The selection cuts for the topological analysis require a high-
lepton,
a large missing 
, and at least four jets. To ensure orthogonality
with the tagged channels, events are rejected if they contain a
-tag.
Two additional variables are used to define the selection cuts. The first
is 
, which is defined as the scalar sum of the transverse energies
of all jets which pass the selection cuts:
A large is a signature of the decay of a massive object.
The second variable used is the
aplanarity 
[8, p. 280] [129].
This is defined in terms of the normalized three-momentum tensor
constructed from the selected jets:
The aplanarity is then
The aplanarity takes on its maximum value of 0.5 for a spherical event. For a planar or linear event, it is zero. Top events tend to be more spherical than events due to radiative QCD background processes [100, pp. 135--138].
Table 5.3: Summary of kinematic selection cuts for the untagged
lepton + jets channels. [1]
The triggers used for these channels varied somewhat over the course
of the two runs. However, the general strategy was to require a relatively
high- central lepton candidate, a central jet in addition to the
lepton, and, for
the e + jets channel, some missing in the calorimeter.
Some additional cuts are made to reject events which are contaminated
by leakage from the Main Ring or by instrumental effects (`hot cells')
in the calorimeter.
The selection cuts used are summarized in Table 5.3.
Figure: Results from the lepton + jets selection, for data,
180 GeV 
top Monte Carlo, QCD fakes,
and 
W + 
Monte Carlo. [130]
The results of this selection are shown in Figure 5.1
as scatter plots in the 
plane for the data, 180 GeV
top Monte Carlo,
and the expected backgrounds. A total of 8
events survive the standard cuts and 23 events survive the loose cuts.
The total normalization of the background is derived entirely
from data. However, the 
Monte Carlo is employed
to find the shapes of the and distributions
for the W + jets background.
The shape of the non-W QCD multijet background
is estimated by using events which contain a `bad' lepton candidate
and several jets. For the e + jets channel, the sample consists of
multijet events which contain a highly electromagnetic jet which fails
the final electron-ID cuts. This jet is then treated as an electron
for the remainder of the analysis. For the + jets channel,
the sample used consists of events containing muons which fail the
isolation cut and are thus embedded in a jet.
Figure: Observed distributions (points) compared to the
distributions expected from background (line) for
for
(a) e + 
and
(b) e + 
. [1]
These background models can be tested by looking at
event selections which are dominated by background.
Figure 5.2 compares the 
distributions for the data and
the calculated backgrounds for
e + 
and e + 
events; good agreement is seen.
(Here, and in what follows, jet multiplicities are inclusive;
i.e., e + 
means `two or more jets.')
The calculation of the background normalization is based on the fact that the background jet multiplicity spectrum for radiative QCD processes falls nearly exponentially; i.e.,
Roughly speaking, each additional jet adds an extra factor of the
strong coupling 
to the cross section.
This was suggested on theoretical grounds in [131],
and has been shown to work well empirically for small n (
)
for W + jets,
Z + jets, QCD multijet, and W + jets samples.
This is illustrated for Z and W events in
Figures 5.3 and 5.4.
Figure 5.4: Jet multiplicity spectrum for
events. [130]
Figure 5.3: Jet multiplicity spectrum for
events. [130]
For the e + jets channel,
the calculation starts by estimating the amount of non-W background
(dominantly QCD multijets)
present in the sample. This is done by taking the data sample before
the lepton-ID and 
cuts and dividing it up into four sets
corresponding to the four possible outcomes for the two cuts.
Label the set containing events which passed both cuts 1 and the
other three 2, 3, and 4. Then the number of
observed events in each set 
can be written as a sum of W and
QCD contributions:
The distribution of W events among the four sets is determined using the
Monte Carlo. This determines the ratios
and gives the three additional equations
One additional constraint is needed in order to obtain a unique solution.
It is assumed that for QCD events, the lepton-ID and
cuts are independent; i.e.,
This system of equations can be solved iteratively to yield 
and 
. This is repeated for each jet multiplicity, and the
resulting estimates for the QCD background are subtracted from the
data. The result for the e + jets channel is plotted
in Figure 5.4.
The e + jets data now consist of a QCD-subtracted event count for
each jet
multiplicity. Change notation slightly and denote these points by
, where i is the jet multiplicity.
The data are now considered to be the sum of
W + jets and top contributions, and are fit to the form
Here, 
is the number of W + 
events,
is the total number of top events,
is the fraction of top events expected at each multiplicity, and
is the ratio from the W + jets scaling law
The top fractions are determined using Monte Carlo, and ,
, and 
are obtained from the fit. This is then evaluated to
yield the expected number of W + jets events with four or more
jets.
The final step is to apply the and cuts.
The efficiencies for these cuts are found separately for the
W + jets and QCD backgrounds using the Monte
Carlo and the QCD multijet samples, respectively. The background estimates
are then multiplied by these efficiencies.
The estimation of the + jets background is similar, except that
the QCD background is not subtracted off before the fit to the scaling
law. Instead, the scaling law is used to obtain the total
background, including both W + jets and QCD multijets. The amount
of non-W background contributing to the final background number is
estimated using the nonisolated muon sample.
The results for the e + jets and + jets channels are
summarized in Table 5.4.
Table: Summary of results from l + jets channels, showing the
efficiency 
branching ratio (
)
and the expected number of top events (
). The central value of the cross section of [17] is used.
Also given are the
expected background, integrated luminosity, and the number of
observed events in each channel.
From [1,132,133].