512 The ATLAS Collaboration / Physics Letters B 789 (2019) 508–529
the invariant mass of the two leptons, φ
is the azimuthal
angle between the two leptons, and max
m
T
is the larger of
m
i
T
=
2 p
i
T
· E
miss
T
·
1 −cosφ
i
, E
miss
T
, where
i
can be ei-
ther
the leading or the subleading lepton. The “outside lepton veto”
requires the two leptons to reside within the rapidity gap spanned
by the two leading jets, and the “central jet veto” rejects events
with additional jets with p
T
> 20 GeV in the rapidity gap between
the two leading jets. In the N
jet
=1 and N
jet
≥2categories, the
invariant mass of the τ -lepton pair (m
ττ
), calculated using the
collinear approximation [71], is used to veto background from Z →
ττ production. Signal regions (SRs) are defined in each N
jet
cate-
gory
after applying all selection criteria. For both the N
jet
=0 and
N
jet
=1 ggF SRs, eight regions, later used for the fit, are defined by
subdividing in m
at m
< 30 GeV and m
≥ 30 GeV, in p
T
of
the subleading lepton at p
sublead
T
< 20 GeV and p
sublead
T
≥ 20 GeV,
and by the flavour of the subleading lepton. For the categories
with zero jets and with exactly one jet, the discriminating vari-
able
between signal and SM background processes is the dilepton
transverse mass, defined as m
T
=
E
T
+ E
miss
T
2
−
p
T
+ E
miss
T
2
where E
T
=
|p
T
|
2
+m
2
and p
T
is the vector sum of the lep-
ton
transverse momenta. The discriminating variable m
T
is used in
the ggF SRs, with eight bins for the N
jet
=0 and six bins for the
N
jet
=1regions. The bin boundaries are chosen such that approxi-
mately
the same number of signal events is expected in each bin.
The m
T
distributions for the N
jet
=0 and N
jet
=1SRs are shown
in Fig. 3. All figures in this Letter, except Fig. 2, use signal and
background normalisations as fitted by the final statistical analysis
of all signal and control regions, including pulls of statistical and
systematic uncertainty parameters (post-fit). For the N
jet
≥2VBF
selection, a boosted decision tree (BDT) [72]is used to enhance
discrimination power between the VBF signal and backgrounds,
including the ggF process. Kinematic variables of the two lead-
ing
jets ( j) and the two leading leptons () are used as inputs
to the BDT: the invariant masses (m
jj
, m
), the difference be-
tween
the two jet rapidities (y
jj
), and the difference between
the azimuthal angles of the two leptons (φ
). Other variables
used in the BDT training are: m
T
, the lepton η-centrality (
C
,
where C
=|2η
−
η
j
|/η
jj
), which quantifies the positions of
the leptons relative to the leading jets in pseudorapidity [73], the
sum of the invariant masses of all four possible lepton–jet pairs
(
, j
m
j
), and the total transverse momentum (p
tot
T
), which is de-
fined
as the magnitude of the vectorial sum of all selected objects.
The observables providing the best discrimination between signal
and background are m
jj
and y
jj
, and are shown in Fig. 4 after
applying all selections. The BDT score reflects the compatibility of
an event with VBF-like kinematics. Signal-like events would tend
to have high BDT score, while background-like events tend to have
low BDT score. The signal purity, therefore, increases at high values
of BDT score. The BDT score is used as the discriminating variable
in the statistical analysis with four bins. The bin boundaries are
chosen to maximise the expected sensitivity for the VBF produc-
tion
mode, resulting in smaller bin widths for larger values of the
BDT score. In the highest-score BDT bin, the expected signal-to-
background
ratio of the VBF signal is approximately 0.6. The BDT
distribution for the VBF-enriched region is presented in Fig. 5.
5. Background estimation
The background contamination in the SRs originates from vari-
ous
processes: non-resonant WW, top-quark pair (t
¯
t) and single-
top-quark
(Wt), diboson (WZ, ZZ, W γ and W γ
∗
) and Drell–Yan
(mainly Z →ττ, hereafter denoted Z /γ
∗
) production. Other back-
Table 4
Post-fit
normalisation factors which scale the corresponding estimated yields in the
signal region; the dash indicates where MC-based normalisation is used. The errors
include the statistical and systematic uncertainties.
Category WW t
¯
t/Wt Z/γ
∗
N
jet,(p
T
>30 GeV)
= 0 ggF 1.06 ± 0.09 0.99 ± 0.17 0.84 ± 0.04
N
jet,(p
T
>30 GeV)
= 1 ggF 0.97 ± 0.17 0.98 ± 0.08 0.90 ± 0.12
N
jet,(p
T
>30 GeV)
≥ 2VBF – 1.01± 0.01 0.93 ± 0.07
Fig. 5. Post-fit BDT score distribution with the signal and the background modelled
contributions
in the VBF signal region. The hatched band shows the total uncer-
tainty
of the signal and background modelled contributions.
ground contributions arise from W +jets and multi-jet production
with misidentified leptons, which are either non-prompt leptons
from decays of heavy-flavour hadrons or jets faking prompt lep-
tons.
Dedicated regions in data, identified hereafter as control re-
gions
(CRs), are used to normalise the predictions of some of the
background processes. CRs are defined for the main background
processes: WW (only for N
jet
≤1 final states), t
¯
t/Wt, and Z /γ
∗
.
Table 3 summarises the event selection for all CRs. For the N
jet
=0
and
N
jet
=1 WW CRs, m
selections orthogonal to those of the
SRs are applied. For the t
¯
t/Wt CRs, the b-veto is replaced with a
b-tag requirement. For the N
jet
=1 and N
jet
≥2VBF Z/γ
∗
CRs, the
m
ττ
selection is inverted, while for the N
jet
=0 Z/γ
∗
CR the φ
selection criterion is inverted. Fig. 6 presents the post-fit m
T
dis-
tributions
in the N
jet
=0 and N
jet
=1CRs.
In
Fig. 7, the post-fit y
jj
distributions in the N
jet
≥2VBF
CRs are shown. Data and simulation are in agreement within un-
certainties
for all the relevant distributions in the different CRs.
The background contributions with misidentified leptons are esti-
mated
using a data-driven technique. A control sample where one
of the two lepton candidates fails to meet the nominal identifica-
tion
and isolation criteria but satisfies looser identification criteria,
referred as an anti-identified lepton, is used. The contribution of
this background in the SRs and CRs is then obtained by scaling
the number of data events, after the subtraction of processes with
two prompt leptons, in the control samples by an extrapolation
factor. The latter is measured in a Z+jets-enriched data sample,
where the Z boson decays to a pair of electrons or muons, and
the misidentified lepton candidate recoils against the Z boson. The
extrapolation factor is defined as the ratio of the numbers of iden-
tified
and anti-identified leptons, and is measured in bins of p
T
and η. Furthermore, a sample composition correction factor is ap-
plied
separately in p
T
< 25 GeV and p
T
> 25 GeV bins, and is
defined in each bin as the ratio of the extrapolation factors mea-
sured
in W +jets and Z +jets MC simulation. The total uncertainty
of the background with misidentified leptons includes uncertain-
ties
due to the difference in sample composition between the