Transcript Document 7638114

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
Ann Arbor Symposium
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)
Ann Arbor Symposium
3
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+
Ann Arbor Symposium
4
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
Ann Arbor Symposium
5
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*)
Ann Arbor Symposium
6
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*)
Ann Arbor Symposium
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
Ann Arbor Symposium
 N  A( x)[c1 Pttbar ( x; F0 )  c2 PW  jets ( x)]dx
8
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
Ann Arbor Symposium
9
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)
Ann Arbor Symposium
10
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
Ann Arbor Symposium
11
PTlepton Details
 Signal and background composition
LJ
Ann Arbor Symposium
LL
12
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
Ann Arbor Symposium
13
PTlepton LL Results
F0 < 0.52 @ 95% CL
Ann Arbor Symposium
14
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
Ann Arbor Symposium
15
Mlb2 Details
 Systematic errors
for the LJ data
(CDF)
Ann Arbor Symposium
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
16
Mlb2 Results
F0 =0.89
Ann Arbor Symposium
+0.30
-0.34
(stat)  0.17(sys)
F0 > 0.25 @ 95% CL
17
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
Ann Arbor Symposium
18
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
Ann Arbor Symposium
19
Cos(θ*) Details
 Cos(θ*) for ttbar signal (b-tag, e+jets channel)
F-=0.3
F+=0.3
Ann Arbor Symposium
20
Cos(θ*) Results
 Topological analysis (no explicit b-tag)
F+ < 0.24 @ 90% CL
Ann Arbor Symposium
21
Cos(θ*) Results
 b-tag analysis
F+ < 0.24 @ 90% CL
Ann Arbor Symposium
22
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)
Ann Arbor Symposium
Result
23
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
Ann Arbor
Symposium
24
W Helicity
 Top decays
b
t
W0
t
W
Ann Arbor Symposium
WR
t
b
b
25
Matrix Element Details
 Systematic errors
Ann Arbor Symposium
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
26
PTlepton Method
Ann Arbor Symposium
27
PTlepton LJ Results
+0.12
f 0 = 0.88-0.47
+0.12
F0 =0.88-0.47
Ann Arbor Symposium
F0 > 0.24 @ 95% CL
28
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
Ann Arbor Symposium
σsys
(LJ+LL)
0.10
0.11
0.05
0.03
0.02
0.01
0.02
0.02
0.17
29
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
Ann Arbor Symposium
30
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
31
Mlb2 Details
 Backgrounds

31 events observed
Ann Arbor Symposium
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
32
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
Ann Arbor Symposium
33
Cos(θ*) Details
 Cos(θ*) for tt signal (b-tag, e+jets channel)
Ann Arbor Symposium
34
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)
Ann Arbor Symposium
35
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
Ann Arbor Symposium
L( x)dx
L( x)dx
 0.68


max
0.0
0.3
0.0
L( x)dx
 0.68
L( x)dx
36