Measurement of suppression of large-radius jets and its dependence on substructure in Pb+Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV with the ATLAS detector

This letter presents a measurement of the nuclear modification factor of large-radius jets in $\sqrt{s_\mathrm{NN}} = 5.02$ TeV Pb+Pb collisions by the ATLAS experiment. The measurement is performed using 1.72 nb$^{-1}$ and 257 pb$^{-1}$ of Pb+Pb and $pp$ data, respectively. The large-radius jets are reconstructed with the anti-$k_{t}$ algorithm using a radius parameter of $R = 1.0$, by re-clustering anti-$k_{t}$ $R = 0.2$ jets, and are measured over the kinematic range of $158<p_{\mathrm{T}}<1000$ GeV and $|y|<2.0$. The large-radius jet constituents are further re-clustered using the $k_{t}$ algorithm in order to obtain the splitting parameters, $\sqrt{d_{12}}$ and $\Delta R_{12}$, which characterize the transverse momentum scale and angular separation for the hardest splitting in the jet, respectively. The nuclear modification factor, $R_{\mathrm{AA}}$, obtained by comparing the Pb+Pb jet yields to those in $pp$ collisions, is measured as a function of jet transverse momentum ($p_{\mathrm{T}}$) and $\sqrt{d_{12}}$ or $\Delta R_{12}$. A significant difference in the quenching of large-radius jets having single sub-jet and those with more complex substructure is observed. Systematic comparison of jet suppression in terms of $R_{\mathrm{AA}}$ for different jet definitions is also provided. Presented results support the hypothesis that jets with hard internal splittings lose more energy through quenching and provide a new perspective for understanding the role of jet structure in jet suppression.

Heavy-ion collisions at high energies lead to the creation of matter composed of unconfined quarks and gluons known as quark-gluon plasma (QGP).Studies of the collective expansion of the QGP [1] have demonstrated that the plasma is strongly coupled.A major goal of the experimental high-energy nuclear physics programs at the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) is to understand how the strong coupling of the QGP arises from a theory that is asymptotically free [2,3].Jets, collimated sprays of hadrons originating in hard scattering processes, represent a key tool for studying the microscopic interactions between color charges within the QGP that ultimately determine its properties.Those interactions can alter the energy and angular distributions of constituents within the jets -a phenomenon referred to as "jet quenching" [4,5].As a result, the jet yields are suppressed and jet properties are significantly modified in heavy-ion collisions relative to those measured in elementary proton-proton ( ) collisions.
At the LHC, jet quenching was studied using many observables [6].Jet substructure observables [7], constructed from measured jet constituents, are versatile tools to measure the changes in jet properties due to jet quenching.These observables, calculated separately for each jet using a variety of algorithms, were originally motivated by studies of highly Lorentz-boosted massive objects in elementary collisions [8].Jet grooming algorithms that remove soft and wide-angle radiation can help mitigate impact of backgrounds from multiple collisions within one bunch crossing (pileup) or the underlying event (UE) on these observables.They also can be used to separate hard components of a parton shower, for example, sub-jets, in a jet with multi-prong structure [9,10].In the context of jet quenching, these methods enable distinguishing sub-jets resulting from hard splittings in the parton shower from soft medium-induced radiation [11], soft particles resulting from jet-induced medium excitations [12], and the UE.Furthermore, the dependence of the jet quenching on such splittings, and more generally, the complexity of the parton shower [13] can be studied using substructure techniques.
One specific phenomenon connected with the parton shower complexity is the color (de)coherence [14][15][16].This phenomenon results from quantum interference between successive splittings, and it is believed to largely dictate the magnitude of the energy loss [17,18].In-medium jet evolution is then characterized by a vacuum-like parton cascade whose constituents are either resolved by the medium due to color decoherence or remain unresolved and radiate coherently as a single color charge.This induces a dependence of the observed jet suppression on the structure of splittings, which may be experimentally accessed by substructure techniques [13].
Jet substructure was measured in lead-lead (Pb+Pb) collisions at the LHC using several observables: the momentum ratio of two leading sub-jets,   [19][20][21], the groomed jet radius,   [21], the groomed jet mass [22], the number of branches obtained in the iterative declustering of the jet [20], and the -subjetiness [23].Typically the per-jet normalized distributions of substructure observables are measured in Pb+Pb collisions and compared with the same quantity measured in   collisions or to that obtained from Monte Carlo (MC) simulations.A recent measurement of   , fully corrected for detector effects and with a robust grooming method to reduce the impact of fluctuating backgrounds on the sub-jet selection, reported no significant change of the   distribution in Pb+Pb collisions [21].A narrowing of the   distribution was observed in Pb+Pb collisions [21] which may be due to the color coherence effects or due to the difference in the relative suppression of quark-and gluon-initiated jets [24].No change of the groomed mass distribution for the core of the jet was observed, and only a hint of an increase for jets with large jet mass was seen [22].Furthermore, no significant change in the per-jet yields of the two-pronged structure was observed in Pb+Pb collisions relative to the MC-based reference in the measurement of -subjetiness [23].
One important conceptual issue associated with jet substructure measurements is that the QGP may not directly modify the hard splittings of a jet since their formation time is much shorter than the formation time of the QGP [18].Thus, changes in substructure distributions can only arise from a substructuredependent quenching mechanism of the jets.Rather than measuring the per-jet normalized distributions of a substructure variable, which are resulting from an admixture of jets suffering different energy loss, it may be advantageous to, instead, quantify the suppression of jets having different substructure using the jet nuclear modification factor,  AA [25].
This Letter provides the first observation and quantification of the dependence of the large-radius jet suppression on the jet substructure, namely on the presence of hard splittings in the parton shower.The suppression of large-radius jets is measured with the ATLAS detector differentially in jet transverse momentum ( T ) and also in two specific substructure observables.The jet suppression is quantified in terms of jet  AA .The two substructure observables are the splitting parameter,

√
12 , and the angular separation, Δ 12 , which characterize the transverse momentum scale and the angular separation, respectively, for the hardest splitting in the jet.This quantification allows direct access to the difference between the energy loss of single-prong jets and the energy loss of jets with more complex structure involving early hard splittings which was not possible with previous measurements.The use of large-radius jets then delimits the measured kinematics of the internal splitting.The results also provide a direct quantification of cone-size dependence of energy loss.Detailed quantification of jet suppression as a function of angular separation at small opening angles using tracks associated with calorimeter small-radius jets follows in a separate study by ATLAS [26].
The principal components of the ATLAS detector [27] used in this measurement are the inner tracking detector, electromagnetic and hadronic calorimeters, and the online trigger system.The inner tracking detector is surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field and it covers the pseudorapidity range || < 2.5. 1 It consists of silicon pixel, silicon microstrip, and transition radiation tracking detectors.Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic (EM) energy measurements with high granularity.A steel/scintillator-tile hadron calorimeter covers the central pseudorapidity range (|| < 1.7).Liquid-argon calorimeters with separate EM and hadronic compartments instrument the endcap (up to || = 3.2) and forward (FCal, up to || = 4.9) regions.Both the inner detector and calorimeter systems have a 2 coverage in azimuth.Two zero-degree calorimeters (ZDC) are composed of four longitudinal layers of tungsten absorbers and quartz rods.They are situated in the far forward region || > 8.3 and primarily measure the spectator neutrons from the struck Pb nuclei.An extensive software suite [28] is used in data simulation, in the reconstruction and analysis of real and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment.
The analysis uses 1.72 nb −1 of Pb+Pb data at √  NN = 5.02 TeV recorded in 2018 and 257 pb −1 of   data collected in 2017 at the same center-of-mass energy.Events were selected using a combination of calorimeter-based jet triggers [29,30].Both the   and Pb+Pb events are required to contain at least one primary vertex.All jets in the analysis are in a kinematic range where the jet trigger was fully efficient.The Pb+Pb data contain only a small fraction of events (<0.5%) with multiple collisions per bunch crossing which are further suppressed using the anti-correlation of signal from ZDC and FCal.The   data were 1 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.
collected with typically 1.4 − 4.4 inelastic interactions per bunch crossing.No pileup rejection is applied in the analysis of   data.
The centrality of Pb+Pb events is defined using the total transverse energy measured in the FCal, Σ FCal T [31,32].Events in Pb+Pb data are classified into four centrality intervals, ordered from the most central to the most peripheral: 0 − 10%, 10 − 30%, 30 − 50%, and 50 − 80%.The values of the mean nuclear thickness function with their uncertainties,  AA (used as an input to  AA ), are evaluated in each centrality interval by a Glauber model analysis of the Σ FCal T distribution [33,34].
Several MC simulation samples are used to evaluate the performance of the analysis procedure and to correct the measured distributions for detector effects.The   MC sample uses 4 × 10 7 P 8 [35] jet events at √  = 5.02 TeV with the A14 ATLAS tune [36] and the NNPDF23LO parton distribution functions (PDF) [37].Pileup from additional   collisions is generated by P 8, with parameter values set to the A2 tune [38] and using the MSTW2008 [39] PDF set, with a distribution of the number of extra collisions matching that of data.
The Pb+Pb MC sample uses 4 × 10 7   P 8 events with the same tune and PDFs as in   MC samples that are overlaid on top of events from a dedicated sample of Pb+Pb data events.This sample was recorded with a combination of minimum-bias and total energy triggers requiring 1.5 TeV or 6.5 TeV to enhance the number of central collisions.This "MC overlay" sample was re-weighted on an event-by-event basis such that it has the same centrality distribution as the jet-triggered data sample.The detector response in all MC samples was simulated using G 4 [40,41].
First, jets with radius parameter  = 0.2 are reconstructed using the anti-  algorithm [42,43] from calorimeter energy deposits as described in Ref. [44].The jet kinematics are corrected event-by-event for the contribution from the UE particles, and are calibrated using simulations of the calorimeter response and in situ measurement of the absolute energy scale [45].
The large-radius jets are defined by clustering the small-radius,  = 0.2, jets with  T > 35 GeV and || < 3.0 using anti-  algorithm with radius parameter  = 1.0.These requirements and procedure limits the impact of UE on the measurement but prohibits recovering the quenched jet energy [11] transferred outside the  = 0.2 sub-jets.The   jet finding algorithm [43,46] is used to re-cluster  = 0.2 jet constituents to obtain two observables of interest, Δ 12 and √  12 .These are defined as the angular separation and the splitting parameter of the   algorithm calculated for two jets before the final clustering step of  = 1.0 jet The large-radius jet yields in Pb+Pb collisions and jet cross-section in   collisions measured in the kinematic range of 158 <  T < 1000 GeV and || < 2.0 are evaluated inclusively and differentially in each of the two substructure observables.The   clustering of large-radius jet constituents with only a single sub-jet defaults to √  12 = 0 and Δ 12 = 0.These jets, which consist of a single  = 0.2 jet, centered on the  = 1.0 jet axis with no other clustered activity in the large-radius cone, populate only the first interval in √  12 and Δ 12 .The fraction of reconstructed large-radius jets with a single sub-jet in   collisions is 75% in the  T interval of 158 − 200 GeV and 62% in the  T interval of 316 − 500 GeV.More details of the sub-jet multiplicity can be found in the Appendix.The jet performance of large-radius reclustered jets was analyzed using MC samples.The jet energy scale (JES) was found to be within a 3% range from 1.
The measured inclusive and differential distributions are corrected for detector effects by the iterative Bayesian unfolding method [47,48] in one dimension and two dimensions, respectively, to return the distributions to the particle level.The unfolding accounts for the effects of bin migrations due to the jet energy resolution (JER) and JES.It also corrects the combinatoric sub-jet contribution originating from fluctuations of the UE and from jets from different hard partonic interactions in the same Pb+Pb collision resulting in migration in the substructure observable.To better represent the data, the simulated distributions are re-weighted along the generator-level jet  T ,

√
12 , and Δ 12 axes by the reconstructionlevel data-to-simulation ratio before the unfolding.The number of iterations in the unfolding was chosen such that the result is stable when changing the number of iterations while minimizing the amplification of statistical uncertainties.Four iterations were used for inclusive  = 0.2 and  = 1.0 jet yields and cross-sections, while six and eight iterations were used in the unfolding of √  12 and Δ 12 distributions, respectively.Generator-level jets that do not match to a reconstructed jet passing the selection criteria are incorporated as an inefficiency correction after the unfolding.
A dominant source of systematic uncertainty is the uncertainty in the JES.For more central collisions, the uncertainty in JER is equally important.The systematic uncertainty on the JES contains components from calorimeter response uncertainties derived from in situ studies [45], a component connected with the JES in the Pb+Pb environment [49], components accounting for inaccuracies in the description of the relative abundances of jets initiated by quarks and gluons and their calorimetric response, and a component connected with the jet radius.The magnitude of the uncertainty in the  AA from the JES uncertainty varies from 5% to 20% as a function of  T , √  12 , Δ 12 , and centrality.The primary component of the JER uncertainty is derived using an in situ technique involving studies of dĳet energy balance [50,51].The resulting uncertainty in  AA reaches ∼20% in 0-10% central collisions at low √  12 and Δ 12 , but it is typically below 5%.The systematic uncertainty of the unfolding procedure is estimated by repeating the analysis with response matrices without the re-weighting to match the shapes of measured distributions in data and it is typically bellow 5%.Other systematic uncertainties consist of the deviation between the unfolded result and the underlying generator-level distribution in simulation, the uncertainty in the determination of  AA values [44], and the uncertainty in the determination of the   luminosity [52].The colored boxes at  AA = 1 represent fractional uncertainty in  AA and   luminosity in this measurement and   luminosity in previous analysis [44], which both affect the overall normalization.
The nuclear modification factor for large-radius jets evaluated in the  T interval of 200 − 251 GeV as a function of the √  12 is shown in the left panel of Figure 1.The  AA values for large-radius jets with a single sub-jet are significantly larger compared with the  AA for large-radius jets with a more complex substructure having a non-zero √  12 .This observation is qualitatively consistent with the scenario in which the medium cannot resolve partonic fragments below a certain transverse scale [53].This result is also consistent with the previous measurement of correlated production of pairs of nearby jets in Pb+Pb collisions [54] where a larger suppression of neighboring jets compared with inclusive jets was observed.For √  12 > 0, the  AA values are constant as a function of √  12 within uncertainties for all the centrality intervals.
The right panel of Figure 1 shows  AA of large-radius jets evaluated as a function of Δ 12 for  T = 200 − 251 GeV.The trends seen for  AA (Δ 12 ) are the same as those seen for  AA ( √  12 ): suppression is significantly smaller for the single sub-jets case, and then constant within uncertainties for non-zero Δ 12 values.The other  T intervals spanning the range of 158 <  T < 500 GeV show the same trends.These observations are in contrast with non-monotonic  T and radial dependence of production of charged particles associated with jets measured using fragmentation functions or jet shapes [55][56][57].The measurement of the   splitting scale by √  12 and radial dependence of sub-jet suppression by Δ 12 thus provide new information relative to previously measured transverse and radial structure of jets using charged particles.
A systematic comparison of jet suppression in terms of jet  AA ( T ) for different jet definitions is provided in Figure 2. The jet  AA is measured for:  = 1.0 re-clustered jets with single sub-jet,  = 1.0 re-clustered jets with multiple sub-jets,  = 1.0 re-clustered inclusive jets,  = 0.2 jets, and  = 0.4 jets [44].
Production of  = 1.0 re-clustered inclusive jets is suppressed more than the production of  = 0.2 or  = 0.4 jets.Various theoretical calculations of the jet quenching where the jet energy is distributed to soft particles predict less suppression when expanding the jet radius by recovering more lost energy, see e.g.Ref. [58].This energy recovery may however not happen in the case of re-clustered large-radius jets where energy radiated outside of  = 0.2 sub-jets is removed.A singular situation when the re-clustered large-radius jet is completely removed due to all sub-jets being suppressed below 35 GeV cut is very unlikely given the minimum  T threshold of 158 GeV on  = 1.0 jet and relatively small multiplicity of sub-jets.Thus, in general, variations in the jet definition used in this study allow including different fractions of the lost energy and energy from the medium response to the showering process.Comparing new results with theoretical calculations may therefore help to understand possible biases in the quantification of energy loss using traditional, small-radius jets.The presented quantification of cone-size dependence of  AA may also be used to constrain theoretical uncertainties in the recently analytically calculated cone-size dependent energy loss [59].
The  = 1.0 re-clustered jets with multiple sub-jets show the largest suppression while the  = 1.0 re-clustered jets with a single sub-jet show the smallest suppression out of all jet definitions.The sizable difference between the  AA for multiple sub-jet and single sub-jet configurations provides an important input for understanding the role of color decoherence in the jet quenching.This sizable difference is not due to missing a contribution from the energy radiated out of the  = 0.2 cone since this radiated energy is not measured in all configurations of  = 1.0 jets with sub-jets.The lack of jet  T dependence in the  AA of  = 1.0 re-clustered jets with multiple sub-jets might be understood to be the consequence of increasing sub-jet multiplicity with increasing jet  T (see sub-jet multiplicity distributions in Appendix).More sub-jets may imply more sources of radiation which may lead to flattening of  AA at high- T .Finally, it should be noted that any direct comparisons of  AA between different jet definitions should be treated with care as the same particles reconstructed with a different procedure might appear in different jet  T intervals.
In conclusion, this Letter provides a measurement of the jet nuclear modification factor for large-radius jets which is differential in  T and in transverse and radial substructure observables.Presented observations are qualitatively consistent with the hypothesis that jets with hard internal splittings lose more energy, and provide a new perspective for understanding the role of jet structure in jet suppression in the QGP.

Figure 1 :
Figure 1: The values of  AA for  = 1.0 re-clustered jets as function of √  12 (left) and Δ 12 (right) in four centrality intervals.The label 'SSJ' on the -axis identifies the single sub-jet configuration.The vertical bars on the data points indicate statistical uncertainties, the shaded boxes indicate systematic uncertainties.The fully correlated fractional uncertainties due to the luminosity and  AA are represented by boxes at  AA = 1.One data point with a relative statistical uncertainty above 50% is not displayed.

Figure 2 :
Figure 2: Comparison of  AA distributions evaluated in 0 − 10% central collisions as a function of  T for several jet definitions:  = 1.0 re-clustered inclusive jets (circles),  = 1.0 re-clustered jets with a single sub-jet (crosses),  = 1.0 re-clustered jets with multiple sub-jets (squares),  = 0.2 jets (diamonds),  = 0.4 jets (stars) [44].The vertical bars on the data points indicate statistical uncertainties, the shaded boxes indicate systematic uncertainties.The colored boxes at  AA = 1 represent fractional uncertainty in  AA and   luminosity in this measurement and   luminosity in previous analysis[44], which both affect the overall normalization.