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Introduction
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In the Standard Model (SM), top quark can be produced
via the strong interaction as a tt pair. It
also allows for top quark to be produced through
electroweak interaction as single top quark plus jets,
which is referred to as single top. There are three
production modes: the t-channel, the s-channel and the
Wt-channel production mode. In this analysis we select
events with W boson only decaying leptonically and two
or three jets with at least one of them is identified as
originated from a b-quark decay. Since a small signal
has to be extracted from a huge amount of background
events in order to have a significant result,
multivariate methods which exploit a large number of
characteristic quantities are used. In this analysis,
neural networks are used to discriminate single
top-quarks events by employing the NeuroBayes package.
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Event Selection and Background Modelling
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The CDF
event selection exploits the kinematic features of
the signal final state, which contains a top quark,
a bottom quark, and possibly additional light quark
jets. To reduce multijet backgrounds, the W boson
originating from the top quark is required to decay
leptonically. One therefore demands a single
high-energetic electron or muon
(ET(lepton) > 20 GeV) and large
missing transverse energy (MET > 25 GeV) from the
undetected neutrino. We selects event with at least
two jets with ET > 20 GeV and |η|
< 2.8 be present in the event. At least one jets
has to be tagged as a b-quark jet by using displaced
vertex information from the silicon vertex detector
(SVX).
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backgrounds belong to the following categories:
Wbb,
Wcc,
Wc, Wqq (mistagged light quarks
misidentified as heavy flavor jets), top pair
production tt events (one lepton or two jets
are lost due to detector acceptance), QCD (non-W
multijet events where a jet is erroneously
identified as a lepton), Z+jets and diboson(WW, WZ,
and ZZ). The top pair, single top, Z+jets and
diboson are nomalized to standard model prediction
according to following table.
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The QCD content of the selected dataset is further
reduced by single top QCD veto, which applies
several requirements to MET, MET significance,
transverse W boson mass, and several angles between
the MET vector, lepton vectors and jet vectors. The
background modelling using the standard CDF "Method
II for you". The numbers of expected and observed
events are listed in the tables below. |
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Neural Network Discriminant
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| Using neural networks,
kinematic or event shape variables are combined to a
powerful discriminant.
We have four categories in total, one for
the 2jet1tag events, one for 2jet2tag events, one for
3jet1tag events, and one for 3jets2tags. We devide
each of the four categories into two separate
channels, one containing triggered electrons and
muons called Triggered Lepton Coverage (TLC), and
the other containing muons from an Extended Muon
Coverage (EMC) accepted through the MET + 2 jets
trigger. We trained one NN for each channel.
Each network was trained with sample mixed
with systematic samples of jet energy scale and Q^2
of W+Heavy flavor in order to contraint the
uncertainty of the cross section.
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| One of the variables is the output of
the KIT flavor separator. The KIT flavor separator gives an
additional handle to reduce the large background components where no
real b quarks are contained, mistags and charm-backgrounds. Both of
them amount to about 50% in the W+2 jets data sample even after
imposing the requirement that one jet is identified by the secondary
vertex tagger of CDF. The following plots show the
most significant input variables in the 2jet1tag channel.
The plots in the third column show the
variables in the 0 Tag sideband sample for modelling validation.
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MC distributions:
the mass of the reconstructed top-quark
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data - MC comparison:
the mass of the reconstructed top-quark |
data - MC comparison:
the mass of the reconstructed top-quark
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MC distributions:
the neural network output of the KIT flavor separator for the b-tagged jet
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data - MC comparison:
the neural network output of the KIT flavor separator for the b-tagged jet |
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MC distributions:
the invariant mass of the two jets
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data - MC comparison:
the invariant mass of the two jets |
data - MC comparison:
the invariant mass of the two jets
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MC distributions:
the product of the lepton-charge and the pseudorapidity of the light quark jet
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data - MC comparison:
the product of the lepton-charge and the pseudorapidity of the light quark jet |
data - MC comparison:
the product of the lepton-charge and the pseudorapidity of the light quark jet
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Systematic
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The measurement of the single top cross section requires
substantial input from theorical models, Monte Carlo
simulations and extrapolations from control samples in
data. We assign systematic uncertainties to our
predictions and include the effects of these
uncertainties on the measured cross section. We
consider three categories of systematic uncertainty:
uncertainty in the predicted rates of the signal and
background processes, uncertainty in the shapes of the
distribution of the discriminant variables, and
uncertainty arising from the limited number of Monte
Carlo events used to predict the signal and background
expectations in each bin of each discriminant
distribution.
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Cross Section and |Vtb|
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Using a Bayesian statistical approach, we measured the total cross section of single top quark production
assuming the SM ratio among t-channel
s-channel and Wt-channel production. The posterior distribution is shown below. From this
distribution, we obtain a single top quark cross section measurement of
3.04+0.57-0.53 pb, assuming a top quark mass of 172.5
GeV/c2.
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To extract Vtb from the combined measurement, we take
advantage of the fact that the production cross section
of single top is directly proportional to Vtb2.
We assumes that Vtb2 is much
larger than
Vts2+Vtd2,
because we are assuming that the top quark decays to Wb
100% of the time, and because we assume that the
production cross section scales with
Vtb2, while the other CKM matrix
elements may contribute as well if they were not very
small. Figure below shows the joint posterior
distribution of all of our independent channels as a
function of Vtb2(which includes
the theoretical uncertainty on the predicted production
rate, which is not part of the cross section posterior),
from which we obtain a 95% confidence level lower limit
of Vtb > 0.78 and extracted
Vtb=0.96 ± 0.09(stat. + syst.)
± 0.05(theory).
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Two-Dimensional Fit Results
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The extraction of the combined signal cross section
proceeds by constructing a one-dimensional Bayesian
posterior with a uniform prior in the cross section to
be measured. An extension of this is to form the
posterior in the two-dimensional plane, s-channel and
t-channel, and to extract the s-channel and the t-and
Wt-channel cross sections separately. Here we combined
the Wt-channel with t-channel due to the small predicted
cross section of Wt-channel at Tevatron and the similar
final state signature with t-channel. Our studies show
that the Wt-channel contributes very negligible effect in this
two-dimensional fit.
The best-fit cross section is the one for which the
posterior is maximized, and corresponds to s-channel =
1.81+0.63-0.58pb and t-channel =
1.49+0.47-0.42pb. The
uncertainties on the measurements are correlated with
each other. Regions of 68.3%, 95.5%, and 99.7%
credibility are derived from the distribution of the
posterior by evaluating the smallest region in area that
contains 68.3%, 95.5% or 99.7% of the integral of the
posterior. We compare them with the SM NNNLO prediction.
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