340 The CMS Collaboration / Physics Letters B 772 (2017) 336–358
Fig. 3. Distribution of the event-level BDT discriminants D
dil
t
¯
tt
¯
t
for the combined
dilepton (μ
+
μ
−
+μ
±
e
∓
+e
+
e
−
) event sample for 4–5 jets (top), 6–7 jets (middle),
and ≥8 jets (bottom). The vertical bars show the statistical uncertainty in the data.
The predicted background distributions from simulation are shown by the shaded
histograms. The hatched area shows the size of the dominant systematic uncer-
tainty
in the simulation, which comes from the choice of the matrix-element (ME)
factorization and renormalization scales used in the simulation. The electroweak
(EW) histogram is the sum of the Drell–Yan and W boson+jets backgrounds. The
expected SM t
¯
tt
¯
tsignal contribution is shown by the open histogram, multiplied by
a factor of 20.
(renormalization and factorization scale) and
+6.2%
−6.4%
(PDF). The
effect of uncertainties in the cross sections for the other back-
grounds
were checked and found to be negligible.
3. The
uncertainties from trigger, lepton identification, and lepton
isolation corrections, which are included as nuisance parame-
ters
in determining the upper limit. Combined, these give an
uncertainty of 1.2% in the single-muon channel, 3.7% in the
single-electron channel, 4.3% in the μμ channel, 4.6% in the
μe channel, and 4.8% in the ee channel.
The
shape uncertainties are:
1. The
uncertainty from the choice of the factorization and renor-
malization
scales in the calculation of the matrix element of
the hard-scattering process, which is estimated by the maxi-
mum
variation in the D
dil
t
¯
tt
¯
t
or D
lj
t
¯
tt
¯
t
distribution obtained when
each scale is changed separately by a factor of 1/2 and 2,
excluding unphysical anticorrelated combinations. This proce-
dure
is performed separately for the t
¯
tt
¯
tsignal and the t
¯
tback-
ground.
In addition, alternative t
¯
tsamples are used to estimate
the impact of a change in the scale at the parton-shower level,
taking into account the uncertainty in α
S
for the hadroniza-
tion [25].
The differences in the distributions with respect to
the nominal ones are taken as the uncertainty. The uncertainty
in the matrix-element scale is the dominant systematic uncer-
tainty
in the analysis.
2. Differences
in the simulation of t
¯
tfrom the choice of the
matrix-element generator, which is estimated by comparing
the nominal t
¯
t simulation using powheg +pythia 8to samples
generated using MadGraph + pythia 8 with MLM matching
[16]. The difference relative to the nominal simulation is used
to estimate the uncertainty from this source.
3. The uncertainty in the fraction of ttbbevents in the t
¯
tback-
ground,
which is estimated using the uncertainty in the mea-
sured
cross section ratio σ
ttbb
: σ
t
¯
tjj
[42] that was used to
correct the ttbb content of the t
¯
t simulation. An anticor-
related
uncertainty in the measured cross section ratio of
(σ
t
¯
tjj
−σ
ttbb
): σ
t
¯
tjj
is applied simultaneously to the light-quark
fraction to maintain the total t
¯
tcross section.
4. The uncertainties in the jet energy scale and the jet energy
resolution [49], which are estimated by varying these within
their uncertainties by ±1 standard deviation. A similar method
is used to estimate the uncertainty from the inelastic proton–
proton
cross section and the procedure used in the pileup
reweighting. These uncertainties have very little influence on
the final limit.
5. The
uncertainty in the corrections to the values of the b tag-
ging
CSV discriminator, where three categories of systematic
uncertainty are applied for each jet flavor: the jet energy scale,
purity of the data sample used to derive the corrections, and
the statistical uncertainties derived from the fits used in the
method. The uncertainty in the b tagging correction caused by
the jet energy scale is treated as fully correlated with the jet
energy scale uncertainty described above. Typical magnitudes
of each of these individual uncertainties on the corrections to
the b tagging CSV discriminator are 10–50% before the fit, de-
pending
on the number of jets and b jets in the event. A full
description of these corrections can be found in Ref. [41].
Each
systematic source was attributed a nuisance parameter in the
limit determination.
7. Results
No deviation from the background-only simulation, which in-
cludes
t
¯
tproduction and negligible single top, t
¯
t+H/Z/Wbo-
son,
Drell–Yan+jets, and W+jets backgrounds, is observed in the
D
dil
t
¯
tt
¯
t
or D
lj
t
¯
tt
¯
t
distributions. An upper limit is derived for the t
¯
tt
¯
t
production
cross section using the asymptotic approximation of
the CL
s
method provided in Refs. [50–54]. The signal and back-
ground
distributions are fitted using a simultaneous maximum-
likelihood
method. The normalization uncertainties are included
using log-normal functions and the shape uncertainties are in-
cluded
as Gaussian-distributed nuisance parameters. The expected
and observed 95% CL upper limits from the two analyses and
their combination are listed in Table 1. For the combination of
the single-lepton and opposite-sign dilepton results, the system-
atic
uncertainties attributed to the integrated luminosity, jet en-
ergy
scale, and modeling of the pileup contribution are assumed