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W Studies at LEP2

W Studies at LEP2. SDM Elements and Polarised Cross-Sections Test of CP and CPT Invariance W Polarisation, W Polarisation vs. cos θ W WW Spin Correlations in Flight Direction WW Decay Plane Correlations. R.Ofierzynski, ETH Z ürich, on behalf of the LEP collaborations.

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W Studies at LEP2

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  1. W Studies at LEP2 • SDM Elements and Polarised Cross-Sections • Test of CP and CPT Invariance • W Polarisation, W Polarisation vs. cos θW • WW Spin Correlations in Flight Direction • WW Decay Plane Correlations R.Ofierzynski, ETH Zürich, on behalf of the LEP collaborations International Europhysics Conference on High Energy Physics 2003

  2. W Polarisations • Mass 0 – photon → helicities (–1), (+1) • Massive W boson → helicities (-1), (+1) and (0) (-1),(+1): transverse polarisation, (0): longitudinal polarisation • Standard Model: longitudinal d.o.f. from electroweak symmetry breaking mechanism • Equivalence theorem: longitudinal gauge bosons ≈ Goldstone bosons R.Ofierzynski

  3. Spin Density Matrix (D,L,O) • Theoretically: [M.Bilenky et al, Nucl.Phys.B409(1993)] e+(l’) e–(l) → W+(t2) W–(t1) → 4f (l = -l’ = ±½, t1,t2 = ±1,0) • Two-particle SDM: • Single-particle SDM: (9 elements) • diagonal elements (real) → probability to produce W- with helicity +1,0,-1 • off-diagonal elements (complex) → test of CP and CPT invariance R.Ofierzynski

  4. SDM Measurement (D,L,O) • Experimentally: divide cos θW in 8 bins • Apply projection operators on the events in bin k • : projection operator for diagonal SDM elements dependent on (cos θ*f) for non-diagonal SDM elements dependent on (cos θ*f) and Φ*f • correct for detector acceptance, resolution effects, background contamination → compare to SM prediction R.Ofierzynski

  5. SDM – Elements DELPHI preliminary measurement performed in three energy bins: 189 GeV, 192-202 GeV, 204-208 GeV SDM elements measured with W→ℓν as function of cos ΘW- R.Ofierzynski

  6. SDM – Test of CP(T) invariance L3, 189-209 GeV, W→ℓν • CPT-invariance: • CP-invariance: compatible with 0, no CP- or CPT-violation at tree level

  7. SDM – Test of CP invariance OPAL, 183-209 GeV, W→ℓν Construct CP-odd observables: consistent with 0 →TGC-parameters ≤O(10-1) — SM prediction R.Ofierzynski

  8. SDM – Polarised Cross-sections DELPHI preliminary Polarised cross-section: — SM MC prediction R.Ofierzynski

  9. SDM – Polarised Cross-sections OPAL preliminary 183-209 GeV 680pb-1, stat.+syst. uncertainty SDM elements ρ00,ρ-- measured with W→ℓν, W→qq as function of cos ΘW- Polarised cross-section — SM prediction (luminosity averaged) R.Ofierzynski

  10. W– (–1) W– (+1) W–(0) Inclusive Measurement (L3) Polar decay angle in W rest frame cos θf* W→ℓν: W→qq: Helicity fractions extracted by fit of corrected cos θ* distributions with R.Ofierzynski

  11. Inclusive W Polarisation L3, 183-209 GeV, 685pb-1, WW→e/μνqq, corrected R.Ofierzynski

  12. Longitudinal Polarisation in D,L,O • DELPHI, OPAL: integration of differential polarised cross-sections, divide by total cross-section • L3: inclusive measurement R.Ofierzynski

  13. Polarisation vs. cos ΘW- Direct measurement 183-209 GeV, W→ℓν and W→qq combined strong variations with W scattering angle, in agreement with Standard Model R.Ofierzynski

  14. WW Spin Correlations (L3) W → qq W → ℓν f–, f+, f0 (±1) depleted (±1) enriched f–, f+, f0 Relative cross-section contributions (0) difference = indicator for correlations 61.7% (±1) 89.2% (±1) (±1) |cos θ*q| R.Ofierzynski

  15. WW Spin Correlations cont. Enlarge possible effects using W scattering angle Forward bin: 0.3 < cos ΘW- < 0.9 f(–+) ≈ 63% (average 43%) Backward bin: -0.9 < cos ΘW- < -0.3 f(00) ≈ 25% (average 9%) cos ΘW- R.Ofierzynski

  16. WW Spin Correlations Results 189-209 GeV, corrected W→ℓν seen with 2.6σ, somewhat stronger than in MC R.Ofierzynski

  17. WW Spin Correlations Results 189-209 GeV, corrected W→ℓν R.Ofierzynski

  18. f f W– W+ f f Decay Plane Correlations (L3) • determine angle between decay plane normal vectors • fit with D = correlation parameter • WW→e/μνqq and WW→qqqq, 189-209 GeV [Duncan,Kane,Repko, Nucl.Phys.B272(1986)] R.Ofierzynski

  19. Decay Plane Correlations Results D = 0.000 ± 0.024 ± 0.014 D = 0.051 ± 0.033 ± 0.020 combined data: D = 0.017 ± 0.019 ± 0.011 (MC: D = 0.010 ± 0.002 ) R.Ofierzynski

  20. Conclusions • Spin Density Matrix measurement (DELPHI,L3,OPAL) Inclusive measurement (L3) • Fraction of longitudinal polarisation, variation with W scattering angle, polarised cross-sections in agreement with SM • SDM provides direct test for CP(T) invariance, no deviations from SM • expect limits on CP-violating couplings • WW spin correlations in flight direction observed with 2.6 standard deviations • WW decay plane correlations very small, in agreement with SM R.Ofierzynski

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