAt LEP W bosons are predominantly produced in pairs through the reaction e+e− → W+W−, with each W sub-sequently decaying either hadronically (qq), or leptonically (ℓν, ℓ = e, µ, or τ). This yields three possible four-fermion final states, hadronic (W+W−→qqqq), semi-leptonic (W+W−→qqℓν), and leptonic (W+W−→ℓ−νℓℓ′+νℓ′),with branching fractions of 45%, 44%, and 11% respectively. The W+W− production cross-section varies from 3.6 pbat√s = 161 GeV to 16.7 pb at√s = 189 GeV. These can be contrasted with the production cross-sections for the dom-inant backgrounds σ (e+e− → Z∗/γ∗ → qq) ≈ 100 pb, σ(e+e− → Z0e+e−)≈ 2.8 pb, σ (e+e− → (Z∗/γ∗)(Z∗/γ∗)) ≈0.6 pb, and σ (e+e− →Weν) ≈ 0.6 pb. Aside from the Z∗/γ∗ → qq process, which falls from ≈ 150 pb at√s = 161 GeV, these background cross-sections vary slowly for√s < 185 GeV, when the e+e− → ZZ processbegins to turn-on.1TABLE I. The W+W− selection efficiency, ε, and purity, P , for the qqqq and qqℓν channels for each of the four LEPexperiments. Delphi employs no explicit qqτν selection.channel experimentA D L Oqqqq ε (%) 83 85 88 85P (%) 83 65 80 80qqeν(µν) ε (%) 89 71 87 90P (%) 96 94 96 94qqτν ε (%) 64 – 59 75P (%) 93 – 87 83B. LEP Measurement TechniquesThere are two main methods available for measuring MW at LEP2. The first exploits the fact that the W+W−production cross-section is particularly sensitive to MW for√s ≈ 2MW. In this threshold (TH) region, assumingSM couplings and production mechanisms, a measure of the production cross-section yields a measure of MW. Inearly 1996 the four LEP experiments collected roughly 10 pb−1 of data at√s = 161 GeV, resulting in a combineddetermination of the W boson mass of MW(TH) = 80.40 ± 0.20(exp) ± 0.03(Ebm) GeV, where the uncertaintiesscorrespond to experimental and LEP beam energy respectively [2,4].The second method uses the shape of the reconstructed invariant mass distribution to extract a measure of MW.This method is particularly useful for√s ≥ 170 GeV where the W+W− production cross-section is larger andphase-space effects on the reconstructed mass distribution are smaller. Each experiment collected roughly 10 pb−1 at√s = 172 GeV [5] in later 1996, and in 1997, roughly 55 pb−1 at√s = 183 GeV. Since most of the LEP2 data hasbeen collected at center-of-mass energies well above the W+W− threshold, the LEP2 MW determination is dominatedby these direct reconstruction (DR) methods. For this reason, the rest of this article will concentrate on the detailsof this method.II. DIRECT RECONSTRUCTION OF MWTo measure MW using direct reconstruction techniques one must1. Select W+W− → ffff events.2. Obtain the reconstructed invariant mass,mrec, for each event.3. Extract a measure of MW from the mrec distribution.Each of these steps are discussed in detail in the section below and in Reference [5]. It should be noted that noneof the LEP experiments presently exploits the W+W−→ℓ−νℓℓ′+νℓ′ final state in the DR methods 1; it is thereforediscussed no further.A. Event SelectionThe expected statistical error on MW varies as, ∆MW(stat) ∼ 1√NWW ·1√Purity, so that high efficiency, high purityselections are important. The W+W− selection efficiencies and purities are given in Table I for each of the four LEPexperiments.1A measure of MW can be obtained from the W+W−→ℓ−νℓℓ′+νℓ′ channel by using the lepton energy spectrum. However, itis estimated to be a factor of 4-5 less sensitive than the measurements available from the other W+W− final states.2For the data taken at√s = 183 GeV, these efficiencies and purities give approximately 700 W+W− candidate eventsper experiment, about 100 of which are non-W+W− background. The selection efficiencies have a total uncertaintyof about 1% (absolute) and have a negligible effect (< 1 MeV) on the MW determination. The accepted backgroundcross-sections have a total uncertainty of 10 − 20% (relative) and effect the MW determination at the 10− 15 MeVlevel (cf. Section IV).B. Invariant Mass ReconstructionThere are several methods available for reconstructing the invariant mass of a W± candidate. The best resolution isobtained by using a kinematic fit which exploits the fact that the center-of-mass energy of the collision is known apriori 2. The are two “flavours” of kinematic fit:1. 4C-fit: Enforces Σ(P,E) = (0,√s) constraints; yields two reconstructed masses per event, (mrec1 ,mrec2), onefor each W± in the final state.2. 5C-fit: In addition to the four constraints above, ignores the finite width of the W± and requires that mrec1 =mrec2; yields a single reconstructed mass per event.The type of fit used depends on the final state. For instance, in the qqeν and qqµν channels, because the promptneutrino from the leptonic W± decay takes three degrees-of-freedom (dof), Pν , the fits effectively become 1C and 2Cfits respectively. For the qqτν channel, high energy neutrinos from the τ -decay itself lose at least one additional dofand so require that all 5 constraints be used, thus yielding a 1C fit 3.In the qqqq channel, since there are (nominally) four jets, there exist three possible jet-jet pairings. This pairingambiguity gives rise to a combinatoric background unique to the qqqq channel. Each LEP experiment employs adifferent technique for choosing the best combination(s). L3 uses the 5C-fit probabilities (the equal mass constraintyields a different fit χ2 for each combination) to choose the two best combinations per event. At the cost of someadditional combinatorics, this algorithm has the correct combination among those chosen about 90% of the time.Opal , Delphi and Aleph employ a 4C-fit and exploit kinematic information to choose the best combination. Thealgorithms employed by Aleph and Opal choose a single combination per event; this combination corresponds tothe correct combination approximately 85% of the time at no additional cost in combinatorics. Delphi uses allcombinations and weights each according to the likelihood that it corresponds to the correct combination.C. Extracting MWThe ensemble of selected events yields a mrec distribution from which a measure of MW is extracted. There areseveral methods available for extracting MW. Aleph , L3 , and Opal all employ a traditional maximum likelihoodcomparison of data to Monte Carlo (MC) spectra corresponding to various MW. In addition to its simplicity, thismethod has the advantage that all biases (ie. from resolution, ISR, selection, etc.) are implicitly included in theMC spectra. The disadvantage of this method is that it does not make optimal use of all available information.Delphi employs a convolution technique, which makes use of all available information; in particular, events withlarge fit-errors are de-weighted relative to fits with small fit-errors. The convolution has the limitations that it2Strictly speaking, this is not true since any initial state radiation (ISR) reduces the collision energy to less than twice thebeam energy. The kinematic fits assume no ISR. The effect of ISR uncertainties is incorporated in the total systematic errordiscussed in Section IV.3Such a fit is possible only if one assumes that the τ -lepton direction is given by the direction of the visible decay productsassociated with the τ .3TABLE II. Results for data taken at√s = 183 GeV. All quantities are given in units of GeVqqℓν channelexp MW ± (stat)± (syst) σˆstatA 80.34 ± 0.19± 0.05 0.20D 80.50 ± 0.26± 0.07 0.25L 80.03 ± 0.24± 0.07 0.21O 80.33 ± 0.17± 0.06 0.19LEP 80.31 ± 0.10± 0.03 χ2 = 1.9/3TABLE III. Results for data taken at√s = 183 GeV. All quantities are given in units of GeV.qqqq channelexp MW ± (stat)± (syst)± (CR/BE) σˆstatA 80.41 ± 0.18 ± 0.05± 0.06 0.18D 80.02 ± 0.20 ± 0.05± 0.06 0.20L 80.51 ± 0.21 ± 0.08± 0.06 0.19O 80.53 ± 0.23 ± 0.07± 0.06 0.19LEP 80.35 ± 0.10 ± 0.04± 0.06 χ2 = 3.7/3requires various approximations (ie. the resolution is often assumed to be Gaussian) and often requires an a posterioricorrection as the fit procedure does not account for all biases, notably from ISR and selection.III. RESULTSThe results from each LEP experiment, using data collected at√s = 183 GeV, are given in Table II for qqℓν channeland in Table III for the qqqq channel4. Also included is the mass obtained when combining all four measurements5.For the LEP combinations, the ISR, hadronization, LEP beam energy, and color-reconnection/Bose-Einstein (CR/BE)uncertainties are taken as completely correlated between the four experiments. The errors given correspond to theobserved statistical and the total systematic (including that associated with the LEP beam energy) uncertaintiesrespectively. For the qqqq channel, the error associated with CR/BE uncertainties is given separately and is taken asa 60 MeV common error. Also shown in Tables II and III is the expected statistical error, σˆstat, for each experiment.As an example, the Opal fits are shown in Figure 1.Using data taken at√s = 172 and 183 GeV, the preliminary LEP combined MW using DR methods for the qqℓνand qqqq channels separately is:MW(qqℓν) = 80.33± 0.09(stat)± 0.03(syst) GeV (3)MW(qqqq) = 80.39± 0.09(stat)± 0.04(syst)± 0.06(CR) GeV (4)Note that these results are statistically consistent with each other.IV. SYSTEMATIC ERRORSThe systematic errors for a typical LEP experiment are given in Table IV. It should be noted that for all four LEPexperiments the errors associated with ISR, hadronization, and four-fermion interference uncertainties are limited by4From these results, only the Opal numbers are final [6] while the rest are the latest available pre-liminary results.5Note that since the Opal numbers have changed since the last “official” LEP combination, the combinations given here arethe author’s own.4TABLE IV. Table of systematic errors on MW for a typical LEP experiment.systematic ∆MW (MeV) ∆MW (MeV)source qqℓν qqqqinitial state radiation 15 15hadronization 25 30four fermion 20 20detector effects 30 35fit procedure 30 30Sub-total 55 60beam energy 22 22CR/BE – 60Total 59 88the statistics of the comparison. Uncertainties associated with the selection efficiencies and accepted backgrounds areincluded in the line labeled “fit procedure”. For the qqℓν channel the largest single contribution to the systematicuncertainty is due to detector effects (eg. energy scales, resolutions, and modelling). These errors are expected todecrease as more data is collected. For the qqqq channel the dominant systematic uncertainty is due to CR/BEeffects.There has been recent progress in experimentally constraining the available CR models by comparing event shapeand charged particle multiplicity distributions as predicted by various MC models (both including and excluding CReffects) with those observed in the data. On the basis of these studies, some of the models have been excluded asthey fail to adequately describe the data [7]. In particular, the VNI [8] model is excluded, which predicted systematicshifts to the measured MW(qqqq) on the order of 100 MeV. The surviving models are used to estimate the systematicuncertainty associated with the modeling of CR effects and yield estimates in the range of 20− 55 MeV. For a morecomplete discussion, see Reference [7]. Additional data should help to further constrain the remaining CR modelsand thus improve these errors.V. CONCLUSIONSUsing approximately 10 pb−1 of data collected at√s = 161 and 172 GeV and 55 pb−1 at√s = 183 GeV the LEPexperiments have measured the mass of the W boson. The LEP combined result, assuming the Standard Model relationbetween the W decay width and mass, is MW = 80.38± 0.07(exp)± 0.03(CR/BE)± 0.02(Ebm) GeV, where the errorscorrespond to experimental, colour-reconnection/Bose-Einstein, and LEP beam energy uncertainties respectively.This value (80.38± 0.08 GeV) is consistent with the direct measurement from the TeVatron (80.41± 0.09 GeV) [9],and the indirect determinations from NuTeV (80.26 ± 0.11 GeV) [10] and SM fits to precision electroweak data(80.37± 0.03) [3].During 1998 LEP delivered approximately 180pb−1 per experiment at√s ≈ 189 GeV. This additional data increasedthe presently available statistics for the DR method by more than a factor of two. Incorporating this data should yielda statistical error for the LEP combined determination of MW of 40− 50 MeV and will allow for tighter experimentalconstraints on various color-reconnection and Bose-Einstein models in the qqqq final state.ACKNOWLEDGEMENTSMany thanks to my colleagues in the LEP Electroweak working group for their comments and suggestions.5[1] W.J. Marciano and A.Sirlin, Phys. Rev. D 29, 945 (1984).[2] LEP Electroweak Working Group, A Combination of Preliminary Electroweak Measurements and Constraints on theStandard Model, LEPEWWG/98-01, April 1998.[3] See for example G. Degressi, et al., Phys. Lett. B 418, 209 (1998); F. Teubert, Precision test of the Standard Modelfrom Z physics, \protect\vrule width0pt\protect\href{http://arxiv.org/abs/hep-ph/9811414}{hep-ph/9811414},November 1998.[4] Opal Collaboration, Phys. Lett. B 389, 416 (1996); Delphi Collaboration, Phys. Lett. B 397, 158 (1997);L3 Collaboration, Phys. Lett. B 398, 223 (1997); Aleph Collaboration, Phys. Lett. B 401, 347 (1997).[5] L3 Collaboration, Phys. Lett. B 413, 176 (1997); Opal Collaboration, Eur. Phys. J. C 1, 395 (1998); Aleph Collaboration,Phys. Lett. B 422, 384 (1998); Delphi Collaboration, Eur. Phys. J. C 2, 581 (1998).[6] Opal Collaboration, Measurement of the W Mass and Width in e+e− Collisions at 183 GeV, CERN-EP/98-197, submittedto Phys. Lett. B.[7] Opal Collaboration, Colour Reconnection studies in e+e− →W+W− at √s = 183 GeV, CERN-EP/98-196, submitted toPhys. Lett. B.[8] J. Ellis and K. Geiger, Phys. Rev. D 54, 1967 (1996); K. Geiger, Comput. Phys. Commun. 104, 70 (1997).[9] D0 Collaboration, Phys. Rev. Lett. 80, 3008 (1998); Cdf Collaboration, Phys. Rev. Lett. 75, 11 (1995).[10] G.P. Zeller, Measurement of sin2 θW in νN scattering from NuTeV, these proceedings.6 OPAL, √s = 183 GeV010203040506070 80 90Mrec / GeVWW→qqqq05101520253070 80 90Mrec / GeVWW→qqe n05101520253070 80 90Mrec / GeVWW→qq mnentries / GeV0510152070 80 90Mrec / GeVWW→qq tnFIG. 1. Fit results for√s = 183 GeV data. The points are Opal data, the histogram is the fit result, and backgroundcontributions are shown as the dark shaded regions.

Measurement of the W Mass from LEP2

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