Measurements of the suppression and correlations of dĳets in Pb+Pb collisions at √ 𝒔 NN = 5 . 02 TeV The ATLAS Collaboration

Studies of the correlations of the two highest transverse momentum (leading) jets in individual Pb+Pb collision events can provide information about the mechanism of jet quenching by the hot and dense matter created in such collisions. In Pb+Pb and 𝑝𝑝 collisions at √ 𝑠 NN = 5 . 02 TeV, measurements of the leading dĳet transverse momentum ( 𝑝 T ) correlations are presented. Additionally, measurements in Pb+Pb collisions of the dĳet pair nuclear modiﬁcation factors projected along leading and subleading jet 𝑝 T are made. The measurements are performed using the ATLAS detector at the LHC with 260 pb − 1 of 𝑝𝑝 data collected in 2017 and 2.2 nb − 1 of Pb+Pb data collected in 2015 and 2018. An unfolding procedure is applied to the two-dimensional leading and subleading jet 𝑝 T distributions to account for experimental eﬀects in the measurement of both jets. Results are provided for dĳets with leading jet 𝑝 T greater than 100 GeV. Measurements of the dĳet-yield-normalized 𝑥 J distributions in Pb+Pb collisions show an increased fraction of imbalanced jets compared to 𝑝𝑝 collisions; these measurements are in agreement with previous measurements of the same quantity at 2.76 TeV in the overlapping kinematic range. Measurements of the absolutely-normalized dĳet rate in Pb+Pb and 𝑝𝑝 collisions are also presented, and show that balanced dĳets are signiﬁcantly more suppressed than imbalanced dĳets in Pb+Pb collisions. It is observed in the measurements of the pair nuclear modiﬁcation factors that the subleading jets are signiﬁcantly suppressed relative to leading jets with 𝑝 T between 100 and 316 GeV for all centralities in Pb+Pb collisions.


Introduction
The principal physics aim of the heavy-ion program at the Large Hadron Collider (LHC) is to produce and measure the properties of the quark-gluon plasma (QGP).In quantum chromodynamics (QCD), the QGP is a high-temperature state of matter in which quarks and gluons are no longer confined in color-neutral hadrons such as protons and neutrons (for a recent review, see Ref. [1]).In order to understand the properties of the QGP at short distances, high transverse momenta ( T ) probes such as jets of correlated particles are used.
The overall rate of jets in a given centrality 1 interval in Pb+Pb collisions at a given  T is characterized by the nuclear modification factor, where  jet and    are the jet yield in Pb+Pb collisions and the jet cross-section in   collisions, respectively, measured as a function of the jet  T , and where  evt is the total number of Pb+Pb events within the chosen centrality interval.Additionally, ⟨ AA ⟩ is the mean nuclear thickness function [2] for the centrality interval.The  AA value is one in the absence of nuclear effects, however in the most central Pb+Pb collisions,  AA is observed to be about a factor of two lower than that in   collisions scaled by ⟨ AA ⟩, up to a  T of approximately 1 TeV [3][4][5].This suppression, referred to as jet quenching, is generally explained by the interplay of radiative and collisional energy loss in reducing the jet  T by moving energy associated with the initial parton to wider angles, with some of it being outside the jet cone.Given the steeply falling jet  T spectrum, this leads to fewer jets being measured at a given jet  T , giving rise to  AA values below one.For recent reviews, see Refs.[6,7].
Jets are mostly produced in pairs in 2 → 2 scattering processes.The QCD evolution of the initial partons gives rise to back-to-back jets, referred to here as "dĳets".Compared to single-jet suppression, dĳets in Pb+Pb collisions provide a cleaner probe for studying jet quenching.The two jets are expected to experience asymmetric energy loss due to traversing unequal path lengths in the QGP [8], driven by the geometry of the overlapping nuclei and the relative orientation of the jet trajectories through the evolving medium.Measurements of the azimuthal anisotropy of jets [9] have already shown that the geometry of the overlapping nuclei affects the relative rates of jets measured in Pb+Pb collisions.Additionally, jets are expected to experience jet-by-jet fluctuations in the energy-loss process [10].The measurement of the  T balance of dĳets provides a way to constrain the relative importance of fluctuations and geometry in jet quenching.
In order to compare the final transverse momenta of the two jets which define a dĳet, the leading dĳet momentum balance: is measured.Here, the leading dĳet is constructed using the highest two  T jets out of the set of jets in an event,  T,1 is the transverse momentum of the highest- T (leading) jet, and  T,2 is the transverse momentum of the second-highest- T (subleading) jet.
In   collisions, the showering process in vacuum (in the absence of a significant QGP), as well as higher-order scattering processes, can lead to imbalanced dĳet transverse momenta.However, the most probable situation is that the jets are nearly balanced in  T [11].Previous dĳet measurements in Pb+Pb collisions have observed that jets are more likely to have a larger momentum imbalance in Pb+Pb collisions than in   collisions [11][12][13].
Previous publications reported only the dĳet imbalance normalized by the measured dĳet yields, in order to study the changes in the shape of the  J distribution as a function of the heavy-ion collision centrality.Past studies did not address the absolute rate at which dĳets are produced in Pb+Pb collisions, which could assess whether leading dĳets are suppressed at levels similar to those for "inclusive jets" (all jets in the event which meet  T and rapidity selections) [3].This paper thus presents both types of measurements with leading dĳets in Pb+Pb and   collisions at √  NN = 5.02 TeV.These measurements use 2.2 nb −1 of Pb+Pb collisions collected in 2015 and 2018 as well as 260 pb −1 of   data collected in 2017 with the ATLAS detector [14] at the LHC.
Jets are reconstructed using the anti-  algorithm [15] with radius parameter  = 0.4.Leading dĳets are constructed from the two highest- T jets in the event and are required to have the two jets nearly back-to-back in azimuth with Δ ≡ | 1 −  2 | ≥ 7/8 and || < 2.1. 2The measurement is performed in logarithmic  T bins from 100 to 562 GeV for leading jets and above 32 GeV for subleading jets.Events whose two highest- T jets do not meet the selection criteria are discarded.
The primary observable for this measurement is the two-dimensional yield of leading dĳets ( pair ) meeting the selection criteria: 2  pair   T,1   T,2 . ( Projections of the two-dimensional distribution in Exp. (3) can be used to construct  J distributions as a function of  T,1 and  T,2 .The  J values, as defined in Eq. ( 2), are reported for 0.32 <  J < 1.0 for selections in  T,1 .The minimum  J value is chosen to be consistent with previous measurements [11].
The  J distributions are presented with two normalizations.The first uses the dĳet yield normalization to extract the dĳet-yield-normalized  J distributions: This normalization, Exp.(4), has been used in previous dĳet measurements by ATLAS and CMS [11][12][13].
The second normalization provides absolutely normalized  J distributions: 1 ⟨ AA ⟩ AA evt  AA pair  J (5) in Pb+Pb collisions and 1       pair  J (6) 2 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector, and the -axis along the beam pipe.The -axis points from the IP to the center of the LHC ring, and the -axis points upward.Cylindrical coordinates (, ) are used in the transverse plane,  being the azimuthal angle around the -axis.The pseudorapidity is defined in terms of the polar angle  as  = − ln tan(/2).The rapidity is defined as  = 0.5 ln[( +   )/( −   )] where  and   are the energy and -component of the momentum along the beam direction, respectively.Transverse momentum and transverse energy are defined as  T =  sin  and  T =  sin , respectively.The angular distance between two objects with relative differences Δ in pseudorapidity and Δ in azimuth is given by Δ in   collisions.Here ⟨ AA ⟩ [2] is the mean nuclear thickness function for the events under consideration,  AA evt is the number of minimum-bias events, and    is the integrated luminosity of the   collisions [16].The absolutely normalized  J distributions allow a direct comparison between the dĳet rates measured in Pb+Pb and   collisions.Additionally, the absolutely normalized  J distributions can be integrated over the measurement range of 0.32 <  J < 1.0 to construct the pair nuclear modification factors for dĳets as a function of the leading and subleading jet  T .These quantities are defined analogously to the nuclear modification factor for inclusive jets, Eq. ( 1), as

ATLAS detector
The ATLAS detector [14] at the LHC covers nearly the full solid angle around the nominal interaction point.It contains an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, a zero-degree calorimeter, and a muon spectrometer which incorporates three large superconducting toroidal magnets.The inner-detector system is immersed in a 2 T axial magnetic field and provides charged-particle tracking within || < 2.5.The ATLAS calorimeter system covers the pseudorapidity range || < 4.9.Within the region || < 3.2, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) calorimeters, with an additional thin LAr presampler covering || < 1.8 to allow corrections for energy lost in material upstream of the calorimeters.Hadronic calorimetry is provided by a steel/scintillator-tile calorimeter which is segmented into three barrel structures within || < 1.7, as well as two copper/LAr hadronic endcap calorimeters.To complete the solid angle coverage, forward copper/LAr and tungsten/LAr calorimeter modules (FCal) are used, optimized for electromagnetic and hadronic measurements respectively.
The zero-degree calorimeters (ZDCs) are located symmetrically at  = ±140 m and cover || > 8.3.They are constructed using tungsten absorber plates with quartz fibers to transmit the Cherenkov light.In Pb+Pb collisions the ZDCs primarily observe "spectator" neutrons, which do not interact during the primary collision.
A two-level trigger system is used within ATLAS to select events of interest [17].The first-level trigger is implemented in hardware and uses a subset of the detector information to reduce the event rate to at most 100 kHz.This is followed by the software-based high-level trigger, which further reduces the event rate to several kHz of triggered events that are recorded to permanent storage.
An extensive software suite [18] is used in the reconstruction and analysis of real and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment.

Data and Monte Carlo selection
The Pb+Pb data used to perform these measurements were collected in 2015 and 2018, and the   data used were collected in 2017 with the average number of inelastic interactions per bunch crossing ranging from 1.4 to 4.4.The events were triggered using a series of various  T -threshold single-jet triggers with the leading jets in the analysis being in a region where the trigger is fully efficient.Although only a small fraction of the Pb+Pb events (< 0.5%) contain multiple collisions, these were suppressed utilizing the observed anti-correlation, expected from the nuclear geometry, between the total transverse energy deposited in both of the forward calorimeters, Σ FCal T , and the energy in the ZDC, which is proportional to the number of observed spectator neutrons.Pileup collisions are not rejected in   collisions.
The overlap area of the two colliding nuclei in Pb+Pb collisions is characterized by the event centrality, which is estimated from the total transverse energy deposited in the FCal [19].This measurement considers five centrality intervals as defined according to successive percentiles of the Σ FCal T distribution obtained from minimum-bias collisions.The centrality intervals considered in this measurement are 0-10% (largest Σ FCal T ), 10-20%, 20-40%, 40-60%, and 60-80% (smallest Σ FCal T ).The values of the mean nuclear thickness function, ⟨ AA ⟩ [2], are determined using the TGlauberMC v3.2 [20]; the uncertainties in ⟨ AA ⟩ are discussed in Ref. [21].The ⟨ AA ⟩ values and their uncertainties are listed in Table 1 for each centrality selection considered in this measurement.[23] and the NNPDF23lo parton distribution functions (PDFs) [24].Pileup due to additional inelastic   interactions is similarly generated using Pythia 8 with the same PDFs and utilizing the A3 tune [25], tuned for inclusive QCD processes, matching the number of extra collisions in the   data.The MC samples for Pb+Pb collisions, one for the 2015 detector conditions and one for the 2018 detector conditions, each use 3.2 × 10 7   Pythia 8 events with the same A14 tune and PDFs as used for the generation of the   jet MC samples.The underlying event contribution to the detector signal is accounted for by overlaying the simulated   events with dedicated Pb+Pb data events from the 2015 Pb+Pb run and 2018 Pb+Pb run respectively.The data events from Pb+Pb collisions were combined with the signal from the Pythia 8 simulation of hard scattering events at the digitization stage, and then reconstructed as a combined event.This procedure enables the "data overlay" sample to accurately reproduce the effects of the underlying event on the jet response.This sample was reweighted on an event-by-event basis to ensure the same centrality distribution as is measured in the jet-triggered data samples.The detector response in all three MC samples was simulated utilizing Geant4 [26,27].Finally,   Herwig++ [28] events using the UEEE5 tune [29] and the CTEQ6L1 PDFs [30] are used for uncertainty studies.

Jet reconstruction and performance
The jet reconstruction procedures follow those used by ATLAS for previous jet measurements in Pb+Pb collisions [3,9].Jets are reconstructed using the anti-  algorithm [15] implemented in the FastJet software package [31].In both   and Pb+Pb collisions, jets with  = 0.2 and  = 0.4 are formed by clustering calorimetric towers of spatial size Δ × Δ = 0.1 × /32.The energies in the towers are obtained by summing the energies of calorimeter cells at the electromagnetic energy scale [32] within the tower boundaries.In Pb+Pb collisions, a background subtraction procedure is applied to estimate, within each event, the underlying event (UE) average transverse energy density, (, ), where the  dependence is due to global azimuthal correlations in the particle production from the hydrodynamic flow [33].The modulation accounts for the contribution to the UE of the second-, third-, and fourth-order azimuthal anisotropy harmonics characterized by values of flow coefficients  UE  [33].Additionally, the UE is also corrected for -and -dependent nonuniformities of the detector response by correction factors derived in minimum-bias Pb+Pb data.In   collisions, the same background subtraction procedure is applied to remove the pileup contribution to the jet, but without the -dependent modulation and without the correction for -and -dependent nonuniformities.
An iterative procedure is used to remove the impact of jets on the estimated  and  UE  values.The first estimate of the average transverse energy density of the UE, (), is evaluated in 0.1 intervals of , excluding towers within Δ = 0.4 of "seed" jets.In the first subtraction step, the seeds are defined to be a combination of  = 0.2 jets and  = 0.4 track-jets.Track-jets are reconstructed by applying the anti-  algorithm with  = 0.4 to charged particles with  T > 4 GeV.The  = 0.2 jets must pass a cut on the minimum value of the tower  T and on a ratio of maximum tower  T to average tower  T , while the track-jets are required to have  T > 7 GeV.The underlying event contribution is then subtracted from each tower constituent and the jet kinematics are recalculated.After the first iteration, the  and   values are updated by excluding from the UE determination the regions within Δ = 0.4 of both the track-jets and the newly reconstructed  = 0.2 jets with  T > 25 GeV (8 GeV) in Pb+Pb ( ) collisions.The updated  and  UE  values are used to update the jet kinematic properties in the second iteration.Jet -and  T -dependent correction factors derived in simulations are applied to the measured jet energy to correct for the calorimeter energy response [34,35].An additional correction based on in situ studies of jets recoiling against photons and jets in other regions of the calorimeter is applied [36].This calibration is followed by a "cross-calibration" which relates the jet energy scale (JES) of jets reconstructed by the procedure outlined in this section to the JES in 13 TeV   collisions [35].
"Truth"-level jets are defined in the MC sample before detector simulation by applying the anti-  algorithm with  = 0.4 to stable particles with a proper lifetime greater than 30 ps, but excluding muons and neutrinos, which do not leave significant energy deposits in the calorimeter.After the detector simulation the truth jets are matched to the nearest reconstructed jet within Δ < 0.  for jets with  truth T < 50 GeV in Pb+Pb collisions stems from jets for which there is an over subtraction of the underlying event.This is caused by the corresponding region of the detector not containing a "seed" jet above 25 GeV resulting in the jets energy contributing to the UE determination; this is corrected for in the unfolding procedure discussed below.The efficiency of reconstructing a jet with  T > 32 GeV, as evaluated from the probability of a truth-jet matching to a reconstructed jet with  T > 32 GeV in the MC simulation, can be seen as a function of  truth T in Figure 2.

Data analysis
The analysis and dĳet selection used here closely follow those in Ref. [11].In each data event, the reconstructed leading dĳet is constructed from the two highest- reco T jets in the event with reconstructed  reco T,1 > 79 GeV and  reco T,2 > 32 GeV, and both jets are required to have || < 2.1.The inclusion of leading jets down to  reco T,1 > 79 GeV provides an underflow region for the unfolding to enable inflow and outflow of jets from the measurement region.These dĳets are required to be back-to-back with |Δ| > 7/8.Events in which the leading dĳets do not meet these criteria are discarded.For dĳets matching the selection criteria, two-dimensional (  reco T,1 ,  reco T,2 ) distributions are constructed symmetrically across  reco T,1 =  reco T,2 .The distributions are symmetrized to account for the possibility of swapping the leading and subleading jet definition due to the finite JER.
The analysis procedure selects at most one dĳet per event and therefore has the potential to produce a biased subsample of the inclusive jets.Figure 3 shows the fraction of the inclusive jets which are also included in the leading dĳets used in this analysis.This quantity is shown as a function of  reco T for both central Pb+Pb and   collisions.The fraction is 47% (69%) at 100 GeV and rises to more than 82% (83%) at 200 GeV in central Pb+Pb collisions (  collisions).Due to the steep falloff of the jet yields with increasing  T and the finite JER, jets reconstructed at a given  T typically arise from jets at a lower truth  T , and thus the fractions shown here at the reconstructed- T scale underestimate the true fraction of inclusive jets included at a given  T .Nevertheless, the large value, and weak  T dependence, of the fraction of inclusive jets that are part of the leading dĳet imply that the dĳet selection in this analysis does not produce a particularly biased sample.The fractions are further broken down by leading and subleading jets.The relative fractions of leading and subleading jets at a given  T are driven largely by the steeply-falling  T spectrum convolved with the shape of the  J distribution.
The measured (  reco T,1 ,  reco T,2 ) distributions are a combination of the dĳet signal and pairs of uncorrelated jets.Since the underlying-event subtraction accounts for azimuthal correlations in the particle production due to hydrodynamic flow, the contribution from uncorrelated dĳets is independent of the Δ of the jets; therefore, a Δ sideband method is used to remove these pairs as a function of (  reco T,1 ,  reco T,2 ).The symmetrized two-dimensional (  reco T,1 ,  reco T,2 ) distribution of background combinatoric dĳets is determined using dĳets with 1 < |Δ| < 1.4 which, after normalizing to the Δ window of the signal band, is subtracted from the dĳet yields.This effect is strongest for 0-10% centrality Pb+Pb events at low  reco T,1 , where combinatoric dĳets constitute 13% of the dĳets for 79 <  reco T,1 < 100 GeV, and drops off rapidly both with increasing  reco T,1 and in more peripheral events.Because of how the leading dĳet is defined, the presence of residual combinatoric dĳets in the sample results in an inefficiency for genuine jet pairs, where one of the jets might be superseded by an uncorrelated third jet.This effect is corrected for using the measured inclusive jet spectrum from minimum-bias events to determine the efficiency loss as a function of the measured jet  T following the method discussed in Ref. [11].The resulting combinatoric-subtracted and efficiency-corrected symmetrized two-dimensional (  reco T,1 ,  reco T,2 ) distributions can be seen in Figure 4 for both central Pb+Pb and   collisions.The ability to remove uncorrelated jets and extract the truth-level leading-dĳet  J distributions in an unbiased way was confirmed by a closure test performed using the data overlay sample.
In order to correct for the effects of the JES and JER, the measured (  reco T,1 ,  reco T,2 ) distributions are unfolded using the iterative Bayesian unfolding procedure [37] as implemented in the RooUnfold [38] software package.A two-dimensional unfolding is used in order to account for bin migrations of both the leading and the subleading jet  T , as well as to account for possible swapping of the leading and subleading jet.A separate response matrix is generated for   collisions as well as for each centrality selection in Pb+Pb collisions.The response matrix used in the unfolding contains the relationship between (  truth T,1 ,  truth T,2 ) and (  reco T,1 ,  reco T,2 ).It is populated by identifying the leading and subleading truth-level jets in the MC sample which are matched to the corresponding reconstructed jets within Δ < 0.3.In order to account for migration from lower jet  reco T , the response matrices are populated with truth-level jets down to  truth T,1 of 20 GeV and  truth T,2 of 10 GeV.As with the reconstructed data, truth dĳets are required to have |Δ truth | > 7/8, with each jet being within | truth | < 2.1.The two selected reconstructed jets from the MC simulations are required to meet the same selection criteria as applied to dĳets measured in data.Truth  dĳets that do not match to a reconstructed dĳet meeting the selection criteria are accounted for by using an efficiency correction in the unfolding.Similarly to the construction of the data distributions, the response matrix is populated symmetrically in  T,1 and  T,2 .To construct a Bayesian prior which is similar to the measured distributions, the response matrices are reweighted along the  truth T,1 and  truth T,2 axes by the ratio of the two-dimensional reconstructed yields in data to those from simulation.The number of iterations used in the unfolding is tuned separately for each centrality in Pb+Pb collisions and for   collisions.The number of iterations in each case was selected to optimize the balance between the accuracy of the final unfolded yield, and the increased statistical uncertainty which results from a larger number of iterations.Six iterations were used for the 0-10% centrality Pb+Pb events, while four iterations were used for all other centralities as well as for   collisions.
In order to evaluate the statistical uncertainties of the data and the MC simulation, 1000 unfoldings were performed by varying each bin in either the data distribution or the response matrix independently according to its statistical uncertainty while preserving the symmetrization across  T,1 =  T,2 .The RMS of the resulting unfolded distributions in each (  T,1 ,  T,2 ) bin was taken as the contribution to the statistical uncertainty on the corresponding unfolded (  T,1 ,  T,2 ) bin.The data and response matrix statistical uncertainty components were combined in quadrature in order to obtain the total statistical uncertainty of the unfolded distributions.Due to the large number of bins in the two-dimensional unfolding, in some cases the uncertainties due to the finite MC sample sizes are comparable to those in the data.
To extract measurements of the dĳet momentum balance observable,  J , the unfolded two-dimensional (  T,1 ,  T,2 ) distributions are first reflected about  T,1 =  T,2 in order to restore the leading/subleading hierarchy.Then, following the procedure discussed in Ref. [11], the two-dimensional distributions are projected in slices of  T,1 into bins of  J .The upper edge of the  th  J bin boundary is defined by ((  T,  / T,0 ) 1/ ) −  , where  is the number of logarithmic  T bins (40), and  T,0 and  T,  are the minimum (10 GeV) and maximum (1 TeV) bin edges covered by the binning, respectively.This enables the mapping of the logarithmic  T,1 and  T,2 bins to  J in such a way that each reported (  T,1 ,  T,2 ) bin is fully contained within two adjacent  J bins.In this analysis, half of the yield in each (  T,1 ,  T,2 ) bin is apportioned to each of the two adjacent  J bins.An exception to this are the bins along the diagonal  T,1 =  T,2 , which contribute solely to the highest  J bin.
By projecting the resulting distributions over selections of  T,1 while normalizing by the number of dĳets ( pair ) and accounting for the  J bin widths, measurements of the dĳet yield-normalized  J distributions are extracted.The absolutely-normalized  J distributions are extracted by instead normalizing the  J distributions by the number of events and either the  AA in Pb+Pb collisions or the integrated luminosity in   collisions, as described by Exp.(5).
In order to quantify the energy losses of the leading and subleading jets within a dĳet, the nuclear modification factor,  pair AA , is measured for each of these selections.The  pair AA compares the per-event differential yield of jets at a given  T in Pb+Pb collisions with the cross-section in   collisions scaled by the  AA , as described in Eqs.(7) and (8).

Systematic uncertainties
Systematic uncertainties for this measurement are attributed to three categories of sources, those which arise from the analysis and unfolding procedure, those which stem from uncertainties in the jet energy resolution (JER) and scale (JES), and those connected with global normalization.For each uncertainty component in the first two categories, the entire analysis procedure, including unfolding, is repeated accounting for the modification to the analysis procedure or the response matrix and the result is compared with the nominal one.The third category applies to the absolutely-normalized  J distributions,  pair AA (  T,1 ), and  pair AA (  T,2 ); it contains the uncertainty in the determination of the mean nuclear thickness function, ⟨ AA ⟩, and the   luminosity.These uncertainties are independent of the jet transverse momentum and are noted on the figures.
The systematic uncertainty in the JES has four parts.First, a centrality-independent baseline component is determined from in situ studies of the calorimeter response to jets reconstructed with the procedure used in 13 TeV   collisions [39].A second, centrality-independent component accounts for the relative energy scale difference between the jet reconstruction procedures used in this analysis and those in 13 TeV   collisions.This is evaluated using the cross-calibration procedure described in Ref. [35].Potential inaccuracies in the Pythia 8 MC sample's description of the relative abundances of jets initiated by quarks and gluons and of the calorimetric response to quark and gluon jets are accounted for by the third, centrality independent, component -based on evaluating these same quantities using the Herwig++ MC sample.The fourth, centrality-dependent, component accounts for modifications of the parton shower due to quenching [40], which is not modeled in the simulations.The modifications to the parton shower can impact the detector response to jets in Pb+Pb collisions resulting in a small disagreement in the JES between data and simulations.The extent of this disagreement, and corresponding uncertainty contribution is evaluated by the method used in Ref. [35] for 2015 and 2011 data, which compares the jet  T measured in the calorimeter with the sum of the transverse momenta of charged particles within the jet, in both the data and MC samples.This uncertainty is determined as a function of event centrality and was found to be independent of jet  T and .The selected charged-particle tracks have  T > 4 GeV in order to exclude particles from the UE.The sum of the charged-particle transverse momenta provides a data-driven estimate of the centrality dependence of the JES arising from the observed centrality-dependent modification of the jet fragmentation due to jet quenching in Pb+Pb collisions [40].The size of this centrality-dependent uncertainty in the JES reaches 1.2% in the most central collisions and the value is applied independent of  J .For each individual component, the JES in the MC simulation was modified as a function of  T and  by one standard deviation, and the response matrix was recomputed.
The uncertainty due to the JER is evaluated by repeating the unfolding procedure with modified response matrices, where an additional contribution is added to the resolution of the reconstructed  T in the MC sample using a Gaussian smearing procedure.The smearing factor is evaluated using an in situ technique in 13 TeV   data that involves studies of dĳet  T balance [41].Further, an uncertainty is included to account for differences between the tower-based jet reconstruction and the jet reconstruction used in analyses of 13 TeV   data, as well as differences in calibration procedures.The modifications to the response are propagated through the unfolding and the resulting uncertainty is symmetrized.
Two sources of systematic uncertainty were included to account for uncertainties in the removal of the combinatoric background.The first contribution stems from the combinatoric subtraction method, and was determined by extracting the two-dimensional (  T,1 ,  T,2 ) distribution of combinatoric jets from an alternative sideband of 1.1 < |Δ| < 1.5 as was done in Ref. [11].The second contribution stems from the sensitivity of the analysis to the efficiency correction for combinatoric jets, and was evaluated by repeating the analysis without the inclusion of this efficiency correction.The deviation from the nominal result is taken as the uncertainty contribution.Additional sources of systematic uncertainty which account for the unfolding procedure were considered.The sensitivity to the Bayesian prior was evaluated by modifying the weights applied when producing the response matrix in a centrality-dependent manner in order to enclose the data (  reco T,1 ,  reco T,2 ) distributions between the corresponding MC distributions based on the nominal and alternative priors.There is a sensitivity to the minimum  jet T in the analysis at small  J and small  T,1 due to the efficiency correction made as part of the unfolding.The sensitivity of the result to this effect is evaluated by varying the minimum reconstructed  jet T , motivated by the magnitude of the JER, from 32 to 39 GeV for both data and simulation.This results in a significant contribution to the systematic uncertainties at low  J in low  T,1 bins.For each of these contributions the deviation of the unfolded result from the nominal is symmetrized and taken as a contribution to the systematic uncertainties.A closure test was performed using the MC samples by splitting them into two equal parts and using one part to produce a response matrix and the other in place of the data sample in the unfolding.The deviation between the unfolded result and the underlying truth-level distribution was taken as an estimate of this uncertainty.The uncertainty from each of these contributions is taken independently and symmetrized.
The magnitude of the systematic uncertainties in the dĳet-yield-normalized  J distributions can be seen in Figure 5 for both central and peripheral Pb+Pb collisions.In the central collisions, the total systematic  uncertainties are largely driven by the sensitivity of the unfolding to the choice of prior.In contrast, in peripheral collisions the total uncertainties are largely driven by the uncertainty in the JES and JER.The fractional uncertainties are largest at low  J in both collision systems; however, the yield in these  J regions is small.The systematic uncertainty contributions are similarly propagated to the calculation of the nuclear modification factor.The centrality-independent components of the JES and JER, as well as the sensitivity of the unfolding to the minimum measured

Dĳet-yield-normalized 𝒙 J distributions
The dĳet-yield-normalized  J distributions in   collisions are shown for three selections of  T,1 from 100 to 562 GeV in Figure 7.The measured distributions are compared with those from the Pythia 8 generator [22] using the A14 tune [23] in combination with the NNPDF23lo PDFs [24].The Pythia 8 sample is able to describe the data over the full  J range considered.
Figure 8 shows the measured dĳet-yield-normalized  J distributions in   collisions and as a function of centrality in Pb+Pb collisions for twelve  T,1 selections between 100 and 562 GeV.In central collisions, at 100 <  T,1 < 112 GeV a broad maximum is observed in the distributions at  J around 0.6.With increasing  T,1 as well as with decreasing centrality, this feature becomes less pronounced.Significant modification from   collisions is observed up to 398 <  T,1 < 562 GeV in the full centrality range; the  J distributions have a reduced fraction of balanced jets and an increased fraction of imbalanced jets.Figure 9 compares the measured distributions in Pb+Pb collisions with the predictions from the LIDO model [42].LIDO is a transport model including both elastic jet-medium collisions and medium-induced radiative processes, with event-by-event fluctuations implemented for both processes, as well as a simple model for the response of the medium.LIDO uses Pythia 8 [22] with the A14 tune [23] and the CTEQL1 PDF [30] to initialize their energy-loss calculation.The calculations are performed using two high likelihood values for the jet-medium coupling cutoff parameter:  min = 1.3 and  min = 1.8.This parameter is related to the strength of the coupling between the jet and the medium, where a smaller  min value corresponds to a larger coupling, and was constrained using inclusive jet and hadron suppression measurements [42].Only minimal sensitivity to the jet-medium coupling cutoff parameter is observed in the dĳet-yield-normalized  J distributions, with  min = 1.3 and  min = 1.8 demonstrating equal ability to reproduce the measured results.The model reproduces the behavior observed at high  T,1 and in 40-60% centrality Pb+Pb collisions while not reproducing the relative enhancement of intermediate  J observed at low  T,1 in 0-10% centrality Pb+Pb collisions.
Figure 10 shows a direct comparison between the dĳet-yield-normalized  J distributions in 0-10% centrality Pb+Pb collisions at 5.02 TeV for 100 <  T,1 < 200 GeV and results at 2.76 TeV from Ref. [11] for the same collision centrality and  T,1 selections.Although these two measurements are performed at different collision energies, similar levels of quenching are expected, based measurements of inclusive jets [3,43].The  J distributions are observed to be consistent within systematic uncertainties at the two collision energies.For 100 <  T,1 < 126 GeV, a peak is observed at intermediate  J for both collision energies.

Absolutely normalized 𝒙 J distributions
The absolutely normalized  J distributions, as calculated with Exps.( 5) and ( 6) for Pb+Pb and   collisions respectively, allow a direct comparison of the absolute dĳet yields between Pb+Pb and   collisions as a function of  J . Figure 11 shows these distributions for   and Pb+Pb collisions as a function of centrality for three  T,1 selections: 100-112 GeV, 200-224 GeV, and 398-562 GeV.Balanced dĳets are suppressed in central Pb+Pb collisions relative to asymmetric dĳets, leading to the peak structure observed in the dĳet-yield-normalized  J distributions at low  T,1 .The depletion of balanced dĳets persists over all  T,1 and centrality selections measured here, with the magnitude of the depletion decreasing with increasing  T,1 and towards more peripheral collisions.When going from central Pb+Pb collisions to   collisions for 100 <  T,1 < 112 GeV, the suppression of dĳets is smaller for  J < 0.6 than for higher  J .For higher  T,1 , there is a smaller difference between   and Pb+Pb collisions at low  J .
Figure 12 shows the absolutely normalized  J distributions compared with the same LIDO calculations [42] as in the previous section for three  T,1 selections from 100 to 562 GeV.The LIDO   calculation is also shown.For   collisions, LIDO uses Pythia 8 [22] with the A14 tune [23] and the CTEQL1 PDF [30].The LIDO model overestimates the   collision results at large  J ; the size of the discrepancy between the model and the data decreases with increasing  T,1 .This trend persists, but with a smaller difference in 40-60% centrality Pb+Pb collisions.In 0-10% centrality Pb+Pb collisions, the LIDO model's prediction is flatter than the data in the lowest  T,1 range, but agrees well at higher  T,1 .

AA of leading and subleading jets
The pair nuclear modification factors projected for leading and subleading jets, as defined in Eqs. ( 7) and ( 8), are shown for three centrality selections as a function of the jet  T in Figure 13.Both  pair AA (  T,1 ) and  pair AA (  T,2 ) show significant modification from a value of one in all but the most peripheral collisions, with a stronger suppression observed at low  jet T .It is observed that the subleading jets are more suppressed than leading jets, particularly at  T > 200 GeV where nearly all the inclusive jets (within the rapidity range of this analysis) are included in the dĳet sample.This behavior is qualitatively reproduced in predictions made by the LIDO [42] model.In the LIDO model, the jet-medium coupling cutoff parameter  min = 1.3 clearly predicts a larger suppression for both jets than is observed in the data.The calculation with  min = 1.8 is closer to the data but does not describe the trends with  T and centrality.
The different levels of suppression observed for leading and subleading jets is quantified as a function of centrality in the ratio  pair AA (  T,2 )/ pair AA (  T,1 ) integrated over  jet T between 100 and 316 GeV as shown in Figure 14, where  pair AA (  T,2 ) is seen to be smaller than  pair AA (  T,1 ) in all centrality selections.The suppression of subleading jets relative to leading jets is most significant in 0-10% centrality Pb+Pb collisions and decreases smoothly towards peripheral Pb+Pb collisions.In 0-10% centrality Pb+Pb events, subleading jets are approximately 20% more suppressed than leading jets, with 60-80% centrality Pb+Pb events seeing only about 5% more suppression for subleading jets than for leading jets.The value of  pair AA (  T,2 )/ pair AA (  T,1 ) in 60-80% centrality Pb+Pb events is 3 away from one, providing evidence of jet quenching in peripheral Pb+Pb collisions.In contrast, in inclusive jet measurements, due to the larger uncertainties, no significant suppression is observed in this  T range for the most peripheral Pb+Pb collisions [3].This is in qualitative agreement with results from CMS [44], which find that, compared to   collisions, the subleading jets in dĳet events in Pb+Pb collisions have stronger modification to their structure than leading jets.

pb pp
Figure 12: The absolutely normalized  J distributions for 100 <  T,1 < 112 GeV (top), 200 <  T,1 < 224 GeV (center), and 398 <  T,1 < 562 GeV (bottom) in   collisions and for two centrality selections in Pb+Pb collisions.For Pb+Pb collisions, the measurements are compared with predictions from LIDO [42] for two values of the jet-medium coupling cutoff parameter,  min = 1.3 and  min = 1.8, and the   collision measurements are compared with the LIDO   collision calculation.

Conclusion
This paper presents a measurement of the unfolded double-differential yields of leading dĳets.The yields are presented as measurements of the dĳet  J distributions and the  pair AA projected for leading and subleading jets, using 2.2 nb −1 of Pb+Pb data and 260 pb −1 of   data collected at √  NN = 5.02 TeV by the ATLAS detector at the LHC.The measurement of the  J distributions is performed differentially in  T,1 and centrality, and the  AA of leading and subleading jets is measured differentially in jet  T and centrality.The presented results are unfolded to correct for detector response and inefficiencies.
The dĳet-yield-normalized  J distributions, across the full  T,1 range considered in this analysis, show significant broadening in central Pb+Pb collisions relative to those in   collisions.Up to the highest  T,1 interval considered in this measurement, 398 <  T,1 < 562 GeV, significant modification from the distributions in   collisions is observed for central Pb+Pb collisions.With decreasing  T,1 the modifications from the distributions in   collisions become larger, with significant modifications observed for all centralities at 100 <  T,1 < 112 GeV.In 0-10% centrality Pb+Pb collisions, between 100 and 112 GeV, the distribution is peaked around  J of 0.6, indicating that the most probable configuration for dĳets is to be highly imbalanced in  T .Measurements of absolutely normalized  J distributions show that this comes from the suppression of balanced dĳets, as opposed to an enhancement of imbalanced jets, in comparison with   collisions.This suppression of balanced dĳets evolves smoothly as a function of the event centrality, with peripheral Pb+Pb collisions demonstrating only slight modification from   collisions.The measurements of the pair nuclear modification factor,  pair AA (  T,1 ) and  pair AA (  T,2 ), show that subleading jets are more suppressed than leading jets.This is observed to be largely independent of jet  T and this behavior is seen in all centralities.In central collisions, subleading jets are observed to be 20% more suppressed than the leading jets.In peripheral collisions, the suppression of subleading jets relative to leading jets is reduced, but the stronger suppression of subleading jets remains significant.These measurements provide new information about the role of path-length dependence and fluctuations in jet energy loss which will help constrain models of parton energy loss in the quark-gluon plasma.

Appendix
For completeness, the data including the full range of  T,1 intervals and centrality selections in Pb+Pb collisions are included here.Figure 15 shows the dĳet-yield-normalized distributions for   collisions, compared to Pythia 8 calculations.Figure 16 shows unfolded 1  pair   pair   J distributions for both Pb+Pb and   collisions over twelve selections in  T,1 between 100 and 562 GeV, for centrality intervals omitted previously.Figure 17 shows absolutely normalized  J distributions for five centrality intervals for both Pb+Pb and   collisions for 12 selections of  T,1 between 100 and 562 GeV.Finally, Figure 18 provides

3 .Figure 1 :
Figure 1: The jet energy scale, JES, (left) and jet energy resolution, JER, (right) as a function of  truth T for centrality selections in Pb+Pb and in   collisions.

Figure 2 :> 32
Figure 2: The efficiency of reconstructing a jet with  reco T > 32 GeV as a function of  truth T for centrality selections in Pb+Pb collisions and   collisions.The statistical uncertainties shown are smaller than the point markers.

Figure 3 :
Figure 3: Measured fractions of the inclusive jets which are part of the leading dĳet (black), the leading jet of the dĳet (red), or subleading jet of the dĳet (blue), all as a function of  reco T for 0-10% centrality Pb+Pb collisions (left) and   collisions (right).

Figure 5 :
Figure 5: The systematic uncertainty breakdown of the  J distributions in central (left) and peripheral (right) Pb+Pb collisions as well as   collisions (bottom).The panels have different vertical axis ranges.
jet T , are treated as correlated between Pb+Pb and   collisions.The remainder of the contributions to the systematic uncertainty, including the centrality-dependent component of the JES, are treated as uncorrelated between Pb+Pb and  .The resulting uncertainties in  pair AA (  T,1 ) and  pair AA (  T,2 ) are shown for 0-10% centrality Pb+Pb collisions in Figure 6; these uncertainties are dominated by the JES uncertainty.In the ratio of  pair AA (  T,2 ) to  pair AA (  T,1 ), each source of systematic uncertainty is treated as fully correlated between  pair AA (  T,2 ) and  pair AA (  T,1 ), including the global systematic uncertainties.

Figure 6 :
Figure 6: The systematic uncertainty breakdown of the  pair AA for leading jets (left) and subleading jets (right).Uncertainty on the  AA and   luminosity are not shown.

Figure 11 :
Figure 11: The absolutely normalized  J distributions for 100 <  T,1 < 112 GeV (top), 200 <  T,1 < 224 GeV (center), and 398 <  T,1 < 562 GeV (bottom) in   collisions and for five centrality selections in Pb+Pb collisions.Statistical uncertainties are shown as error bars (which are smaller than the markers in many cases) and systematic uncertainties are shown as boxes.The global normalization uncertainties due to the  AA for each centrality as well as the   luminosity are listed in the legends.

Figure 13 :
Figure 13: The leading and subleading jet  pair AA distributions measured for a selection of centrality regions compared with predictions from LIDO [42].Statistical uncertainties are shown as error bars (which are smaller than the markers in many cases) and systematic uncertainties are shown as boxes.

Figure 14 :
Figure 14: The ratio of the subleading-jet to leading-jet nuclear modification factors integrated over jet  T between 100 and 316 GeV.Statistical uncertainties are shown as error bars (which are smaller than the markers in many cases) and systematic uncertainties are shown as boxes.

Figure 17 :
Figure 17: Comparison of the absolutely normalized  J distributions in   collisions and five centrality selections in Pb+Pb collisions.

Table 1 :
The ⟨ AA ⟩ values and uncertainties for the centrality selections used in this measurement.These are the results from TGlauberMC v3.2 modeling of the summed transverse energy in the forward calorimeters, Σ FCal T .
[22]rality selection ⟨AA ⟩ ± ⟨ AA ⟩ [1/This analysis uses four Monte Carlo (MC) samples to evaluate the detector performance and correct for detector effects.The   MC sample used in this analysis includes 3.2 × 10 7 Pythia 8[22]  jet events generated at √  = 5.02 TeV with parameter values set according to the A14 tune