Edinburgh Research Explorer Measurement of jet $p_{\mathrm{T}}$ correlations in Pb+Pb and $pp$ collisions at $\sqrt{s_{\mathrm{NN}}}=$ 2.76 TeV with the ATLAS detector

Measurements of dijet p T correlations in Pb + Pb and pp collisions at a nucleon–nucleon centre-of- mass energy of √ s NN = 2 . 76 TeV are presented. The measurements are performed with the ATLAS detector at the Large Hadron Collider using Pb + Pb and pp data samples corresponding to integrated luminosities of 0 . 14 nb − 1 and 4 . 0 pb − 1 , respectively. Jets are reconstructed using the anti- k t algorithm with radius parameter values R = 0 . 3 and R = 0 . 4. A background subtraction procedure is applied to correct the jets for the large underlying event present in Pb + Pb collisions. The leading and sub-leading jet transverse momenta are denoted p T 1 and p T 2 . An unfolding procedure is applied to the two-dimensional ( p T 1 , p T 2 ) distributions to account for experimental effects in the measurement of both jets. Distributions of ( 1 / N ) d N / d x J , where x J = p T 2 / p T 1 , are presented as a function of p T 1 and collision centrality. The distributions are found to be similar in peripheral Pb + Pb collisions and pp collisions, but highly modiﬁed in central Pb + Pb collisions. Similar features are present in both the R = 0 . 3 and R = 0 . 4 results, indicating that the effects of the underlying event are properly accounted for in the measurement. The results are qualitatively consistent with expectations from partonic energy loss models.


Introduction
Jets have long been considered an important tool for studying the matter produced in ultra-relativistic heavy-ion collisions. In these collisions, a hot medium of deconfined colour charges is produced, known as the quark-gluon plasma (QGP). Jets produced in the initial stage of the collision lose energy as they propagate through the medium. This phenomenon, known as jet quenching, was first observed at the Relativistic Heavy Ion Collider (RHIC) [1,2]. Early measurements using fully reconstructed jets in Pb+Pb collisions at the LHC provided a direct observation of this phenomenon [3]. In Pb+Pb collisions the transverse momentum (p T ) balance between two jets was found to be distorted, resulting from configurations in which the two jets suffer different amounts of energy loss. This measurement was the experimental confirmation of some of the initial pictures of jet quenching and signatures of a deconfined medium [4].
Subsequent measurements of jets in Pb+Pb collisions have improved the understanding of properties of quenched jets and the empirical features of the quenching mechanism [5][6][7][8][9][10][11][12][13][14]. Significant theoretical advances also occurred in this period, and while a complete description of jet quenching is not available, some models are capable of reproducing its key features and provid-E-mail address: atlas.publications@cern.ch. ing testable predictions. Measurements of the dijet asymmetry, A J ≡ (p T 1 − p T 2 )/(p T 1 + p T 2 ), where p T 1 and p T 2 are the transverse momenta of the jets with the highest and second highest p T in the event, respectively, have been crucial in facilitating these developments. The experimental results demonstrate that the measured asymmetries in central collisions, where the geometric overlap of the colliding nuclei is almost complete, differ from those in pp collisions more than is expected from detector-specific experimental effects [3,9,10]. However, such effects, in particular the resolution of the measured jet p T , must be corrected for in order for the measurement to be directly compared to theoretical calculations. Unfolding procedures have been applied to correct for such effects for single-jet measurements [6]; however, the dijet result requires a two-dimensional unfolding to account for migration in the p T of each jet separately. The measurement reported here is the first unfolded Pb+Pb dijet measurement and as such can be directly compared to theoretical models.
This Letter presents a measurement of dijet p T correlations in Pb+Pb and pp collisions at a nucleon-nucleon centre-of-mass energy of 2.76 TeV performed with the ATLAS detector. Jets are reconstructed with the anti-k t algorithm with radius parameter values R = 0.3 and R = 0.4 [15]. The analysis is described mostly for the example of R = 0.4 jets. A background subtraction procedure is applied to account for the effects of the large underlying event (UE) present in Pb+Pb collisions on the measured jet kinematics. The momentum balance of the dijet system is expressed by the variable x J ≡ p T 2 /p T 1 . Measurements of the dijet yield normalised by the total number of jet pairs in a given p T 1 interval, (1/N)dN/dx J , are presented as a function of x J in intervals of p T 1 and collision centrality. The results are obtained by first measuring the two-dimensional distribution, (p T 1 , p T 2 ), and unfolding in the two-dimensional space. The binning in the (p T 1 , p T 2 ) distribution is chosen such that the bins in the two-dimensional space correspond to fixed ranges of x J , and the (1/N)dN/dx J results are obtained by projecting into these x J bins. The (p T 1 , p T 2 ) distributions are less strongly correlated for jets reconstructed with a smaller value of R due to the effects of parton radiation outside the jet cone, which makes them less suitable as a probe of medium-induced effects in Pb+Pb collisions. However, for smaller jet sizes the effect of the UE on the measurement is significantly reduced. It is therefore interesting to compare the results obtained using R = 0.3 and R = 0.4 jets, to see if the same features are visible.

Experimental set-up
The measurements presented in this Letter are performed using the ATLAS inner detector, calorimeter and trigger systems [16]. The inner detector provides measurements of charged-particle tracks over the range |η| < 2.5. 1 It is composed of silicon pixel detectors in the innermost layers, followed by silicon microstrip detectors and a straw-tube tracker, all immersed in a 2 T axial magnetic field provided by a solenoid. The minimum-bias trigger scintillators (MBTS) measure charged particles over 2.1 < |η| < 3.9 using two planes of counters placed at z = ±3.6 m and provide timing measurements used in the event selection [17]. The ATLAS calorimeter system consists of a liquid argon (LAr) electromagnetic (EM) calorimeter (|η| < 3.2), a steel-scintillator sampling hadronic calorimeter (|η| < 1.7), a LAr hadronic calorimeter (1.5 < |η| < 3.2), and a forward calorimeter (FCal) (3.2 < |η| < 4.9). The hadronic calorimeter has three sampling layers longitudinal in shower depth and has a η × φ granularity of 0.1 × 0.1 for |η| < 2.5 and 0.2 × 0.2 for 2.5 < |η| < 4.9. 2 The EM calorimeters are longitudinally segmented in shower depth into three compartments following a pre-sampler layer (|η| < 1.8). The EM calorimeter has a granularity that varies with layer and pseudorapidity, but which is generally much finer than that of the hadronic calorimeter. The first layer has high η granularity (between 0.003 and 0.006) that can be used to identify photons and electrons. The middle sampling layer, which typically has the largest energy deposit in EM showers, has a granularity of 0.025 × 0.025 over |η| < 2.5.
A total transverse energy (TE) trigger is implemented by requiring a hardware-based determination of the total transverse energy in the calorimeter system, E tot T , to be above a threshold. The zero-degree calorimeters (ZDCs) are located symmetrically at z = ±140 m and cover |η| > 8.3. In Pb+Pb collisions the ZDCs primarily measure "spectator" neutrons: neutrons that do not interact hadronically when the incident nuclei collide. A ZDC coincidence trigger is implemented by requiring the pulse height from each ZDC to be above a threshold set below the single-neutron peak.
In addition to the ZDC and TE hardware-based triggers, a software-based high-level trigger is used to further reduce the ac-1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). cepted event rate. This trigger applies a jet reconstruction procedure, including a UE subtraction, similar to that used in the offline analysis, which is described in Section 4.

Data and Monte Carlo samples
The Pb+Pb data used for these measurements were recorded in 2011 and obtained using a combination of jet and minimum-bias triggers. The minimum-bias trigger is defined by a logical OR of the TE trigger with a threshold of E tot T = 50 GeV and the ZDC coincidence trigger. The combined trigger is fully efficient in the range of centralities presented here. In the events selected by the ZDC coincidence trigger alone, at least one track is required to remove empty events. The jet trigger [18] first selects events satisfying the TE trigger with a threshold of E tot T = 20 GeV. A jet reconstruction procedure is then applied using the anti-k t algorithm with R = 0.2 and utilising a UE subtraction procedure similar to that used in the offline reconstruction described in Section 4. Events with at least one jet with E T > 20 GeV at the electromagnetic scale [19] are selected by the jet trigger. The use of R = 0.2 for jets in the trigger, as opposed to the values of R = 0.3 and 0.4 applied in the measurement, is motivated by the need to define an algorithm that is robust against UE fluctuations, which grow with R. The effects of the different R values on the trigger efficiency are discussed in Section 5. The minimum-bias trigger operated with a prescale of approximately 18 while no prescale was applied to the jet trigger. After accounting for these prescales, the recorded events correspond to integrated luminosities of 8 μb −1 and 0.14 nb −1 for the minimum-bias and jet-triggered samples, respectively.
Events are further subjected to criteria designed to remove noncollision background and inelastic electromagnetic interactions between the nuclei. Events are required to have a reconstructed primary vertex and have a timing difference of less than 5 ns between the times measured by the two MBTS planes. After the trigger and event selection criteria, the resulting data samples contain 53 and 14 million events in the minimum-bias and jet triggered samples, respectively. The average number of collisions per bunch-crossing in the Pb+Pb data sample was less than 0.001, and the effects of multiple collisions are neglected in the data analysis.
The centrality of the Pb+Pb collisions is characterised by the total transverse energy measured in the FCal modules, E FCal T . The E FCal T distribution obtained in minimum-bias collisions is partitioned into separate ranges of E FCal T referred to as centrality classes [17,20,21]. Each class is defined by the fraction of the distribution contained by the interval, e.g. the 0-10% centrality class, which corresponds to the most central collisions, contains the 10% of minimum-bias events with the largest E FCal T . The centrality boundaries used in this analysis are 0%, 10%, 20%, 30%, 40%, 60% and 80%.
The pp data sample, recorded in 2013, was composed of events selected by a jet trigger and used a series of different p T thresholds each selected with a different prescale. The jet trigger is the same used in other ATLAS measurements in pp collisions [18] and applies the anti-k t algorithm with R = 0.4. The events are further required to contain at least one primary reconstructed vertex. The average number of pp collisions per bunch-crossing varied between 0.3 and 0.6 during data taking. The sample corresponds to a luminosity of 4.0 pb −1 .
The impact of experimental effects on the measurement is evaluated using the Geant4-simulated detector response [22,23] in a Monte Carlo (MC) sample of pp hard-scattering events. Dijet events at √ s = 2.76 TeV are generated using Pythia version 6.423 [24] with parameter values chosen according to the AUET2B tune [25] using the CTEQ6L1 parton distribution function (PDF) set [26]. To fully populate the kinematic range considered in the measurement, hard-scattering events are generated for separate intervals of p T , the transverse momentum of outgoing partons in the 2 → 2 hard-scattering, and combined using weights proportional to their respective cross sections. Separate samples are generated for the Pb+Pb and pp analyses, with the simulated detector conditions chosen to match those present during the recording of the respective data samples. In the pp data sample, the contribution of additional collisions in the same bunch crossing (pile-up) is accounted for by overlaying minimum-bias pp collisions produced at the same rate as in the data, generated by Pythia version 8.160 [27] using the A2 [28] tune with CT10 PDF set [29]. In the Pb+Pb sample, the UE contribution to the detector signal is accounted for by overlaying the simulated events with minimum-bias Pb+Pb data. The vertex position of each simulated event is selected to match the data event that is overlaid. Through this procedure the MC sample contains contributions from underlying-event fluctuations and harmonic flow that match those present in the data. The combined signal is then reconstructed using the same procedure as is applied to the data. So-called truth jets are defined by applying the anti-k t algorithm with R = 0.3 and R = 0.4 to stable particles in the MC event generator's output, defined as those with a proper lifetime greater than 10 ps, but excluding muons and neutrinos, which do not leave significant energy deposits in the calorimeter. The detector's response to quenched jets is studied with an additional sample using Pyquen [30]. This event generator applies medium-induced energy loss to parton showers produced by Pythia. It is used to generate a sample of jets with fragmentation functions that differ from those in the nominal Pythia sample in a fashion consistent with measurements of fragmentation functions in quenched jets [11][12][13].

Jet reconstruction
The procedure used to reconstruct jets in heavy-ion collisions is described in detail in Ref.
[5] and is briefly summarised here. First, energy deposits in the calorimeter cells are assembled into η × φ = 0.1 × π 32 logical towers. Jets are formed from the towers by applying the anti-k t algorithm [15] as implemented in the FastJet software package [31].
An estimate of the UE contribution to each tower within the jet is performed on an event-by-event basis by estimating the transverse energy density, ρ(η, φ). Global azimuthal modulation in the UE arises due to the physics of flow and is traditionally described in terms of the Fourier expansion of the φ dependence of the transverse energy density. In the subtraction procedure, the UE estimate is assigned a φ dependence using the measured magnitudes and phases of the modulation: where v n and n are the magnitudes and phases of the harmonic modulation, respectively, and ρ(η) is the average transverse energy density measured from energy deposits in the calorimeter as a function of η. In Ref.
[5], only the second-order harmonic modulation (n = 2) was considered, but in this measurement the procedure has been extended to account for n = 3 and 4 harmonic modulations as well. The subtraction is applied to each tower within the jet. The quantities in Eq. (1) may be biased if the energy in a jet is included in their calculation, which results in an over-subtraction of the average UE contribution to the jet energy or incomplete removal of the harmonic modulation. To mitigate such effects, the contribution from jets is excluded from the estimate of the background. The typical background energy subtracted from the jets varies from a few GeV in peripheral collisions to 150 GeV in the most central collisions.
A calibration factor, derived from MC studies, is then applied after the subtraction to account for the non-compensating hadronic response. A final in situ calibration is applied to account for known differences in detector response between data and the MC sample used to derive the initial calibration [32]. This calibration is derived in 8 TeV pp data and adapted to the different beam energy and pile-up conditions relevant for the samples considered here. It uses the balance between jet pairs in different η regions of the detector to provide an evaluation of the relative response to jets as a function of η. It subsequently uses jets recoiling against objects with an independently-determined energy scale such as Z bosons or photons to provide constraints on the absolute energy measurement.

Data analysis
In this analysis, jet pairs are formed from the two highest-p T jets in the event with p T > 25 GeV and |η| < 2.1. The pair is required to have φ > 7π /8, where φ ≡ |φ 1 − φ 2 |. For events selected by a jet trigger, the leading jet is required to match a jet identified by the trigger algorithm responsible for selecting the jet.
The two-dimensional (p T 1 , p T 2 ) distributions obtained from different triggered samples are combined such that intervals of p T 1 are populated by a single trigger. In the pp data analysis, the trigger with the most events that is more than 99% efficient for selecting a jet with p T > p T 1 is used, with the reciprocal of the luminosity for the respective trigger samples used as a weight.
The Pb+Pb jet trigger efficiency has a broad turn-on as a function of p T since the trigger jets are identified using R = 0.2 and have no energy scale calibration applied. This effect is the strongest in central collisions where the UE fluctuations are the largest and further weaken the correlation between jets reconstructed with different values of R. In the most central collisions, the single-jettrigger efficiency does not reach a plateau until p T ∼ 90 GeV. The jet-triggered sample is used where the efficiency is found to be greater than 97%, which occurs at a p T of approximately 85 GeV in the most central collisions. A trigger efficiency correction is applied in the region where there is an inefficiency.
In addition to the dijet signal, the measured (p T 1 , p T 2 ) distribution receives contributions from so-called combinatoric jet pairs. Such pairs arise when two jets, which are not from the same hardscattering process, fulfil the pair requirements through random association. Jets forming such pairs may originate from independent hard scatterings or from upward UE fluctuations identified as jets, referred to as UE jets. The rate for such occurrences is highest in the most central collisions, and the reduction in the true sub-leading jet p T due to quenching effects further enhances the likelihood of forming a combinatoric pair.
The shape of the φ distribution for the combinatoric jet pairs is influenced by the harmonic flow. Since the jet p T spectrum falls steeply, the jets most likely to be measured at a given p T value are those lying on top of larger-than-average UE. If the effects of the modulation of the UE are not fully accounted for in the background subtraction, more jets would be observed at angles corresponding to the flow maxima (φ ∼ n ). Thus combinatoric jet pairs, without any underlying angular correlation, are expected to acquire a modulation to their φ distribution determined by the dominant flow harmonics [33]. Although the second-, third-and fourth-order harmonic modulations are considered event-by-event in the jet reconstruction procedure described in Section 4, only the effects of the second-order modulation on the φ distribution are observed to be completely removed. The residual effects are an indication that the method of estimating the modulation of the UE under- and c 4 are obtained by fitting the φ distribution for jet pairs with | η| > 1 in the region 0 < φ < π 2 , which is indicated by the red squares (scaled to match the black circles in the yellow region for presentation purposes). The error bars denote statistical errors. (For interpretation of the references to colour in this figure, the reader is referred to the web version of this article.) neath the jet is less accurate for the higher-order harmonics than for n = 2.
To account for the residual modulation, the combinatoric contribution is assumed to be of the form: (2) The c 3 and c 4 values are determined by fitting the φ distributions over the range 0 < φ < π/2 where the real dijet contribution is expected to be small. The region 0 < φ 0.8 is also expected to receive real dijet contributions arising from parton radiation which results in pairs of jets at nearby angles. To remove this contribution, the fit to obtain c 3 and c 4 is performed only using jet pairs with a separation of | η| > 1. Once c 3 and c 4 are obtained, the φ distribution without this | η| requirement is integrated over the range 1 < φ < 1.4 to obtain Y . This proce-dure is performed separately in each (p T 1 , p T 2 ) interval. In intervals where the c 3 and c 4 are found to not be statistically significant their values are taken to be zero. The expected combinatorial contribution, B, in the signal region is obtained by integrating C ( φ) from 7π /8 to π .
The φ distribution of jet pairs is shown in Fig. 1 for pairs with 89 < p T 1 < 100 GeV in the 0-10% centrality interval. Also shown is the φ distribution obtained from such jet pairs with | η| > 1, which is fitted to obtain c 3 and c 4 . The background subtraction is most significant in central collisions, where the fraction subtracted from the total yield in the signal region is as large as 10% for small x J and is less than 1% for x J values greater than 0.5. The background contribution in more peripheral collisions is less than 1% for all values of x J . This background subtraction is not applied in the pp data because the pile-up is small.
The presence of combinatoric jet pairs also reduces the efficiency for genuine pairs. The measured inclusive jet spectrum is used to estimate the likelihood that another jet in the event, uncorrelated with the dijet system, is measured with a transverse momentum greater than p T 2 . For the 40-60% and 60-80% centrality intervals the effect is negligible. In the 0-10% centrality bin the efficiency is approximately 0.9 for p T 2 = 25 GeV and increases with p T 2 , reaching unity at 45 GeV. The effects of the combinatoric jet pairs are accounted for by first subtracting the estimated background and then correcting for the efficiency, ε, in each (p T 1 , p T 2 ) bin. The number of jet pairs corrected for such effects is defined to be: where N raw is the number of jet pairs after correcting for trigger efficiency and luminosity/prescale weighting as described above.
In a given event, the p T resolution may result in the jet with the highest true p T being measured with the second highest p T and vice-versa. To properly account for such migration effects, (p T 1 , p T 2 ) distributions are symmetrised prior to the unfolding by apportioning half of the yield in a given (p T 1 , p T 2 ) bin, after combinatoric subtraction, to the bin related to the original by p T 1 ↔ p T 2 .
The two-dimensional distributions after symmetrisation are shown in Fig. 2 for central and peripheral Pb+Pb collisions and for pp collisions. The choice of binning in (p T 1 , p T 2 ) is motivated by the mapping to the x J variable, and is described in more detail in the following section.

Unfolding
The calorimetric response to jets is evaluated in the MC sample by matching truth and reconstructed jets; the nearest recon- and p reco T 2 . The matched reconstructed jets are not required to have the highest p T in the event, but are subject to all other requirements applied to the data and truth jets. The response matrix is populated symmetrically in both truth and reconstructed p T . The full fourdimensional response behaves similarly to the factorised product of separate single-jet response distributions, and the migration effects can be understood in terms of the above discussion. While this provides intuition for the nature of the unfolding problem, such a factorisation is not explicitly assumed, and any correlations between the response of the two jets are accounted for in the procedure.
After unfolding, the leading/sub-leading distinction is restored by reflecting the distribution over the line p T 1 = p T 2 : for each bin with p T 2 > p T 1 the yield is moved to the corresponding bin with p T 2 < p T 1 . The bins along the diagonal, e.g. those containing pairs with p T 2 = p T 1 , are not affected by this procedure. The twodimensional distribution is constructed using binning along each axis such that the upper edge of the ith bin obeys, where N is the total number of bins and p T 0 and p T N are the minimum and maximum bin edges covered by the binning, respectively. As a consequence, the bins are of the same size when plotted with logarithmic axes. With these choices of binning, the range of x J values in any given (p T 1 , p T 2 ) bin is fully contained within two adjacent x J bins, which have boundaries at In this analysis, half of the yield in each (p T 1 , p T 2 ) bin is apportioned to each of the x J bins. The exceptions are the bins along the diagonal. These bins contribute solely to the x J bin with bin edges (α −1 , 1). The effects of such a mapping on the x J distribution are studied and found to not significantly distort the shape of the distribution for a variety of input x J distributions.
The Bayesian unfolding method is an iterative procedure that requires both a choice in a number of iterations, n iter , and assumption of a prior for the underlying true distribution. An increase in n iter reduces sensitivity to the choice of prior but may amplify statistical fluctuations that are already present in the input distribution. As Pythia does not include the effects of jet quenching, the x J distributions obtained from the MC sample are not expected to be optimal choices for the prior. In particular, the x J distributions in Pythia increase monotonically with x J , whereas the distributions in the data become flatter and develop a peak near x J ∼ 0.5 in lower p T 1 intervals and in the most central collisions. The (p T 1 , p T 2 ) distributions from Pythia are reweighted in a centrality-dependent way to obtain features that qualitatively match those present in the data.
The effects of the reweighting procedure are shown in the left panel of Fig. 3 in the 100 < p T 1 < 126 GeV range and 0-10% centrality interval, where the largest difference between the data and Pythia is observed. The "nominal" distribution, or the reweighted distribution, is used as the prior in the unfolding of the data. An "alternate" reweighting is also shown, which has a shape significantly different from the nominal, but does not increase as much as the Pythia distribution. The features in the data are observed to be robust with respect to the choice of prior for a broad set of reweighting functions. The systematic uncertainty due to the choice of prior is estimated by comparing the results of the unfoldings using the "nominal" and "alternate" x J distributions. The results of applying unfoldings with these two choices of priors are shown in the right panels of Fig. 3 for the same p T 1 and centrality selection. An alternative study is performed in the MC sample to validate the estimation of this uncertainty. The "alternate" reweighting is applied to obtain input truth and reconstructed distributions in which no peak structure is present. The reconstructed distribution is then unfolded using the nominal prior. The unfolded distribution does not develop the strong peak present in the nominal prior. The differences between the unfolded result and the input truth distribution are similar to the uncertainty obtained by varying the prior used to unfold the data.
The value of n iter is selected separately in each centrality interval by examining the uncertainty, √ δ 2 , in (1/N)dN/dx J after unfolding considering statistical uncertainties and systematic uncertainties attributed to the unfolding procedure, δ 2 = δ 2 stat + δ 2 prior , and summing over all x J bins. Here δ prior is the uncertainty due to the choice of prior, obtained using the procedure described above. The statistical uncertainties are evaluated using a pseudoexperiment technique. Stochastic variations of the data are generated based on its statistical uncertainty and each variation is unfolded and projected into x J . The statistical covariance of the set is taken as the statistical uncertainty. An additional covariance is obtained from applying the pseudo-experiment procedure to the response matrix and combined with that obtained from applying the procedure to the data. The δ 2 stat for each x J bin is taken to be the diagonal element of the resulting covariance matrix. The statistical covariance matrices exhibit similar trends across all p T 1 and centrality ranges. Nearby x J bins show a strong positive correlation that diminishes for bins separated in x J , and is expected from the effects of the procedures for unfolding and mapping to x J . Bins well separated in x J show an anti-correlation attributable to the normalisation of (1/N)dN/dx J .
The left panel of Fig. 4 shows √ δ 2 as a function of n iter along with its various contributions for the 100 < p T 1 < 126 GeV range and 0-10% centrality interval. Since the unfolding is performed in two dimensions, the value of n iter cannot be chosen separately for each range of p T 1 . At higher values of p T 1 the effects of the unfolding are smaller while the effects of the statistical fluctuations can be more severe. The right panel of Fig. 4 shows the total √ δ 2 for each range of p T 1 considered in the measurement along with the total combined over all p T 1 ranges. The value of n iter for each centrality bin and R value is chosen by considering the n iter dependence of √ δ 2 for each p T 1 bin and selecting a value that maintains comparable uncertainties across all p T 1 ranges. The more central bins require the most iterations, resulting from the larger jet energy resolution in these events. The number of iterations for R = 0.4 jets is at most 20 for 0-10% centrality and at the least 6 for 60-80% centrality. The √ δ 2 distributions for R = 0.3 jets show behaviour similar to those for R = 0.4 jets in the same centrality bin.
It is possible for a third jet present in the event to be reconstructed as the jet with the second highest p T through the experimental resolution. As a check to study the impact of such effects on the measurement, an alternative response matrix is constructed where no R matching is required between the truth and reconstructed jets. A weighting is applied such that the p T distribution of the reconstructed third jet matches that observed in the data. Differences between the unfolded distributions obtained with this response matrix and the nominal one are observed to be small and well within the systematic uncertainty associated with the unfolding procedure.
The (1/N)dN/dx J distributions before and after unfolding are shown in Fig. 5

for central and peripheral Pb+Pb collisions and for
pp collisions for jet pairs with 100 < p T 1 < 126 GeV. The systematic uncertainties indicated contain all of the contributions to the total systematic uncertainty described in Section 7. In the pp and 60-80% centrality interval, the resolution effects before unfolding reduce the sharpness of the peak near x J ∼ 1. In the case of the 0-10% centrality interval, the effect is to smear out the peak near x J ∼ 0.5. The lowest x J bins exhibit instability in the unfolding procedure due to the MC sample having too few events in this region. However, including this range in the unfolding improves the stability of the adjacent x J bins. Thus, after unfolding, only the range 0.32 < x J < 1 is reported in the results even though pairs with p T 2 > 25 GeV are included in the measurement.

Systematic uncertainties
Systematic uncertainties attributed to the response matrix used in the unfolding arise due to uncertainties in the JES and JER. To account for these effects, new response matrices are constructed with a systematically varied relationship between the truth and In the pp data analysis, the JES uncertainty is described by a set of 11 independent nuisance parameters; these include effects from uncertainties derived through the in situ calibration [32]. In the MC sample used to determine the calibration, the calorimetric response to jets initiated by the fragmentation of quarks and gluons is observed to differ. Potential inaccuracies in the MC sample describing both this flavour-dependent response and the relative abundances of quark and gluon jets are accounted for using separate nuisance parameters. A source of uncertainty related to the adaptation of the in situ calibration derived at √ s = 8 TeV to 2.76 TeV data is also included.
In the Pb+Pb data analysis, two additional uncertainties in the JES are considered. The first accounts for differences between the detector operating conditions in the Pb+Pb and pp data, which were recorded in 2011 and 2013, respectively. This is derived by using charged-particle tracks reconstructed in the inner detector to provide an independent check on the JES, which only uses information from the calorimeter. For each jet, all reconstructed tracks within R < 0.4 and having p trk T > 2 GeV, are matched to the jet and the scalar sum of the track transverse momenta is evaluated. The ratio of this sum to the jet's p T is evaluated both in data and in the MC sample, and a double ratio of the two quantities is formed. The double ratio obtained in peripheral Pb+Pb data is compared with that in pp data. The precision of the comparison is limited by having too few events in the peripheral Pb+Pb data and at high jet p T , and a p T -and η-independent uncertainty of 1.46% is assigned to account for potential differences. The second additional uncertainty is a centrality-dependent JES uncertainty to account for potential differences in the detector response to quenched jets. This is estimated by comparing the detector response evaluated in the Pythia and Pyquen MC samples. This estimate is checked in data using a track-based study similar to the one described above, but comparing central and peripheral Pb+Pb collisions and accounting for the measured variation of the fragmentation function with centrality [11][12][13]. An uncertainty of up to 1% in the most central collisions and decreasing linearly with centrality percentile to 0% in the 60-80% centrality class is assigned.
The uncertainty attributed to the JER is obtained by adding Gaussian fluctuations to each reconstructed jet p T value when populating the response matrix. The magnitude of this uncertainty is fixed by a comparison of the data and MC descriptions of the JER in 8 TeV data [36]. Since the MC sample is constructed using the data overlay procedure, it is expected that the centrality dependence of the JER should be well described in the MC sample. This is checked by studying the distribution of UE fluctuations using random, jet-sized groups of calorimeter towers in Pb+Pb data. The standard deviations of these distributions describe the typical UE contribution beneath a jet. The centrality dependence of the UE fluctuations is compared to that of the JER in the MC sample, and a systematic uncertainty is included to account for the observed differences. As expected, these differences are much smaller than the centrality-independent contribution to the JER uncertainty.
The data-driven estimates of the JES and JER uncertainties described above are derived using R = 0.4 jets. Additional uncertainties are included in the R = 0.3 jet measurement to account for potential differences between data and the MC sample in the relative energy scale of R = 0.3 jets with respect to R = 0.4 jets.
These uncertainties are estimated from a study that matched jets reconstructed with the two R values and compared the means of the p R=0.3 T /p R=0.4 T distributions in data and the MC sample. Differences may arise between the data and MC sample from differences in the calorimetric response or because the jets in the two samples have different internal structure. The contribution of the latter is constrained by using existing jet shape measurements [37]. An uncertainty in the energy scale is applied to account for residual differences, which are 1.5% at the lowest p T and decrease sharply as a function of p T to a limiting value of 0.3% at high p T . A similar study comparing the variances of the p R=0.3 T distributions is used to constrain the uncertainty in the relative resolution. This uncertainty is applied in the R = 0.3 jet measurement in the same fashion as the other JER uncertainties described above. Although larger than the centrality-dependent contribution, it is also much smaller than the centrality-independent contribution.
As the response matrix is sparsely populated (containing 40 4 bins), statistical fluctuations could introduce instabilities in the unfolding. To evaluate the sensitivity to such effects, along with any other defects in the response, a new response matrix is constructed as a factorised product of single-jet response distributions, i.e. assuming the responses in p T 1 and p T 2 are independent. The data are unfolded using this new response and the differences between the unfolded distributions are taken as a systematic uncertainty. Systematic uncertainties in the unfolding due to the choice of prior are estimated as described in the previous section and are also included. Uncertainties due to the correction for the combinatoric effects described in Section 5 affect the number of jet pairs before the unfolding and are thus included as additional contributions to the previously described statistical uncertainties in the data. These include statistical uncertainties in ε and the uncertainties in the values of the fit parameters c 3 and c 4 , accounting for their covariance. Uncertainties in the normalisation are estimated by varying the region of φ used to estimate Y from 1.0-1.4 to 1.1-1.5. The uncertainty due to this correction is smaller than the other uncertainties in all p T and centrality bins, and is only greater than 5% at values of x J < 0.4. This correction was not applied to the pp data so there is no corresponding systematic uncertainty.
The breakdown of different contributions to the total systematic uncertainty is shown in the 100 < p T 1 < 126 GeV range for the 0-10% centrality interval and for pp collisions in Fig. 6. Each contribution to the uncertainty, and thus the total uncertainty, tends to decrease with increasing x J . The total uncertainty at x J ∼ 1 reaches approximately 12% in most p T 1 and centrality bins in the Pb+Pb data. For x J < 0.4, the relative uncertainty becomes large, but this region represents only a small contribution to the total (1/N)dN/dx J distribution. The JER uncertainty is the largest contribution. In the Pb+Pb data it reaches values of approximately 10% and 15% at x J ∼ 1 and x J = 0.5, respectively. The JES contributions are the second largest contribution to the uncertainties, typically between 5% and 10%. In the most central bins the unfolding uncertainty can become as large as the JES contribution. The contributions to the uncertainty in the other centrality intervals and in the pp data follow trends similar to those described for the 0-10% centrality interval, but the magnitudes are smaller in more peripheral collisions. In the pp data they are typically smaller by a factor of two compared to the 0-10% Pb+Pb data. The uncertainties for the R = 0.3 result follow the same trends as those for the R = 0.4 result but are slightly larger due to the two additional sources included in that measurement to describe the relative energy scale and resolution between the two R values.

Results
The unfolded (1/N)dN/dx J distribution in pp collisions for 100 < p T 1 < 126 GeV is shown in Fig. 7. Also shown are the corresponding distributions obtained from the Pythia 6 sample used in the MC studies and also from Pythia 8 using the AU2 tune and Herwig++ [38] with the UE-EE-3 [39] tune. An additional sample, referred to as Powheg+Pythia 8 is generated using Powheg-Box 2.0 [40-42], which is accurate to next-to-leading order in perturbative QCD, and interfaced with Pythia 8 to provide a description of the parton shower and hadronisation. All samples used the CTEQ6L1 PDF set [26] except the Powheg+Pythia 8, which used the CT10 PDF set [29]. All four models describe the data fairly well with the Herwig++ and Powheg+Pythia 8 showing the best agreement over the full x J range.
The unfolded (1/N)dN/dx J distributions in Pb+Pb collisions are shown in Fig. 8, for jet pairs with 100 < p T 1 < 126 GeV for different centrality intervals. The distribution in pp collisions is shown on each panel for comparison. In the 60-80% centrality bin, where the effects of quenching are expected to be the smallest, the Pb+Pb data are consistent with the pp data. In more central Pb+Pb collisions, the distributions become significantly broader than that in pp collisions and the peak at x J ∼ 1, corresponding to nearly symmetric dijet events, is reduced. At lower centrality percentiles the distribution becomes almost constant over the range 0.6 x J 1, and develops a peak at x J ∼ 0.5 in the 0-10% centrality interval. In pp collisions, the x J distribution becomes increasingly narrow with increasing p T 1 , indicating that higher-p T dijets tend to be better balanced in momentum (fractionally). At higher p T 1 , the x J distribution begins to fall more steeply from x J ∼ 1, but appears to  Fig. 11 shows the (1/N)dN/dx J distributions for 79 < p T 1 < 100 GeV for different collision centralities but for jets reconstructed with R = 0.3. This indicates that the trends present in p T 1 and centrality are robust with respect to the UE and that UE effects are properly accounted for by the combinatoric subtraction and unfolding procedures applied in the data analysis.
The distributions are flatter for R = 0.3 jets in all p T and centrality bins, including in pp collisions. This is consistent with the expectation that the (p T 1 , p T 2 ) correlation is weaker for smaller-R jets due to the effects of parton radiation outside the nominal jet cone.

Conclusion
This Letter presents a measurement of dijet x J distributions in 4.0 pb −1 of pp and 0.14 nb −1 of Pb+Pb collisions at √ s NN = 2.76 TeV. The measurement is performed differentially in leadingjet transverse momentum, p T 1 , and in collision centrality using data from the ATLAS detector at the LHC. The measured distributions are unfolded to account for the effects of experimental resolution and inefficiencies on the two-dimensional (p T 1 , p T 2 ) distributions and then projected into bins of fixed ratio x J = p T 2 /p T 1 .
The distributions show a larger contribution of asymmetric dijets in Pb+Pb data compared to that in pp data, a feature that becomes more pronounced in more central collisions and is consistent with expectations of medium-induced energy loss due to jet quenching.
In the 0-10% centrality bin for 100 < p T 1 < 126 GeV, the x J distribution develops a significant peak at x J ∼ 0.5 indicating that the most probable configuration for dijets is for them to be highly unbalanced. This is in sharp contrast to the situation in the pp data where the most probable values are near x J ∼ 1. The centralitydependent modifications evolve smoothly from central to peripheral collisions, and the results in the 60-80% centrality bin and the pp data are consistent. At larger values of p T 1 the x J distributions are observed to narrow and the differences between the distributions in central Pb+Pb and pp collisions lessen. This is qualita-tively consistent with a picture in which the fractional energy loss decreases with increasing jet p T . The features in the data are compatible with those observed in previous measurements of dijets in Pb+Pb collisions by the ATLAS and CMS collaborations, however, the trends in this measurement are more prominent due to the application of the unfolding procedure. This result constitutes an important benchmark for theoretical models of jet quenching and the dynamics of relativistic heavy-ion collisions.