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57:2 Æ 4:2ðestÞ "
tt samples from a subset of the
the ﬁnal state and whether or not
Observed
yield b tag
required? Expt.
Ref. 246
98
39
17
13
8
6
284
87
200 0
!1
no CDFa
D0b !1
¼1
!2
!1 CDFc
D0d a Aaltonen et al., 2009b.
Abazov et al., 2009i.
c
Aaltonen et al., 2009c.
d
Abazov et al., 2008f.
b These loose initial selections have minimal topquark mass
bias and form the basis for further analysis.
Typical signal and background estimates are given in
Table XXII for various channels. In the selections, tradeoffs are made between signal acceptance and purity. In
particular, the requirement that an event have one or more
jets consistent with being initiated by b quarks considerably
improves the signal purity.
After the initial selections, various methods are used to
determine the top mass. Among these are (1) template methods in which data are ﬁt to the predicted signal plus background distribution for a variable that is sensitive to the top
mass, (2) ME methods similar to those discussed in
"
Sec. III.E.4 in which tt event kinematics determined by
matrix element calculations are convoluted with detector
resolution functions to predict measured kinematic distributions as a function of the top mass used in the matrix element
calculations, and (3) other weighting methods in which missing information is supplied by trying possible reconstructed
"
jet and true tt decay parton assignments and computing a
probability for the particular assignment as a function of top
mass. The ME and various weighting methods compute
eventbyevent likelihoods as a function of top mass, and
then compute the total likelihood for a data set as the products
of the event likelihoods. Combinations of these methods are
also used.
For lepton þ jet events, the momenta of the four jets and
the lepton are fully measured, and the neutrino momentum in
the plane transverse to the beam is inferred from the event ET .
6
This gives 17 measured values. Two constraints are available.
The ﬁrst is that the invariant mass of one pair of reconstructed
jets should be consistent with that of the W boson, and the
second is that the reconstructed mass of the two top quarks
should be consistent with each other. This information allows
a 1 degreeoffreedom ﬁt to be performed in which the top
mass is a free parameter. The resulting event top mass values
are not simply averaged to determine the mass, but provide an
input variable to the various methods described above. The ﬁt
2 can also be used to determine (or weight) the most likely
partonjet assignment in an event. Complications to this ﬁt
Rev. Mod. Phys., Vol. 84, No. 4, October–December 2012 arise from the presence of intrinsic transverse momentum of
"
the tt system ptt" and from ﬁnalstate gluon radiation giving
T
rise to additional jets. The ptt" can be incorporated by adding
T
an additional variable for the unknown transverse momentum
~
X to the ﬁt and constraining it using a priori estimates...
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 Fall '13
 Energy

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