358 The ATLAS Collaboration / Physics Letters B 773 (2017) 354–374
The uncertainty in the C factor in Eq. (1) is dominated by ex-
perimental
sources. Uncertainties in the lepton and jet reconstruc-
tion
affect the signal acceptance in the fiducial phase space. The ef-
fects
are estimated by varying the energy or momentum scale and
the resolution of leptons and jets, and the correction factors for
the trigger, reconstruction, identification and isolation efficiencies,
within their uncertainties estimated in dedicated data analyses [50,
51,54].
Uncertainties in the E
miss
T
reconstruction and b-tagging are
also taken into account based on the studies in Ref. [59] and
Ref. [57] respectively. The impact of the hard-object uncertainties
in the E
miss
T
is estimated by individually varying each of their as-
sociated
uncertainties and recalculating E
miss
T
for each variation. In
addition, uncertainties in the scale and resolution of the E
miss
T
soft
term are estimated using data as discussed in Refs. [59] and [60].
The
full set of detector-related uncertainties is taken into ac-
count
in the background estimation. The statistical uncertainties
stemming from the size of the MC samples used for the back-
ground
estimates and from the size of the data samples used for
data-driven estimations in the control regions are also considered
as systematic uncertainties. The uncertainties due to the modelling
of background processes in the signal and control regions are es-
timated
by comparing different event generators, as discussed in
Sections 3 and 5.
The
MC samples are reweighted to reproduce the distributions
in data of the average number of interactions per bunch cross-
ing,
and additionally the number of reconstructed primary ver-
tices
per event. The uncertainty due to pile-up is estimated as the
difference between the two. An uncertainty of 2.1% in the inte-
grated
luminosity affects the cross-section measurement and the
MC-based estimate of backgrounds. It is determined following the
same methodology as that detailed in Ref. [61] based on a cali-
bration
of the luminosity scale using x–y beam-separation scans
performed in August 2015. The beam energy uncertainty of 0.66%
(from Ref. [62]) gives a 1.7% uncertainty in the theoretical cross
section, which is not accounted for in the predictions quoted in
this Letter.
Uncertainties
in the C factor due to theoretical sources are also
included. The uncertainties associated with PDFs are taken as the
largest of either the CT10 NLO eigenvector uncertainty band at
68% confidence level, or the difference among the central val-
ues
of CT10 NLO, MSTW2008nlo [63] and NNPDF3.0 [64] PDFs.
The uncertainty associated with higher-order QCD corrections is
estimated by varying renormalisation (μ
R
) and factorisation (μ
F
)
scales independently by factors of 2 and 0.5 with the constraint
0.5 ≤ μ
F
/μ
R
≤ 2. The effects of parton shower, hadronisation and
underlying event models (referred to here as parton shower for sim-
plicity)
are accounted for by comparing the default MC prediction
for WW production, which uses PYTHIA v8.210 for modelling
of these effects, with the prediction obtained with the models im-
plemented
in HERWIG++.
A
full list of systematic uncertainties and their impact on the
cross-section measurement is given in Table 4.
8. The fiducial cross-section measurement
The fiducial cross section σ
fid
WW
→eμ
is extracted by minimising
a negative log-likelihood function, based on observed and expected
numbers of events in the signal region, as defined by the signal
event selection, and in the top-quark and Drell–Yan control re-
gions,
as defined in Section 5. The likelihood consists of a product
of Poisson probability density functions for the orthogonal regions.
This procedure allows a simultaneous measurement of the signal
process cross section and of the contributions from the top-quark
and Drell–Yan processes. Systematic uncertainties are taken into
account as constrained nuisance parameters in the log-likelihood
Table 3
Observed
number of events in data and estimated numbers of events from
signal and background processes in the signal and control regions. The
numbers of events from signal and background processes are the result
of the simultaneous fit, i.e. are constrained to match the data in the sig-
nal
and control regions. The quoted uncertainties account for statistical and
systematic components on the number of events for each process and do
not include the uncertainties in the C factor. The correlations among pro-
cesses
for common systematic uncertainties are accounted for in the total
uncertainties.
Process Signal region Top-quark
control region
Drell–Yan
control region
WW signal 997 ±69 49 ±12 75.3 ±5.4
Drell–Yan 62
±23 49 ±29 1568 ±45
t
¯
t +single top 177 ± 33 2057 ± 81 3.5 ± 1.6
W
+jets/multi-jet 78 ±41 70 ±55 0 ±17
Other dibosons 38
±12 6.3 ±3.519.2 ±6.1
Total 1351
±37 2232 ±47 1666 ± 41
Data 1351 2232 1666
Table 4
Breakdown
of the relative uncertainties in the fiducial cross-section measurement as
a result of the simultaneous fit to signal and control regions. “Electron” and “Muon”
uncertainties include contributions from trigger, energy/momentum reconstruction,
identification and isolation.
Sources of uncertainty Relative uncertainty for σ
fid
WW
→eμ
Jet selection and energy scale & resolution 7.3%
b-tagging 1.3%
E
miss
T
and p
miss
T
1.7%
Electron 1.0%
Muon 0.4%
Pile-up 0.9%
Luminosity 2.1%
Top-quark background theory 2.4%
Drell–Yan background theory 1.5%
W
+jet and multi-jet background 3.8%
Other diboson backgrounds 1.1%
Parton shower 3.1%
PDF 0.2%
QCD scale 0.2%
MC statistics 1.2%
Data statistics 3.7%
Total uncertainty 11%
function. The methodology accounts for uncertainties and their
correlations across signal and background processes. It is found
that the Drell–Yan and top-quark processes need to be scaled rel-
ative
to their MC predictions by 1.03 ± 0.03 and 0.875 ± 0.035
respectively
to match the observed data yields in the correspond-
ing
control regions. The uncertainties of the quoted scale factors
are driven by the data statistics in the respective control regions
and do not include modelling uncertainties on the respective pro-
cesses.
The number of events observed in data and the estimated
numbers of signal and background events together with their to-
tal
uncertainties are reported in Table 3. The correction factor C is
calculated to be 0.60 ± 0.04, where the uncertainty accounts for
the systematic effects discussed in Section 7. The measured signal
cross section is
σ
fid
WW
→eμ
= 529 ±20 (stat.) ±50 (syst.) ± 11 (lumi.) fb.
The total uncertainty is dominated by systematic sources, as de-
scribed
in Section 7, of which the largest contribution originates
from the experimental jet selection and calibration. The correla-
tions
of the fit parameters in the signal and control regions are
taken into account in the computation of the total uncertainties.
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