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 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


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


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 '


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


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


SDM – Polarised Cross-sections

Polarised cross-section:

DELPHI preliminary

WW

W

L

d

d

d

d

cos)(cos

cos 00

— SM MC prediction


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)


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:


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


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


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


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


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


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


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


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)]


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 )


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

W Studies at LEP2

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