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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. - PowerPoint PPT Presentation
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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
EPS Aachen, 19.07.03 R.Ofierzynski 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
EPS Aachen, 19.07.03 R.Ofierzynski 3
Spin Density Matrix (D,L,O)• Theoretically:
[M.Bilenky et al, Nucl.Phys.B409(1993)]
e+(’) e–() → W+() W–() → 4f
( = -’ = ±½, 1,2 = ±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
2,,
*''
'' ||
)()cos,(
2121
2121
2211
F
FFs W
)cos,()cos,(2
221111 ''' WWW ss
EPS Aachen, 19.07.03 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
k
k
N
iiff
WN
W k1
**'
1' ),(cos)(
W '
EPS Aachen, 19.07.03 R.Ofierzynski 5
SDM – ElementsDELPHI 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-
6
SDM – Test of CP(T) invariance
L3, 189-209 GeV, W→ℓν
• CPT-invariance:
• CP-invariance:
0)Im()Im( ',',
WW
0)Im()Im( ',',
WW
compatible with 0,no CP- or CPT-violation
at tree level
5.0~
Z
EPS Aachen, 19.07.03 R.Ofierzynski 7
SDM – Test of CP invariance
OPAL, 183-209 GeV, W→ℓν
Construct CP-odd observables:
1
1 '' coscos
)Im( WW
WW dd
d
WWCP
WWCP
WWCP
000
000
consistent with 0
→TGC-parameters ≤ O(10-1)
— SM prediction
EPS Aachen, 19.07.03 R.Ofierzynski 8
SDM – Polarised Cross-sections
Polarised cross-section:
DELPHI preliminary
WW
W
L
d
d
d
d
cos)(cos
cos 00
— SM MC prediction
EPS Aachen, 19.07.03 R.Ofierzynski 9
SDM – Polarised Cross-sections
OPAL preliminary 183-209 GeV680pb-1, stat.+syst. uncertainty
SDM elements ρ00,ρ--
measured with W→ℓν, W→qqas function of cos ΘW-
Polarised cross-section
— SM prediction (luminosity averaged)
EPS Aachen, 19.07.03 R.Ofierzynski 10
Inclusive Measurement (L3)
W– (–1)
W– (0)
W– (+1)
2*f8
3*f
243
02*
f83
*f
)cos1()(sin)cos1(cos
1
fffd
dN
N
Polar decay anglein W rest frame
cos θf*
Helicity fractions extracted by fit of corrected cos θ* distributionswith 1 if
W→qq:2*
f23
02*
f43
*f
||||||
sin)cos1(cos
1
ffd
dN
N
W→ℓν:
EPS Aachen, 19.07.03 R.Ofierzynski 11
Inclusive W Polarisation
W→ℓν, W→qq combined ƒ– [%] ƒ+ [%] ƒ0 [%]
Data 59.2 ± 2.7 ± 1.6 19.0 ± 1.7 ± 1.5 21.8 ± 2.7 ± 1.6
SM MC 59.0 ± 0.3 16.9 ± 0.2 24.1 ± 0.3
L3, 183-209 GeV, 685pb-1, WW→e/μνqq, corrected
EPS Aachen, 19.07.03 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
fraction of helicity (0) [%]
DELPHI 189-209GeV
W→e/μν24.9 ± 3.3 (preliminary)
OPAL 183-209GeV
W→e/μ/ν, W→qq23.8 ± 2.1 ± 1.4 (preliminary)
L3 183-209GeV
W→e/μν, W→qq21.8 ± 2.7 ± 1.6 (published)
SM 24.0
EPS Aachen, 19.07.03 R.Ofierzynski 13
Polarisation vs. cos ΘW-
Direct measurement
183-209 GeV,
W→ℓν and W→qq combined
strong variations withW scattering angle,
in agreement with Standard Model
EPS Aachen, 19.07.03 R.Ofierzynski 14
WW Spin Correlations (L3)
W → qq W → ℓν
(±1)enriched
(±1)depleted
(±1)
(0)
89.2%(±1)
61.7% (±1)
|cos θ*q|
f–, f+, f0
f–, f+, f0
difference=
indicator forcorrelations
Relative cross-section contributions
EPS Aachen, 19.07.03 R.Ofierzynski 15
WW Spin Correlations cont.
cos ΘW-
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%)
Enlarge possibleeffects using
W scattering angle
EPS Aachen, 19.07.03 R.Ofierzynski 16
WW Spin Correlations Results
W→ℓν helicity
(fdep – fenr)
Data
(fdep – fenr)
MC
(-1)
[%]
-31.8
±10.3±6.5
-11.1
±1.1
(+1)
[%]
3.4
±6.7±5.2
5.7
±0.7
(0)
[%]
28.4
±13.7±9.5
5.4
±1.5
seen with 2.6σ, somewhat stronger than in MC
189-209 GeV, corrected W→ℓν
EPS Aachen, 19.07.03 R.Ofierzynski 17
WW Spin Correlations Results
W→ℓν helicity
(fdep – fenr)
Data
(fdep – fenr)
MC
(-1)
[%]
23.5
±15.9±13.4
2.8
±2.0
(+1)
[%]
-13.2
±15.8±12.1
-18.1
±2.3
(0)
[%]
-10.3
±38.2±19.4
15.3
±3.5
189-209 GeV, corrected W→ℓν
EPS Aachen, 19.07.03 R.Ofierzynski 18
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
W–W+
f
ff
f
|)|2cos(1||
1
Dd
dN
N[Duncan,Kane,Repko, Nucl.Phys.B272(1986)]
EPS Aachen, 19.07.03 R.Ofierzynski 19
Decay Plane Correlations Results
D = 0.051 ± 0.033 ± 0.020 D = 0.000 ± 0.024 ± 0.014
combined data: D = 0.017 ± 0.019 ± 0.011 (MC: D = 0.010 ± 0.002 )
EPS Aachen, 19.07.03 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