A measurement of the polarization of W bosons in semi-leptonically decaying W
pairs produced at 189 GeV is presented. Rates of longitudinally and
transversely polarized W bosons and correlation between two W bosons are
studied. The spin properties of the leptonically decaying W boson in the W
pairs was used to measure the CP-violating trilinear gauge boson couplings.
These results are compared with Standard Model expectations.Comment: Proceedings of the XXXth International Symposium on Multiparticle
  Dynamics (ISMD2000), 9-15 October 2000, Tihany, Hungary. 6 pages, 2 figures
  (LaTex, encapsulated PostScript

Trigger, I.

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A measurement of the polarization of W bosons in semi-leptonically decaying W pairs produced at 189 GeV is presented. Rates of longitudinally and transversely polarized W bosons and correlation between two W bosons are studied. The spin properties of the leptonically decaying W boson in the W pairs was used to measure the CP-violating trilinear gauge boson couplings. These results are compared with Standard Model expectations

Trigger, I

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CONSTRAINING CP-VIOLATING TGCS AND MEASURINGW-POLARIZATION AT OPALISABEL TRIGGERDivision EP, CERN, CH-1211 Gene`ve-23, SwitzerlandE-mail: Isabel.Trigger@cern.chOPAL Conference Report CR456December 15, 2001A measurement of the polarization of W bosons in semi-leptonically decaying Wpairs produced at 189 GeV is presented. Rates of longitudinally and transverselypolarized W bosons and correlation between two W bosons are studied. The spinproperties of the leptonically decaying W boson in the W pairs was used to measurethe CP-violating trilinear gauge boson couplings. These results are compared withStandard Model expectations.1 The Spin Density Matrix for W+W−Polarization properties of W+W− produced in e+e− collisions are summarizedby the two-particle joint spin density matrix (SDM). The SDM is the productof the amplitudes for producing a W+ and W− of respective helicities +, −:− 0−+ 0+(s; cos W) =∑ F()−+(F() 0−0+)∑+− jF()−+ j2: (1)The diagonal elements are probabilities of producing W+W− with the corre-sponding helicity combinations, and are strictly real. The potentially complexoff-diagonal terms represent interference between helicity states. The dataconsidered in the analysis were collected with the OPAL detector in 1998,at a centre-of-mass energy of 189 GeV. They correspond to an integratedluminosity of  183 pb−1, with 1065 events identified as W+W− ! qq¯‘.Only semi-leptonic decays are used for this analysis, as fully leptonic andfully hadronic decays cannot be unambiguously reconstructed. Due to therestricted sample size, it is not possible to measure all 81 elements of the jointSDM; however, all elements of the nine-element single-particle SDM, obtainedby summing over the helicity states of the W+, may be measured:W−− 0−(s; cos W) =∑+− 0−++(s; cos W) : (2)Its diagonal elements are the probabilities of producing a W− with helicity+1; 0 or −1. In order to use both qq¯‘−¯ and qq¯‘+, CPT is assumed.The five kinematic variables used in the analysis are the cosine of the polarproduction angle of the W− in the laboratory frame (cos W ), and the decay0101010: submitted to World Scientific on December 15, 2001 1angles given by the directions of the fermion and anti-fermion with respect tothe W+ and W− respectively in the W rest-frames (cos ‘ ; ‘ ; cos j ; j ), withan ambiguity of  for both jet angles due to the difficulty of distinguishingthe up-quark jet from the anti–down-quark jet. With the hadronic part of theevent, it is therefore only possible to measure combinations of SDM elementswhich are symmetric under cos  ! − cos  and  !  + . Fortunately,these include ++ + −− and 00, so the full two-particle SDM element 0000and the combinations +++++++−−+−−+++−−−− and ++00+−−00+00++ + 00−− may be measured.SDM elements are measured by forming histograms of the cos W distribu-tion obtained in the data, and weighting each event by a projection operatorwhich is a function of cos ‘ ; ‘ ; cos j ; j . Different operators project outeach independent element of the SDM. Results are shown in figure 1.Constraints arise from imposing tree-level CPT-invariance:Re(W−12) − Re(W+−1−2) = 0 (3)Im(W−12) + Im(W+−1−2) = 0 : (4)Since CPT has already been assumed, any deviation from these must arisefrom loop effects. CP-invariance would further imply that:Im(W−12)− Im(W+−1−2) = 0 : (5)Combining equations 4 and 5 shows that all single-particle SDM coefficientsmust be strictly real in the absence of CP-violation.2 Helicity Cross-SectionsDifferential production cross-sections for W of particular helicities are:dhdcos W= fhddcos W; (6)where fT = ++ + −−, fL = 00, fTT = ++++ + ++−− + −−++ +−−−−, fLL = 0000, fTL = ++00 + −−00 + 00++ + 00−−. Correspondingtotal cross-sections may be obtained by integrating over the full range ofdcos W. Results are given in table 1. Correction factors are included fordetector and reconstruction effects. The W+ and W− polarizations are about7% correlated. This effect is included in the systematic errors. Total cross-sections for the various helicity states are very strongly correlated. It shouldbe noted that 0000 can have no CP-violating contributions,1 and dLLdcos W isthus completely insensitive to CP-violation. The helicity fractions for TT, LL0101010: submitted to World Scientific on December 15, 2001 2OPALρW-++ ρW-−−ρW-00Re(ρW-+− ) Re(ρW-+0 ) Re(ρW-−0 )Im(ρW-+− ) Im(ρW-+0 ) Im(ρW-−0 )−1 0 ±1 0 ±1 0 +1−0.750−10−0.25+0.5cosθWFigure 1. SDM elements from leptonically decaying W bosons in qq`ν data events. Pointsare OPAL data, with statistical and systematic errors. Histograms show Monte Carlopredictions with full detector simulation. The solid line shows the SM expectation and thedotted (dashed) line that for ∆gz1 = +0.5 (−0.5).and TL differ by about 2 from Standard Model (SM) predictions, giving a2 probability of about 10% for SM compatibility.0101010: submitted to World Scientific on December 15, 2001 3Data SM Exp.T=totalW! ‘ 0.842  0.048  0.023 0.746  0.006W! qq 0.738  0.045  0.025 0.741  0.006All 0.790  0.033  0.016 0.743  0.004L=totalW! ‘ 0.158  0.048  0.023 0.254  0.006W! qq 0.262  0.045  0.025 0.259  0.006All 0.210  0.033  0.016 0.257  0.004Measured ExpectedTT=total 0.781  0.090  0.033 0.572  0.010LL=total 0.201  0.072  0.018 0.086  0.008TL=total 0.018  0.147  0.038 0.342  0.016Table 1. Fractions of W polarizations, and of W+W− pairs of each helicity combination.Expected values are from generator level EXCALIBUR Monte Carlo.3 Triple Gauge Boson CouplingsOf nine possible W+W− helicity pairings, seven are allowed in the s-channelprocesses e+e− ! Z=γ ! W+W− (+−, −+ occur only in t-channel -exchange, as j+ − −j = 2). There are then seven free parameters in theLagrangian describing each of the triple gauge boson couplings W+W−Z0and W+W−γ, here called V ; gV1 ; V ; gV5 ; ˜V ; gV4 ; ˜V (V = Z0; γ). The firsttwo are unity in the SM, and the others zero. The first three conserve C andP, gV5 violates C and P but conserves CP, and the last three violate CP.The real elements of the SDM are sensitive to all of the coupling param-eters; the imaginary elements are also sensitive to CP-violating parameters.It is impossible to fit all fourteen parameters simultaneously with the limiteddata sample. Each is measured separately, with the others set to their SMvalues, except those related to the tested parameter through SU(2)  U(1)symmetry2 (˜Z = − tan2 W ˜γ ; ˜Z = ˜γ ; gZ4 = gγ4 ). This leaves three inde-pendent parameters to test, chosen to be ˜Z ; ˜Z ; gZ4 . There are strong con-straints on CP-violation in electromagnetic interactions from the constraintson the electric dipole moment of the neutron,3 which is why an alternativewould be to ignore the gauge symmetry constraints and set W+W−γ cou-plings to zero. Coupling values from a fit to the SDM elements are given intable 2. Table 2 also includes results from a 2 fit to the cos W distribution.0101010: submitted to World Scientific on December 15, 2001 4Fit ˜z gz4 ˜zSDM Elements −0:19+0:08−0:07 0:00+0:21−0:20 −0:12+0:17−0:16cos W −0:19+0:46−0:08 0:7+0:4−1:8 −0:29+0:69−0:11Combined −0:19+0:06−0:05 0:01+0:22−0:22 −0:19+0:18−0:13Expected Stat. Error 0.11 0.19 0.12Final FitIncluding Systematics−0:20+0:10−0:07 −0:02+0:32−0:33 −0:18+0:24−0:16Table 2. Measured values of CP-violating TGC parameters. Both the SDM elements andthe cos θW production distribution are used in the calculation. Errors are statistical onlyexcept in the case of the final combined fit.The cos W distribution is the most sensitive to variations in CP-conservingcouplings, but is relatively insensitive to CP-violating couplings. Figure 2shows 2 curves for TGCs measured from SDM elements and from cos Wdistributions. The real SDM elements and cos W are sensitive only to themagnitude of CP-violating couplings (their dependence on the couplings isquadratic), and so have a double minimum. The imaginary SDM elementsdepend linearly on the CP-violating couplings and can thus lift the degener-acy. The CP-conserving couplings measured from the SDM elements are fullycompatible with the results of the OPAL optimal observable analysis.44 ConclusionsThe SDM method allows direct measurement of the fraction of W bosons pro-duced with longitudinal polarization. This longitudinal component of the Wis a result of the electroweak symmetry breaking mechanism. It also providesconstraints on CP-violation in TGCs. All results are compatible with SMpredictions. This analysis is more fully described elsewhere.5References1. G. Gounaris, J. Layssac, G. Moultaka and F.M. Renard, Int. Journal ofModern Physics A8, 3285 (1993).2. G. Gounaris, C.G. Papadopoulos, Eur. Phys. J. C2, 365 (1998).C.G. Papadopoulos, Comput. Phys. Commun. 101, 183 (1997).3. P.G. Harris et al., Phys. Rev. Lett. 82, 904 (1999).K.F. Smith et al., Phys. Lett. B234, 191 (1990).4. OPAL Collaboration, G. Abbiendi et al., “Measurement of Triple Gauge0101010: submitted to World Scientific on December 15, 2001 5OPAL∆κγ∆χ2κ~z∆χ2∆gz1∆χ2gz4∆χ2λ∆χ2λ~z∆χ205-1 0 105-1 -0.5 0 0.5 105-1 -0.5 0 0.5 105-2 -1 0 1 205-1 -0.5 0 0.5 105-1 -0.5 0 0.5 1Figure 2. The χ2 plots for the fits to the CP-conserving and CP-violating anomalous cou-plings. The dotted line is the fit to just the cos θW distribution. The solid line is thecombined fit. All fits include systematic uncertainties.Boson Couplings from e+e− Production at LEP Energies up to 189 GeV,”CERN-EP-2000-114, Submitted to Eur. Phys. J. C.5. OPAL Collaboration, G. Abbiendi et al., “Measurement of W BosonPolarisations and CP-violating Triple Gauge Couplings from e+e− Pro-duction at LEP,” CERN-EP-2000-113, Submitted to Eur. Phys. J. C.0101010: submitted to World Scientific on December 15, 2001 6

Constraining CP-Violating TGCs and Measuring W-Polarization at OPAL

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