ATLAS Collaboration / Physics Letters B 728 (2014) 562–578 565
Fig. 2. The 95% CL upper limits on σ × BR × A × ε for a hypothetical signal with
a Gaussian-shaped m
γ j
distribution as a function of the signal mass m
G
for four
values of the relative width
σ
G
/m
G
.
high p
T
(0.1%) and pileup effects (0.1%). Uncertainties on the jet
and photon energy scale contribute 1.0–1.5% and 0.3%, respectively,
through their effects on the shape and yield of the signal distri-
bution. The sizes of the systematic uncertainties are similar for
the q
∗
and QBH signals. These systematic uncertainties are treated
as marginalized nuisance parameters in the limit calculation. Sys-
tematic uncertainties on the value and shape of the signal accep-
tance due to the PDF uncertainties were examined and found to be
negligible. To account for the statistical uncertainties on the back-
ground fit parameters, the background function is repeatedly fit to
pseudodata for which the content of each bin is drawn from Pois-
son distributions. The mean of the Poisson distribution for a given
bin corresponds to the number of entries actually observed in that
bin in the data. The variations in the fit predictions for a given bin,
1% of the background at 1 TeV to about 20% of the background
at 3 TeV, are taken as indicative of the systematic uncertainty. This
bin-by-bin uncertainty is treated in the limit as fully correlated, us-
ing a single nuisance parameter that scales the entire background
distribution. Several other fit functions from Ref. [50] were tested,
and a negligible systematic uncertainty was found.
Fig. 2 sho
ws the model-independent limits on the visible cross-
section, define
d as the product of the cross-section (
σ )times
branching fraction (BR) times acceptance (A) times efficiency (
ε),
of a potential signal as a function of the mass of each signal tem-
plate, and includes the systematic uncertainties discussed above.
The signal line shape is modelled as a Gaussian distribution, with
one of four relative widths:
σ
G
/m
G
= 5%, 7%, 10%, and 15%, where
σ
G
(m
G
) is the width (mean mass) of the Gaussian. The differ-
ences between the limits for different widths are driven by the
increased sensitivity to local fluctuations for the narrower signals.
Beyond the highest-mass event recorded, 2.57 TeV, the limits begin
to converge due to the absence of observed events. At 1 TeV and
4TeVthelimitsare8fband0.1fb,respectively,for
σ
G
/m
G
= 5%.
At 3 TeV, the new limit improves the earlier ATLAS result in this
channel by an order of magnitude.
The limit on the visible cross-section in the QBH model is
shown i
n Fig. 3 as a function of M
th
. The observed (expected)
lower limit on the QBH mass threshold is found to be 4.6 (4.6) TeV,
at 95% CL. The uncertainty on the QBH theoretical cross-section
arising from PDF uncertainties moves the uppermost excluded
mass by 0.2%.
Fig. 3. The 95% CL upper limits on σ × BR × A × ε for QBHs decaying to a photon
and a jet, as a function of the threshold mass M
th
, assuming M
D
= M
th
and n = 6.
The limits take into account statistical and systematic uncertainties. Points along
the solid black line indicate the mass of the signal where the limit is computed.
The black short dashed line is the central value of the expected limit. Also shown
are the
±1σ and ±2σ uncertainty bands indicating the underlying distribution of
possible limit outcomes under the background-only hypothesis. The predicted visi-
ble cross-section for QBHs is shown as the long dashed line.
Fig. 4. The 95% CL upper limits on σ × BR × A × ε for excited quarks decaying
to a photon and a jet, as a function of the signal mass m
q
∗
. The limits take into
account statistical and systematic uncertainties. Points along the solid black line
indicate the mass of the signal where the limit is computed. The black short dashed
line is the central value of the expected limit. Also shown are the
±1σ and ±2σ
uncertainty bands indicating the underlying distribution of possible limit outcomes
under the background-only hypothesis. The long dashed line shows the predicted
visible cross-section for excited-quark production from pythia.
The limit on the visible cross-section in the excited-quark
model as a function of the q
∗
mass, assumed to be the same for u
∗
and d
∗
, is shown in Fig. 4. The rise in the expected and observed
limits at high m
q
∗
is due to the increased fraction of off-shell pro-
duction of the q
∗
, which alters the signal distribution to lower
masses with a wider peak. The observed (expected) lower limit
on the excited-quark mass is found to be 3.5 (3.4) TeV, at 95% CL.
With a much lower branching fraction than the dijet channel but
also smaller backgrounds, this result improves on the present ex-
clusion limits in the dijet final state: 3.32 TeV from CMS with