Observation and studies of jet quenching in PbPb collisions at nucleon-nucleon center-of-mass energy = 2.76 TeV

Jet production in PbPb collisions at a nucleon-nucleon center-of-mass energy of 2.76 TeV was studied with the CMS detector at the LHC, using a data sample corresponding to an integrated luminosity of 6.7 inverse microbarns. Jets are reconstructed using the energy deposited in the CMS calorimeters and studied as a function of collision centrality. With increasing collision centrality, a striking imbalance in dijet transverse momentum is observed, consistent with jet quenching. The observed effect extends from the lower cut-off used in this study (jet transverse momentum = 120 GeV/c) up to the statistical limit of the available data sample (jet transverse momentum approximately 210 GeV/c). Correlations of charged particle tracks with jets indicate that the momentum imbalance is accompanied by a softening of the fragmentation pattern of the second most energetic, away-side jet. The dijet momentum balance is recovered when integrating low transverse momentum particles distributed over a wide angular range relative to the direction of the away-side jet.


Introduction
The data provide information on the evolution of the dijet imbalance as a function of both collision centrality (i.e., the degree of overlap of the two colliding nuclei) and the energy of the leading jet. By correlating the dijets detected in the calorimeters with charged hadrons reconstructed in the high-resolution tracker system, the modification of the jet fragmentation pattern can be studied in detail, thus providing a deeper insight into the dynamics of the jet quenching phenomenon.
The paper is organized as follows: the experimental setup, event triggering, selection and characterization, and jet reconstruction are described in Section 2. Section 3 presents the results and a discussion of systematic uncertainties, followed by a summary in Section 4.

Experimental method
The CMS detector is described in detail elsewhere [20]. The calorimeters provide hermetic coverage over a large range of pseudorapidity, |η| < 5.2, where η = −ln [ tan(θ/2)] and θ is the polar angle relative to the particle beam. In this study, jets are identified primarily using the energy deposited in the lead-tungstate crystal electromagnetic calorimeter (ECAL) and the brass/scintillator hadron calorimeter (HCAL) covering |η| < 3. In addition, a steel/quartzfiber Cherenkov calorimeter, called Hadron Forward (HF), covers the forward rapidities 3 < |η| < 5.2 and is used to determine the centrality of the PbPb collision. Calorimeter cells are grouped in projective towers of granularity in pseudorapidity and azimuthal angle given by ∆η × ∆ϕ = 0.087 × 0.087 at central rapidities, having a coarser segmentation at forward rapidities. The central calorimeters are embedded in a solenoid with 3.8 T central magnetic field. The event display shown in Fig. 1 illustrates the projective calorimeter tower granularity over the full pseudorapidity range. The CMS tracking system, located inside the calorimeter, consists of pixel and silicon-strip layers covering |η| < 2.5, and provides track reconstruction down to p T ≈ 100 MeV/c, with a track momentum resolution of about 1% at p T = 100 GeV/c. A set of scintillator tiles, the Beam Scintillator Counters (BSC), are mounted on the inner side of the HF calorimeters for triggering and beam-halo rejection. CMS uses a right-handed coordinate system, with the origin located at the nominal collision point at the center of the detector, the x-axis pointing towards the center of the LHC ring, the y-axis pointing up (perpendicular to the LHC plane), and the z-axis along the counterclockwise beam direction. The detailed Monte Carlo (MC) simulation of the CMS detector response is based on GEANT4 [21].

Data samples and triggers
The expected cross section for hadronic inelastic PbPb collisions at √ s NN = 2.76 TeV is 7.65 b, corresponding to the chosen Glauber MC parameters described in Section 2.3. In addition, there is a sizable contribution from large impact parameter ultra-peripheral collisions (UPC) that lead to the electromagnetic breakup of one, or both, of the Pb nuclei [22]. particles per unit of pseudorapidity, depending on the impact parameter.
For online event selection, CMS uses a two-level trigger system: Level-1 (L1) and High Level Trigger (HLT). The events for this analysis were selected using an inclusive single-jet trigger that required an L1 jet with p T > 30 GeV/c and an HLT jet with p T > 50 GeV/c, where neither p T value was corrected for the p T -dependent calorimeter energy response discussed in Section 2.4.3. The efficiency of the jet trigger is shown in Fig. 2 (a) for leading jets with |η| < 2 as a function of their corrected p T . The efficiency is defined as the ratio of the number of triggered events over the number of minimum bias events (described below). The trigger becomes fully efficient for collisions with a leading jet with corrected p T greater than 100 GeV/c.  Figure 2: (a) Efficiency curve for the HLT 50 GeV/c single-jet trigger, as a function of the corrected leading jet transverse momentum. Error bars shown are statistical. (b) Correlation between the number of pixel hits and HF total energy for a single run containing 60 k minimum bias events, after selections as described in the text.
In addition to the jet data sample, a minimum bias event sample was collected using coincidences between the trigger signals from the +z and −z sides of either the BSC or the HF. This trigger has an efficiency of more than 97% for hadronic inelastic collisions. In order to suppress non-collision related noise, cosmic rays, double-firing triggers, and beam backgrounds, the minimum bias and jet triggers used in this analysis were required to fire in time with the presence of both colliding ion bunches in the interaction region. It was checked that the events selected by the jet trigger described above also satisfy all triggers and selections imposed for minimum bias events. The total hadronic collision rate varied between 1 and 210 Hz, depending on the number of colliding bunches (between 1×1 and 129×129) and on the bunch intensity.

Event selection
In order to select a pure sample of inelastic hadronic collisions for analysis, a number of offline selections were applied to the triggered event sample, removing contaminations from UPC events and non-collision beam backgrounds (e.g. beam-gas). Table 1 shows the number of events remaining after the various selection criteria are applied. First, beam halo events were vetoed based on the timing of the +z and −z BSC signals. Then, to veto UPC and beam-gas events, an offline HF coincidence of at least three towers on each side of the interaction point was required, with a total deposited energy of at least 3 GeV. Next, a reconstructed vertex was required with at least two tracks of p T > 75 MeV/c, consistent with the transverse beam spot position and the expected collision region along the z-axis. Finally, to further reject beam-gas and beam-scraping events, the length of pixel clusters along the beam direction were required to be compatible with particles originating from the primary vertex. This last selection is identical to the one used for the study of charged hadron pseudorapidity density and p T spectrum in 7 TeV pp collisions [23]. Figure 2 (b) shows the correlation between the total energy deposited in the HF calorimeters and the number of hits in the first layer of the silicon pixel barrel detector after these event selections. A tight correlation between the two detectors is observed, with very few of the events showing HF energy deposits that deviate significantly (at any given number of pixel hits) from the expectations for hadronic PbPb collisions. This correlation is important to verify the selection of a pure collision event sample, and also to validate the HF energy sum as a measure of event centrality (Section 2.3).
Starting from inelastic hadron collisions based on the selections described above, the basic offline selection of events for the analysis is the presence of a leading calorimeter jet in the pseudorapidity range of |η| < 2 with a corrected jet p T > 120 GeV/c. By selecting these leading jets we avoid possible biases due to inefficiencies close to the trigger threshold. Furthermore, the selection of a rather large leading jet momentum expands the range of jet momentum imbalances that can be observed between the leading and subleading jets, as the subleading jets need a minimum momentum of p T > 35-50 GeV/c to be reliably detected above the high-multiplicity underlying event in PbPb collisions (Section 2.4). In order to ensure high quality dijet selection, kinematic selection cuts were applied. The azimuthal angle between the leading and subleading jet was required to be at least 2π/3. Also, we require a minimum p T of p T,1 > 120 GeV/c for leading jets and of p T,2 > 50 GeV/c for subleading jets. No explicit requirement is made either on the presence or absence of a third jet in the event. Prior to jet finding on the selected events, a small contamination of noise events from uncharacteristic ECAL and HCAL detector responses was removed using signal timing, energy distribution, and pulse-shape information [24,25]. As a result, about 2.4% of the events were removed from the sample.

Centrality determination
For the analysis of PbPb events, it is important to know the "centrality" of the collision, i.e., whether the overlap of the two colliding nuclei is large or small. In this analysis, the observable used to determine centrality is the total energy from both HF calorimeters. The distribution of the HF signal used in this analysis is shown in Fig. 3 (a). The shape of the energy distribution is characteristic of all observables related to (soft) particle production in heavy ion collisions. The more frequent peripheral events with large impact parameter produce very few particles, while the central ones with small impact parameter produce many more particles because of the increased number of nucleon-nucleon interactions.
The distribution of this total energy was used to divide the event sample into 40 centrality bins, each representing 2.5% of the total nucleus-nucleus interaction cross section. Because of inefficiencies in the minimum bias trigger and event selection, the measured multiplicity distribution does not represent the full interaction cross section. MC simulations were used to estimate the distribution in the regions where events are lost. Comparing the simulated distribution to the measured distribution, it is estimated that the minimum bias trigger and event selection efficiency is 97 ± 3%.
For the jet analysis, these fine-grained bins were combined into five larger bins corresponding to the most central 10% of the events (i.e., smallest impact parameter), the next most central 10% of the events (denoted 10-20%), and further bins corresponding to the 20-30%, 30-50%, and 50-100% selections of the total hadronic cross section.
Simulations can be used to correlate centrality, as quantified using the fraction of the total interaction cross section, with more detailed properties of the collision. The two most commonly used physical quantities are the total number of nucleons in the two lead ( 208 Pb) nuclei which experienced at least one inelastic collision, denoted N part , and the total number of binary nucleon-nucleon collisions, N coll .
The centrality bins can be correlated to the impact parameter, b, and to average values and variances of N part and N coll using a calculation based on a Glauber model in which the nucleons are assumed to follow straight-line trajectories as the nuclei collide (for a review, see [26]). The bin-to-bin smearing of the results of these calculations due to the finite resolution and fluctuations in the HF energy measurement was obtained from fully simulated and reconstructed MC events generated with the AMPT event generator [27]. Standard parameters of the Woods-Saxon function used to model the distribution of nucleons in the Pb nuclei were used [28]. The nucleon-nucleon inelastic cross section, which is used to determine how close the nucleon trajectories need to be in order for an interaction to occur, was taken to be 64 ± 5 mb, based on a fit of the existing data for total and elastic cross-sections in proton-proton and proton-antiproton collisions [29]. The uncertainties in the parameters involved in these calculations contribute to the systematic uncertainty in N part and N coll for a given bin. The other source of uncertainty in the centrality parameters comes from the determination of the event selection efficiency.
Using the procedure outlined above, the mean and spread (RMS) values of the impact parameter, N part , and N coll for the five bins used in this analysis, and their systematic uncertainties,  The centrality-bin labels run from 100% for the most peripheral to 0% for the most central events.
were extracted and are listed in Table 2. The RMS values for the centrality parameters are due to their correlation with the percentage cross section and the width of the chosen centrality bins.
It is important to note that the selection of rare processes, such as the production of high-p T jets, leads to a strong bias in the centrality distribution of the underlying events towards more central collisions, for which N coll is very large. This can be seen in Fig. 3 (a), where the HF energy distribution for events selected by the jet trigger is shown in comparison to that for minimum bias events. The bias can be seen more clearly in Fig. 3 (b), where the distribution of minimum bias and jet-triggered events in the 40 centrality bins is shown.

Jet algorithm
The baseline jet reconstruction for heavy ion collisions in CMS is performed with an iterative cone algorithm modified to subtract the soft underlying event on an event-by-event basis [30]. Each cone is selected with a radius ∆R = ∆φ 2 + ∆η 2 = 0.5 around a seed of minimum transverse energy of 1 GeV. The underlying event subtraction algorithm is a variant of an iterative "noise/pedestal subtraction" technique [31]. Initially, the mean value, E cell , and dispersion, σ(E cell ), of the energies recorded in the calorimeter cells are calculated for all rings of cells that have at least 0.3 GeV transverse energy deposit at constant pseudorapidity. The algorithm subtracts E cell + σ(E cell ) from each cell. If a cell energy is negative after subtraction, the value is set to zero. Subtracting the mean plus the dispersion, as opposed to simply the mean, compensates for the bias caused by the "zeroing" of negative-energy cells. Jets are then reconstructed, using a standard iterative cone algorithm [32,33], from the remaining cells with non-zero energy. In a second iteration, the pedestal function is recalculated using only calorimeter cells outside the area covered by reconstructed high-p T jets (p T > 10 GeV/c). The threshold of 10 GeV/c was chosen in studies optimizing the final extracted jet p T resolution. The cell energies are updated with the new pedestal function (again subtracting mean plus dispersion) and the jets are reconstructed again, using the updated calorimeter cells. The performance of this algorithm is documented in Ref. [30]. Jet corrections for the calorimeter response have been applied, as determined in studies for pp collisions [34]. When applying the algorithm to PbPb data, the subtracted background energy for R = 0.5 jet cones ranges from 6-13 GeV for peripheral events (centrality bins 50-100%) to 90-130 GeV for central collisions (0-10%), before applying jet energy scale corrections.
To perform a cross-check of the main results, the anti-k T algorithm [35] with a resolution parameter of 0.5 was used to reconstruct jets, as was done for the pp reference measurements presented here. The energy attributed to the underlying event was estimated and subtracted using the "average energy per jet area" procedure provided by the FASTJET package [36,37]. In order to eliminate biases in the underlying event estimation, an η-strip of total width ∆η = 1.6 centered on the jet position was used, with the two highest energy jets in each event excluded [38].
In addition, the anti-k T jets were reconstructed based on particle flow objects [39,40] instead of calorimeter-only information. A good agreement was found with the calorimeter-based, iterative cone algorithm results.

Simulated data samples
For the analysis of dijet properties in PbPb events, it is crucial to understand how the jet reconstruction is modified in the presence of the high multiplicity of particles produced in the PbPb underlying event. The jet-finding performance was studied using dijets in pp collisions simulated with the PYTHIA event generator (version 6.423, tune D6T) [41], modified for the isospin content of the colliding nuclei [42]. In order to enhance the number of Pythia dijets in the momentum range studied, a minimump T selection of 80 GeV/c was used. Lowerp T selections, as discussed in [43], were also investigated and found to agree with thep T = 80 GeV/c results within uncertainties. The PYTHIA dijet events were processed with the full detector simulation and analysis chain. Additional samples were produced in which the PYTHIA dijet events were embedded into a minimum bias selection of PbPb events at the raw data level. For this embedding procedure, both real PbPb data events (PYTHIA+DATA), and PbPb events simulated with the HYDJET event generator [42] (PYTHIA+HYDJET) were used. The HYDJET parameters were tuned to reproduce the total particle multiplicities at all centralities and to approximate the underlying event fluctuations seen in data. The HYDJET events included the simulation of hard-scattering processes for which radiative parton energy loss was simulated, but collisional energy loss was turned off [42]. Both embedded samples were propagated through the standard reconstruction and analysis chain.
The PYTHIA+DATA sample was used in several ways for studies of calorimeter jets. First, by matching the same PYTHIA dijet event reconstructed with and without the PbPb underlying event, the degradation of the jet p T and position resolution, the jet p T scale, and the jet-finding efficiency were determined as a function of collision centrality and jet p T (Section 2.4.3). In addition, PYTHIA+DATA events were compared to non-embedded PYTHIA for dijet observables such as azimuthal correlations and momentum balance distributions. Finally, to separate effects due to the medium itself from effects simply due to reconstructing jets in the complicated environment of the underlying PbPb event, a direct comparison of results for PYTHIA+DATA and actual data events was made (Section 3.1).
The PYTHIA+HYDJET sample was used for studies of track momentum balance and track-jet correlations (Sections 3.2 and 3.3), where access to the full MC particle level (truth) information for charged tracks is important for systematic studies.

Jet-finding performance
A detailed characterization of the CMS calorimeter jet-finding performance in pp collisions can be found in [44]. The dependence of the jet energy scale and of the jet energy resolution on centrality was determined using the PYTHIA+DATA sample ( Fig. 4, standard pp jet energy corrections are applied). In this study, reconstructed jets were matched to the closest generatorlevel jet in η-φ within a cone of ∆R = 0.3. The residual jet energy scale dependence and the relative jet energy resolution are derived from the mean and standard deviation of the approximately Gaussian distributions of the ratio of the reconstructed calorimeter jet transverse momentum p CaloJet T and the transverse momentum of jets reconstructed based on event generator level final state particles p GenJet T . For peripheral events in the 50-100% centrality selection, the jet energies are under-corrected by 5% after applying the standard pp jet energy corrections, and the jet energy resolution is found to be about 15% worse than in pp collisions. For the most central events, the large transverse energy per unit area of the underlying event leads to an over-correction of low-p T jet energies by up to 10% and a degradation of the relative resolution by about 30% to σ(p CaloJet T /p GenJet T ) = 0.16 at p T = 100 GeV/c. The effect of the underlying event on the jet angular resolution was also studied. Integrated over jet p T > 50 GeV/c, the angular resolution in φ worsens from 0.03 for peripheral events (50-100%) to 0.04 for central events (0-10%), while the resolution in η changes from 0.02 to 0.03 over the same centrality range.
The jet reconstruction efficiency as a function of jet p T and centrality was extracted from the PYTHIA+DATA sample as well, with the results shown in Fig. 5. For peripheral events, a jetfinding efficiency of 95% was found for a jet p T = 50 GeV/c, while for central collisions the efficiency drops to 88% at the same p T . Jets with p T > 70 GeV/c are found with an efficiency greater than 97% for all collision centralities. No correction for the inefficiency near the threshold was applied in the subsequent analysis, as the effects of the reconstruction inefficiency are included in the PYTHIA+DATA reference analysis.
Finally, the rate of calorimeter jets reconstructed from fluctuations in the underlying event without the presence of a fragmenting p T parton, so called fake jets, for the jet selection used in this paper was determined using fully simulated 0-10% central HYDJET   is found within an η-φ distance to the reconstructed jet axis smaller than 0.3. For leading jets with p T,1 > 120 GeV/c, a fake jet fraction of less than 0.02% is found. In events with a p T,1 > 120 GeV/c leading jet, the fake jet fraction on the away-side of the leading jet (∆φ 12 > 2π/3) is determined to be 3.5% for reconstructed jets with p T,2 > 50 GeV/c and less than 0.02% for p T,2 > 120 GeV/c. The effects of the degradation of jet performance in terms of energy scale, resolution, efficiency, and fake rate on the dijet observables are discussed in Section 3.1.

Results
The goal of this analysis is to characterize possible modifications of dijet properties as a function of centrality in PbPb collisions. In addition to the standard event selection of inelastic hadronic collisions and the requirement of a leading jet with p T,1 > 120 GeV/c (Section 2.2), most of the subsequent analysis required the subleading jet in the event to have p T,2 > 50 GeV/c, and the azimuthal angle between the leading and subleading jet (∆φ 12 ) to be larger than 2π/3. Only jets within |η| < 2 were considered for the analysis of calorimeter jets in Section 3.1. For a data set of L int = 6.7 µb −1 , this selection yields 3514 jet pairs. For studies of correlations of calorimeter jets with charged particles (Sections 3.2 and 3.3), a more restrictive pseudorapidity selection was applied. The analysis was performed mostly in five bins of collision centrality: 0-10%, 10-20%, 20-30%, 30-50%, and 50-100%.
Thus far, no pp reference data exist at the PbPb collision energy of √ s NN = 2.76 TeV. Throughout the paper, the results obtained from PbPb data will be compared to references based on the PYTHIA and PYTHIA+DATA samples described in Section 2.4.2.
For most results, the PYTHIA+DATA events will be used for direct comparisons. To calibrate the performance of PYTHIA for the observables used in this analysis, the dijet analysis was also performed using the anti-k T algorithm on 35 pb −1 of pp data at √ s = 7 TeV, collected by CMS prior to the heavy ion data taking and compared to PYTHIA simulations for the same collision system and energy. The same jet selection criteria used for the 2.76 TeV PbPb data were applied to both pp data and PYTHIA.

Dijet properties in pp and PbPb data
The correlation between the transverse momentum of the reconstructed leading and subleading jets in the calorimeters is plotted in Fig. 6. The top row contains PbPb data for peripheral, mid-central, and central events, the second row shows pp jets simulated by PYTHIA and embedded into PbPb data, and the bottom panel shows pp jets from PYTHIA without embedding. One can already observe a downward shift in the subleading jet p T for the more central PbPb events. In the following discussion, a more quantitative and detailed assessment of this phenomenon will be presented.  It is important to note that the jet momentum spectra at detector level presented here have not been corrected for smearing due to detector resolution, fluctuations in/out of the jet cone, or underlying event fluctuations. Therefore, a direct comparison of these spectra to analytical calculations or particle-level generator results is not possible. For the jet asymmetry and dijet ∆φ distributions discussed below, the effect of the finite jet energy resolution is estimated using the PYTHIA+DATA events.

Dijet azimuthal correlations
One possible medium effect on the dijet properties is a change of the back-to-back alignment of the two partons. This can be studied using the event-normalized differential dijet distribution, (1/N)(dN/d∆φ 12 ), versus ∆φ 12 . Figure 8 shows distributions of ∆φ 12 between leading and subleading jets which pass the respective p T selections. In Fig. 8 (a), the dijet ∆φ 12 distributions are plotted for 7 TeV pp data in comparison to the corresponding PYTHIA simulations using the anti-k T algorithm for jets based on calorimeter information. PYTHIA provides a good de- scription of the experimental data, with slightly larger tails seen in the PYTHIA simulations. A recent study of azimuthal correlations in pp collisions at 7 TeV can be found in [45]. For the PYTHIA comparison to PbPb results at √ s NN = 2.76 TeV, this discrepancy seen in the higher energy pp comparison is included in the systematic uncertainty estimation. It is important to note that the PYTHIA simulations include events with more than two jets, which provide the main contribution to events with large momentum imbalance or ∆φ 12 far from π.
show the dijet ∆φ 12 distributions for PbPb data in five centrality bins, compared to PYTHIA+DATA simulations. The distributions for the four more peripheral bins are in good agreement with the PYTHIA+DATA reference, especially for ∆φ 12 2. The three centrality bins spanning 0-30% show an excess of events with azimuthally misaligned dijets (∆φ 12 2), compared with more peripheral events. A similar trend is seen for the PYTHIA+DATA simulations, although the fraction of events with azimuthally misaligned dijets is smaller in the simulation. The centrality dependence of the azimuthal correlation in PYTHIA+DATA can be understood as the result of the increasing fake-jet rate and the drop in jet reconstruction efficiency near the 50 GeV/c threshold from 95% for peripheral events to 88% for the most central events. In PbPb data, this effect is magnified since low-p T away-side jets can undergo a sufficiently large energy loss to fall below the 50 GeV/c selection criteria.
Furthermore, a reduction of the fraction of back-to-back jets above ∆φ 12 3 is observed for the most central bin. This modification of the ∆φ 12 distribution as a function of centrality can be quantified using the fraction R B of dijets with ∆φ 12 > 3.026 , as plotted in Fig. 9, for p T,1 > 120 GeV/c and p T,2 > 50 GeV/c. The threshold of 3.026 corresponds to the median of the ∆φ 12 distribution for PYTHIA (without embedding). The results for both the PbPb data and PYTHIA+DATA dijets are shown as a function of the reaction centrality, given by the number of participating nucleons, N part , as described in Section 2.3. This observable is not sensitive to the shape of the tail at ∆φ 12 < 2 seen in Fig. 8, but can be used to measure small changes in the back-to-back correlation between dijets. A decrease in the fraction of back-to-back jets in PbPb data is seen compared to the pure PYTHIA simulations. Part of the observed change in R B (∆φ) with centrality is explained by the decrease in jet azimuthal angle resolution from σ φ = 0.03 in peripheral events to σ φ = 0.04 in central events, due to the impact of fluctuations in the PbPb underlying event. This effect is demonstrated by the comparison of PYTHIA and PYTHIA+DATA results. The difference between the pp and PYTHIA+DATA resolutions was used for the uncertainty estimate, giving the dominant contribution to the systematic uncertainties, shown as brackets in Fig. 9.

Dijet momentum balance
To characterize the dijet momentum balance (or imbalance) quantitatively, we use the asymmetry ratio,  Figure 9: Fraction of events with ∆φ 12 > 3.026 as a function of N part , among events with p T,1 > 120 GeV/c and p T,2 > 50 GeV/c. The result for reconstructed PYTHIA dijet events (blue filled star) is plotted at N part = 2. The other points (from left to right) correspond to centrality bins of 50-100%, 30-50%, 20-30%, 10-20%, and 0-10%. The red squares are for reconstruction of PYTHIA+DATA events and the filled circles are for the PbPb data, with statistical (vertical bars) and systematic (brackets) uncertainties.
where the subscript 1 always refers to the leading jet, so that A J is positive by construction. The use of A J removes uncertainties due to possible constant shifts of the jet energy scale. It is important to note that the subleading jet p T,2 > 50 GeV/c selection imposes a p T,1 -dependent limit on the magnitude of A J . For example, for the most frequent leading jets near the 120 GeV/c threshold, this limit is A J < 0.41, while the largest possible A J for the present dataset is 0.7 for 300 GeV/c leading jets. Dijets in which the subleading jet is lost below the 50 GeV/c threshold are not included in the A J calculation.
In Fig. 10 (a), the A J dijet asymmetry observable calculated by PYTHIA is compared to pp data at √ s = 7 TeV. Again, data and event generator are found to be in excellent agreement. This observation, as well as the good agreement between PYTHIA+DATA and the most peripheral PbPb data shown in Fig. 10 (b), suggests that PYTHIA at √ s = 2.76 TeV can serve as a good reference for the dijet imbalance analysis in PbPb collisions.
The centrality dependence of A J for PbPb collisions can be seen in Figs. 10 (b)-(f), in comparison to PYTHIA+DATA simulations. Whereas the dijet angular correlations show only a small dependence on collision centrality, the dijet momentum balance exhibits a dramatic change in shape for the most central collisions. In contrast, the PYTHIA simulations only exhibit a modest broadening, even when embedded in the highest multiplicity PbPb events.
Central PbPb events show a significant deficit of events in which the momenta of leading and subleading jets are balanced and a significant excess of unbalanced pairs. The large excess of unbalanced compared to balanced dijets explains why this effect was apparent even when simply scanning event displays (see Fig. 1). The striking momentum imbalance is also confirmed when studying high-p T tracks associated with leading and subleading jets, as will be shown in Section 3.2. It is consistent with a degradation of the parton energy, or jet quenching, in the medium produced in central PbPb collisions. The evolution of the dijet momentum balance illustrated in Fig. 10 can be explored more quantitatively by studying the fraction of balanced jets in the PbPb events. The balanced fraction, R B (A J < 0.15), is plotted as a function of collision centrality (again in terms of N part ) in Fig. 11. It is defined as the fraction of all events with a leading jet having p T,1 > 120 GeV/c for which a subleading partner with A J < 0.15 and ∆φ 12 > 2π/3 is found. Since R B (A J < 0.15) is calculated as the fraction of all events with p T,1 > 120 GeV/c, it takes into account the rate of apparent "mono-jet" events, where the subleading partner is removed by the p T or ∆φ selection.
The A J threshold of 0.15 corresponds to the median of the A J distribution for pure PYTHIA dijet events passing the criteria used for Fig. 10. By definition, the fraction R B (A J < 0.15) of balanced jets in PYTHIA is therefore 50%, which is plotted as a dashed line in Fig. 11. As will be discussed in Section 3.3, a third jet having a significant impact on the dijet imbalance is present in most of the large-A J events in PYTHIA.
The change in jet-finding performance from high to low p T , discussed in Section 2.4.3, leads to only a small decrease in the fraction of balanced jets, of less than 5% for central PYTHIA+DATA dijets. In contrast, the PbPb data show a rapid decrease in the fraction of balanced jets with collision centrality. While the most peripheral selection shows a fraction of balanced jets of close to 45%, this fraction drops by close to a factor of two for the most central collisions. This again suggests that the passage of hard-scattered partons through the environment created in PbPb collisions has a significant impact on their fragmentation into final-state jets.  Figure 11: Fraction of all events with a leading jet with p T,1 > 120 GeV/c for which a subleading jet with A J < 0.15 and ∆φ 12 > 2π/3 was found, as a function of N part . The result for reconstructed PYTHIA dijet events (blue filled star) is plotted at N part = 2. The other points (from left to right) correspond to centrality bins of 50-100%, 30-50%, 20-30%, 10-20%, and 0-10%. The red squares are for reconstruction of PYTHIA+DATA events and the filled circles are for the PbPb data, with statistical (vertical bars) and systematic (brackets) uncertainties.
The observed change in the fraction of balanced jets as a function of centrality, shown in Fig. 11, is far bigger than the estimated systematic uncertainties, shown as brackets. The main contributions to the systematic uncertainties include the uncertainties on jet energy scale and resolution, jet reconstruction efficiency, and the effects of underlying event subtraction. The uncertainty in the subtraction procedure is estimated based on the difference between pure PYTHIA and PYTHIA+DATA simulations. For central events, the subtraction procedure contributes the biggest uncertainty to R B (A J ), of close to 8%. The uncertainty on the residual jet energy scale was estimated based on the results shown in the top row of Fig. 4. The full difference between the observed residual correction and unity, added in quadrature with the systematic uncertainty obtained for pp [34], was used as the systematic uncertainty on the jet p T and propagated to R B (A J ). For the jet p T resolution uncertainty, the full difference of the PYTHIA+DATA result to the pp resolution, as shown in Fig. 4 (bottom), was used as an uncertainty estimate for the PbPb jet p T resolution. The uncertainties in jet energy scale and jet resolution contribute 5% and 6%, respectively, to the 11% total systematic uncertainty in central events. For peripheral events, the total uncertainty drops to 9%, mostly due to the smaller uncertainty related to the PbPb background fluctuations for lower multiplicity events.

Leading jet p T dependence of dijet momentum imbalance
The dependence of the jet modification on the leading jet momentum can be studied using the fractional imbalance ∆p T rel = (p T,1 − p T,2 )/p T,1 . The mean value of this fraction is presented as a function of p T,1 in Fig. 12 for three bins of collision centrality, 30-100%, 10-30% and 0-10%. PYTHIA is shown as stars, PYTHIA+DATA simulations are shown as squares, while the data are shown as circles. Statistical and systematic uncertainties are plotted as error bars and brackets, respectively. The dominant contribution to the systematic uncertainty comes from the observed p T dependence of the residual jet energy correction in PbPb events (6% out of a total systematic uncertainty of 8%). The jet energy resolution and underlying event subtraction uncertainties contribute about 4% each.  Figure 12: Mean value of the fractional imbalance (p T,1 − p T,2 )/p T,1 as a function of leading jet p T for three centrality bins. The PbPb data are shown as circles with vertical bars and brackets indicating the statistical and systematic uncertainties, respectively. Results for PYTHIA are shown with blue stars, and PYTHIA+DATA with red squares. The dot-dashed line to guide the eye is drawn at the value for pure PYTHIA for the lowest p T bin.
The fractional imbalance exhibits several important features: the imbalance seen in PbPb data grows with collision centrality and reaches a much larger value than in PYTHIA or PYTHIA+DATA. In addition, the effect is clearly visible even for the highest-p T jets observed in the data set, demonstrating that the observed dijet imbalance is not restricted to the threshold region in our leading jet selection. Within the present uncertainties, the p T,1 dependence of the excess imbalance above the PYTHIA prediction is compatible with either a constant difference or a constant fraction of p T,1 .
The main contributions to the systematic uncertainty in (p T,1 − p T,2 )/p T,1 are the uncertainties in the p T -dependent residual energy scale (based on results shown in the top row of Fig. 4), and the centrality-dependent difference observed between PYTHIA and PYTHIA+DATA seen in Fig. 12. As before, the uncertainty on the residual jet energy scale was estimated using the full difference between the observed residual correction and unity, and also assuming that within these limits the low-p T and high-p T response could vary independently.

Track-jet correlations
The studies of calorimeter jets show a strong change of the jet momentum balance as a function of collision centrality. This implies a corresponding modification in the distribution of jet fragmentation products, with energy being either transported out of the cone area used to define the jets, or to low-momentum particles which are not measured in the calorimeter jets. The CMS calorimeter is less sensitive to these low momentum particles, or they do not reach the calorimeter surface. Information about changes to the effective fragmentation pattern as a function of A J can be obtained from track-jet correlations. For this analysis, PYTHIA+HYDJET simulations are used as MC reference, to allow full access to MC truth (i.e., the output of the generator) information for tracks in the dijet signal and in the PbPb underlying event. The event selection for PYTHIA+HYDJET was based on reconstructed calorimeter jet information, as for the previous studies.  Figure 13: Distribution of the transverse momentum sum of tracks for three p T ranges, as a function of the distance ∆R to the leading and subleading jet axes. Results for the 0-30% centrality selection are shown for PYTHIA+HYDJET (upper row) and PbPb data (lower row). For each figure, the requirements on the dijet asymmetry A J are given. Note that events with A J > 0.22 are much rarer in the PYTHIA+HYDJET sample than in the data. Vertical bars are statistical and systematic uncertainties, combined in quadrature, the systematic contributions being 20%, independent of the bin.
To derive the associated track spectrum for a given jet selection in data, the p T distribution of tracks inside a ring of radius ∆R = ∆φ 2 + ∆η 2 and width of 0.08 around the jet axes was summed over all selected jets. The contribution of tracks from the underlying event, not associated with the jet, was estimated by summing the track p T distributions using an equalsize ring that was reflected around η = 0, but at the same φ coordinate as the individual jet. For this procedure, jets in the region |η| < 0.8 were excluded and only ring-radii up to ∆R = 0.8 around the jet axes were considered, to avoid overlap between the signal jet region and the region used for background estimation. In addition, jets in the region |η| > 1.6 were excluded to ensure the 0.8 radius rings would lie within the tracker acceptance. Statistical fluctuations in the underlying event limit this procedure to tracks with transverse momenta p T > 1 GeV/c. The summed p T spectra from the jet regions and the underlying event regions were then subtracted, yielding the momentum distribution of charged tracks associated with the jets as a function of ∆R.
The resulting distributions of associated track momentum as a function of track p T and ∆R are presented in Fig. 13 for four selections in dijet asymmetry, from A J < 0.11 (left) to A J > 0.33 (right). For both data and PYTHIA+HYDJET results, the jet selections and A J values are based on the reconstructed calorimeter jet momenta (Section 2.4) in order to have consistent event selections for comparison. The middle bin boundary (A J = 0.22) corresponds to the median of the A J distribution for the 0-30% central PbPb events shown here. The top row shows the results for PYTHIA+HYDJET simulations. The track results shown for the PYTHIA+HYDJET simulations were found using the known ("truth") values of the track momenta from the embedded PYTHIA events. The bottom row presents results for PbPb data. The track results shown for PbPb data were corrected for tracking efficiency and fake rates using corrections that were derived from PYTHIA+HYDJET simulations and from the reconstruction of single tracks embedded in data. In each panel, the area of each colored region in p T and ∆R corresponds to the total transverse momentum per event carried by tracks in this region.
For the balanced-jet selection, A J < 0.11, one sees qualitative agreement in the leading and subleading jet momentum distributions between PYTHIA+HYDJET (top) and data (bottom). In data and simulation, most of the leading and subleading jet momentum is carried by tracks with p T > 8 GeV/c, with the data tracks having a slightly narrower ∆R distribution. A slightly larger fraction of the momentum for the subleading jets is carried by tracks at low p T and ∆R > 0.16 (i.e., beyond the second bin) in the data.
Moving towards larger dijet imbalance, the major fraction of the leading jet momentum continues to be carried by high-p T tracks in data and simulation. For the A J > 0.33 selection, it is important to recall that less than 10% of all PYTHIA dijet events fall in this category, and, as will be discussed in Section 3.3, those that do are overwhelmingly 3-jet events.
While the overall change found in the leading jet shapes as a function of A J is small, a strong modification of the track momentum composition of the subleading jets is seen, confirming the calorimeter determination of the dijet imbalance. The biggest difference between data and simulation is found for tracks with p T < 4 GeV/c. For PYTHIA, the momentum in the subleading jet carried by these tracks is small and their radial distribution is nearly unchanged with A J . However, for data, the relative contribution of low-p T tracks grows with A J , and an increasing fraction of those tracks is observed at large distances to the jet axis, extending out to ∆R = 0.8 (the largest angular distance to the jet in this study).
The major systematic uncertainties for the track-jet correlation measurement come from the p T -dependent uncertainty in the track reconstruction efficiency. The algorithmic track reconstruction efficiency, which averages 70% over the p T > 0.5 GeV/c and |η| < 2.4 range included in this study, was determined from an independent PYTHIA+HYDJET sample, and from simulated tracks embedded in data. Additional uncertainties are introduced by the underlying event subtraction procedure. The latter was studied by comparing the track-jet correlations seen in pure PYTHIA dijet events for generated particles with those seen in PYTHIA+HYDJET events after reconstruction and background subtraction. The size of the background subtraction systematic uncertainty was further cross-checked in data by repeating the procedure for random ring-like regions in 0-30% central minimum bias events. In the end, an overall systematic uncertainty of 20% per bin was assigned. This uncertainty is included in the combined statistical and systematic uncertainties shown in Fig. 13.

Overall momentum balance of dijet events
The requirements of the background subtraction procedure limit the track-jet correlation study to tracks with p T > 1.0 GeV/c and ∆R < 0.8. Complementary information about the overall momentum balance in the dijet events can be obtained using the projection of missing p T of reconstructed charged tracks onto the leading jet axis. For each event, this projection was calculated as where the sum is over all tracks with p T > 0.5 GeV/c and |η| < 2.4. The results were then averaged over events to obtain p T . No background subtraction was applied, which allows  this study to include the |η jet | < 0.8 and 0.5 < p Track T < 1.0 GeV/c regions not accessible for the study in Section 3.2. The leading and subleading jets were again required to have |η| < 1.6.
In Fig. 14, p T is shown as a function of A J for two centrality bins, 30-100% (left) and 0-30% (right). Results for PYTHIA+HYDJET are presented in the top row, while the bottom row shows the results for PbPb data. Using tracks with |η| < 2.4 and p T > 0.5 GeV/c, one sees that indeed the momentum balance of the events, shown as solid circles, is recovered within uncertainties, for both centrality ranges and even for events with large observed dijet asymmetry, in both data and simulation. This shows that the dijet momentum imbalance is not related to undetected activity in the event due to instrumental (e.g. gaps or inefficiencies in the calorimeter) or physics (e.g. neutrino production) effects. The figure also shows the contributions to p T for five transverse momentum ranges from 0.5-1 GeV/c to p T > 8 GeV/c. The vertical bars for each range denote statistical uncertainties. For data and simulation, a large negative contribution to p T (i.e., in the direction of the leading jet) by the p T > 8 GeV/c range is balanced by the combined contributions from the 0.5-8 GeV/c regions. Looking at the p T < 8 GeV/c region in detail, important differences between data and simulation emerge. For PYTHIA+HYDJET both centrality ranges show a large balancing contribution from the intermediate p T region of 4-8 GeV/c, while the contribution from the two regions spanning 0.5-2 GeV/c is very small. In peripheral PbPb data, the contribution of 0.5-2 GeV/c tracks relative to that from 4-8 GeV/c tracks is somewhat enhanced compared to the simulation. In central PbPb events, the relative contribution of low and intermediate-p T tracks is actually the opposite of that seen in PYTHIA+HYDJET. In data, the 4-8 GeV/c region makes almost no contribution to the overall momentum balance, while a large fraction of the negative imbalance from high p T is recovered in low-momentum tracks.
The dominant systematic uncertainty for the p T balance measurement comes from the p Tdependent uncertainty in the track reconstruction efficiency and fake rate described in Section 3.2. A 20% uncertainty was assigned to the final result, stemming from the residual difference between the PYTHIA generator-level and the reconstructed PYTHIA+HYDJET tracks at high p T . This is combined with an absolute 3 GeV/c uncertainty that comes from the imperfect cancellation of the background tracks. The background effect was cross-checked in data from a random cone study in 0-30% central events similar to the study described in Section 3.2. The overall systematic uncertainty is shown as brackets in Figs. 14 and 15.
Further insight into the radial dependence of the momentum balance can be gained by studying p T separately for tracks inside cones of size ∆R = 0.8 around the leading and subleading jet axes, and for tracks outside of these cones. The results of this study for central events are shown in Fig. 15 for the in-cone balance and out-of-cone balance for MC and data. As the underlying PbPb event in both data and MC is not φ-symmetric on an event-by-event basis, the back-to-back requirement was tightened to ∆φ 12 > 5π/6 for this study.
One observes that for both data and MC an in-cone imbalance of p T ≈ −20 GeV/c is found for the A J > 0.33 selection. In both cases this is balanced by a corresponding out-of-cone imbalance of p T ≈ 20 GeV/c. However, in the PbPb data the out-of-cone contribution is carried almost entirely by tracks with 0.5 < p T < 4 GeV/c whereas in MC more than 50% of the balance is carried by tracks with p T > 4 GeV/c, with a negligible contribution from p T < 1 GeV/c. The PYTHIA+HYDJET results are indicative of semi-hard initial or final-state radiation as the underlying cause for large A J events in the MC study. This has been confirmed by further studies which showed that in PYTHIA the momentum balance in the transverse plane for events with large A J can be restored if a third jet with p T > 20 GeV/c, which is present in more than 90% of these events, is included. This is in contrast to the results for large-A J PbPb data, which show that a large part of the momentum balance is carried by soft particles (p T < 2 GeV/c) and radiated at large angles to the jet axes (∆R > 0.8).

Summary
The CMS detector has been used to study jet production in PbPb collisions at √ s NN = 2.76 TeV.
Jets were reconstructed using primarily the calorimeter information in a data sample corresponding to an integrated luminosity of L int = 6.7 µb −1 . Events having a leading jet with p T > 120 GeV/c and |η| < 2 were selected. As a function of centrality, dijet events with a subleading jet of p T > 50 GeV/c and |η| < 2 were found to have an increasing momentum imbalance. Data were compared to PYTHIA dijet simulations for pp collisions at the same energy which were embedded into real heavy ion events. The momentum imbalances observed in the data were significantly larger than those predicted by the simulations. While the relative imbalance between the leading and subleading jets increased with increasing collision centrality, it was found to be largely independent of the leading jet p T , up to the highest p T region studied (≈210 GeV/c).
The angular distribution of jet fragmentation products has been explored by associating charged tracks with the dijets observed in the calorimeters. The calorimeter-based momentum imbalance is reflected in the associated track distributions, which show a softening and widening of the subleading jet fragmentation pattern for increasing dijet asymmetry, while the high-p T components of the leading jet remain nearly unchanged.
Studies of the missing transverse momentum projected on the jet axis have shown that the overall momentum balance can be recovered if tracks at low p T are included. In the PbPb data, but not in the simulations, a large fraction of the balancing momentum is carried by tracks having p T < 2 GeV/c. Comparing the momentum balance inside and outside of cones of ∆R = 0.8 around the leading and subleading jet axes demonstrates that a large contribution to the momentum balance in data arises from soft particles radiated at ∆R > 0.8 to the jets, a feature which is also not reproduced in PYTHIA calculations.
In conclusion, a strong increase in the fraction of highly unbalanced jets has been seen in central PbPb collisions compared with peripheral collisions and model calculations, consistent with a high degree of jet quenching in the produced matter. A large fraction of the momentum balance of these unbalanced jets is carried by low-p T particles at large radial distance, in contrast to PYTHIA simulations embedded into heavy ion events. The results provide qualitative constraints on the nature of the jet modification in PbPb collisions and quantitative input to models of the transport properties of the medium created in these collisions. [44] CMS Collaboration, "Jet Performance in pp Collisions at √ s=7 TeV", CMS Physics Analysis Summary CMS-PAS-JME-10-003 (2010).