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Physics Letters B 694 (2011) 327–345
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Search for quark contact interactions in dijet angular distributions in pp collisions
at√s = 7 TeV measured with the ATLAS detector✩
.ATLAS Collaboration
a r t i c l e i n f oa b s t r a c t
Article history:
Received 27 September 2010
Received in revised form 12 October 2010
Accepted 13 October 2010
Available online 16 October 2010
Editor: H. Weerts
Keywords:
ATLAS
LHC
7 TeV
Dijets angular distributions
Quark compositeness
Contact interactions
Dijet angular distributions from the first LHC pp collisions at center-of-mass energy√s = 7 TeV have been
measured with the ATLAS detector. The dataset used for this analysis represents an integrated luminosity
of 3.1 pb−1. Dijet χ distributions and centrality ratios have been measured up to dijet masses of 2.8 TeV,
and found to be in good agreement with Standard Model predictions. Analysis of the χ distributions
excludes quark contact interactions with a compositeness scale Λ below 3.4 TeV, at 95% confidence level,
significantly exceeding previous limits.
© 2010 CERN. Published by Elsevier B.V. All rights reserved.
1. Introduction
At hadron colliders, most events with large transverse momen-
tum (pT) transfer occur when a constituent parton from one of
the incoming hadrons scatters from a parton in the other. At high
pT, these ‘2 → 2’ scattering processes are well described within
the Standard Model by perturbative Quantum Chromodynamics
(QCD), the quantum field theory of strong interactions. As each
high-momentum parton emerges from the collision, the subse-
quent parton shower and hadronization create a collimated jet of
particles aligned with the direction of the original parton. In most
of these collisions, two high-pT jets emerge from the interaction.
These ‘dijet’ events are particularly useful for measuring quantities
associated with the initial interaction, such as the polar scattering
angle in the two-parton center-of-mass (CM) frame, θ∗, and the di-
jet invariant mass, mjj. Precise tests of QCD may be carried out by
comparing the theoretical predictions to the experimental distribu-
tions. If discrepancies between data and QCD are found to be well
beyond experimental and theoretical uncertainties, this would in-
dicate that the QCD description needs improvement, or that a new
process, not included in the Standard Model, has appeared.
This analysis focuses on dijet angular distributions, which have
been shown by previous experiments [1–4] to be sensitive mea-
sures for testing the predictions of QCD and searching for new
processes. Dijet angular distributions are well suited to the analysis
✩© CERN, for the benefit of the ATLAS Collaboration.
E-mail address: atlas.publications@cern.ch.
of early LHC data, since they are little affected by the main sys-
tematic uncertainties associated with the jet energy scale (JES) and
the luminosity. QCD calculations predict that high-pT dijet produc-
tion is dominated by t-channel gluon exchange, leading to angular
distributions that are peaked at |cosθ∗| close to 1. By contrast,
models of new processes characteristically predict angular distri-
butions that would be more isotropic than those of QCD.
This Letter reports on the first search with the ATLAS detec-
tor for quark contact interactions leading to modifications of dijet
angular distributions in proton–proton (pp) collisions at a center-
of-mass energy of√s = 7 TeV at the LHC. The data sample repre-
sents an integrated luminosity of 3.1 pb−1, recorded in periods of
stable collisions, through August 2010. The two distributions under
study – dijet χ distributions, and dijet centrality ratios – have been
used repeatedly as benchmark measures, and will be described in
detail below.
The highest exclusion limits on quark contact interactions set
by any previous experiment [4], for several statistical analyses,
ranged from 2.8 to 3.1 TeV at 95% confidence level (CL) for the
compositeness scale Λ.
2. Kinematics and angular distributions
The θ∗distribution for 2 → 2 parton scattering is predicted
by QCD in the partonic CM frame of reference. Event by event,
the momentum fraction (Bjorken x) of one incoming parton dif-
fers from that of the other, causing the partonic reference frame
to be boosted relative to the detector frame by an amount which
can be determined from the dijet kinematics. A natural variable
0370-2693/ © 2010 CERN. Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.physletb.2010.10.021
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ATLAS Collaboration / Physics Letters B 694 (2011) 327–345
for analysis of parton–parton interactions is therefore the rapidity,
y =1
momentum, of the given particle. The variable y transforms un-
der Lorentz boosts along the z-direction as y → y − yB= y −
tanh−1(βB), where βB is the velocity of the boosted frame, and
yBis its rapidity boost.
The ATLAS coordinate system is a right-handed Cartesian sys-
tem with the x-axis pointing to the center of the LHC ring, the
z-axis following the counter-clockwise beam direction, and the y-
axis going upwards. The polar angle θ is referred to the z-axis, and
φ is the azimuthal angle about the z-axis.
Rapidity differences are boost invariant, so that under Lorentz
boosts jets retain their shapes in (y,φ) coordinates. The pseudora-
pidity, η = −ln(tan(θ
and can be used as an approximation to rapidity. The variables η
and φ are employed in the reconstruction of jets.
The variable χ, used in the first angular distributions consid-
ered in this study, is derived from the rapidities of the two jets
defining the dijet topology (y1and y2). For a given scattering an-
gle θ∗, the corresponding rapidity in the CM frame (in the massless
particle limit) is y∗=1
be found from the rapidities of the two jets using y∗=1
and yB=1
tonic CM angle θ∗. Additionally, y∗is the basis for the definition
of χ: χ = exp(|y1− y2|) = exp(2|y∗|).
The utility of the χ variable becomes apparent when mak-
ing comparisons of angular distributions predicted for new pro-
cesses to those of QCD. In QCD, gluon (massless, spin-1) exchange
diagrams have approximately the same angular dependence as
Rutherford scattering: dN/dcosθ∗∝ 1/sin4(θ∗/2). Evaluation of
dN/dχ shows that this distribution is constant in χ. By contrast,
the angular distributions characteristic of new processes are more
isotropic, leading to additional dijet events at low χ. In QCD, sub-
dominant diagrams also cause χ distributions to rise slightly at
low χ.
The other important kinematic variable derivable from jet ob-
servables is the dijet invariant mass, mjj, which is also the CM
energy of the partonic system. In reconstruction, mjj is found
from the two jet four-vectors: mjj≡
where E and ? p are the energy and momentum of the jets. Both
distributions used in this Letter are binned in this variable.
The second angular distribution considered is the dijet central-
ity ratio, RC. For this analysis, the detector is divided into two
pseudorapidity regions: central and non-central. RC is defined as
the ratio of the number of events in which the two highest pT jets
both fall into the central region to the number of events in which
the two highest pT jets both fall into the non-central region. For
the current study, the central region is defined as |η1,2| < 0.7, and
the non-central region as 0.7 < |η1,2| < 1.3. Since new processes
are expected to produce more central activity than QCD, their sig-
nal would appear as an increase in RC above some mjjthreshold,
with the increase being directly related to the cross section of the
new signal.
RC distributions are complementary to χ distributions by be-
ing sensitive to different regions of phase space. χ distributions
are fine measures of θ∗and coarse measures of mjj, while the
opposite is true for RC distributions as they can be binned more
finely in mjjfor the given amount of data. This gives RC distribu-
tions greater discrimination in determining mass scales associated
with hypothetical signals. Ideally, when a signal is present, the two
distributions together can be used to narrow the list of viable hy-
potheses and to establish the associated scale parameters.
The measured RC and χ distributions include corrections for
the jet energy scale but are not unfolded to account for resolution
2ln(E+pz
E−pz), where E is the energy and pz, the z-component of
2)), approaches rapidity in the massless limit
2ln(1+|cosθ∗|
1−|cosθ∗|). The variables y∗and yB can
2(y1− y2)
2(y1+ y2). Then y∗may be used to determine the par-
?
(Ej1+ Ej2)2−(? pj1+ ? pj2)2,
effects. They are compared to theoretical predictions processed
through the detector simulation software that, similarly, includes
the jet energy corrections but not resolution unfolding.
3. The ATLAS detector
The ATLAS detector [5] covers almost the whole solid an-
gle around the collision point with layers of tracking detectors,
calorimeters, and muon chambers. Jet measurements depend most
strongly on the calorimeter system. The ATLAS calorimeter is seg-
mented in intervals of pseudorapidity and φ to exploit the prop-
erty that jet shapes are nearly boost invariant in (η,φ) coordinates.
Liquid argon (LAr) technology is used in the electromagnetic
sampling calorimeters, with excellent energy and position reso-
lution, to cover the pseudorapidity range |η| < 3.2. The hadronic
calorimetry in the range |η| < 1.7 is provided by a sampling
calorimeter made of steel and scintillating tiles. In the end-caps
(1.5 < |η| < 3.2), LAr technology is also used for the hadronic
calorimeters, matching the outer |η| limits of the electromag-
netic calorimeters. To complete the η coverage, the LAr forward
calorimeters provide both electromagnetic and hadronic energy
measurements, extending the coverage to |η| = 4.9. In ATLAS,
the calorimeter (η,φ) granularities are 0.1 × 0.1 for the hadronic
calorimeters up to |η| < 2.5 (except for the third layer of the tile
calorimeter, which has a segmentation of 0.2×0.1 up to |η| = 1.7),
and then 0.2 × 0.2 up to |η| < 5.0. The EM calorimeters feature a
much finer readout granularity varying by layer, with cells as small
as 0.025 × 0.025 extending to |η| < 2.5. This segmentation of the
calorimeter is sufficiently fine to assure that angular resolution un-
certainties in dijet analyses are negligible. In the data taking period
considered approximately 187,000 calorimeter cells (98% of the to-
tal) were active for event reconstruction.
ATLAS has a three-level trigger system, with the first level (L1)
being custom built hardware. The two higher level triggers (HLT)
are realized in software. The HLT was not set to reject events ac-
cepted by the L1 single-jet triggers chosen for this analysis.
4. Event selection and reconstruction
In the current 3.1 pb−1data sample, specific L1 jet trigger se-
lections have been exploited for optimal analysis of the angular
observables. For both observables, bins of mjjare associated with
distinct L1 jet trigger requirements selected to provide maximal
statistics while being fully efficient, as will be detailed for χ in
Section 7.
Jets have been reconstructed using the infrared-safe anti-kt jet
clustering algorithm [6] with the radius parameter R = 0.6. The
inputs to this algorithm are clusters of calorimeter cells seeded
by energy depositions significantly above the measured noise. Jet
four-vectors are constructed by the vectorial addition of cell clus-
ters, treating each cluster as an (E, ? p) four-vector with zero mass.
The jet four-vectors are then corrected, as a function of η and pT,
for the effects of hadronic shower response and detector material
distributions by using a calibration scheme based on Monte Carlo
(MC) studies including full detector simulation, and validated with
extensive test-beam studies [7] and collision data [8].
In order to suppress cosmic-ray and beam-related backgrounds,
events are required to contain at least one primary collision vertex
with a position of |z| < 30 cm and reconstructed from at least five
charged-particle tracks. Events with at least two jets are retained if
the highest pT jet (the ‘leading’ jet) satisfies pj1
next-to-leading jet satisfies pj2
olds are required so as to avoid suppression of events where a
third jet has been radiated, while the 30 GeV threshold ensures
T> 60 GeV and the
T> 30 GeV. The asymmetric thresh-
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ATLAS Collaboration / Physics Letters B 694 (2011) 327–345
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that reconstruction is fully efficient for both leading jets. Those
events containing a poorly measured jet [9] with pT > 15 GeV
are vetoed to avoid cases where such a jet would cause incorrect
identification of the two leading jets. This criterion results in a re-
jection rate of 0.5% in the current data sample. The two leading
jets are required to satisfy quality criteria, such as being associated
with in-time energy deposits in the calorimeter. To be considered
as one of the two leading jets, a jet is required to be found within
the pseudorapidity region |η| < 2.8, where the jet energy scale is
known to highest precision.
5. Monte Carlo simulations
The Monte Carlo simulation used for the analysis presented in
this Letter has the following components. The MC samples have
been produced with the PYTHIA 6.4.21 event generator [10] and
the ATLAS MC09 parameter tune [11], using the modified leading-
order MRST2007 [12] parton distribution functions (PDF). The gen-
erated events are passed through the detailed simulation of the
ATLAS detector [13], which uses GEANT4 [14] for simulation of
particle transport, interactions, and decays. This yields QCD MC
samples that have been smeared by detector effects for compar-
ison with collision data. These simulated events are then subjected
to the same reconstruction process as the data to produce dijet
angular distributions.
As the next step, bin-by-bin correction factors (K-factors) have
been applied to the angular distributions derived from MC events
to account for next-to-leading order (NLO) contributions. The K-
factors are derived from dedicated samples generated separately,
and are defined as the ratio NLOME/PYTSHOW. The NLOME sample
is produced using matrix elements in NLOJET++ [15–17] and the
NLO PDF from CTEQ6.6 [18]. The PYTSHOWsample is produced with
PYTHIA restricted to leading-order (LO) matrix elements and par-
ton showering using the modified leading order MRST2007 PDF.
The angular distributions generated with full PYTHIA already
contain various non-perturbative effects modeled by this event
generator (such as multiple parton interactions and hadronization).
The K-factors defined above are designed to retain these effects
while adjusting for differences in the perturbative sector. Multiply-
ing the full PYTHIA predictions of angular distributions by these
bin-wise K-factors results in a reshaped spectrum which includes
corrections originating from NLO matrix elements.
Over the full range of χ, the K-factors change the normalized
distributions by up to 6%, with little variability from one mass bin
to the other. In the case of RC, the K-factors change the distribu-
tion by less than 1%.
The QCD predictions used for comparison to data in this Letter
are the end product of the two-step procedure described above.
Other ATLAS jet studies [19] have shown that the use of dif-
ferent event generators and different sets of parameters for non-
perturbative effects has a negligible effect on the studied observ-
ables in the phase space being considered. For the high-pT dijet
shape observables studied here, χ and RC, differences between
PDF sets were found to be consistently smaller than the uncer-
tainty associated with the CTEQ6.6 PDF set, and are not taken into
account.
6. Quark contact interaction term
The benchmark beyond-the-Standard-Model process considered
in this Letter is a quark contact interaction, which may be used to
model the onset of kinematic properties that would characterize
quark compositeness: the hypothesis that quarks are composed of
more fundamental particles. The model Lagrangian for this bench-
mark process is a four-fermion contact interaction [20–22], the
analog of the Fermi four-fermion interaction used to describe ef-
fects of the weak interaction. The effects of the contact interaction
would be expected to appear below or near a characteristic en-
ergy scale Λ. If Λ is much larger than the partonic CM energy,
these interactions are suppressed by inverse powers of Λ and the
quarks would appear to be point-like. The dominant effect would
then come from the lowest dimensional four-fermion interactions
(contact terms).
While a number of contact terms are possible, the Lagrangian
in standard use since 1984 [20] is the single (isoscalar) term:
Lqqqq(Λ) =
quark fields ΨL
q
are left-handed. The full Lagrangian used for
hypothesis testing is then the sum of Lqqqq(Λ) and the QCD La-
grangian. The relative phase of these terms is controlled by the
interference parameter, ξ, which is set for destructive interference
(ξ = +1) in the current analysis. Previous analyses [4] showed that
the choice of constructive (ξ = −1) or destructive (ξ = +1) inter-
ference changed exclusion limits by ∼ 1%.
MC samples are calculated in PYTHIA 6.4.21 using this La-
grangian, with each sample corresponding to a distinct value of Λ.
Angular distributions of these samples are processed in the same
fashion as QCD distributions, including the application of bin-wise
K-factors.
Notably, in addition to quark compositeness, this same La-
grangian could be applied to a number of other beyond-the-
Standard-Model theories (albeit with different coupling constants),
so that it serves as a template for models of new processes with
similar scattering distributions.
ξg2
2Λ2
q
¯ ΨL
qγμΨL
q¯ ΨL
qγμΨL
q, where g2/4π = 1 and the
7. Kinematic criteria for angular distributions
The χ distributions described here are normalized to unit area,
(1/Nev)dNev/dχ where Nevis the number of observed events, to
reduce the effects of uncertainties associated with absolute nor-
malization.
Detector resolution effects smear the χ distributions, causing
events to migrate between neighboring bins. This effect is reduced
by configuring the χ bins to match the natural segmentation of
the calorimeter, by making them intervals of constant ?η, ap-
proximating ?y. This is achieved by placing the χ bin boundaries
at positions χn= e(0.3×n), where n is the index for the lower χ
boundary of the nth bin, starting with n = 0. In doing this, not
only is the migration reduced, it is also equalized across the span
of χ.
The χ distributions are divided, in turn, into intervals of dijet
invariant mass, mjj. For massless partons, the following approx-
imate form shows the dependence of mjj on pT and χ: mjj=
√pT1pT2·?χ + 1/χ − 2cos(?φ). Since mjj is the CM energy of
in the high mass bins. Several mjjintervals are analyzed to exploit
the fact that the χ distributions in low mass bins would be similar
to the QCD prediction, while these distributions would be modified
by new physics processes acting in high mjj bins. The sensitivity
to these processes depends strongly on their cross sections relative
to QCD and on the number of events in the highest mass bin.
For χ distributions, events are rejected if |yB| > 0.75 or |y∗| >
1.7. The combined criteria limit the rapidity range of both jets
to |y1,2| < 2.45. The |y∗| criterion determines the maximum χ,
which is 30 for this analysis. Taken together, these two criteria de-
fine a region within the space of accessible y1and y2where the
acceptance is uniform to better than 1% in χ, for all mass bins.
This ensures that the expected shapes of the distributions are not
significantly changed by the acceptance. Also, in low mass bins,
the |yB| criterion emphasizes the contribution from the matrix el-
the partonic system, new processes would be expected to appear
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ATLAS Collaboration / Physics Letters B 694 (2011) 327–345
ements and reduces the influence of the effects of PDF convolution.
In the highest mjj bin, used for limit setting, the |yB| criterion
reduces the sample by 16%. These kinematic cuts have been opti-
mized through full MC simulation to assure high acceptance in all
dijet mass bins.
Since event migration also occurs between bins of mjj, studies
of fully simulated jets are used to ensure that migration is small.
This criterion, along with the requirement of a sufficient number of
events, lead to mjjbin boundaries of 340, 520, 800, and 1200 GeV,
with no upper bound on the highest bin. As noted earlier, single-
jet triggers are carefully selected for each bin to be 100% efficient.
Prescaling of triggers leads to a different effective integrated lu-
minosity in each mass bin, with the corresponding numbers being
0.12, 0.56, 2.0, and 3.1 pb−1in the current data sample for the bins
listed above.
Like the χ distributions, the RC distribution has reduced sen-
sitivity to the absolute JES. However, relative differences in jet
response in η could have a significant impact on the sensitivity.
Hence, for these early studies, the η range is restricted to the
more central regions of the calorimeter where the JES is uniform
to within 1% as determined from cross-calibration studies [8]. The
RC region has been chosen to end at a maximum of |η| = 1.3,
just before the transition region between the central and end-cap
calorimeters.
8. Convolution of systematic uncertainties
As mentioned before, the angular distributions have a reduced
sensitivity to the JES uncertainties compared to other dijet mea-
surements. Nevertheless, the JES still represents the dominant un-
certainty for this analysis. The ATLAS JES has been determined by
extensive studies [23], and its uncertainty has been tabulated in
the variables η, pT, and NV, the number of vertices in the event.
The average NV over the full current data sample is 1.7. Typi-
cal values of the JES uncertainty in the considered phase space
are between 5% and 7%. The resulting bin-wise uncertainties are
up to 9% for the χ observable, and up to 7% for the RC observ-
able.
The dominant sources of theoretical uncertainty are NLO QCD
renormalization and factorization scales, and the PDF uncertainties.
The corresponding bin-wise uncertainties for normalized χ distri-
butions are typically up to 3% for the combined NLO QCD scales
and 1% for the PDF error.
Convolution of these experimental and theoretical uncertainties
is done for all angular distributions through Monte Carlo pseudo-
experiments (PE’s). For all events in the MC sample 1000 PE’s
are performed, three random numbers being drawn from a Gaus-
sian distribution for each PE. The first is applied to the absolute
JES, obtained from the tabulation described above and assumed
to be fully correlated across η. The second number is applied to
the relative JES, extracted from the same tabulation, which de-
pends only on η and restores the decorrelation due to η depen-
dence of the energy scale. The third number is applied to the
PDF uncertainty, provided by the CTEQ6.6 PDF error sets. In a
fourth and final step, the uncertainty due to the NLO QCD renor-
malization (μR) and factorization (μF) scales is found by letting
μR and μF vary independently between 0.5, 1 and 2 times the
average transverse momentum of the two leading jets, resulting
in nine samples drawn from a uniform distribution. In a given
PE, the data dijet selection criteria described previously are ap-
plied.
Other sources of uncertainty have been studied in separate sim-
ulations, and have not been included in the PE’s described above.
As determined by in situ studies comparing data to detector sim-
ulation [24], the jet energy resolution (JER) in ATLAS evolves from
Fig. 1. The normalized χ distributions for 340 < mjj< 520 GeV, 520 < mjj<
800 GeV, 800 < mjj< 1200 GeV, and mjj> 1200 GeV, with plotting offsets shown
in parentheses. Shown are the QCD predictions with systematic uncertainties
(bands), and data points with statistical uncertainties. The prediction for QCD with
an added quark contact term with Λ = 3.0 TeV is shown for the highest mass bin
mjj> 1200 GeV.
Fig. 2. Dijet centrality ratio, RC, as a function of mjj, with all events above a mass
of 1400 GeV plotted in the last bin. Shown are the QCD prediction with systematic
uncertainties (bands), and data points with statistical uncertainties. The prediction
for QCD with an added quark contact term with Λ = 2.0 TeV is also shown.
12% to 7% over the pT range from 60 GeV to 1 TeV. To estimate
the effect of JER smearing, the χ and RC distributions were gen-
erated with and without JER variation of this magnitude, and the
differences were found to be negligible. Detector angular resolution
effects in φ and η were studied in a similar fashion, with smear-
ing functions specific to the ATLAS calorimeter segmentation, and
also found to be negligible.
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ATLAS Collaboration / Physics Letters B 694 (2011) 327–345
331
9. Comparison of data to theory
In Fig. 1 the measured dijet χ distributions are compared to
the QCD predictions, along with 1σ systematic error bands deter-
mined from the PE’s, and statistical errors on the data. Fig. 2 shows
the measured dijet-centrality distribution and QCD prediction. The
statistical uncertainties are obtained using Poisson probabilities. In
the highest mass bins, the numerator and denominator of the ratio
typically contain 1 or 2 events each.
To evaluate the agreement between data and QCD in Figs. 1
and 2 a statistical significance test was performed using p-values.
The p-value is the probability to obtain a fit to data further from
the theoretical prediction than the observed fit, under the assump-
tion that the QCD prediction is the correct description of physics.
A chi-square goodness-of-fit is used as the test statistic, and the
p-values are derived from the ensemble of PE’s generated as de-
scribed above, including bin-to-bin correlations due to systematic
effects, but with additional statistical fluctuations. For the χ distri-
butions shown in Fig. 1, the resulting p-value for each dijet mass
bin is (from lowest to highest) 0.19, 0.11, 0.27 and 0.54, indicating
good agreement with the QCD prediction. Similarly, in Fig. 2, the
dijet RC comparison has a p-value equal to 0.85, also indicating
good agreement with the QCD prediction.
The best fit of the RC distribution in Fig. 2 is obtained for a
compositeness scale of 2.9 TeV. This is not statistically significant,
as the QCD prediction lies within the shortest 68% confidence in-
terval in 1/Λ4.
10. Determination of exclusion limits
Since no signal from new physics processes is apparent in these
distributions, limits have been obtained on the compositeness scale
Λ of quark contact interactions, based on analyses of the χ distri-
butions. The contact term hypothesis is tested in the highest dijet
mass bin in Fig. 1, which begins at mjj= 1200 GeV. For the χ dis-
tribution in this mass bin, the parameter Fχ is defined as the ratio
of the number of events in the first four χ bins to the number in
all χ bins. The upper boundary of the fourth bin is at χ = 3.32.
This choice of the bin boundary has been determined through a
MC study that varies the number of bins in the numerator, as well
as the dijet mass bin, and determines the setting that maximizes
the sensitivity to quark contact interactions, given the current in-
tegrated luminosity.
A frequentist analysis is employed as follows. Predictions of Fχ
are obtained for a range of Λ by interpolation between distinct
samples generated with different 1/Λ2values. The QCD sample
provides a bound with Λ = ∞, and additional samples are gen-
erated with Λ values of 500, 750, 1000, 1500, and 3000 GeV. A
full set of PE’s is made for each hypothesis to construct one-sided
95% CL intervals for Fχ, and the Neyman construction [25] is then
applied to obtain a limit on Λ.
The result is shown in Fig. 3. The measured value of Fχ is
shown by the dashed horizontal line. The value of Fχ expected
from QCD is the solid horizontal line, and the band around it al-
lows one to obtain the 1σ variation of the expected limit. The
dotted line is the 95% CL contour of the Fχ prediction for quark
contact interactions plus QCD, as a function of Λ and including all
systematic uncertainties. This contour decreases as a function of Λ
since, for a small Λ scale, there would be more events at low χ.
The observed limit on Λ is 3.4 TeV. This limit is found from
the point where the Fχ 95% CL contour crosses the measured Fχ
value. All values of Λ less than this value are excluded with 95%
confidence. This corresponds to a distance scale of ∼ 6 · 10−5fm,
from conversion of the limit using ¯ hc. The expected limit, found
from the crossing at the QCD prediction, is 3.5 TeV.
Fig. 3. The dashed horizontal line is the measured Fχ (see text) and the solid hor-
izontal line is the QCD prediction, with a band to illustrate a 1σ variation of the
expected limit. The dotted curve is the 95% CL exclusion contour for Fχ with quark
contact interactions, used to set the exclusion limit on Λ.
The impact of systematic uncertainties is as follows. If all sys-
tematic uncertainties were excluded, the observed limit reported
above would increase by 6% to 3.6 TeV, mainly due to the JES
uncertainty. Inclusion of NLO scales and PDF uncertainties does
not change the limit measurably, as shape differences arising from
these are well below the statistical uncertainties.
Confirming analyses have been done using a Bayesian approach
with Poisson likelihoods for all χ bins, calculated using priors flat
in 1/Λ2or 1/Λ4. These have resulted in observed exclusion limits
on Λ of 3.3 TeV and 3.2 TeV, respectively, very close to the limit
found in the frequentist analysis.
Similarly, an analysis has been performed to establish 95% CL
limits using the dijet centrality ratio shown in Fig. 2. The likeli-
hood for RC is constructed as a product of likelihoods of inner and
outer event counts for all mass bins, which is then analyzed with a
Bayesian approach similar to that of the χ Bayesian analysis. Using
priors flat in 1/Λ2(1/Λ4) the observed exclusion limit is 2.0 TeV
(also 2.0 TeV), with an expected limit of 2.6 TeV (2.4 TeV), pro-
viding an additional benchmark for comparison with other exper-
iments. A weaker limit than the one derived from the χ analysis
is expected due to the lower η acceptance associated with the RC
observable.
11. Conclusion
Dijet angular distributions have been measured by the ATLAS
experiment over a large angular range and spanning dijet masses
up to 2.8 TeV. These distributions are in good agreement with QCD
predictions. Using 3.1 pb−1of data, quark contact interactions with
a scale Λ below 3.4 TeV are excluded at the 95% CL. The sensitiv-
ity of this analysis extends significantly beyond that of previously
published studies.
Acknowledgements
We are profoundly grateful to everyone at CERN involved in
operating the LHC in such a superb way during this initial high-
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energy data-taking period. We acknowledge equally warmly all
the technical and administrative staff in the collaborating in-
stitutions without whom ATLAS could not be operated so effi-
ciently.
We acknowledge the support of ANPCyT, Argentina; Yerevan
Physics Institute, Armenia; ARC and DEST, Australia; Bundesminis-
terium für Wissenschaft und Forschung, Austria; National Academy
of Sciences of Azerbaijan; State Committee on Science & Technolo-
gies of the Republic of Belarus; CNPq and FINEP, Brazil; NSERC,
NRC, and CFI, Canada; CERN; CONICYT, Chile; NSFC, China; COL-
CIENCIAS, Colombia; Ministry of Education, Youth and Sports of the
Czech Republic, Ministry of Industry and Trade of the Czech Repub-
lic, and Committee for Collaboration of the Czech Republic with
CERN; DNRF, DNSRC and the Lundbeck Foundation, Denmark; Eu-
ropean Commission, through the ARTEMIS Research Training Net-
work; IN2P3-CNRS and CEA-DSM/IRFU, France; Georgian Academy
of Sciences; BMBF, DFG, HGF and MPG, Germany; Ministry of Ed-
ucation and Religion, through the EPEAEK program PYTHAGORAS
II and GSRT, Greece; ISF, MINERVA, GIF, DIP, and Benoziyo Center,
Israel; INFN, Italy; MEXT, Japan; CNRST, Morocco; FOM and NWO,
Netherlands; The Research Council of Norway; Ministry of Science
and Higher Education, Poland; GRICES and FCT, Portugal; Ministry
of Education and Research, Romania; Ministry of Education and
Science of the Russian Federation and State Atomic Energy Corpo-
ration ROSATOM; JINR; Ministry of Science, Serbia; Department of
International Science and Technology Cooperation, Ministry of Edu-
cation of the Slovak Republic; Slovenian Research Agency, Ministry
of Higher Education, Science and Technology, Slovenia; Ministerio
de Educación y Ciencia, Spain; The Swedish Research Council, The
Knut and Alice Wallenberg Foundation, Sweden; State Secretariat
for Education and Science, Swiss National Science Foundation, and
Cantons of Bern and Geneva, Switzerland; National Science Coun-
cil, Taiwan; TAEK, Turkey; The STFC, the Royal Society and The
Leverhulme Trust, United Kingdom; DOE and NSF, United States
of America.
Open Access
This article is published Open Access at sciencedirect.com. It
is distributed under the terms of the Creative Commons Attribu-
tion License 3.0, which permits unrestricted use, distribution, and
reproduction in any medium, provided the original authors and
source are credited.
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L. Feligioni83, C.U. Felzmann86, C. Feng32d, E.J. Feng30, A.B. Fenyuk128, J. Ferencei144b, D. Ferguson172,
J. Ferland93, B. Fernandes124a,o, W. Fernando109, S. Ferrag53, J. Ferrando118, V. Ferrara41, A. Ferrari166,
P. Ferrari105, R. Ferrari119a, A. Ferrer167a,167b, M.L. Ferrer47, D. Ferrere49, C. Ferretti87,
A. Ferretto Parodi50a,50b, F. Ferro50a,50b, M. Fiascaris118, F. Fiedler81, A. Filipˇ ciˇ c74, A. Filippas9,
F. Filthaut104, M. Fincke-Keeler169, M.C.N. Fiolhais124a,i, L. Fiorini11, A. Firan39, G. Fischer41,
P. Fischer20, M.J. Fisher109, S.M. Fisher129, J. Flammer29, M. Flechl48, I. Fleck141, J. Fleckner81,
P. Fleischmann173, S. Fleischmann20, T. Flick174, L.R. Flores Castillo172, M.J. Flowerdew99, F. Föhlisch58a,
M. Fokitis9, T. Fonseca Martin16, J. Fopma118, D.A. Forbush138, A. Formica136, A. Forti82, D. Fortin159a,
J.M. Foster82, D. Fournier115, A. Foussat29, A.J. Fowler44, K. Fowler137, H. Fox71, P. Francavilla122a,122b,
S. Franchino119a,119b, D. Francis29, M. Franklin57, S. Franz29, M. Fraternali119a,119b, S. Fratina120,
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G. Gagliardi50a,50b, P. Gagnon61, C. Galea98, E.J. Gallas118, M.V. Gallas29, V. Gallo16, B.J. Gallop129,
P. Gallus125, E. Galyaev40, K.K. Gan109, Y.S. Gao143,p, V.A. Gapienko128, A. Gaponenko14,
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H. Garitaonandia105, V. Garonne29, J. Garvey17, C. Gatti47, G. Gaudio119a, O. Gaumer49, B. Gaur141,
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T. Hansl-Kozanecka137, P. Hansson143, K. Hara160, G.A. Hare137, T. Harenberg174, R. Harper139,
R.D. Harrington21, O.M. Harris138, K. Harrison17, J.C. Hart129, J. Hartert48, F. Hartjes105, T. Haruyama66,
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J. Mechnich105, M. Mechtel174, M. Medinnis41, R. Meera-Lebbai111, T. Meguro116, R. Mehdiyev93,
S. Mehlhase41, A. Mehta73, K. Meier58a, J. Meinhardt48, B. Meirose79, C. Melachrinos30,
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C. Menot29, E. Meoni11, D. Merkl98, P. Mermod118, L. Merola102a,102b, C. Meroni89a, F.S. Merritt30,
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M. Mikestikova125, B. Mikulec49, M. Mikuž74, D.W. Miller143, R.J. Miller88, W.J. Mills168, C. Mills57,
A. Milov171, D.A. Milstead146a,146b, D. Milstein171, S. Mima110, A.A. Minaenko128, M. Miñano167a,167b,
I.A. Minashvili65, A.I. Mincer108, B. Mindur37, M. Mineev65, Y. Ming130, L.M. Mir11, G. Mirabelli132a,
L. Miralles Verge11, S. Misawa24, S. Miscetti47, A. Misiejuk76, A. Mitra118, J. Mitrevski137,
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N. Möser20, B. Mohn13, W. Mohr48, S. Mohrdieck-Möck99, A.M. Moisseev128,ax, R. Moles-Valls167a,167b,
J. Molina-Perez29, L. Moneta49, J. Monk77, E. Monnier83, S. Montesano89a,89b, F. Monticelli70,
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J. Morin75, Y. Morita66, A.K. Morley29, G. Mornacchi29, M.-C. Morone49, S.V. Morozov96, J.D. Morris75,
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S.V. Mouraviev94, T.H. Moye17, E.J.W. Moyse84, M. Mudrinic12b, F. Mueller58a, J. Mueller123,
K. Mueller20, T.A. Müller98, D. Muenstermann42, A. Muijs105, A. Muir168, A. Munar120, Y. Munwes153,
K. Murakami66, R. Murillo Garcia163, W.J. Murray129, I. Mussche105, E. Musto102a,102b, A.G. Myagkov128,
M. Myska125, J. Nadal11, K. Nagai160, K. Nagano66, Y. Nagasaka60, A.M. Nairz29, D. Naito110,
K. Nakamura155, I. Nakano110, G. Nanava20, A. Napier161, M. Nash77,ag, I. Nasteva82, N.R. Nation21,
T. Nattermann20, T. Naumann41, F. Nauyock82, G. Navarro162, S.K. Nderitu85, H.A. Neal87, E. Nebot80,
P. Nechaeva94, A. Negri119a,119b, G. Negri29, A. Nelson64, S. Nelson143, T.K. Nelson143, S. Nemecek125,
P. Nemethy108, A.A. Nepomuceno23a, M. Nessi29, S.Y. Nesterov121, M.S. Neubauer165, L. Neukermans4,
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I.M. Nugent159a, A.-E. Nuncio-Quiroz20, G. Nunes Hanninger20, T. Nunnemann98, E. Nurse77,
T. Nyman29, S.W. O’Neale17,ax, D.C. O’Neil142, V. O’Shea53, F.G. Oakham28,h, H. Oberlack99, J. Ocariz78,
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A. Oyarzun31b, O.K. Øye13, V.E. Ozcan77, K. Ozone66, N. Ozturk7, A. Pacheco Pages11,
C. Padilla Aranda11, E. Paganis139, F. Paige24, K. Pajchel117, S. Palestini29, J. Palla29, D. Pallin33,
A. Palma124a,c, J.D. Palmer17, M.J. Palmer27, Y.B. Pan172, E. Panagiotopoulou9, B. Panes31a,
N. Panikashvili87, V.N. Panin107, S. Panitkin24, D. Pantea25a, M. Panuskova125, V. Paolone123,
A. Paoloni133a,133b, Th.D. Papadopoulou9, A. Paramonov5, S.J. Park54, W. Park24,aj, M.A. Parker27,
S.I. Parker14, F. Parodi50a,50b, J.A. Parsons34, U. Parzefall48, E. Pasqualucci132a, A. Passeri134a,
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S. Patricelli102a,102b, T. Pauly29, L.S. Peak150, M. Pecsy144a, M.I. Pedraza Morales172, S.J.M. Peeters105,
S.V. Peleganchuk107, H. Peng172, R. Pengo29, A. Penson34, J. Penwell61, M. Perantoni23a, K. Perez34,ad,
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