predictions after the event selection are presented in Fig. 2,
where the hatched band indicates the overall uncertainty on
the SM predictions. It includes a sizable statistical compo-
nent besides the systematic uncertainties, which are all
propagated to the final results.
The BDT is trained to distinguish signal from
background and provides a single discriminant value
for every event. The BDT output distribution in data is
parametrized as
FðxÞ¼C
sig
S
sig
ðxÞþC
t
¯
tγ
S
t
¯
tγ
ðxÞþC
Wγj
S
Wγj
ðxÞ
þ C
Zγj
S
Zγj
ðxÞþC
misid
S
misid
ðxÞþC
B
S
B
ðxÞ; ð1Þ
where x is the BDT output, S
sig
ðxÞ, S
Wγj
ðxÞ, S
Zγj
ðxÞ,
S
misid
ðxÞ, and S
B
ðxÞ are the normalized distributions
(templates) for the signal, t
¯
t þγ, Wγ þ jets, Zγ þ jets,
the misidentified photon background, and the sum of all
other backgrounds which includes single top quark pro-
duction and VVγ, respectively. The quantities C
sig
, C
t
¯
tγ
,
C
Wγj
, C
Zγj
, C
misid
, and C
B
are the corresponding normal-
izations from which C
sig
and C
t
¯
tγ
are left free in the fit,
while the other terms are constrained by their associated
uncertainties. The different templates, SðxÞ, are taken from
simulation except for t
¯
t þγ and misidentified photons. The
distribution S
misid
ðxÞ is obtained with the method described
above, calculating the yield as a function of BDT output.
The template S
t
¯
tγ
ðxÞ is estimated from data using a control
region defined by requiring exactly two b-tagged jets, while
keeping all other selection criteria the same as for the signal
region. The requirement of two b-tagged jets ensures a high
contribution from t
¯
t þ γ, while suppressing the contribu-
tions from all other processes. The uncertainty in the
difference of shape between events with two b-tagged
and one b-tagged jet is calculated using simulation and
accounted for as a systematic uncertainty. In addition,
S
Wγj
ðxÞ is validated in data, in a control region enriched in
Wγ þ jets events, via the substitution of the signal b jet
requirement by a b jet veto.
γlight-flavor jet,
RΔ
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.5
1
1.5
Events
100
200
300
400
500
600
700
800
900
1000
Data γtt
syst.⊕Stat. jetsγZ
j)γSignal ( t γVV
(s- and tW-)γt Misidentified photon
jetsγW
(13 TeV)
-1
35.9 fb
CMS
θcos
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
0.5
1
1.5
Events
100
200
300
400
500
600
Data γtt
syst.⊕Stat. jetsγZ
j)γSignal ( t γVV
(s- and tW-)γt Misidentified photon
jetsγW
(13 TeV)
-1
35.9 fb
CMS
light-flavor jet
η
-5 -4 -3 -2 -1 0 1 2 3 4 5
0.5
1
1.5
100
200
300
400
500
600
700
800
Data γtt
syst.⊕Stat. jetsγZ
j)γSignal ( t γVV
(s- and tW-)γt Misidentified photon
jetsγW
(13 TeV)
-1
35.9 fb
CMS
[GeV]
bνμ
m
100 150 200 250 300 350 400 450 500 550 600
0.5
1
1.5
Events / 60 GeV
200
400
600
800
1000
1200
Data γtt
syst.⊕Stat. jetsγZ
j)γSignal ( t γVV
(s- and tW-)γt Misidentified photon
jetsγW
(13 TeV)
-1
35.9 fb
CMS
EventsData/Prediction
Data/Prediction
Data/Prediction
Data/Prediction
FIG. 2. Distributions of some of the input variables to the BDT: ΔRðlight jet; γÞ (upper left), cos θ (upper right), η of the light-flavor jet
(lower left), and m
μνb
(lower right) after the final event selection in data (points), and the SM prediction (filled histograms). The hatched
band shows the statistical and systematic uncertainties in the estimated signal and background yields, and the vertical bars on the points
represent the statistical uncertainties of the data. The ratios of the data to the SM predictions are shown in the bottom panels.
PHYSICAL REVIEW LETTERS 121, 221802 (2018)
221802-4