The ATLAS Collaboration / Physics Letters B 798 (2019) 134913 5
Table 1
List
of input variables used in the multivariate analysis for each of the WVZ channels, denoted by ×. The subscripts
1, 2and 3 refer to the leading, subleading and third leading lepton or jet. The definitions of “best Z candidate” and
“other leptons” are given in the text. The variable m
T
(W
) is the W -boson transverse mass of the leptonically decaying
W -boson candidate. Among the invariant masses formed by all possible jet pairs, the one closest to the W -boson mass
defines the “m
jj
of best W candidate” and the smallest one defines the “smallest m
jj
”. Finally, the leptonic and hadronic
H
T
are calculated as the scalar sum of the p
T
of all leptons or all jets, respectively.
Variable 3-1j 3-2j 3-3j 4 DF 4 SF on-shell 4 SF off-shell
p
T
(
1
) ××
p
T
(
2
) ×××
p
T
(
3
) ×××
Sum of p
T
() ×××
m
1
2
××
m
1
3
××
m
2
3
××
m
of best Z candidate ××
m
of other leptons ×× ×
m
3
×××
m
4
×× ×
Sum of lepton charges ×××
p
T
( j
1
) ××
p
T
( j
2
) ××
Sum of p
T
( j) ×
Number of jets ×× × ×
m
j
1
j
2
×
m
T
(W
) ×
m
jj
of best W candidate ×
Smallest m
jj
×
E
miss
T
××× × ×
H
T
×× × ×
Leptonic H
T
×
Hadronic H
T
×
Invariant mass of all leptons, jets and E
miss
T
××
Invariant mass of the best Z leptons and j
1
×
of the three leptons has to be smaller than 150 GeV. Data and ex-
pectation
agree in the 3-1j validation region, as shown in Fig. 3(a)
for the transverse momentum distribution of the third-highest-p
T
lepton.
The
t
¯
tZ background is determined in a region defined like the
3-3j region with the exception that no requirement on H
T
is ap-
plied,
and at least four jets are required, of which at least two are
b-tagged. This region is included as a single-bin control region (CR)
in the fit model, outlined in Section 6. Data and expectation agree,
as shown in Fig. 3(b) for the t
¯
tZ control region.
6. Signal extraction and combination
The WWW, WWZ and WZZ regions are combined using the
profile likelihood method described in Ref. [60]based on a simul-
taneous
fit to distributions in the signal and background control
regions. A total of eleven signal regions are considered: four re-
gions
(ee, eμ, μe, and μμ) for the ννqq channel, one region
(μee and eμμ combined) for the ννν channel, three regions
(3-1j, 3-2j, and 3-3j) for the WVZ three-lepton channel, and
three regions (4-DF, 4-SF-Z, and 4-SF-noZ) for the WVZ four-
lepton
channel. One control region is considered: the t
¯
tZ control
region described in Section 5. The distributions used in the fit are
the m
jj
distributions for the ννqq channel and the BDT distri-
butions
for the WVZ three-lepton and four-lepton channels. The
number of selected events in the ννν channel and the t
¯
tZ con-
trol
region are each included as a single bin in the fit. In total, 186
bins are used in the combined fit.
A
binned likelihood function L(μ, θ ) is constructed as a prod-
uct
of Poisson probability terms over all bins considered. This
likelihood function depends on the signal-strength parameter μ,
a multiplicative factor that scales the number of expected signal
events, and θ , a set of nuisance parameters that encode the effect
of systematic uncertainties in the signal and background expecta-
tions.
The nuisance parameters are implemented in the likelihood
function as Gaussian, log-normal or Poisson constraints. The same
value for μ = μ
WVV
is assumed for the on- and off-mass-shell
WWW, WWZ and WZZ processes. Correlations of systematic
uncertainties arising from common sources are maintained across
processes and channels.
Experimental
uncertainties are related to the lepton trigger, re-
construction
and identification efficiencies [49,48], lepton isolation
criteria [50], lepton energy (momentum) scale and resolution [48,
61],
jet energy scale and resolution [54], jet vertex tagging [55,
62],
b-tagging [57], modelling of pile-up and missing transverse
momentum [58], and integrated luminosity [63,64]. Nuisance pa-
rameters
related to these uncertainties are treated as correlated
between all channels. The time-dependence of the efficiencies,
scales and resolutions across the various run periods is taken into
account.
For
each of the background processes evaluated using simula-
tion,
a nuisance parameter representing its normalisation uncer-
tainty
is included. The following prior uncertainties in the nor-
malisations
are assumed: 20% for WZ and ZZ; 40% for Z +jets,
10% [65]for WtZ, 30% [66,67]for tZ, 11% [68]for t
¯
tZ, and 30%
for VH not producing three massive bosons. For dominant back-
grounds
from the WZ and ZZ processes, the simultaneous fit
model has the power to constrain their normalisations at the ∼5%
level, independently of the assumed prior. In addition, shape-only
variations for backgrounds from the WZ and ZZ processes are de-
rived
from alternative samples, generated using Powheg [69]with
Pythia 8
for the parton shower to account for differences in the
modelling of diboson production and showering. Shape variations
due to renormalisation and factorisation scales are also consid-
ered
for these two processes. The prior uncertainties assumed for
Z+jets and VH cover the observed data/simulation agreement in
validation regions, and the calculations in Ref. [68], respectively.
The impact of these uncertainties on the measurement is small.
Uncertainties
in data-driven background evaluations mainly
come from statistical and systematic uncertainties in the charge
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