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spectrum. The impact of ﬁnalstate radiation can be controlled by requiring exactly four reconstructed (good) jets in
the event.
For dilepton events, the number of measurements minus
the number of constraints does not give enough information
to fully determine the ﬁnalstate kinematics, and one assumption must be made. A variety of methods are used including
ME weighting and neutrino weighting. The ME weighting
method (Kondo, 1988, 1991; Dalitz and Goldstein, 1992) is
related to the general ME method described below (and also
used for ‘ þ jets analyses). The neutrino weighting method
(Abbott et al., 1998, 1999) is unique to dilepton events. In
this method, an event weight is deﬁned as a function of
hypothesized topquark mass Mt using a comparison of the
measured ET to ETi values predicted for a set of possible
6~
6~
neutrino pseudorapidity values ð1Þ , ð2Þ . Large weights cori
i
respond to situations in which the measured and predicted ET
6~
are similar and thus give a probability for different values
for the neutrinos in each event.
The use of the ME approach has become widespread,
especially for ‘ þ jets ﬁnal states. It is used either as the
ﬁnal analysis variable used to determine the measured mass
or to provide information used in joint likelihoods for determining the top mass. In this approach, the probability that the
jet momenta, lepton momentum, and missing transverse en"
ergy observed in a given event, assuming it arises from tt
production and decay, is computed by (Abazov et al. (2008f)
Ptt" ¼ 1ZX
dðy; Mt Þdq1dq2fðq1 Þfðq2 ÞW ðy; xÞ
N in which d is the differential cross section for production of
the ﬁnalstate partons in (momentum) conﬁguration y for a
given Mt , fðq1 Þ and fðq2 Þ are the parton density functions for
the proton and antiproton, W ðy; xÞ is the transfer function for Hobbs, Neubauer, and Willenbrock: Tests of the standard electroweak model at . . . Pðx; Mt Þ ¼ AðxÞ½fPtt"ðx; Mt Þ þ ð1 À fÞPbkg ðxÞ ∆ log(L) = 0.5 1 ∆ log(L) = 2.0
∆ log(L) = 4.5 ∆JES (σc) 0.5 0 0.5 1 166 168 170 172 174 176 1507 178 2 M top (GeV/c ) FIG. 43 (color online). Contours of constantlog(L) in the
Ájes kjes À 1 vs Mt plane. A perfect a priori jet energy calibration
used as input to this analysis results in kjes ¼ 1 corresponding to
Ájes ¼ 0. From Aaltonen et al., 2009d. computing the probability that a partonic ﬁnal state y gives
the observed reconstructed ﬁnal state x, and 1=N is a normalization factor equal to the expected observed cross section
for a given Mt . For each event, this probability and the
corresponding probability computed assuming the event is a
background event Pbkg ðxÞ are combined to give an event
probability as a function of top mass in which AðxÞ is a normalization factor incorporating accep"
tance and efﬁciency effects and f is the fraction of tt events in
the total sample. The overall normalization of P is forced to
unity so that i...
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 Fall '13
 Energy

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