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Unformatted text preview: 0:20 5:18 Æ 0:29 0:71 Æ 0:10
Total expected
23:46 Æ 1:90 68:64 Æ 3:88 10:79 Æ 0:58
Data
22
64
14 Hobbs, Neubauer, and Willenbrock: Tests of the standard electroweak model at . . . 1492 TABLE X. Expected number of signal (WW ) and background
events along with the total number of expected and observed events
in the data for the CDF WW crosssection measurement (Aaltonen
et al., 2010a).
Z=
Ã Events
79:8 Æ 18:4
13:8 Æ 1:9
91:7 Æ 24:8
112:7 Æ 31:2
20:7 Æ 2:8
1:3 Æ 0:2
320:0 Æ 46:8
317:6 Æ 43:8
637:6 Æ 73:0
654 (DrellYan) WZ
W W þ 1 À jet
ZZ
"
tt
Total background
WþWÀ
Total expected
Data alone. Table X shows the expected number of signal and
background events along with the observed events in the
data used to ﬁt for the signal. For each event passing the
signal selection criteria, four matrixelementbased (ME)
event probabilities are calculated corresponding to the production and decay processes WW ! ‘‘, ZZ ! ‘‘,
W þ 1 À jet ! ‘ þ 1 À jet, and W ! ‘ þ . In the latter two processes, the jet or is assumed to have been
reconstructed as a chargedlepton candidate. The event
probability for a process X is given by
~
P X ð xÞ ¼ ~
1 Z dðyÞ
~
~~ ~
ðyÞGðx; yÞdy;
~
hi
dy SM W+W
100 Events / 0.04 Process 120 Background 80 Data 60
40
20
0 0 0.1 ~
where x represents the observed lepton momenta and ET
6
~~
vectors, Gðx; yÞ is a transfer function representing the detector
~
resolution, and ðyÞ is an efﬁciency function parametrized by
which quantiﬁes the probability for a particle to be recon~
~
structed as a lepton. The differential cross section dðyÞ=dy
is calculated using leadingorder matrix elements from the
MCFM program (Campbell and Ellis, 1999) and integrated
over all possible true values of the ﬁnalstate particle four~
vectors y. The normalization factor hi is determined from
the leadingorder cross section and detector acceptance for
each process. These event probabilities are combined into a
likelihood ratio 0.2 0.3
0.4
0.5
0.6
0.7
0.8
0.9
Matrix Element Likelihood Ratio (LR WW ) L¼ Y
i
ni eÀi Y ÀS2 =2
i
Á ec;
ni !
c (9) where
i ¼ X k Y
Exp
c
ð1 þ fk Sc Þ ðNk Þi ; c
fk is the fractional uncertainty for the process k due to the
systematic c, and Sc is a ﬂoating parameter associated with
the systematic uncertainty c. The correlations of systematic
uncertainties between processes are accounted for in the
deﬁnition of i . The expected number of events from process
Exp
k in the ith bin is given by ðNk Þi . The parameter k is an
overall normalization parameter for process k and is ﬁxed to
unity for all processes other than WW , for which it is freely
ﬂoating. The likelihood is maximized with respect to the
systematic parameters Sc and WW . The WW cross section
is then given by the ﬁtted value of WW multiplied by
"
NLO ðpp ! WW Þ. + (8) j where j ¼ fZZ; W þ 1 À jet; W
g and kj is the relative fraction of the expected number of events for the...
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 Fall '13
 Energy

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