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Version 1.
Measurement of the W helicity in t¯t decays at
s = 1.96 TeV
in the Lepton+jets Final States using a lifetime tag
Christian Schmitt
(Dated: June 28, 2004)
A measurement of the W helicity in t¯t decays at
s = 1.96 TeV has been carried out using data
collected by the DØ detector. Semileptonic t¯t events in the electron and muon channel with b-jets
identified by secondary vertices were used. In these events the distribution of the angle between the
lepton and the direction of the intermediate W boson measured in its restframe is sensitive to the
helicities of the W. With an integrated luminosity of 168.7pb−^1 and 158.4pb−^1 in the e+jets and
μ+jets channels respectively, an upper limit on the fraction f+ of positive helicity W ’s of f+ < 0. 207
is set at 90% confidence level.
Preliminary Results for the Conferences 2004
Contents
W
l
b
cos θ
w(cos
SM
- +
FIG. 1: Definition of the decay angle θ in the W restframe (left): θ is the angle between the down-type particle from the W
decay (lepton or d,s quark) and the original W momentum. The right plot shows the angular functions ω(cos θ) for W+, W−
and W 0. The solid line shows the prediction of the Standard Model
A. b-tag
One of the main ingredients for this analysis is the usage of secondary vertex information to identify heavy flavor
jets, allowing a further background reduction. A detailed description of the Secondary Vertex Tagger (SVT) algorithm
in the tight configuration and its performance in both Monte Carlo and data is given in [4].
The algorithm consists of three main steps:
- reconstruction of the primary vertex,
- reconstruction of track-based jets and
- reconstruction of secondary vertices within these jets.
Only tracks with pT > 1 GeV, χ^2 < 3, at least 2 SMT hits and impact parameter significance |dca|/σ(dca) > 3 .5 are
considered in the reconstruction of the secondary vertices.
A calorimeter jet is tagged if it contains a secondary vertex within ∆R < 0 .5 and the secondary vertex fulfills the
following conditions:
- the vertex must consist of at least two tracks,
- the vertex transverse decay length |Lxy| = |~rSV − ~rP V | must be less than 2.6 cm,
- the decay length significance |Lxy /σ(Lxy)| is greater than 7.0,
- the χ^2 of the vertex must be less than 100 and
- the absolute value of the collinearity, defined as the inner product of ~Lxy and the vertex momentum computed as the vector sum of the momenta of all attached tracks after the constrained fit, must be greater than 0.9.
As the tracking performance is currently not properly described by the detector simulation, the tagging efficiency
for b and c quarks as well as the mistag efficiency for light quarks is parametrized as a function of jet ET and η.
These parametrizations are then applied to the t¯t and the different W +jets Monte Carlo samples. The flavor
composition of the W +jets background is estimated using the procedure described in [5]. Table I shows the composition
of the W +jets background before and after applying the b-tag.
Channel W jjjj W bbJj W ccJj W cjjj
μ+jets 83 .3% 4 .4% 7 .0% 5 .3%
e+jets 82 .5% 4 .4% 7 .9% 5 .2%
Channel W jjjj W bbJj W ccJj W cjjj
μ+jets 20 .9% 47 .5% 21 .8% 9 .8%
e+jets 19 .3% 46 .7% 24 .1% 10 .0%
TABLE I: Expected fraction of each W +jets flavor after preselection for each channel before (left) and after (right) applying
the b-tag. In the above tables j is any of u, d, s, g and J is any of u, d, s, c, g partons.
IV. EVENT PRESELECTION
The event preselection in the e+jets and the μ+jets channel requires, respectively, a high pT tight electron or
isolated muon, high missing ET and at least four jets. These requirements are identical to the ones used in the
topological cross section analysis [6] with the following changes:
- a soft muon veto is not applied to jets,
- a veto on a second lepton (e, μ) with pT > 15 GeV is applied to reduce dilepton background,
- at least one jet that is tagged by the SVT algorithm in the tight configuration is required and
- the kinematic fit described in Section VI has to converge.
All preselection cuts are summarized in Table II for the muon channel and in Table III for the electron channel.
Object Selection Cut (μ+jets)
Primary vertex ≥ 3 tracks attached
|zP V | < 60 cm
Muon medium muon with nseg = 3
matched to central track
satisfies cosmic veto
∆R(μ, jet) > 0. 5
Halo(0. 1 , 0 .4)/pTμ < 0 .08 and TrkCone(0.5)/pTμ < 0. 06 (tight requirement)
|dca|/σdca < 3 and |∆z(μ, P V )| < 1 cm
pT > 20 GeV
no second tight μ with pT > 15 GeV
Electron no electron with pT > 15 GeV
Jets ≥ 4 jets with pT > 15 GeV and |η| < 2. 5
≥ 1 jet tagged as b-jet
Missing ET 6 ET > 17 GeV
∆φ(μ, 6 ET ) > 1. 2 − 6 ET · 1. 2 / 38
∆φ(μ, 6 ET ) < 1 .3 + 6 ET · (π − 1 .3)/ 24
∆φ(μ, jet) < 2 .2 + 6 ET · (π − 2 .2)/ 26
Event μ+jets trigger requirement
kinematic fit converges
TABLE II: Preselection cuts for the muon channel.
V. SIGNAL-TO-BACKGROUND DISCRIMINATION
The two main backgrounds to t¯t pair production in the lepton+jets channel arise from the W multijet production
and from QCD multijet events in which one jet fakes an electron or a muon.
A. Estimation of QCD background
The QCD background is estimated using the matrix method [6]. Two samples of events, a loose and a tight set,
are selected, the latter being a subset of the first. The efficiency of the tight selection is higher for real leptons from
W+jets and t¯t events than from fake leptons from QCD as can bee seen in Table IV. This difference can then be used
to extract the expected number of QCD events in the tight sample. In this analysis the matrix method is applied to
the tagged sample.
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FIG. 2: Input variables for the likelihood discriminant in the muon channel after all preselection cuts and after applying the
b-tag. From top left to bottom right: sphericity, aplanarity, centrality, H T^3 , minimal dijet mass and the χ^2 from the kinematic
fit.
Variable Centrality Aplanarity H^3 T Sphericity Mmin χ^2 cos θ
Centrality 1.000 0.177 0.158 0.177 -0.025 -0.009 -0.
Aplanarity 0.177 1.000 0.164 0.635 0.105 -0.085 0.
H T^3 0.158 0.164 1.000 0.085 0.521 0.040 0.
Sphericity 0.177 0.635 0.085 1.000 0.043 -0.101 0.
Mmin -0.025 0.105 0.521 0.043 1.000 -0.009 0.
χ^2 -0.009 -0.085 0.040 -0.101 -0.009 1.000 0.
cos θ -0.032 0.009 0.094 0.012 0.074 0.178 1.
TABLE V: Correlation between the input variables for the Likelihood discriminant and the decay angle in the muon channel.
Centrality: the centrality C is defined as
C =
HT
HE
=
∑Njets jet=1 ET^ (jet) ∑Njets jet=1 E(jet)^
, (9)
where HT is the sum of the transverse jet energies and HE is the total jet energy in the event. It provides a handle on what fraction of the energy deposited in the proton-antiproton collision is transverse energy.
H T^3 : is defined as
H
T =^ HT^ −^ ET^ (jet1)^ −^ ET^ (jet2),^ (10)
where jet1 and jet2 are the leading and second-leading jet, respectively.
Mmin: the smallest invariant mass of any two jets in the event.
HitFit χ^2 : the χ^2 from the kinematic fit described in Section VI provides a measure on how top-like the event is.
Only the four leading jets are used to determine these variables. This does not reduce the statistical separation power
but it reduces the dependence on systematic effects on the modeling of soft radiation (e.g. underlying event).
The likelihood discriminant is built in the following way [6]:
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FIG. 3: Input variables for the likelihood discriminant in the electron channel after all preselection cuts and after applying the
b-tag from top left to bottom right: sphericity, aplanarity, centrality, H T^3 , minimal dijet mass and the χ^2 from the kinematic
fit.
Variable Centrality Aplanarity H^3 T Sphericity Mmin χ^2 cos θ
Centrality 1.000 0.156 0.166 0.153 0.002 -0.033 -0.
Aplanarity 0.156 1.000 0.125 0.639 0.105 -0.088 0.
H T^3 0.166 0.125 1.000 0.053 0.521 0.097 0.
Sphericity 0.153 0.639 0.053 1.000 0.033 -0.099 0.
Mmin 0.002 0.105 0.521 0.033 1.000 -0.023 0.
χ^2 -0.033 -0.088 0.097 -0.099 -0.023 1.000 0.
cos θ -0.071 0.041 0.112 0.029 0.089 0.079 1.
TABLE VI: Correlation between the input variables for the Likelihood discriminant and the decay angle in the electron channel.
- The variables are transformed using functions in order to be less sensitive to statistical fluctuations in rapidly varying regions. The functions used are: - ln(S) - exp (− 11 · A) - exp (− 2 · C) - ln(H T^3 ) -
√ Mmin
- ln(χ^2 )
- The distributions are normalized to unity and the ratio of signal (t¯t) over background (W + jets) is built for each of the six distributions. Only the light-jets sample is used as background.
- The logarithm of the ratios is built and fitted with a polynomial. Fitting the logarithm simplifies the fit function and symmetrises the errors on the points.
- Data in the tail of a distribution is consolidated including over- and underflow bins.
- The likelihood output L is given by
L =
exp
(∑ i (ln^
S
B )
i
fitted
)
exp
(∑ i (ln^
S
B )
i
fitted
)
, (11)
ln(S)
-2.5 -2 -1.5 -1 -0. ln(S)
-2.5 -2 -1.5 -1 -0.
1/N dN/dln(S)
0
ttbar
W+Jets
Sphericity
exp(-11.*A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 exp(-11.*A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1/N dN/dexp(-11.A)*
0
ttbar
W+Jets
Aplanarity
exp(-2.*C)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0. exp(-2.*C)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.
1/N dN/dexp(-2.C)*
0
0.12 ttbar
W+Jets
Centrality
ln(S)
-2.5 -2 -1.5 -1 -0.
χ^2 / ndf 12.5 / 21
p0 1.4±0.
p1 2.079±0.
p2 1.01±0.
p3 0.2729±0.
ln(S)
-2.5 -2 -1.5 -1 -0.
ln(S/B)
-1.
-0.
0
1
χ^2 / ndf 12.5 / 21
p0 1.4±0.
p1 2.079±0.
p2 1.01±0.
p3 0.2729±0.
Sphericity
exp(-11.*A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
χ^2 / ndf 12.4 / 15 p0 1.134±0. p1 1.135±2. p2 -15.94±10. p3 24.94±14. p4 -12.97±6.
exp(-11.*A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ln(S/B)
-1.
-0.
0
1
χ^2 / ndf 12.4 / 15 p0 1.134±0. p1 1.135±2. p2 -15.94±10. p3 24.94±14. p4 -12.97±6.
Aplanarity
exp(-2.*C)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.
χ^2 / ndf 3.997 /
p0 3.104±0. p1 -24.58±9. p2 71.48±29. p3 -87.08±29.
exp(-2.*C)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.
ln(S/B)
-1.
-0.
0
χ^2 / ndf 3.997 /
p0 3.104±0. p1 -24.58±9. p2 71.48±29. p3 -87.08±29.
Centrality
ln(HT3/GeV)
3.6 3.8 4 4.2 4.4 4.6 4.8 5 ln(HT3/GeV)
3.6 3.8 4 4.2 4.4 4.6 4.8 5
1/N dN/dln(HT3/GeV)
0
ttbar
W+Jets
HT
m/GeV
4 5 6 7 8 9 10 11 m/GeV
4 5 6 7 8 9 10 11
m/GeV
1/N dN/d
0
0.14 ttbar
W+Jets
minimal dijet mass
ln( χ^2 )
-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 ln( χ^2 )
-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
2 ) χ
1/N dN/dln(
0
ttbar
W+Jets
HitFit χ^2
ln(HT3/GeV)
3.6 3.8 4 4.2 4.4 4.6 4.8 5
χ^2 / ndf 17.94 / 19 p0 -4527±0. p1 5307 ±0. p2 -2481±0. p3 577.4±0. p4 -66.83±0. p5 3.074±0.
ln(HT3/GeV)
3.6 3.8 4 4.2 4.4 4.6 4.8 5
ln(S/B)
-1.
-0.
0
1
χ^2 / ndf 17.94 / 19 p0 -4527±0. p1 5307 ±0. p2 -2481±0. p3 577.4±0. p4 -66.83±0. p5 3.074±0.
HT
m/GeV
4 5 6 7 8 9 10 11
χ^2 / ndf 6.249 / 10 p0 -23.49±0. p1 13.99±0. p2 -3.202±0. p3 0.3251±0. p4 -0.01209±4.762e-
m/GeV
4 5 6 7 8 9 10 11
ln(S/B)
-0.
-0.
-0.
-0.
0
χ^2 / ndf 6.249 / 10 p0 -23.49±0. p1 13.99±0. p2 -3.202±0. p3 0.3251±0. p4 -0.01209±4.762e-
minimal dijet mass
ln( χ^2 )
-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
χ^2 / ndf 13.63 / 16 p0 1.001±0. p1 -0.2951±0. p2 -0.2196±0. p3 0.03596±0.
ln( χ^2 )
-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
ln(S/B)
-1.
-0.
0
1
1.5 (^) χ (^2) / ndf 13.63 / 16 p0 1.001±0. p1 -0.2951±0. p2 -0.2196±0. p3 0.03596±0.
HitFit χ^2
FIG. 4: Normalized distribution for the input variables used in the likelihood discriminant and the fit to the logarithm of signal
over background in the muon channel after all preselection cuts and after applying the b-tag. From top left to bottom right:
sphericity, aplanarity, centrality, H T^3 , minimal dijet mass and the χ^2 from the kinematic fit.
ln(S)
-2.5 -2 -1.5 -1 -0. ln(S)
-2.5 -2 -1.5 -1 -0.
1/N dN/dln(S)
0
ttbar
W+Jets
Sphericity
exp(-11.*A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 exp(-11.*A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1/N dN/dexp(-11.A)*
0
ttbar
W+Jets
Aplanarity
exp(-2.*C)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0. exp(-2.*C)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.
1/N dN/dexp(-2.C)*
0
ttbar
W+Jets
Centrality
ln(S)
-2.5 -2 -1.5 -1 -0.
χ^2 / ndf 23.65 / 16 p0 1.309±0. p1 2.133±0. p2 1.181±0. p3 0.322±0.
ln(S)
-2.5 -2 -1.5 -1 -0.
ln(S/B)
-1.
-0.
0
1
χ^2 / ndf 23.65 / 16 p0 1.309±0. p1 2.133±0. p2 1.181±0. p3 0.322±0.
Sphericity
exp(-11.*A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
χ^2 / ndf 16.14 / 16 p0 1.45±0. p1 -4.048±1. p2 3.912±3. p3 -2.803±1.
exp(-11.*A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
ln(S/B)
-1.
-0.
0
1
χ^2 / ndf 16.14 / 16 p0 1.45±0. p1 -4.048±1. p2 3.912±3. p3 -2.803±1.
Aplanarity
exp(-2.*C)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.
χ^2 / ndf 15.61 / 15 p0 -1.851±0. p1 46.2±0. p2 -283.2±2. p3 658.2±5. p4 -556.4±8.
exp(-2.*C)
0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.
ln(S/B)
-1.
-0.
0
1
χ^2 / ndf 15.61 / 15 p0 -1.851±0. p1 46.2±0. p2 -283.2±2. p3 658.2±5. p4 -556.4±8.
Centrality
ln(HT3/GeV)
3.6 3.8 4 4.2 4.4 4.6 4.8 5 ln(HT3/GeV)
3.6 3.8 4 4.2 4.4 4.6 4.8 5
1/N dN/dln(HT3/GeV)
0
ttbar
W+Jets
HT
m/GeV
4 5 6 7 8 9 10 m/GeV
4 5 6 7 8 9 10
m/GeV
1/N dN/d
0
0.1 ttbar
W+Jets
minimal dijet mass
ln( χ^2 )
-1 0 1 2 3 4 ln( χ^2 )
-1 0 1 2 3 4
2 ) χ
1/N dN/dln(
0
0.12 ttbar
W+Jets
HitFit χ^2
ln(HT3/GeV)
3.6 3.8 4 4.2 4.4 4.6 4.8 5
χ^2 / ndf 10.97 / 21 p0 -24.4±0. p1 5.187±0. p2 1.223±0. p3 -0.2535±0.
ln(HT3/GeV)
3.6 3.8 4 4.2 4.4 4.6 4.8 5
ln(S/B)
-1.
-0.
0
1
χ^2 / ndf 10.97 / 21 p0 -24.4±0. p1 5.187±0. p2 1.223±0. p3 -0.2535±0.
HT
m/GeV
4 5 6 7 8 9 10
χ^2 / ndf 13.91 / 13 p0 -240.4±0. p1 224.7±0. p2 -87.44±0. p3 18.02±0. p4 -2.069±7.311e- p5 0.1252±7.498e- p6 -0.003123±6.254e-
m/GeV
4 5 6 7 8 9 10
ln(S/B)
-1.
-0.
0
1
χ^2 / ndf 13.91 / 13 p0 -240.4±0. p1 224.7±0. p2 -87.44±0. p3 18.02±0. p4 -2.069±7.311e- p5 0.1252±7.498e- p6 -0.003123±6.254e-
minimal dijet mass
ln( χ^2 )
-1 0 1 2 3 4
χ^2 / ndf 24.37 / 14 p0 0.9601±0. p1 -0.3199±0. p2 -0.1405±0. p3 0.006472±0.
ln( χ^2 )
-1 0 1 2 3 4
ln(S/B)
-1.
-0.
0
1
1.5 χ^2 / ndf 24.37 / 14 p0 0.9601±0. p1 -0.3199±0. p2 -0.1405±0. p3 0.006472±0.
HitFit χ^2
FIG. 5: Normalized distribution for the input variables used in the likelihood discriminant and the fit to the logarithm of signal
over background in the electron channel after all preselection cuts and after applying the b-tag. From top left to bottom right:
sphericity, aplanarity, centrality, H T^3 , minimal dijet mass and the χ^2 from the kinematic fit.
VI. RECONSTRUCTION OF THE TOP QUARK
The top quarks are reconstructed using a kinematic fit as described in [7]. The fit is performed by minimizing a χ^2
defined as
χ^2 = (~x − ~xM )G(~x − ~xM )T^ , (12)
where ~xM is a vector of measured variables, ~x is a vector of fitted variables and G is the inverse error matrix of the
measured quantities. The minimization is subject to the following constraints:
- two jets must form the invariant mass of the W ,
- the lepton and the missing transverse energy must form the invariant mass of the W ,
- the masses of the two reconstructed top quarks must be equal.
Up to this point the usage of the kinematic fit is the same as for the top mass measurement. Since this analysis is not
targeted at measuring the top mass, it is possible to also constrain the top mass to be 175 GeV. The mass constraint
improves the resolution of the reconstructed decay angle by 10%, as can be seen in Figure 7.
Without any knowledge about the jets, there are 12 possible jet permutations. The b-tag information is not used
to reduce the number of possible permutations as the correct implementation of the b-tagging parametrization inside
HitFit is nontrivial and needs more studies.
Among the possible combinations the one with the lowest χ^2 is chosen.
∆ cos θ
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
χ^2 / ndf 131.9 / 71 Constant 0 31.74 ± 2. Mean 0 0.00731 ± 0. Sigma 0 0.1288 ± 0. Constant 1 16.68 ± 2. Mean 1 0.07188 ± 0. Sigma 1 0.4358 ± 0.
∆ cos θ
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Entries
0
10
20
30
40
50
60
70
χ^2 / ndf 131.9 / 71 Constant 0 31.74 ± 2. Mean 0 0.00731 ± 0. Sigma 0 0.1288 ± 0. Constant 1 16.68 ± 2. Mean 1 0.07188 ± 0. Sigma 1 0.4358 ± 0.
∆ Decay angle in W restframe
∆ cos θ
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
χ^2 / ndf 110.7 / 62
Constant 0 42.57 ± 3.
Mean 0 -0.02207 ± 0.
Sigma 0 0.1156 ± 0.
Constant 1 15.03 ± 2.
Mean 1 0.1309 ± 0.
Sigma 1 0.3606 ± 0.
∆ cos θ
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Entries
0
10
20
30
40
50
60
70
80
χ^2 / ndf 110.7 / 62
Constant 0 42.57 ± 3.
Mean 0 -0.02207 ± 0.
Sigma 0 0.1156 ± 0.
Constant 1 15.03 ± 2.
Mean 1 0.1309 ± 0.
Sigma 1 0.3606 ± 0.
∆ Decay angle in W restframe
FIG. 7: Resolution of the reconstructed decay angle without top mass constraint (left) and constraining the top mass to be
175 GeV (right). Both distributions are fitted with a double Gaussian. With the top mass constraint the resolution improves
by about 10%.
VII. MEASUREMENT OF THE W HELICITY
The normalization of the signal and background templates is derived by performing a likelihood fit to the likelihood
discriminant from Section V B. A cut on the likelihood discriminant is then applied to further reduce the background.
Due to resolution and reconstruction effects it is not possible to directly fit the measured decay angle distribution
with the theoretical prediction and obtain the fraction of right handed W ’s. Therefore templates for different values
of f+ and for the background are compared to the data.
A. Final selection
The number of t¯t events in the selected data sample can directly be extracted by performing a likelihood fit to the
likelihood discriminant. Since the relative fractions of W+jets and tt¯ events is already known from the matrix method
a likelihood L can be constructed containing this constraint [6]. This is realized by defining the likelihood as follows:
L(Nt¯t, NW , NQCD) =
∏
i
P (n
obs
i , νi)^ ·^ P^ (N^
obs
−t, N−t)^ (13)
where P (n, ν) generically denotes the Poisson probability density function for n observed events given an expectation
of ν. The product runs over all bins, i, in the Likelihood discriminant and N (^) obs−t = N − Nt is the observed number
of events in the loose sample minus the number of events in the tight sample, whereas N`−t is the predicted number.
Figure 8 shows the distribution obtained in data of the likelihood discriminant after all preselection cuts. As a
crosscheck that the likelihood discriminant has a reasonable Monte Carlo description, it has been applied to the data
before applying the b-tag. Figure 9 shows that the agreement between data and Monte Carlo is reasonable.
The result from this fit is summarized in Table VII.
Channel t¯t W +jets QCD
μ+jets 10. 2 ± 2. 9 3. 1 ± 2. 2 0. 9 ± 0. 2
e+jets 16. 9 ± 4 .1 14. 9 ± 4 .0 1. 0 ± 0. 3
TABLE VII: Fitted number of events for the three different samples in each of the two channels.
L
0 0.2 0.4 0.6 0.8 1
Entries
0
1
2
3
4
5
6
7
8
L
0 0.2 0.4 0.6 0.8 1
Entries
0
1
2
3
4
5
6
7
8 Data
ttbar
W+jets
QCD
Likelihood D ∅ Run II Preliminary
L
0 0.2 0.4 0.6 0.8 1
Entries
0
2
4
6
8
10
12
L
0 0.2 0.4 0.6 0.8 1
Entries
0
2
4
6
8
10
12 Data
ttbar
W+jets
QCD
Likelihood D ∅ Run II Preliminary
FIG. 8: Likelihood discriminant after all preselection cuts in the muon channel (left) and the electron channel (right). All
Monte Carlo samples are normalized to the result from the Fit to the likelihood discriminant.
To further reduce the background, a cut on the likelihood discriminant is applied. This cut is optimized to maximize
the statistical significance between the V+A and the V-A scenarios. The significance is here defined to be
S =
N∑bins
i=
(ni,V −A − ni,V +A)^2 ni,V −A + ni,V +A
, (14)
Channel t¯t 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
TABLE IX: Predicted number of events for the three different samples in each of the two channels after the cut on the likelihood
discriminant.
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
1/N dN/dcos
0
V-A V+A
Decay angle in W restframe
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
1/N dN/dcos
0
V-A V+A
Decay angle in W restframe
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
1/N dN/dcos
0
V-A V+A
Decay angle in W restframe
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
1/N dN/dcos
0
V-A V+A
Decay angle in W restframe
FIG. 11: Decay angle distribution in the muon (left) and electron channel (right) after all preselection cuts (top) and after the
cut on the likelihood discriminant (bottom). The cut on the likelihood discriminant doesn’t change the decay angle distribution
significantly.
B. Templates
The decay angle templates for the signal and the W+jets background sample are taken from Monte Carlo, while
the template for the QCD background is derived from the tagged data, by reversing the tight criteria for the isolation
in the muon channel and for the electron likelihood in the electron channel.
The 7 different signal templates have a sizable statistical uncertainty. To reduce this uncertainty the 7 templates
are interpolated to create just two templates: a template for V-A and a template for V+A. This is possible, because
the interference Term between V-A and V+A is negligible [8] and therefore all f+ fractions can be reproduced by a
linear combination of the V-A and the V+A template.
The templates are interpolated in the following way:
- for each of the 7 signal samples the decay angle distribution is plotted into a histogram;
- the content of each bin i of these histograms is plotted against the corresponding V+A fraction;
- the resulting graph is fitted with a straight line;
- the templates for V-A and for V+A are created using the parameters and uncertainties from the fit.
Figures 12 and 13 show the fits to the bin content and Figures 14 and 15 show the templates of the decay angle
distribution for the two extreme values of f+, 0.0 and 0.3.
C. Limit calculation
To extract a limit on f+ or, if that’s possible, quote a value of f+ two different methods are used:
- a frequentist approach based on the prescription given by Feldman and Cousins and
- a maximum likelihood fit together with a Bayesian interpretation of the result
The final result will be based on the first method.
1. Feldman & Cousins
The confidence interval construction based on the prescription by Feldman & Cousins [9] is one of the recommended
procedures by the Particle Data Group for bounded parameters.
The different possible values for f+ are caused by a mixture between a V-A and a V+A interaction:
α · V-A + (1 − α) · V+A with α ∈ [0, 1]. (15)
Values outside of the interval [0, 1] have no physical meaning.
The measured data consists of a set N ≡ {ni}, together with an assumed known mean expected background
B ≡ {bi} and a signal contribution T ≡ {μi|α}. Each bin i corresponds to a Poisson process:
P (ni|μi) = (μ + b)n^ ·
exp[−(μ + b)]
n!
. (16)
To construct the confidence region, the large number of possible N sets have to be ordered according to the ratio
of the probabilities,
R =
P (N |T )
P (N |Tbest)
, (17)
where Tbest(α) gives the highest probability for P (N |T ) for the physically allowed values of α. By using χ^2 = −2 ln(P )
the following equation is obtained
R′^ = ∆χ^2 = 2
∑
i
[
μi − μbesti + ni ln
( μbesti + bi
μi + bi
)]
. (18)
To perform the actual confidence interval calculation the following procedure is used:
FIG. 13: Interpolation of the signal templates in the muon channel. Each plot corresponds to one bin in the decay angle
- I. Introduction - II. Data Sets - III. Object identification - A. b-tag - IV. Event preselection - V. Signal-to-background discrimination - A. Estimation of QCD background - B. Discrimination of W +jets background - VI. Reconstruction of the top quark
- VII. Measurement of the W helicity - A. Final selection - B. Templates - C. Limit calculation - 1. Feldman & Cousins - 2. Bayes
- VIII. Systematics - A. Feldman & Cousins - B. Bayes - IX. Ensemble tests - X. Result - XI. Summary - A. Additional control plots - References - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0.
- χ^2 / ndf 3.442 / - p0 0.03682 ± 0. - p1 -0.02368 ± 0. - χ^2 / ndf 3.442 / - p0 0.03682 ± 0. - p1 -0.02368 ± 0.
- Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 7.026 / - p0 0.09924 ± 0. - p1 -0.03953 ± 0. - χ^2 / ndf 7.026 / - p0 0.09924 ± 0. - p1 -0.03953 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 4.889 / - p0 0.1267 ± 0. - p1 -0.04607 ± 0. - χ^2 / ndf 4.889 / - p0 0.1267 ± 0. - p1 -0.04607 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0.
- Content
- χ^2 / ndf 6.326 / - p0 0.1408 ± 0. - p1 -0.01756 ± 0. - χ^2 / ndf 6.326 / - p0 0.1408 ± 0. - p1 -0.01756 ± 0.
- Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 6.096 / - p0 0.1349 ± 0. - p1 0.002841 ± 0. - χ^2 / ndf 6.096 / - p0 0.1349 ± 0. - p1 0.002841 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - χ^2 / ndf 4.087 / - p0 0.1299 ± 0. - p1 -0.002572 ± 0. - χ^2 / ndf 4.087 / - p0 0.1299 ± 0. - p1 -0.002572 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0.
- Content - 0.
- 0.
- χ^2 / ndf 1.04 / - p0 0.1156 ± 0. - p1 0.01811 ± 0. - χ^2 / ndf 1.04 / - p0 0.1156 ± 0. - p1 0.01811 ± 0.
- Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 3.29 / - p0 0.09053 ± 0. - p1 0.04343 ± 0. - χ^2 / ndf 3.29 / - p0 0.09053 ± 0. - p1 0.04343 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 2.415 / - p0 0.06971 ± 0. - p1 0.03208 ± 0. - χ^2 / ndf 2.415 / - p0 0.06971 ± 0. - p1 0.03208 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0.
- χ^2 / ndf 3.843 / - p0 0.05176 ± 0. - p1 0.03171 ± 0. - χ^2 / ndf 3.843 / - p0 0.05176 ± 0. - p1 0.03171 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content
- 0. - χ^2 / ndf 2.216 / - p0 0.03385 ± 0. - p1 -0.0194 ± 0. - χ^2 / ndf 2.216 / - p0 0.03385 ± 0. - p1 -0.0194 ± 0.
- Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 6.133 / - p0 0.09291 ± 0. - p1 -0.02589 ± 0. - χ^2 / ndf 6.133 / - p0 0.09291 ± 0. - p1 -0.02589 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 4.086 / - p0 0.1243 ± 0. - p1 -0.03328 ± 0. - χ^2 / ndf 4.086 / - p0 0.1243 ± 0. - p1 -0.03328 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 5.488 / - p0 0.1365 ± 0. - p1 -0.04376 ± 0. - χ^2 / ndf 5.488 / - p0 0.1365 ± 0. - p1 -0.04376 ± 0.
- Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 4.443 / - p0 0.1356 ± 0. - p1 0.004175 ± 0. - χ^2 / ndf 4.443 / - p0 0.1356 ± 0. - p1 0.004175 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 2.967 / - p0 0.1262 ± 0. - p1 -0.0003424 ± 0. - χ^2 / ndf 2.967 / - p0 0.1262 ± 0. - p1 -0.0003424 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 6.147 / - p0 0.1092 ± 0. - p1 0.03653 ± 0. - χ^2 / ndf 6.147 / - p0 0.1092 ± 0. - p1 0.03653 ± 0.
- Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 5.62 / - p0 0.08918 ± 0. - p1 0.02187 ± 0. - χ^2 / ndf 5.62 / - p0 0.08918 ± 0. - p1 0.02187 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - χ^2 / ndf 1.745 / - p0 0.07294 ± 0. - p1 0.02796 ± 0. - χ^2 / ndf 1.745 / - p0 0.07294 ± 0. - p1 0.02796 ± 0. - Bin - α -0. - -0.6 -0.4 -0.2 0 0.2 0.4 0. - 0. Content - 0. - 0. - 0. - 0. - 0. - χ^2 / ndf 3.997 / - p0 0.07557 ± 0. - p1 0.03697 ± 0. - χ^2 / ndf 3.997 / - p0 0.07557 ± 0. - p1 0.03697 ± 0.
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
θ
1/N dN/dcos
Decay angle in W restframeDecay angle in W restframe
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
θ
1/N dN/dcos
0
Decay angle in W restframeDecay angle in W restframe
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
θ
1/N dN/dcos
0
Decay angle in W restframeDecay angle in W restframe
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
θ
1/N dN/dcos
0
Decay angle in W restframeDecay angle in W restframe
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
θ
1/N dN/dcos
0
Decay angle in W restframeDecay angle in W restframe
cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1 cos θ
-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1
θ
1/N dN/dcos
0
Decay angle in W restframeDecay angle in W restframe
FIG. 14: Templates of the decay angle in the muon channel after all selection cuts: t¯t at parton level with f+ = 0.0 (top left),
t¯t at parton level with f+ = 0.3 (top right), t¯t at detector level with f+ = 0.0 (middle left), t¯t at detector level with f+ = 0. 3
(middle right), W+jets background (bottom left) and QCD background (bottom right).The signal templates at detector level
are the interpolated templates. The difference in the statistical uncertainty compared to the parton level shows the improvement
due to the interpolation.
