ATLAS search for new phenomena in dijet mass and angular distributions using pp collisions at √ s = 7 TeV

: Mass and angular distributions of dijets produced in LHC proton-proton collisions at a centre-of-mass energy √ s = 7 TeV have been studied with the ATLAS detector using the full 2011 data set with an integrated luminosity of 4.8 fb − 1 . Dijet masses up to ∼ 4 . 0 TeV have been probed. No resonance-like features have been observed in the dijet mass spectrum, and all angular distributions are consistent with the predictions of QCD. Exclusion limits on six hypotheses of new phenomena have been set at 95% CL in terms of mass or energy scale, as appropriate. These hypotheses include excited quarks below 2.83 TeV, colour octet scalars below 1.86 TeV, heavy W bosons below 1.68 TeV, string resonances below 3.61 TeV, quantum black holes with six extra space-time dimensions for quantum gravity scales below 4.11 TeV, and quark contact interactions below a compositeness scale of 7.6 TeV in a destructive interference scenario.


Introduction
and LAr/tungsten modules to provide electromagnetic and hadronic energy measurements, respectively.

Overview of the dijet mass and angular analyses
The dijet invariant mass, m jj , is calculated from the vectorial sum of the four-momenta of the two highest p T jets in the event. A search for resonances is performed on the m jj spectrum, employing a data-driven background estimate that does not rely on QCD calculations.
The angular analyses employ ratio observables and normalised distributions to substantially reduce their sensitivity to systematic uncertainties, especially those associated with the jet energy scale (JES), parton distribution functions (PDFs) and the integrated luminosity. Unlike the m jj analysis, the angular analyses use a background estimate based on QCD. The basic angular variables and distributions used in the previous ATLAS dijet studies [18,23] are also employed in this analysis. A convenient variable that emphasises the central scattering region is χ. If E is the jet energy and p z is the z-component of the jet's momentum, the rapidity of the jet is given by y ≡ 1 2 ln( E+pz E−pz ). In a given event, the rapidities of the two highest p T jets in the pp centre-of-mass frame are denoted by y 1 and y 2 , and the rapidities of the jets in the dijet CM frame are y * = 1 2 (y 1 − y 2 ) and −y * . The longitudinal motion of the dijet CM system in the pp frame is described by the rapidity boost, y B = 1 2 (y 1 + y 2 ). The variable χ is: χ ≡ exp(|y 1 − y 2 |) = exp(2|y * |). The χ distributions predicted by QCD are relatively flat compared to those produced by new phenomena. In particular, many NP signals are more isotropic than QCD, causing them to peak at low values of χ. For the χ distributions in the current studies, the rapidity coverage extends to |y * | < 1.7 corresponding to χ < 30.0. This interval is divided into 11 bins, with boundaries at χ i = exp(0.3 × i) with i = 0, ..., 11, where 0.3 corresponds to three times the coarsest calorimeter segmentation, ∆η = 0.1. These χ distributions are measured in five dijet mass ranges with the expectation that low m jj bins will be dominated by QCD processes and NP signals would be found in higher mass bins. The distributions are normalised to unit area, restricting the analysis to a shape comparison.
To facilitate an alternate approach to the study of dijet angular distributions, it is useful to define a single-parameter measure of isotropy as the fraction F χ ≡ N central N total , where N total is the number of events containing a dijet that passes all selection criteria, and N central is the subset of these events in which the dijet enters a defined central region. It was found that |y * | < 0.6, corresponding to χ < 3.32, defines an optimal central region where many new processes would be expected to deviate from QCD predictions. This value corresponds to the upper boundary of the fourth bin in the χ distribution.
As in previous ATLAS studies [18], the current angular analyses make use of the F χ (m jj ) distribution, which consists of F χ binned finely in m jj : using the same mass binning as the dijet mass analysis. This distribution is more sensitive to mass-dependent changes in the rate of centrally produced dijets than the χ distributions but is less sensitive to the detailed angular shape. The distribution of F χ (m jj ) in the central region defined above is similar to the m jj spectrum, apart from an additional selection criterion on the boost of the system (as explained in section 4). Dijet distributions from collision data are not corrected (unfolded) for detector resolution effects. Instead, the measured distributions are compared to theoretical predictions passed through detector simulation.

Jet calibration
The calorimeter cell structure of ATLAS is designed to follow the shower development of jets. Jets are reconstructed from topological clusters (topoclusters) [28] that group together cells based on their signal-to-noise ratio. The default jet algorithm in ATLAS is the anti-k t algorithm [29,30]. For the jet collection used in this analysis, the distance parameter of R = 0.6 is chosen. Jets are first calibrated at the electromagnetic scale (EM calibration), which accounts correctly for the energy deposited by electromagnetic showers but does not correct the scale for hadronic showers.
The hadronic calibration is applied in steps, using a combination of techniques based on Monte Carlo (MC) simulation and in situ measurements [31]. The first step is the pileup correction which accounts for the additional energy due to collisions in the same bunch crossing as the signal event (in-time) or in nearby bunch crossings (out-of-time). Since the pile-up is a combination of these effects, the net correction may add or subtract energy from the jet. In the second step, the position of the jet origin is corrected for differences between the geometrical centre of the detector and the collision vertex. The third step is a jet energy correction using factors that are functions of the jet energy and pseudorapidity. These calibration factors are derived from MC simulation using a detailed description of the ATLAS detector geometry, which simulates the main detector response effects. The EM and hadronic calibration steps above are referred to collectively as the "EM+JES" scheme [32], which restores the hadronic jet response in MC to within 2%.
The level of agreement between data and MC simulation is further improved by the application of calibration steps based on in situ studies. First, the relative response in |η| is equalised using an inter-calibration method obtained from balancing the transverse momenta of jets in dijet events [33]. Then the absolute energy response is brought into closer agreement with MC simulation by a combination of various techniques based on momentum balancing methods between photons or Z bosons and jets, and between highmomentum jets and a recoil system of low-momentum jets. This completes all the stages of the jet calibration.
The jet energy scale uncertainty is determined for jets with transverse momenta above 20 GeV and |η| < 4.5, based on the uncertainties of the in situ techniques and on systematic variations in MC simulations. For the most general case, covering all jet measurements made in ATLAS, the correlations among JES uncertainties are described by a set of 58 sources of systematic uncertainty (nuisance parameters). Uncertainties due to pile-up, jet flavour, and jet topology are described by five additional nuisance parameters. The total uncertainty from in situ techniques for central jets with a transverse momentum of 100 GeV is as low as 1% and rises to about 4% for jets with transverse momentum above 1 TeV.
For the high-p T dijet measurements made in the current analysis, the number of nuisance parameters is reduced to 14, while keeping a correlation matrix and total magnitude equivalent to the full configuration. This is achieved using a procedure that diagonalises the total covariance matrix found from in situ techniques, selects the largest eigenvalues as effective nuisance parameters, and groups the remaining parameters into one additional term.
The jet energy resolution is estimated both in data and in simulation using transverse momentum balance studies in dijet events, and they are found to be in good agreement [34]. Monte Carlo studies are used to assess the dijet mass resolution. Jets constructed from final state particles are compared to the calorimeter jets obtained after the same particles have been passed through full detector simulation. While the dijet mass resolution is found to be 10% at 0.20 TeV, it is reduced to approximately 5% within the range of high dijet masses considered in the current studies.

Event selection criteria
The triggers employed for this study select events that have at least one large (100 GeV or more) transverse energy deposition in the calorimeter. These triggers are also referred to as "single jet" triggers. To match the data rate to the processing and storage capacity available to ATLAS, a number of triggers with low-p T thresholds were "prescaled". For these triggers only a preselected fraction of all events passing the threshold is recorded.
A single, unprescaled trigger is used for the dijet mass spectrum analysis. This single trigger is also used for the angular analyses at high dijet mass, but in addition several prescaled triggers are used at lower dijet masses. Each χ distribution is assigned a unique trigger, chosen to maximise the statistics, leading to a different effective luminosity for each distribution. Similar choices are made for the F χ (m jj ) distribution, assigning triggers to specific ranges of m jj to maximise the statistics in each range. In all analyses, kinematic selection criteria ensure a trigger efficiency exceeding 99% for the events under consideration.
Events are required to have a primary collision vertex defined by two or more charged particle tracks. In the presence of additional pp interactions, the primary collision vertex chosen is the one with the largest scalar sum of p 2 T for its associated tracks. In this analysis, the two highest-p T jets are invariably associated with this largest sum of p 2 T collection of tracks, which ensures that the correct collision vertex is used to reconstruct the dijet. Events are rejected if the data from the electromagnetic calorimeter have a topology as expected for non-collision background, or there is evidence of data corruption [35]. There must be at least two jets within |y| < 4.4 in the event, and all jets with |y| ≥ 4.4 are discarded. The highest p T jet is referred to as the "leading jet" (j 1 ), and the second highest as the "next-to-leading jet" (j 2 ). These two jets are collectively referred to as the "leading jets". Following the criteria in ref. [35], there must be no poorly measured jets with p T greater than 30% of the p T of the next-to-leading jet for events to be retained. Poorly measured jets correspond to energy depositions in regions where the energy measurement is known to be inaccurate. Furthermore, if either of the leading jets is not attributed to in-time energy depositions in the calorimeters, the event is rejected.
A selection has been implemented to avoid a defect in the readout electronics of the electromagnetic calorimeter in the region from −0.1 to 1.5 in η, and from −0.9 to −0.5 in φ that occurred during part of the running period. The average response for jets in this region is 20% to 30% too low. For the m jj analysis, events in the affected running period with jets near this region are rejected if such jets have a p T greater than 30% of the next-to-leading jet p T . This requirement removes 1% of the events. A similar rejection has been made for the angular analysis. In this case the complete η slice from −0.9 to −0.5 in φ is excluded in order to retain the shape of the distributions. The event reduction during run periods affected by the defect is 13%, and the overall reduction in the data set due to this effect is 4%.
Additional kinematic selection criteria are used to enrich the sample with events in the hard-scattering region of phase space. For the dijet mass analysis, events must satisfy |y * | < 0.6 and |η 1,2 | < 2.8 for the leading jets, and m jj > 850 GeV.
For the angular analyses, events must satisfy |y * | < 1.7 and |y B | < 1.1, and m jj > 800 GeV. The combined y * and y B criteria limit the rapidity range of the leading jets to |y 1,2 | < 2.8. This |y B | selection does not affect events with dijet mass above 2.8 TeV since the phase space is kinematically constrained. The kinematic selection also restricts the minimum p T of jets entering the analysis to 80 GeV. Since at lowest order y B = 1 2 ln( x 1 x 2 ) and m 2 jj = x 1 x 2 s, with x 1,2 the parton momentum fractions of the colliding protons, the combined m jj and y B criteria result in limiting the effective x 1,2 -ranges in the convolution of the matrix elements with the PDFs. The QCD matrix elements for dijet production lead to χ distributions that are approximately flat. Without the selection on y B , the χ distributions predicted by QCD would have a slope becoming more pronounced for the lower m jj bins. Restricting the x 1,2 -ranges of the PDFs reduces this shape distortion, and also reduces the PDF and jet energy scale uncertainties associated with each χ bin of the final distribution.

Comparing the dijet mass spectrum to a smooth background
In the dijet mass analysis, a search for resonances in the m jj spectrum is made by using a data-driven background estimate. The observed dijet mass distribution after all selection cuts is shown in figure 1. Also shown in the figure are the predictions for an excited quark for three different mass hypotheses [1,2]. The m jj spectrum is fit to a smooth functional form, where the p i are fit parameters, and x ≡ m jj / √ s. In previous studies, ATLAS and other experiments [15,17,19,23] have found this ansatz to provide a satisfactory fit to the QCD prediction of dijet production. The use of a full Monte Carlo QCD background prediction would introduce theoretical and systematic uncertainties of its own, whereas this smooth background form introduces only the uncertainties associated with its fit parameters. A feature of the functional form used in the fitting is that it allows for smooth background variations but does not accommodate localised excesses that could indicate the presence of NP signals. However, the effects of smooth deviations from QCD, such as contact interactions, could be absorbed by the background fitting function, and therefore the m jj analysis is used only to search for resonant effects. The χ 2 -value of the fit is 17.7 for 22 degrees of freedom, and the reduced χ 2 is 0.80. The middle part of figure 1 shows the data minus the background fit, divided by the fit. The lower part of figure 1 shows the significance, in standard deviations, of the difference between the data and the fit in each bin. The significance is calculated taking only statistical uncertainties into account, and assuming that the data follow a Poisson distribution. For each bin a p-value is determined by assessing the probability of the background fluctuating higher than the observed excess or lower than the observed deficit. This p-value is transformed to a significance in terms of an equivalent number of standard deviations (the z-value) [36]. Where there is an excess (deficit) in data in a given bin, the significance is plotted as positive (negative) 2 . To test the degree of consistency between the data and the fitted background, the p-value of the fit is determined by calculating the χ 2 -value from the data and comparing this result to the χ 2 distribution obtained from pseudo-experiments drawn from the background fit, as described in a previous publication [23]. The resulting p-value is 0.73, showing that there is good agreement between the data and the fit.
As a more sensitive test, the BumpHunter algorithm [37,38] is used to establish the presence or absence of a resonance in the dijet mass spectrum, as described in greater detail in previous publications [23,24]. Starting with a two-bin window, the algorithm increases the signal window and shifts its location until all possible bin ranges, up to half the mass range spanned by the data, have been tested. The most significant departure from the smooth spectrum ("bump") is defined by the set of bins that have the smallest probability of arising from a background fluctuation assuming Poisson statistics.
The BumpHunter algorithm accounts for the so-called "look-elsewhere effect" [39], by performing a series of pseudo-experiments drawn from the background estimate to determine the probability that random fluctuations in the background-only hypothesis would create an excess anywhere in the spectrum at least as significant as the one observed. Furthermore, to prevent any NP signal from biasing the background estimate, if the most significant local excess from the background fit has a p-value smaller than 0.01, this region is excluded and a new background fit is performed. No such exclusion is needed for this data set.
The most significant discrepancy identified by the BumpHunter algorithm in the observed dijet mass distribution in figure 1 is a four-bin excess in the interval 2.21 TeV to 2.88 TeV. The probability of observing such an excess or larger somewhere in the mass spectrum for a background-only hypothesis is 0.69. This test shows no evidence for a resonance signal in the m jj spectrum.

QCD predictions for dijet angular distributions
In the dijet angular analyses, the QCD prediction is based on MC generation of event samples which cover the kinematic range in χ and m jj spanned by the selected dijet events. The QCD hard scattering interactions are simulated using the Pythia 6 [40] event generator with the ATLAS AUET2B LO** tune [41] which uses the MRSTMCal [42] modified leading-order (LO) parton distribution functions (PDFs).
To incorporate detector effects, these QCD events are passed through a fast detector simulation, ATLFAST 2.0 [43], which employs FastCaloSim [44] for the simulation of electromagnetic and hadronic showers in the calorimeter. Comparisons with detailed simulations of the ATLAS detector [45,46] using the Geant4 package [46] show no differences in the angular distributions exceeding 5%.
To simulate in-time pile-up, separate samples of inelastic interactions are generated using Pythia 8 [47], and these samples are passed through the full detector simulation. To simulate QCD events in the presence of pile-up, hard scattering events are overlaid with µ inelastic interactions, where µ is Poisson distributed, and the distribution of µ is chosen to match the distribution of average number of interactions per bunch crossings in data. The combined MC events, containing one hard interaction and several soft interactions, are then reconstructed in the same way as collision data and are subjected to the same event selection criteria as applied to collision data.
Bin-by-bin correction factors (K-factors) are applied to the angular distributions de-rived from MC calculations to account for NLO contributions. These K-factors are derived from dedicated MC samples and are defined as the ratio N LO M E /P Y T SHOW . The N LO M E sample is produced using NLO matrix elements in NLOJET++ [48][49][50] with the NLO PDF from CT10 [51]. The P Y T SHOW sample is produced with the Pythia 6 generator restricted to leading-order matrix elements and with parton showering but with non-perturbative effects turned off. This sample also uses the AUET2B LO** tune. The angular distributions generated with the full Pythia simulation include various non-perturbative effects including hadronisation, underlying event, and primordial k ⊥ . The K-factors defined above are designed to retain these effects while adjusting for differences in the treatment of perturbative effects. The full Pythia predictions of angular distributions are multiplied by these bin-wise K-factors to obtain reshaped spectra that include corrections originating from NLO matrix elements. K-factors are applied to χ distributions before normalising them to unit area. The K-factors change the normalised χ distributions by 2% at low dijet mass, by as much as 11% in the highest dijet mass bins, and the effect is largest at low χ. The K-factors for F χ (m jj ) are close to unity for dijet masses of around 1 TeV, but increase with dijet mass, and are as large as 20% for dijet masses of 4 TeV. Electroweak corrections are not included in the theoretical predictions [52]. The χ distributions are compared to the predictions from QCD, which include all systematic uncertainties, and the signal predictions of one particular NP model, a quantum black hole (QBH) scenario with a quantum gravity mass scale of 4.0 TeV and six extra dimensions [7,8].
Pseudo-experiments are used to convolve statistical, systematic and theoretical uncertainties on the QCD predictions, as has been done in previous studies of this type [18]. The primary sources of theoretical uncertainty are NLO QCD renormalisation and factorisation scales, and PDF uncertainties. The QCD scales are varied by a factor of two independently around their nominal values, which are set to the mean p T of the leading jets, while the PDF uncertainties are determined using CT10 NLO PDF error sets [53]. The resulting bin-wise uncertainties for the cross-section normalised χ distributions can be as high as 8% for the combined NLO QCD scale variations and are typically below 1% for the PDF uncertainties. These theoretical uncertainties are convolved with the JES uncertainty and applied to all MC angular distributions. Other experimental uncertainties such as those due to pile-up and to the jet energy and angular resolutions have been investigated and found to be negligible. The JES uncertainties are largest at low χ and are as small as 5% for the lowest dijet mass bin but increase to above 15% for the highest bin. Variations based on the resulting systematic uncertainties are used in generating statistical ensembles for the estimation of p-values when comparing QCD predictions to data. A statistical analysis is performed on each of the five χ distributions to test the overall consistency between data and QCD predictions. A binned log-likelihood is calculated for each distribution assuming that the sample consists only of QCD dijet production. The expected distribution of this likelihood is then determined using pseudo-experiments drawn from the QCD MC sample and convolved with the systematic uncertainties as discussed above. Finally the p-value is defined as the probability of obtaining a log-likelihood value less than the value observed in data.
The p-values determined from the observed likelihoods are shown in table 1. These indicate that there is no statistically significant evidence for new phenomena in the χ distributions, and that these distributions are in reasonable agreement with QCD predictions.
As with the dijet resonance analysis, the BumpHunter algorithm is applied to the five χ distributions separately, in this case to test for the presence of features that might indicate disagreement with the QCD prediction. The results are shown in table 1. In this particular application, the BumpHunter is required to start from the first χ bin, and the excess must be at least three bins wide. For each of the bin combinations, the binomial p-value for observing the data given the QCD-background-only hypothesis is calculated. The bin sequence with the smallest binomial p-value is listed in table 1. Statistical and systematic uncertainties, and look-elsewhere effects, are included using pseudo-experiments drawn from the QCD background. For each of the pseudo-experiments the most discrepant bin combination is found and its p-value is used to construct the expected binomial p-value distribution. The final BumpHunter p-value is then defined as the probability of finding a binomial p-value as extreme as the one observed in data. The p-values listed in the last column of table 1 indicate that the data are consistent with the QCD prediction in all five mass bins.  Table 1. Comparing χ distributions to QCD predictions. The abbreviations in the first line of the table stand for "log-likelihood" (LL), and "BumpHunter" (BH). The second line labels the "p-values" (p-value) and the "most discrepant region" (Discrep).
In addition, the BumpHunter algorithm is applied to all χ distributions at once, which increases the effect of the correction for the look-elsewhere effect. The most discrepant region in all distributions is in bins 1-9 of the 800-1200 GeV mass distribution. The resulting p-value, including the look-elsewhere effect, is now 0.43, again indicating good agreement with QCD predictions.
8 Comparing the F χ (m jj ) distribution to the QCD prediction The observed F χ (m jj ) data distribution is shown in figure 3, where it is compared to the QCD prediction, which includes all systematic uncertainties. Also shown in the figure is the expected behaviour of F χ (m jj ) if a contact interaction with the compositeness scale Λ = 7.5 TeV were present [54][55][56]. Furthermore the predictions for an excited quark with a mass of 2.5 TeV and a QBH signal with M D = 4.0 TeV are shown. The blue vertical line at 1.8 TeV included in figure 3 indicates the mass boundary above which the search phase of the analysis is performed, as explained below.
The observed F χ (m jj ) distribution is obtained by forming the finely-binned m jj distributions for N central and N total -the "numerator" and "denominator" distributions of F χ (m jj ) -separately and taking the ratio. The handling of systematic uncertainties, including JES, PDF and scale uncertainties, uses a procedure similar to that for the χ distributions.
Two statistical tests are applied to the high-mass region to determine whether the data are compatible with the QCD prediction. The first test uses a binned likelihood, which includes the systematic uncertainties, and is constructed assuming the presence of QCD processes only. The p-value calculated from this likelihood is 0.38, indicating that these data are in agreement with the QCD prediction.  The second test consists of applying the BumpHunter and TailHunter algorithms [37,38] to the F χ (m jj ) distributions, including systematic uncertainties and assuming binomial statistics. For this test only data with dijet masses above 1.8 TeV, associated with the single unprescaled trigger, are used to obtain a high sensitivity at high mass and to avoid diluting the test with the large number of low-mass bins. The test scans the data using windows of varying widths and identifies the window with the largest excess of events with respect to the background. The BumpHunter finds the most discrepant interval to be from 1.80 TeV to 2.88 TeV, with a p-value of 0.20. The TailHunter finds the most discrepant interval to be from 1.80 TeV onwards, with a p-value of 0.21. The p-values indicate that there is no significant excess in the data .
A number of these NP models are available in the Pythia 6 event generator. In these cases, the corresponding MC samples are generated using the AUET2B LO** tune and the MRSTMCal PDF. For NP models provided by other event generators, with other PDFs, partons originating from the initial two-parton interaction are used as input to Pythia which performs parton showering and the remaining event generation steps. In all cases, the renormalisation and factorisation scales are set to the mean p T of the leading jets.
The quark contact interaction, CI, is used to model the appearance of kinematic properties that characterise quark compositeness. In the current analysis, only destructive interference is studied, but constructive interference is expected to give less conservative limits. Pythia 6 is used to create MC event samples for distinct values of the compositeness scale, Λ.
Excited quarks, q * , a possible manifestation of quark compositeness, are also simulated in all decay modes with Pythia 6 for selected values of the q * mass. Excited quarks are assumed to decay to common quarks via standard model couplings, leading to gluon emission approximately 83% of the time. Recent studies comparing this benchmark model to the same excited quark model in Pythia 8 show that the q * m jj distribution in Pythia 8 is significantly broader than that in Pythia 6. The Pythia authors have identified a long-standing misapplication of QCD p T -ordered final state radiation (FSR) vetoing in Pythia 6, which is resolved in Pythia 8. The q * m jj distributions from Pythia 6 can be brought into close correspondence with Pythia 8 by setting the Pythia 6 MSTJ(47) parameter to zero, restoring the correct behaviour for final state radiation. The resulting widening of the peak affects the search sensitivity and exclusion limits. The q * MC samples used in the current studies are generated using both the default and corrected Pythia 6 settings, to determine the impact on the q * exclusion limit.
The colour octet scalar model, s8, is a typical example of possible exotic coloured resonances decaying to two gluons. MadGraph 5 [61] with the CTEQ6L1 PDF [62] is employed to generate parton-level event samples at leading-order approximation for a selection of s8 masses, which are used as input to Pythia 6.
A model for quantum black holes, QBH, that decay to two jets is simulated using BlackMax [63] with the CT10 PDF to produce a simple two-body final state scenario of quantum gravitational effects at the reduced Planck Scale M D , with n = 6 extra spatial dimensions. The QBH model is used as a benchmark to represent any quantum gravitational effect that produces events containing dijets. Event samples for selected values of M D are used as input to Pythia for further processing.
The first new NP phenomenon used in the current dijet analysis, the production of heavy charged gauge bosons, W ′ , has been sought in events containing a charged lepton (electron or muon) and a neutrino [59,60], but no evidence has been found. In the current studies, dijet events are searched for the decays of W ′ to qq ′ . The specific model used in this study [57,58] assumes that the W ′ has V-A SM couplings but does not include interference between the W ′ and the W . The W ′ signal sample is generated with the Pythia 6 event generator. Instead of the LO cross section values, the NNLO electroweakcorrected cross section values [60,[64][65][66] calculated using the MSTW2008 PDF [67], are used in this analysis. For a given W ′ mass, the width of the resonance in m jj is very similar to that of the q * , and the angular distribution peaks at low χ. The limit analysis for this W ′ model includes the branching ratio to the chosen qq ′ final state and, for each simulated mass, this fraction is taken from Pythia 6.
The second new NP model considered, string resonances (SR), results from excitations of quarks and gluons at the string level [9][10][11][12]. The dominant decay mode is to qg, and the SR model described in ref. [11] is implemented in the CalcHEP generator [68] with the MRSTMCal PDF. As with other models, MC samples are created for selected values of the mass parameter, m SR , by passing the CalcHEP output at parton level to Pythia 6.
All MC signal samples are passed through fast detector simulation using ATLFAST 2.0, except for string resonances, which are fully simulated using Geant4.

Limits on new resonant phenomena from the m jj distribution
For each NP process under study, Monte Carlo samples have been simulated at a number of selected mass points, m NP . The Bayesian method documented in ref.
[23] is applied to data at these same mass points to set a 95% CL limit on the cross section times acceptance, σ × A, for the NP signal as a function of m NP , using a prior constant in signal strength. The limit on σ × A from data is interpolated between mass points to create a continuous curve in m jj . The exclusion limit on the mass (or energy scale) of the given NP signal occurs at the value of m jj where the limit on σ × A from data is the same as the theoretical value, which is derived by interpolation between the generated mass values.
This form of analysis is applicable to all resonant phenomena where the NP couplings are strong compared to the scale of perturbative QCD at the signal mass, so that interference with QCD terms can be neglected. The acceptance calculation includes all reconstruction steps and analysis cuts described in section 4. For all resonant models except for the W ′ , all decay modes have been simulated so that the branching ratio into dijets is implicitly included in the acceptance through the analysis selection. For the W ′ model, only dijet final states have been simulated, and the branching ratio is included in the cross section instead of in the acceptance.
The effects of systematic uncertainties due to luminosity, acceptance, and jet energy scale are included. The luminosity uncertainty for the 2011 data is 3.9% [25] and is combined in quadrature with the acceptance uncertainty. The correlated systematic uncertainties corresponding to the 14 JES nuisance parameters are added in quadrature and represented by a single nuisance parameter which shifts the resonance mass peaks by less than 4%. The background parameterisation uncertainty is taken from the fit results, as described in ref. [23]. The effect of the jet energy resolution uncertainty is found to be negligible.
These uncertainties are incorporated into the fit by varying all sources according to Gaussian probability distributions and convolving them with the posterior probability distribution. Credibility intervals are then calculated numerically from the resulting convolutions. No uncertainties are associated with the theoretical model, as in each case the  . The 95% CL upper limits on σ × A as a function of particle mass (black filled circles) using m jj . The black dotted curve shows the 95% CL upper limit expected in the absence of any resonance signal, and the green and yellow bands represent the 68% and 95% contours of the expected limit, respectively. Theoretical predictions of σ × A are shown (dashed) in (a) for excited quarks, and in (b) for colour octet scalars. For a given NP model, the observed (expected) limit occurs at the crossing of the dashed σ × A curve with the observed (expected) 95% CL upper limit curve.
NP model is a benchmark that incorporates a specific choice of model parameters, PDF set, and MC tune. Previous ATLAS studies using the q * theoretical prediction [23] showed that the variation among three different choices of MC tune and PDF set was less than 4% for the expected limits.
The resulting limits for excited quarks, based on the corrected Pythia 6 samples (as explained in section 9), are shown in figure 4(a). The acceptance A ranges from 40% to 51% for m q * between 1.2 TeV and 4.0 TeV, and is never lower than 46% for masses above 1.4 TeV. The largest reduction in acceptance arises from the rapidity selection criteria. The expected lower mass limit at 95% CL for q * is 2.94 TeV, and the observed limit is 2.83 TeV. For comparison, this limit has also been determined using Pythia 6 samples with the default q * settings, leading to narrower mass peaks. The expected limit determined from these MC samples is 0.1 TeV higher than the limit based on the corrected samples. This shift is an approximate indicator of the fractional correction that is expected when comparing the current ATLAS results to all previous analyses that found q * mass limits using Pythia 6 and p T -ordered final state radiation without corrections, including all previous ATLAS results.
The limits for colour octet scalars are shown in figure 4(b). The expected mass limit at 95% CL is 1.97 TeV, and the observed limit is 1.86 TeV. For this model the acceptance values vary between 34% and 48% for masses between 1.3 TeV and 4.0 TeV.
The limits for heavy charged gauge bosons, W ′ , are shown in figure 5(a)  . In (a), 95% CL upper limits on σ × A × BR as a function of particle mass (black filled circles) from m jj analysis are shown for heavy gauge bosons, W ′ . The black dotted curve shows the 95% CL upper limit expected in the absence of any resonance signal, and the green and yellow bands represent the 68% and 95% contours of the expected limit, respectively. The observed (expected) limit occurs at the crossing of the dashed theoretical σ ×A× BR curve with the observed (expected) 95% CL upper limit curve. In (b), 95% CL upper limits on σ × A are shown for string resonances, SR, with the equivalent set of contours for this model, and the same method of limit determination. model, only final states with dijets have been simulated. The branching ratio, BR, to the studied qq ′ final state varies little with mass and is 0.75 for m W ′ values of 1.1 TeV to 3.6 TeV, and the acceptance ranges from 29% to 36%. The expected mass limit at 95% CL is 1.74 TeV, and the observed limit is 1.68 TeV. This is the first time that an ATLAS limit on W ′ production is set using the dijet mass distribution. Searches for leptonic decays of the W ′ are however expected to be more sensitive.
The W ′ hypothesis used in the current study assumes SM couplings to quarks. If a similar model were to predict stronger couplings, for example, figure 5(a) could be used to estimate the new mass limit by shifting the theoretical curve upward by the ratio of the squared couplings. Alternately, the current limit on W ′ decaying to dijets could be of interest for comparison with leptophobic W ′ models, where all final states would be hadronic [69][70][71][72].
The limits for string resonances are shown in figure 5(b). The SR acceptance ranges from 45% to 48% for masses varying from 2.0 TeV to 5.0 TeV. The expected mass limit at 95% CL is 3.47 TeV, and the observed limit is 3.61 TeV.
Tables with acceptance values and limits for all models discussed here can be found in appendix A.
11 Model-independent limits on dijet resonance production As in previous dijet resonance analyses, limits on dijet resonance production are determined here using a Gaussian resonance shape hypothesis. Limits are set for a collection of hypothetical signals that are assumed to be Gaussian-distributed in m jj with means (m G ) ranging from 1.0 TeV to 4.0 TeV and with standard deviations (σ G ) from 7% to 15% of the mean.
Systematic uncertainties are treated using the same methods as applied in the modeldependent limit setting described above. The only difference between the Gaussian analysis and the standard analysis is that the decay of the dijet final state is not simulated. In place of this, it is assumed that the dijet signal mass distribution is Gaussian in shape, and the JES uncertainty is modelled as an uncertainty of 4% in the central value of the Gaussian signal. This approach has been validated by shifting the energy of all jets in Pythia 6 signal templates by their JES uncertainty and evaluating the relative shift of the mass peak. The resulting limits on σ×A for the Gaussian template model are shown in figure 6 and detailed in table 2. These results may be utilised to set limits on NP models beyond those considered in the current studies, under the condition that their signal shape approaches a Gaussian distribution after applying the kinematic selection criteria on y * , m jj and η of the leading jets (section 4). The acceptance should include the branching ratio of the particle decaying into dijets and the physics selection efficiency. The ATLAS m jj resolution is about 5%, hence NP models with a width smaller than 7% should be compared to the 7% column of table 2. Models with a greater width should use the column that best matches their width. A detailed description of the recommended procedure, including the treatment of detector resolution effects, is given in ref. [24].

Limits on CI and QBH from the χ distributions
The χ distribution in the highest mass bin of figure 2 is used to set 95% CL limits on two NP hypotheses, CI and QBH.
In the contact interaction analysis, four MC samples of QCD production modified by a contact interaction are created for values of Λ ranging from 4.0 TeV to 10.0 TeV. For the CI distributions, QCD K-factors are applied to the QCD-only component of the cross section, as follows: before normalising the χ-distributions to unit area, the LO QCD part of the cross section, determined from a QCD-only simulation sample, is replaced by the QCD cross section corrected for NLO effects.
Using the QCD distribution and the finite set of MC CI distributions, each χ-bin is fit as function of Λ against a four-parameter interpolation function 3 , allowing for a smooth integration of the posterior probability density functions over Λ. From the signal fits, a posterior probability density is constructed as a function of Λ. The systematic uncertainties described in section 7 are convolved with the posterior distribution through pseudoexperiments drawn from the NP hypotheses. For the expected limit, pseudo-experiments are performed on the QCD background and used as pseudo-data.
This analysis sets a 95% CL lower limit on Λ at 7.6 TeV with an expected limit of 7.7 TeV. The observed posterior probability density function is shown in figure 7.
To test the sensitivity of the CI limit to the choice of prior, this analysis is repeated for a constant prior in 1/Λ 2 , which has been used in previous publications. As anticipated, the expected limit is less conservative, increasing by 0.40 TeV. Since the constant prior in 1/Λ 4 more accurately follows the cross section predicted for CI, the 1/Λ 2 result is not reported in the final results of the current studies.
The second model is QBH with n = 6 and with a constant prior in 1/M 4 D , which is for n = 6 proportional to the cross section. Similarly to what is done for CI, the QCD sample, together with a set of eleven QBH samples with M D ranging from 2.0 TeV to 6.0 TeV, is fit to the same smooth function in every χ-bin to enable integration of the posterior probability density functions over M D . The expected and observed 95% CL lower limits on M D are 4.20 TeV and 4.11 TeV, respectively.

Limits on new resonant phenomena from the F χ (m jj ) distribution
The Bayesian approach employed to set exclusion limits on new resonant phenomena with the dijet mass spectrum may be applied to the F χ (m jj ) distribution (see figure 3), provided that the NP models under consideration do not include interference with QCD. Unlike the m jj resonance analysis, the background prediction is based on the QCD MC   samples processed through detector simulation and corrected for NLO effects. The likelihood is constructed from two m jj distributions and their associated uncertainties, one distribution being the numerator spectrum of the F χ (m jj ) distribution and the other being the denominator. Here too, pseudo-experiments are used to convolve all systematic uncertainties, which in this case include the JES uncertainties, and the PDF and scale uncertainties associated with the QCD prediction. Figure 8 shows the limits expected and observed from data on the production cross section σ times the acceptance A, along with theoretical predictions for the QBH model [7,8], for n ranging from two to seven. For this model, generator-level studies have shown that the acceptance does not depend on the number of extra dimensions within this range. Therefore only the QBH MC sample for n = 6 has been processed through the ATL-FAST 2.0 detector simulation, and the acceptance calculated from this sample is used for all values of n. The acceptance is close to 90% for all M D values. The resulting 95% CL exclusion limits for the number of extra dimensions n ranging from 2 to 7 are shown in table 3.
The same analysis is applied to detect resonances in F χ (m jj ) due to excited quarks. With an acceptance close to 90% for all masses this analysis sets a 95% CL lower limit on m q * at 2.75 TeV with an expected limit of 2.85 TeV.  14 Limits on CI from the F χ (m jj ) distribution As was done previously with the ATLAS 2010 data sample [23], the F χ (m jj ) distribution (see figure 3) is used in the current study to set limits on quark contact interactions.
The procedure is very similar to the one used for limits obtained with χ discussed in section 12. MC samples of QCD production modified by a contact interaction are created for values of Λ ranging from 4.0 TeV to 10.0 TeV. For the CI distributions, QCD K-factors are applied to the QCD-only components of the numerator and denominator of F χ (m jj ) separately. This is done by subtracting the LO QCD cross section and adding the QCD cross section corrected for NLO effects.
Simulated F χ (m jj ) distributions are statistically smoothed by a fit in m jj . For the pure QCD sample (corresponding to Λ = ∞), a second-order polynomial is used, while for the MC distributions with finite Λ, a Fermi function is added to the polynomial, which gives a good representation of the onset of contact interactions.
Next, all m jj bins of the MC F χ (m jj ) distributions are interpolated in Λ using the same four-parameter interpolation function used for the χ analysis, creating a smooth predicted F χ (m jj ) surface as a function of m jj and Λ. This surface enables integration in m jj vs. Λ for continuous values of Λ.
Pseudo-experiments are then employed to construct a posterior probability, assuming a prior that is flat in 1/Λ 4 . This analysis sets a 95% CL lower limit on Λ at 7.6 TeV with an expected limit of 7.7 TeV.

Conclusions
Dijet mass and angular distributions have been measured by the ATLAS experiment over a large angular range and spanning dijet masses up to approximately 4.0 TeV, using 4.8 fb −1 of pp collision data at √ s = 7 TeV. No resonance-like features have been observed in the dijet mass spectrum, and all angular distributions are consistent with QCD predictions. This analysis places limits on a variety of hypotheses for physics phenomena beyond the Standard Model, as summarised in table 4.
For √ s = 7 TeV pp collisions at the LHC, the integrated luminosity used in the current studies represents a substantial increase over that available in previously published ATLAS dijet searches. Table 5 lists the previous and current expected limits from ATLAS studies using dijet analyses for three benchmark models: excited quarks, colour octet scalars, and contact interactions with destructive interference. The increase in the excited quark mass limit would have been greater by 0.10 TeV had there not been the long-standing problem with the default Pythia 6 q * model, discussed in earlier sections. For 2012 running, the collision energy of the LHC has been raised from 7 TeV to 8 TeV. The higher energy, and the associated rise in parton luminosity, will increase search sensitivities and the possibility of discoveries. The current 2011 analysis provides a reference for the study of energy-dependent effects once the 2012 data set has been analysed.  [32] ATLAS Collaboration, Jet energy measurement with the ATLAS detector in proton-proton collisions at √ s = 7 TeV, [arXiv:1112.6426].
[33] ATLAS Collaboration, In situ jet pseudorapidity intercalibration of the ATLAS detector using dijet events in [35] ATLAS Collaboration, Selection of jets produced in proton-proton collisions with the ATLAS detector using 2011 data, CERN (2012). ATLAS-CONF-2012-020.