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The CMS Collaboration / Physics Letters B 781 (2018) 244–269 249
Fig. 6. The reduced mass distributions m
jj,red
for the LL (upper) and TT (lower)
signal region categories. The points with bars show the data, the histogram with
shaded band shows the estimated background and associated uncertainty. The
m
jj,red
spectrum for the background is obtained by weighting the m
jj,red
spectrum
in the antitag region by the ratio R
p/f
of Fig. 5. The signal predictions for a bulk
graviton of mass 1000 GeV, are overlaid for comparison, assuming a cross section
σ (pp → X → HH → bbbb) of 10 fb. The last bins of the distributions contain all
events with m
jj,red
> 3000 GeV. The differences between the data and the predicted
background, divided by the data statistical uncertainty (data unc.) as given by the
Garwood interval [76], are shown in the lower panels.
For resonance masses of 1200 GeV and above, the background
estimation is improved by simultaneously fitting a parametric
model for the background and signal to the data in the signal
and the antitag regions for m
jj,red
≥ 1100 GeV. In the fit, the ratio
R
p/f
obtained from the sidebands is used to constrain the relative
number of background events in the two regions. To account for
possible R
p/f
dependence on m
jj,red
at high m
jj,red
values, the R
p/f
obtained from the fits shown in Fig. 5 is also parametrized as a lin-
ear
function of m
jj,red
. The signal normalization is unconstrained in
the fit, while the uncertainties in the parameters of the functions
used to model the background and R
p/f
are treated as nuisance
parameters. For the background modelling, a choice among an
exponential function Ne
−am
jj,red
, a “levelled exponential” function
Ne
−am
jj,red
/(1+abm
jj,red
)
, and a “quadratic levelled exponential func-
tion”
Ne
[−am
jj,red
/(1+abm
jj,red
)]−[−cm
2
jj,red
/(1+bcm
2
jj,red
)]
was made, using
a Fisher F-test [77]. At a confidence level of 95%, the levelled ex-
ponential
function was found to be optimal. Since the background
shapes in the signal regions, as predicted using the antitag re-
gions,
were found to be similar (Fig. 6), the parametric background
modelling was tested using the antitag region in the data before
applying it to the signal region.
The
simultaneous fits to the antitag and the signal regions
are shown in Figs. 7 and 8, respectively, using the background
model only. These are labelled as “post-fit” curves with the signal
region background yields constrained to be R
p/f
times the back-
ground
yields from the antitag regions. The “pre-fit” curves, ob-
tained
by fitting the antitag and the signal regions separately to
the background-only model, with the background event yields un-
constrained,
are also shown for comparison. In the post-fit results,
the R
p/f
dependence on m
jj,red
was found to be negligible.
Among
the four fitted regions, corresponding to the antitag and
the signal regions in the LL and TT categories, the events with the
highest value of m
jj,red
occur in the antitag region of the LL cate-
gory,
at around m
jj,red
= 2850 GeV. As the parametric background
model is only reliable within the range of observed events, the
likelihood is only evaluated up to m
jj,red
= 3000 GeV. This results
in a truncation of the signal distribution for resonances having m
X
of 2800 GeV and above, with signal efficiency losses increasing to
30% for m
X
= 3000 GeV, as shown in Fig. 4.
Closure
tests of the background estimation methods were per-
formed
using simulated multijet samples with signals of various
cross sections. The tests indicated a good consistency between the
expected and the assumed signal strengths.
5. Systematic uncertainties
The following sources of systematic uncertainty affect the ex-
pected
signal yields. None of these lead to a significant change in
the signal shape.
Trigger
response modelling uncertainties are particularly im-
portant
for m
jj,red
< 1200 GeV, where the trigger efficiency drops
below 99%. A scale factor is applied to correct for the difference in
efficiency observed between the data and simulation. The control
trigger used to measure this scale factor requires a single AK4 jet
with p
T
> 260 GeV, and it too is subject to some inefficiency when
m
jj,red
is close to 750 GeV, because of a difference between the jet
energy scale used in the trigger and that used in the offline recon-
struction.
This inefficiency is measured using simulations, and has
an associated total uncertainty of between 1% and 15%.
The jet energy scale and resolution uncertainty is about 1% [63,
64].
The jet mass scale and resolution, and τ
21
selection efficiency
data-to-simulation scale factor are measured using a sample of
merged Wjets in semileptonic ttevents. The corresponding uncer-
tainties
are extrapolated to a higher p
T
range than that associated
with ttevents, using simulations. A correction factor is applied to
account for the difference in the jet shower profile of W → qq
and H → bbdecays, by comparing the ratio of the efficiency of
H and Wjets using the pythia 8 and herwig++ shower gener-
ators.
The jet mass scale and resolution has a 2% effect on the
signal yields because of a change in the mean of the Hjet mass
distribution. The τ
21
selection efficiency uncertainty amounts to
a +30/−26% change in the signal yields. The uncertainty in the
H tagging correction factor is in the range 7–20% depending on
the resonance mass m
X
. The double-b tagger efficiency scale fac-
tor
uncertainty is about 2–5%, depending on the double-b tagger
requirement threshold and jet p
T
, and is propagated to the total
uncertainty in the signal yield.
The impact of the PDFs and the theoretical scale uncertainties
are estimated to be 0.1–2%, using the PDF4LHC procedure [50], and
affect the product of the signal acceptance and the efficiency. The
PDF and scale uncertainties have negligible impact on the signal
m
jj,red
distributions. Additional systematic uncertainties associated