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Measurements of the W Helicity
in Top Quark Decays
Kenneth Johns
University of Arizona
for the
DØ and CDF
Collaborations
Ann Arbor Symposium
1
W Helicity
The heavy mass of the top quark makes it a prime
target for searches of physics beyond the Standard
Model
Measurement of the W helicity is a measurement of
the tbW vertex
Top quark lifetime < hadronization time
V-A weak interaction determines the top quark decay in SM
b
t
WL
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W0
WR
t
t
b
b
2
W Helicity
In the mb=0 limit,
mt2
2M W2
F0 2
0.70 F 2
0.30
2
2
mt 2M W
mt 2M W
F 0
Finite mb and O(αs) corrections change the above
values by < 2%
We look for new physics by searching
for F0 ≠ 0.7 (assuming F+=0)
for F+ > 0 (assuming F0=0.7 )
F+ is indirectly constrained to a few percent by b→sγ
data (e.g. Fujikawa&Yamada, PRD 49 (1994) 5890)
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W Helicity
The angular decay distribution for unpolarized top
w(cosθ) = 3/8(1+cosθ)2F+ + 3/8(1-cosθ)2F- + 3/4(sin2θ)F0
b
W+ direction
in
top rest frame
θ
W boson rest frame
l+
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W Helicity
The angular factors are also reflected in the shape of
the lepton PT distribution
The lepton PT spectrum for F+ will be harder than that for F0
The lepton PT spectrum for F- will be softer than that for F0
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W Helicity Measurements
Expt
Published?
Ldt
Method
CDF Run I
PRL 2000
106 pb-1
PTlepton
CDF Run I
PRD 2005
109 pb-1
Mlb2
DØ Run I
N
125 pb-1
Matrix
Element
CDF Run II
N
162 pb-1
PTlepton
CDF Run II
N
162 pb-1
Mlb2
DØ Run II
N
163 pb-1
cos(θ*)
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W Helicity Measurements
Expt
CDF Run I
Method
PTlepton
CDF Run I
Mlb2
DØ Run I
CDF Run II
ME
PTlepton
CDF Run II
DØ Run II
Mlb2
cos(θ*)
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Samples
LJ (w/wo b-tag)
LL (eμ)
LJ (w b-tags)
LL (eμ)
Notes
SVT, SLT
LJ
LJ w b-tags
LL
LJ w b-tag
4 jets only
SVT
3, 4 jets
SVT
LJ w/wo b-tag
SVT
SVT
SVT = Secondary Vertex Tag
SLT = Soft Lepton Tag
7
Matrix Element Method
ME method offers the possibility of increased
statistical precision by using all measured quantities in
an event
Write the probability density
1
P( x; F0 ) d n ( y; F0 )dq1dq2 f (q1 ) f (q2 )W ( x, y )
Include background
P( x; c1 , c2 , F0 ) c1Pttbar ( x; F0 ) c2 PW jets ( x)
N
Form a likelihood
ln L( F0 ) ln[c1 Pttbar ( xi ; F0 ) c2 PW jets ( xi )]
i 1
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N A( x)[c1 Pttbar ( x; F0 ) c2 PW jets ( x)]dx
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Matrix Element Details
Mttbar
qqbar only (no gg)
4 jets only (no NLO)
Mbkg
W+jets only
Selection cut on Pbkg
used to reduce
background
Ensemble tests are used
to estimate bias
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Matrix Element Results
mt
F0
Assuming mt =175 GeV, F0 = 0.60 ± 0.30 (stat)
Uncertainty in mt is accounted for by integrating L(F0,mt)
over mt
Including the remaining systematic errors gives
F0 = 0.56 ± 0.31 (stat+mt) ± 0.07 (sys)
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PTlepton Method
PTlepton is sensitive to the W helicity
Charged leptons tend to be emitted opposite to WL direction
Charged leptons tend to be emitted transverse to W0 direction
F+ = 0 (hence measure F0)
Select LJ b-tag and LL events
Determine backgrounds ala cross section analyses
Construct PTlepton PDF’s for signal and background
S
L
Construct unbinned
L
Including bias correction
G( ; , ) P ( p ; F , )
s
s 1
s
s
s
l
t
0
s
l 1
Estimate systematic uncertainties using ensemble testing
Method of Feldman-Cousins is used to make a coherent
statement about the true F0 given an estimated F0
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PTlepton Details
Signal and background composition
LJ
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LL
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PTlepton Combined Results
+0.35
Run II F0 =0.27-0.21
F0 < 0.88 @ 95% CL
Run I F0 =0.91 0.37 0.13 F+ < 0.28 @ 95% CL
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PTlepton LL Results
F0 < 0.52 @ 95% CL
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Mlb2 Method
This method exploits the approximation
2
2
M
cos( * ) 2 lb 2 - 1
mt - M W
A kinematic χ2 is used to match a reconstructed jet with the b
parton
Top-specific corrections derived from Monte Carlo are used to
convert jet energies into parton energies
F0 is extracted using a binned maximum likelihood fit
Nb
P( x ; )
L G( ; 0 , )
i 1
i
i
Again, the results are interpreted using Feldman-Cousins
confidence belts
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Mlb2 Details
Systematic errors
for the LJ data
(CDF)
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Source
Background shape
Top mass uncertainty
Jet energy scale
PDF uncertainty
MC modeling
ISR/FSR
SVT b-tagging
MC statistics
Total
ΔF0
0.12
0.09
0.06
0.04
0.03
0.02
0.01
0.01
0.17
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Mlb2 Results
F0 =0.89
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+0.30
-0.34
(stat) 0.17(sys)
F0 > 0.25 @ 95% CL
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Mlb2 Run I Results
Similar to the Run II analysis
b-tagged jets are chosen to form Mlb2
Neyman construction for upper limit
F+ < 0.24 @ 95% CL
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Cos(θ*) Method
Use topological likelihood to determine signal and
background contributions
Use kinematic fit (assuming mt=175 GeV) to select bjet associated with leptonically decaying W
Selects correct b-jet ~57% of the time
Produce cos(θ*) templates using Monte Carlo
Perform binned likelihood fit to data
Nbkg
L
G(n ; n
i 1
b
b0
Nbins
N sources
j 1
k 1
, 0 ) P(d j ; n j ) B(a jk ; Ajk , pk )
Use Bayesian approach to set a confidence interval
Use ensemble tests for systematic errors
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Cos(θ*) Details
Cos(θ*) for ttbar signal (b-tag, e+jets channel)
F-=0.3
F+=0.3
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Cos(θ*) Results
Topological analysis (no explicit b-tag)
F+ < 0.24 @ 90% CL
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Cos(θ*) Results
b-tag analysis
F+ < 0.24 @ 90% CL
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Measurement Summary
Expt
Method
Ldt
CDF Run I
PTlepton
106 pb-1
F0 = 0.91 ± 0.37 ± 0.13
F+ < 0.28 (95%CL)
CDF Run I
Mlb2
109 pb-1
F+ < 0.24 (95%CL)
DØ Run I
ME
125 pb-1
F0 = 0.56 ± 0.31
CDF Run II
PTlepton
162 pb-1
F0 < 0.88 (95% CL)
F0 = 0.27 + 0.31 -0.21
CDF Run II
Mlb2
162 pb-1
F0 > 0.25 (95% CL)
F0 = 0.89 ± 0.32 ± 0.17
DØ Run II
cos(θ*)
163 pb-1
F+ < 0.24 (90%CL)
F+ < 0.24 (90%CL)
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Result
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Conclusions
Good effort in measuring the W helicity in top decay
Variety of methods, variety of data samples
All measurements are consistent with the SM
CDF PTlepton spectrum in the LL sample is interesting
Presently statistical errors are x2 systematic errors
Very useful to combine results from DØ and CDF
Dominant systematic errors arise from uncertainties in top
quark mass, backgrounds, and jet energy scale
Look forward to exploiting the full statistical power of
Run II data
Look forward to exploiting the top quark factory at the
LHC
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Symposium
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W Helicity
Top decays
b
t
W0
t
W
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WR
t
b
b
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Matrix Element Details
Systematic errors
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Source
σ(F0)
Acceptance
0.05
Jet energy scale
0.01
Spin correlations
0.01
PDF
0.01
Signal model
0.02
Multiple interactions
0.006
QCD background
0.02
Subtotal
0.07
Statistical + mass
0.31
Total
0.314
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PTlepton Method
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PTlepton LJ Results
+0.12
f 0 = 0.88-0.47
+0.12
F0 =0.88-0.47
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F0 > 0.24 @ 95% CL
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PTlepton Details
Systematic errors
Source
Background normalization
Top mass uncertainty
ISR/FSR
PDF uncertainty
PTlepton shape uncertainty
Monte Carlo statistics
Acceptance correction
Trigger correction
Total
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σsys
(LJ+LL)
0.10
0.11
0.05
0.03
0.02
0.01
0.02
0.02
0.17
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Feldman-Cousins
The result of the maximum likelihood fit for F0 can
be outside the physical region
The procedure of Feldman-Cousins can be used to
construct a confidence interval in the physical region
Ensemble tests are used to map true F0’s to a
distribution of estimated F0’s using the FeldmanCousins ordering principle
Systematic errors can be included by adding in
quadrature σ(F0est) and σ(sys)
The resulting 2D figure then gives the confidence
interval on true F0 for a measured (estimated) F0
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Mlb2 Details
Systematic errors
Source
Bkg shape
Top mass uncertainty
Jet energy scale
PDF uncertainty
MC modeling
ISR/FSR
SVT b-tagging
MC statistics
Total
Ann Arbor Symposium
ΔF0
0.12
0.09
0.06
0.04
0.03
0.02
0.01
0.01
0.17
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Mlb2 Details
Backgrounds
31 events observed
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Background
Total
QCD
3.4±1.0
W+jets (mistags)
Wbb
2.8±0.6
1.6±0.7
Wcc
Wc
WW/WZ
0.6±0.3
0.7±0.3
0.29±0.05
Single top
Total
Total * χ2 acceptance
0.49±0.07
9.9±1.7
6.4±1.1
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Cos(θ*) Details
Systematic errors
(topological)
Systematic errors
(b-tag)
Source
Top mass
σ (F+)
0.06
Jet energy scale
0.06
Source
σ (F+)
Top mass
0.11
Jet energy scale
0.04
Background
model
Signal model
0.08
0.05
Likelihood fit
0.02
Background
0.01
model
Underlying event 0.06
Total
0.15
MC statistics
0.01
Total
0.11
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Cos(θ*) Details
Cos(θ*) for tt signal (b-tag, e+jets channel)
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Cos (θ*) Details
Signal and background are determined using a
topological likelihood
b-tag
Channel
tt
W+jets
QCD
μ+jets
9.6 ± 2.7
2.0 ± 1.4
0.7 ± 0.4
e+jets
14.2 ± 3.4
6.6 ± 1.8
0.6 ± 0.3
QCD
topological
Channel
tt
W+jets
μ+jets
11.3 ± 1.3
17.6 ± 1.2 2.1 ± 0.5
e+jets
25.9 ± 1.5 20.3 ± 1.5 2.7 ± 0.5
b-tag (μ+jets)
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Bayesian Limit
DØ uses a Bayesian technique to set a confidence
interval in the physical region of F+
Let xML be the result of the maximum likelihood fit
xML
xmin
0.3
0.0
xmax
L( x)dx
L( x)dx
xML
0.3
0.0
L( x)dx
0.34
L( x)dx
If xML is outside the physical range (or close to the
physical 0.3
x
xmin
0.3
0.0
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L( x)dx
L( x)dx
0.68
max
0.0
0.3
0.0
L( x)dx
0.68
L( x)dx
36