Regular Article -Experimental Physics Determination of jet calibration and energy resolution in . proton–proton collisions at s = 8 TeV using the ATLAS detector ATLAS Collaboration CERN, 1211 Geneva 23, Switzerland Received: 11 October 2019 / Accepted: 13 September 2020 / Published online: 1 December 2020 © CERN for the beneft of the ATLAS collaboration 2020 Abstract The jet energy scale, jet energy resolution, and their systematic uncertainties are measured for jets recon­structed with the ATLAS detector in 2012 using proton– proton data produced at a centre-of-mass energy of 8 TeV with an integrated luminosity of 20 fb-1. Jets are recon­structed from clusters of energy depositions in the ATLAS calorimeters using the anti-kt algorithm. A jet calibration scheme is applied in multiple steps, each addressing spe­cifc effects including mitigation of contributions from addi­tional proton–proton collisions, loss of energy in dead mate-rial, calorimeter non-compensation, angular biases and other global jet effects. The fnal calibration step uses several in situ techniques and corrects for residual effects not cap­tured by the initial calibration. These analyses measure both the jet energy scale and resolution by exploiting the trans-verse momentum balance in . +jet, Z + jet, dijet, and multi­jet events. A statistical combination of these measurements is performed. In the central detector region, the derived calibra­tion has a precision better than 1% for jets with transverse momentum 150 GeV < pT < 1500 GeV, and the relative energy resolution is (8.4 ± 0.6)%for pT = 100 GeV and (23 ± 2)%for pT = 20 GeV. The calibration scheme for jets with radius parameter R = 1.0, for which jets receive a dedicated calibration of the jet mass, is also discussed. Contents 1 Introduction..................... 2 2 The ATLAS detector and data-taking conditions .. 3 3 Simulation of jets in the ATLAS detector ..... 3 4 Overview of ATLAS jet reconstruction and calibration 4 4.1 Jet reconstruction and preselection ...... 4 4.2 Matching between jets, jet isolation, and calorime­terresponse .................. 6 4.3 Jetcalibration ................. 6 4.4 Defnition of the calibrated jet four momentum 9 5 Global sequential calibration ............ 11  e-mail: atlas.publications@cern.ch 5.1 Descriptionofthemethod ........... 11 5.2 Jet observables sensitive to the jet calorimeter response.................... 11 5.3 Derivation of the global sequential jet calibration 12 5.4 Jet transverse momentum resolution improve­mentinsimulation ............... 12 5.5 Flavour dependence of the jet response in sim­ulation..................... 15 5.6 In situ validation of the global sequential calibration 15 5.7 Comparison of jet resolution and favour depen­dence between different event generators ... 20 6 Intercalibration and resolution measurement using dijetevents ..................... 21 6.1 Techniques to determine the jet calibration and resolution using dijet asymmetry ....... 21 6.2 Determining the jet resolution using the dijet bisectormethod ................ 22 6.3 Dijetselection ................. 23 6.4 Method for evaluating in situ systematic uncer­tainties..................... 23 6.5 Relative jet energy scale calibration using dijet events ..................... 24 6.6 Jet energy resolution determination using dijet events ..................... 27 7 Calibration and resolution measurement using . +jet and Z +jetevents ................. 27 7.1 The direct balance and missing projection fractionmethods ................ 28 7.2 Eventandobjectselection ........... 29 7.3 Jet response measurements using Z + jet and . +jetdata ................... 30 7.4 Calibration of large-R jets .......... 35 7.5 Measurement of the jet energy resolution usingtheDBmethod ............. 39 8 High-pT-jet calibration using multijet balance ... 41 8.1 Eventselection ................ 43 8.2 Results..................... 43 8.3 Systematic uncertainties ............ 44 9 Final jet energy calibration and its uncertainty ... 44 123 9.1 Combination of absolute in situ measurements 44 9.2 Jet energy scale uncertainties ......... 47 9.3 Simplifed description of uncertainty correlations .49 9.4 Alternative uncertainty confgurations .... 53 9.5 Large-R jetuncertainties ........... 53 10 Final jet energy resolution and its uncertainty ... 54 10.1JERinsimulation ............... 54 10.2 Determination of the noise term in data .... 56 10.3 Combined in situ jet energy resolution mea­ surement.................... 61 11Conclusions ..................... 65 References........................ 66 1 Introduction Collimated sprays of energetic hadrons, known as jets, are the dominant fnal-state objects of high-energy proton–proton ( pp) interactions at the Large Hadron Collider (LHC) located at CERN. They are key ingredients for many physics mea­surements and for searches for new phenomena. This paper describes the reconstruction of jets in the ATLAS detector [1] using 2012 data. Jets are reconstructed using the anti-kt [2] jet algorithm, where the inputs to the jet algorithm are typically energy depositions in the ATLAS calorimeters that have been grouped into “topological clusters” [3]. Jet radius parameter values of R = 0.4, R = 0.6, and R = 1.0are considered. The frst two values are typically used for jets initiated by gluons or quarks, except top quarks. The last choice of R =1.0 is used for jets containing the hadronic decays of massive particles, such as W/Z/Higgs bosons and top quarks. The same jet algorithm can also be used to form jets from other inputs, such as inner-detector tracks associ­ated with charged particles or simulated stable particles from the Monte Carlo event record. Calorimeter jets, which are reconstructed from calorime­ter energy depositions, are calibrated to the energy scale of jets created with the same jet clustering algorithm from sta­ble interacting particles. This calibration accounts for the following effects: • Calorimeter non-compensation Different energy scales for hadronic and electromagnetic showers. • Dead material Energy lost in inactive areas of the detec­tor. • Leakage Showers reaching the outer edge of the calorimeters. • Out-of-calorimeter jet Energy contributions which are included in the stable particle jet but which are not included in the reconstructed jet. • Energy depositions below noise thresholds Energy from particles that do not form calorimeter clusters or have energy depositions not included in these clusters 123 due to the noise suppression in the cluster formation algo­rithm. • Pile-up Energy deposition in jets is affected by the pres­ence of multiple pp collisions in the same pp bunch crossing as well as residual signals from other bunch crossings. A frst estimate of the jet energy scale (JES) uncertainty of 5%-9% was based on information available prior to pp collision data and initial analysis of early data taken in 2010 [4]. An improved jet calibration with an uncertainty evaluated to be about 2.5% for jets with pseudorapidity1 |.| < 0.8 over a wide range of transverse momenta ( pT) was achieved with the full 2010 dataset using test-beam measurements, single-hadron response measurements, and in situ techniques [5]. A much larger dataset, recorded during the 2011 data­taking period, improved the precision of JES measurements to 1-3% for jets with pT > 40 GeV within |.|< 2.5using a statistical combination of several in situ techniques [6]. This paper describes the derivation of the ATLAS jet cal­ibration and jet energy resolution using the full 2012 pp collision dataset, which is more than four times larger than the 2011 dataset used for the previous calibration [6]. Due to the increased instantaneous luminosity, the beam conditions in 2012 were more challenging than those in 2011, and the ability to mitigate the effects of additional pp interactions is of major importance for robust performance, especially for jets with low pT. The jet calibration is derived using a combination of methods based both on Monte Carlo (MC) simulation and on in situ techniques. The jet energy resolu­tion (JER), which previously was studied using events with dijet topologies [7], is determined using a combination of several in situ JER measurements for the frst time. A subset of these jet calibration techniques were subsequently used for R =0.4 jets recorded during the 2015 data-taking period [8], and for R = 1.0 jets recorded during the 2015-2016 data-taking period [9]. The outline of the paper is as follows. Section 2 describes the ATLAS detector and the dataset used. The MC simula­tion framework is presented in Sect. 3, and the jet recon­ struction and calibration strategy is summarized in Sect. 4. Section 5 describes the global sequential calibration method, which exploits information from the tracking system (includ­ing the muon chambers) and the topology of the energy depo­sitions in the calorimeter to improve the JES uncertainties and 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r,.) are used in the transverse plane, . being the azimuthal angle around the z-axis. The pseudorapidity . is an approximation of rapidity y .  0.5ln (E + pz)/(E -pz) in the high-energy limit and is defned in terms of the polar angle . as . .-ln tan(./2). the JER. The in situ techniques based on a pT balance are described in Sects. 6–8. First, the intercalibration between the central and forward detector, using events with dijet-like topologies, is presented in Sect. 6. The methods based on the pT balance between a jet and a well-calibrated photon or Z boson are discussed in Sect. 7, while the study of the balance between a high-pT jet and a system of several low-pT jets is presented in Sect. 8. The combination of the JES in situ results and the corresponding uncertainties are discussed in Sect. 9, while the in situ combination and the results for the JER are presented in Sect. 10. 2 The ATLAS detector and data-taking conditions The ATLAS detector consists of an inner tracking detec­tor, sampling electromagnetic and hadronic calorimeters, and muon chambers in a toroidal magnetic feld. A detailed description of the ATLAS detector is in Ref. [1]. The inner detector (ID) has complete azimuthal coverage and spans the pseudorapidity range of |.| < 2.5. It con­sists of three subdetectors: a high-granularity silicon pixel detector, a silicon microstrip detector, and a transition radia­tion tracking detector. These are placed inside a solenoid that provides a uniform magnetic feld of 2 T. The ID reconstructs tracks from charged particles and determines their transverse momenta from the curvature in the magnetic feld. Jets are reconstructed from energy deposited in the ATLAS calorimeter system. Electromagnetic calorimetry is provided by high-granularity liquid argon (LAr) sampling calorimeters, using lead as an absorber, which are split into barrel (|.| < 1.475) and endcap (1.375 < |.| < 3.2) regions, where the endcap is further subdivided into outer and inner wheels. The hadronic calorimeter is divided into the barrel (|.| < 0.8) and extended barrel (0.8 < |.| < 1.7) regions, which are instrumented with tile scintilla­tor/steel modules, and the endcap region (1.5 < |.| < 3.2), which uses LAr/copper modules. The forward calorimeter region (3.1 < |.| < 4.9) is instrumented with LAr/copper and LAr/tungsten modules to provide electromagnetic and hadronic energy measurements, respectively. The electro­magnetic and hadronic calorimeters are segmented into lay­ers, allowing a determination of the longitudinal profles of showers. The electromagnetic barrel, the electromagnetic endcap outer wheel, and tile calorimeters consist of three layers. The electromagnetic endcap inner wheel consists of two layers. The hadronic endcap calorimeter consists of four layers. The forward calorimeter has one electromagnetic and two hadronic layers. There is also an additional thin LAr presampler, covering |.| < 1.8, dedicated to correcting for energy loss in material upstream of the calorimeters. The muon spectrometer surrounds the ATLAS calorime­ter. A system of three large air-core toroids with eight coils each, a barrel and two endcaps, generates a magnetic feld in the pseudorapidity range |.| < 2.7. The muon spectrometer measures muon tracks with three layers of precision tracking chambers and is instrumented with separate trigger cham-bers. Events are retained for analysis using a trigger system [10] consisting of a hardware-based level-1 trigger followed by a software-based high-level trigger with two levels: level-2 and subsequently the event flter. Jets are identifed using a sliding-window algorithm at level-1 that takes coarse­granularity calorimeter towers as input. This is refned with an improved jet reconstruction based on trigger towers at level-2 and on calorimeter cells in the event flter [11]. The dataset consists of pp collisions recorded from April . to December 2012 at a centre-of-mass energy ( s)of8TeV. All ATLAS subdetectors were required to be operational and events were rejected if any data quality issues were present, resulting in a usable dataset with a total integrated luminos­ity of 20 fb-1. The LHC beams were operated with pro­ton bunches organized in bunch trains, with bunch crossing intervals (bunch spacing) of 50 ns. The average number of pp interactions per bunch crossing, denoted µ, was typically between 10 and 30 [12]. The typical electron drift time within the ATLAS LAr calorimeters is 450 ns [13]. Thus, it is not possible to read out the full detector signal from one event before the next event occurs. To mitigate this issue, a bipolar shaper [14] is applied to the output, creating signals with a pulse suf­fciently short to be read between bunch crossings. After bipolar shaping, the average energy induced by pile-up inter­actions should be zero in the ideal situation of suffciently long bunch trains with the same luminosity in each pair of colliding bunches. A bunch-crossing identifcation number dependent offset correction is applied to account for the fnite train length such that the average energy induced by pileup is zero for every crossing. However, fuctuations in pile-up activity, both from in-time and out-of-time collisions, con-tribute to the calorimeter energy read out of the collision of interest. Multiple methods to suppress the effects of pile-up are discussed in subsequent sections. 3 Simulation of jets in the ATLAS detector Monte Carlo event generators simulate the type, energy, and direction of particles produced in pp collisions. Table 1 presents a summary of the various event generators used to determine the ATLAS jet calibration. A detailed overview of the MC event generators used in ATLAS analyses can be found in Ref. [15]. The baseline simulation samples used to obtain the MC­based jet calibration were produced using Pythia version 8.160 [24]. Pythia uses a 2 › 2 matrix element interfaced 123 1104 Page 4 of 81 Eur. Phys. J. C (2020) 80 :1104 Table 1 Summary of the simulated samples used to Process Event generator PDF set MPI/shower tune set derive the jet calibration and to assess systematic uncertainties Dijet & multijet Pythia 8.160 Herwig++ 2.5.2 CT10 [16] CTEQ6L1 [18] AU2 [17] EE3 MRST LO** [19] Powheg + Pythia 8.175 CT10 AU2 Powheg + Herwig 6.520.2 CT10 AUET2 [20] Sherpa 1.4.5 CT10 Sherpa-default [21] Z +jet Powheg + Pythia8 CT10 AU2 Sherpa CT10 Sherpa-default .+jet Pythia8 CTEQ6L1 AU2 Herwig++ CTEQ6L1 UE-EE-3 [19] Pile-up Pythia8 MSTW2008LO [22] AM2 [23] with a parton distribution function (PDF) to model the hard process. Additional radiation was modelled in the leading­logarithm approximation using pT-ordered parton showers. Multiple parton–parton interactions (MPI), also referred to as the underlying event (UE), were also simulated, and mod­elling of the hadronization process was based on the Lund string model [25]. Separate samples produced using other generators were used to derive the fnal jet calibration and resolution and associated uncertainties using in situ techniques. The Her-wig [26] and Herwig++ [27] event generators use a 2 › 2 matrix element convolved with a PDF for the hard process just as Pythia8 does, but use angle-ordered parton showers and a different modelling of the UE and hadronization. The Sherpa event generator [28] was used to produce multi-leg 2 › N matrix elements matched to parton showers using the CKKW [29] prescription. Fragmentation was simulated using the cluster-hadronization model [30], and the UE was modelled using the Sherpa AMISIC model based on Ref. [21]. Samples were also produced using the Powheg Box [31–34] software that is accurate to next-to-leading order (NLO) in perturbative QCD. Parton showering and modelling of the hadronization and the UE were provided by either Pythia8 or Herwig, resulting in separate samples referred to as Powheg+Pythia8 and Powheg+Herwig, respec­tively. Tuned values of the modelling parameters affecting the parton showering, hadronization, and the UE activity were determined for each generator set-up to match various dis­tributions in data as summarized in Table 1 and references therein. The generated stable particles, defned as those with a lifetime .such that c.>10 mm, were input to the detec­tor simulation that models the particles’ interactions with the detector material. Such particles are used to build jets as explained in Sect. 4. Most MC samples were generated with a full detector simulation of the ATLAS detector [35] based on Geant4[36], in which hadronic showers are simulated with the QGSP BERT model [37]. Alternative samples were produced using the Atlfast-II (AFII) fast detector simulation based on a simplifed modelling of particle interactions with the calorimeter, yielding a factor of ten more events produced for the same CPU time [38]. The output of the detector sim­ulation were detector signals with the same format as those from real data. Pile-up events, i.e. additional pp interactions that are not correlated with the hard-scatter event of interest, were simu­lated as minimum-bias events produced with Pythia8 using the AM2 tuned parameter set [23] and the MSTW2008LO PDF [22]. The simulated detector signals from these events were overlaid with the detector signals from the hard-scatter event based on the pile-up conditions of the 2012 data-taking period. Pile-up events were overlaid both in the hard-scatter bunch crossing (in-time pile-up) and in nearby bunch cross­ings (out-of-time pile-up) with the detector signals offset in time accordingly. These out-of-time pile-up signals are over­laid in such a manner as to cover the full read-out window of each of the ATLAS calorimeter sub-detectors. The number of pile-up events to overlay in each bunch crossing was sampled from a Poisson distribution with a mean µcorresponding to the expected number of additional pp collisions per bunch crossing. 4 Overview of ATLAS jet reconstruction and calibration 4.1 Jet reconstruction and preselection Jets are reconstructed with the anti-kt algorithm [2]using the FastJet software package [39,40] version 2.4.3. Jets are formed using different inputs: stable particles from the event generator record of simulated events resulting in truth­particle jets; reconstructed calorimeter clusters, producing calorimeter jets; or inner-detector tracks to form track jets. The generated stable particles used to defne truth-particle jets are required to originate (either directly or via a decay 123 chain) from the hard-scatter vertex, and hence do not include particles from pile-up interactions. Muons and neutrinos are excluded to ensure that the truth-particle jets are built from particles that leave signifcant energy deposits in the calorimeters. Calorimeter jets are built from clusters of adjacent calorimeter read-out cells that contain a signifcant energy signal above noise levels, referred to as topological clus­ters or topo-clusters. Details of the formation of topo-clust­ers are provided in Ref. [3]. In its basic defnition, a topo­cluster is assigned an energy equal to the sum of the associ­ated calorimeter cell energies calibrated at the electromag­netic scale (EM-scale) [41–44], which is the basic signal scale accounting correctly for the energy deposited in the calorimeter by electromagnetic showers. The direction (. and .) of a topo-cluster is defned from the centre of the ATLAS detector to the energy-weighted barycentre of the associated calorimeter cells, and the mass is set to zero. Topo-clusters can further be calibrated using the local cell signal weighting (LCW) method [3] designed to give the correct scale for charged pions produced in the interaction point. The LCW method reduces fuctuations in energy due to the non-compensating nature of the ATLAS calorimeters, out-of-cluster energy depositions, and energy deposited in dead material, improving the energy resolution of the recon­structed jets in comparison with jets reconstructed using EM­scale clusters [5]. The calorimeter jet four-momentum directly after jet fnd­ing is referred to as the constituent scale four-momentum pconst and is defned as the sum of the constituent topo-clust­er four-momenta pi topo: Nconst   const E const consttopo p = , p = p i i=1  Nconst Nconst  Etopo topo = i , p i . (1) i=1 i=1 The constituent scales considered in this paper are EM or LCW depending on the calibration of the constituent topo­clusters. At this stage, all angular coordinates are defned from the centre of the ATLAS detector, and the detector pseu­dorapidity .det . .const and detector azimuth .det . .const are recorded for each jet. The most common choice in ATLAS analyses of the anti-kt radius parameter is R = 0.4, but R = 0.6 is also used frequently. Analyses that search for hadronic decays of highly boosted (high pT) massive objects often use larger values of R than these since the decay prod­ucts of the boosted objects can then be contained within the resulting large-R jets. Due to the larger radius parameter, this class of jets spans a larger solid angle and hence are more sen­sitive to pile-up interactions than jets with R . 0.6. To miti­gate the infuence of pile-up and hence improve the sensitivity of the analyses, several jet grooming algorithms have been designed and studied within ATLAS [45–48]. In this paper, the trimming algorithm [49] (one type of grooming method) is applied to anti-kt jets built with R = 1.0. This grooming procedure starts from the constituent topo-clusters of a given R = 1.0 anti-kt jet to create subjets using the kt jet algorithm [50] with radius parameter Rsub = 0.3. The topo-clusters subjet/ pTjet belonging to subjets with fcut . pT< 0.05 are discarded, and the jet four-momentum is then recalculated from the remaining topo-clusters. For each in situ analysis, jets within the full calorime­ter acceptance |.det| < 4.5 with calibrated pT > 8GeV ( pT > 25 GeV in case of the multijet analysis) are considered. These pT thresholds do not bias the kinematic region of the derived calibration, which is pT . 17 GeV ( pT . 300 GeV for the multijet analysis). The jets are also required to satisfy “Loose” quality criteria, designed to reject fake jets originat­ing from calorimeter noise bursts, non-collision background, or cosmic rays [6], and to fulfl a requirement designed to reject jets originating from pile-up vertices. The latter crite­rion is based on the jet vertex fraction (JVF), computed as the track scalar sum pT of the tracks matched to the jet that are associated with the hard-scatter primary vertex divided by track pT using all tracks matched to the jet (see Ref. [51]for further details). The default hard-scatter vertex is the primary vertex with the largest T2, but other defnitions are tracks pused for certain analyses [52]. Each jet with pT < 50 GeV within the tracking acceptance |.det| < 2.4 is required to have JVF > 0.25, which effectively rejects pile-up jets in ATLAS 2012 pp data [51]. Jets with a radius parameter of R = 0.4or R = 0.6have been built using both EM-and LCW-scale topo-clusters as inputs. These four jet reconstruction options have been stud­ied in similar levels of detail, but for brevity the paper will focus on presenting the results for jets built using EM-scale topo-clusters with a radius parameter of R = 0.4, which better demonstrates the importance of the GS calibration as described in Sect. 5. Key summary plots will present the results for all four jet defnitions thus showing the fnal per­formance of each of the different options. In contrast, jets with a radius parameter of R = 1.0 have only been studied in detail using LCW-scale topo-clusters as inputs. This choice is motivated by the common usage of such jets for tagging of hadronically-decaying particles, where the energy and angu­lar distribution of constituents within the jet is important. For such a situation, LCW topo-clusters are advantageous because they fatten the detector response, and thus the tag­ging capabilities are less impacted by where a given energy deposit happens to be within the detector. 123 4.2 Matching between jets, jet isolation, and calorimeter response To derive a calibration based on MC simulation, it is neces­sary to match a truth-particle jet to a reconstructed jet. Two methods are used for this: a simple, angular matching as well as a more sophisticated approach known as jet ghost associ­ation [53]. For the angular matching, a R < 0.3 require­ment is used, where R is the pseudorapidity and azimuthal angle separation between the two jets added in quadrature, i.e. R = . . . . (.)2 + (.)2. The angular cri­terion R < 0.3 is chosen to be smaller than the jet radius parameter used for ATLAS analyses (R = 0.4 or larger) but much larger than the jet angular resolution (Sect. 4.3.2). Jet matching using ghost association treats each MC sim­ulated particle as a ghost particle, which means that they are assigned an infnitesimal pT, leaving the angular coordi­nates unchanged. The calorimeter jets can now be built using both the topo-clusters and ghost particles as input. Since the ghost particles have infnitesimal pT, the four-momenta of the reconstructed jets will be identical to the original jets built only from topo-clusters, but the new jets will also have a list of associated truth particles for any given reconstructed jet. A truth-particle jet is matched to a reconstructed jet if the sum of the energies of the truth-particle jet constituents which are ghost-associated with the reconstructed jet is more than 50% of the truth-particle jet energy, i.e. the sum of the energies of all constituents. This ensures that only one reconstructed jet is matched to any given truth-particle jet. If several truth­particle jets fulfl the matching requirement, the truth-particle jet with the largest energy is chosen as the matched jet. Matching via ghost association results in a unique match for each truth-particle jet and hence performs better than the sim-ple angular matching in cases where several jets have small angular separation from each other. The simulated jet energy response is defned by Ereco RE = , Etruth where Ereco is the reconstructed energy of the calorimeter jet, Etruth is the energy of the matching truth-particle jet, and the brackets denote that RE is defned from the mean parame­ter of a Gaussian ft to the response distribution Ereco/Etruth. The pT and mass responses are defned analogously as the Gaussian means pT,reco/ pT,truth and mreco/mtruth of the reconstructed quantity divided by that of the matching truth­particle jet. When studying the jet response for a popula­tion of jets, both the reconstructed and the truth-particle jets are typically required to fulfl isolation requirements. For the analyses presented in this paper, reconstructed jets are required to have no other reconstructed jet with pT > 7GeV within R < 1.5R, where R is the anti-kt jet radius parame­ter used. Truth-particle jets are similarly required to have no jets with pT > 7 GeV within R < 2.5R. After requiring the particle and reconstructed jets to be isolated, the jet energy response distributions for jets with fxed Etruth and . have nearly Gaussian shapes, and RE and the jet resolution .R are defned as the mean and width parameters of Gaussian fts to these distributions, respectively. For all results presented in this paper, the mean jet response is defned from the mean parameter of a ft to a jet response or momentum balance distribution as appropriate rather than the mean or median of the underlying distribution, as the ft mean is found to be signifcantly more robust against imperfect modelling of the tails of the underlying distribution. 4.3 Jet calibration An overview of the ATLAS jet calibration applied to the 8 TeV data is presented in Fig. 1. This is an extension of the procedure detailed in Ref. [6] that was applied to the 7 TeV data collected in 2011. The calibration consists of fve sequential steps. The derivation and application of the frst three calibration steps are described in this section, while the global sequential calibration (GS) is detailed in Sect. 5, and the relative in situ correction and the associated uncertainties are described in Sects. 6–9. 4.3.1 Jet origin correction The four-momentum of the initial jet is defned according to Eq. (1) as the sum of the four-momenta of its constituents. As described in Sect. 4.1, the topo-clusters have their angular directions (., .) defned from the centre of the ATLAS detec­tor to the energy-weighted barycentre of the cluster. This direction can be adjusted to originate from the hard-scatter vertex of the event. The jet origin correction frst redefnes the (., .) directions of the topo-clusters to point to the selected hard-scatter vertex, which results in a updated set of topo­cluster four-momenta. The origin-corrected calorimeter jet four-momentum porig is the sum of the updated topo-cluster four-momenta, Nconst  orig topo,orig p= p. i i=1 Since the energies of the topo-clusters are not affected, the energy of the jet also remains unchanged. Figure 2 presents the impact of the jet origin correction on the jet angular resolution by comparing the axis of the calorime­ter jet (.reco,.reco) with the axis of the matched truth­particle jet (.truth,.truth). A clear improvement can be seen for the pseudorapidity resolution, while no change is seen for the azimuthal resolution. This is expected as the spread of the beamspot is signifcantly larger along the beam axis (~50 mm) than in the transverse plane ( 1mm). 123 Fig. 1 Overview of the ATLAS jet calibration described in this paper. All steps are derived and applied separately for jets built from EM-scale and LCW calibrated calorimeter clusters, except forthe global sequential calibration, which is only partially applied to LCW-jets (Sect. 5). The notations EM + JES and LCW + JES typically refer to the fully calibrated jet energy scale; however, inthe sections of this paper that detail the derivations of the GS and the in situ corrections, these notations refer to jets calibrated by all steps up to the correction that is being described 4.3.2 Pile-up correction The reconstruction of the jet kinematics is affected by pile-up interactions. To mitigate these effects, the contribution from pile-up is estimated on an event-by-event and jet-by-jet basis as the product of the event pT-density .[53] and the jet area A in (y,.)-space, where y is the rapidity of the jet [54]. The jet area is determined with the FastJet 2.4.3 program [39,40] using the active-area implementation, in which the jets are rebuilt after adding randomly distributed ghost particles with infnitesimal pT and randomly selected y and .from uniform distributions. The active area is estimated for each jet from the relative number of associated ghost particles (Sect. 4.2). As can be seen in Fig. 3a, the active area for a given anti-kt jet tends to be close to .R2. The event pT-density .is esti­mated event-by-event by building jets using the kt jet-fnding algorithm [50] due to its tendency to naturally include uni­form soft background into jets [53]. Resulting kt jets are only considered within |.| < 2 to remain within the calorimeter regions with suffcient granularity [51]. No requirement is placed on the pT of the jets, and the median of the pT/A distribution is taken as the value of .. The median is used to reduce the sensitivity of the method to the hard-scatter activity in the tails. The .distributions of events with aver­age interactions per bunch crossing µin the narrow range of 20 <µ<21 and several fxed numbers of primary vertices NPV are shown in Fig. 3b. It can be seen that . increases with NPV as expected, but for a fxed NPV, . still has size­able event-by-event fuctuations. A typical value of the event pT-density in the 2012 ATLAS data is . = 10 GeV, which for a R = 0.4 jet corresponds to a subtraction in jet pT of .A . 5GeV. After subtracting the pile-up contribution based on .A, jet the pileup dependence of pT is mostly removed, especially within the region where the value of .is derived. However, jet the value of pT has a small residual dependence on NPV and µ, particularly in the region beyond where .is derived and where the calorimeter granularity changes. To mitigate this, an additional correction is derived, parameterized in terms of NPV and µ, which is the same approach and parameterization as was used for the full pile-up correction of the ATLAS 2011 jet calibration [6]. A typical value for this correction is ±1 GeV for jets in the central detector region. The full pile-up correction to the jet pT is given by pT › pT - .A - .(NPV - 1)- ßµ, (2) where the .and ßparameters depend on jet pseudorapidity and the jet algorithm, and are derived from MC simulation. Further details of this calibration, including evaluation of the associated systematic uncertainties, are in Ref. [51]. No pile-up corrections are applied to the trimmed large-R jets 123 Fig. 2 Jet angular resolution as a function of transverse momentum matching details) in simulated events and are shown both with (circles) for anti-kt jets with R = 0.4. The resolutions are defned by the spread and without (triangles) the jet origin correction, which adjusts the direc­of the difference between the reconstructed jet axis (.reco,.reco)and tion of the reconstructed jet to point to the hard-scatter vertex instead the axis of the matched truth-particle jet (.truth,.truth) (see Sect. 4.2 for of the geometrical centre of the detector (a) (b) Fig.3 a Ratio of the jet active area to .R2,where R is the jet radius parameter and b the event pT-density .. The jet area ratio is shown separately for R = 0.4and R = 0.6 jets reconstructed with the anti-kt since this is found to be unnecessary after applying the trim­ming procedure. 4.3.3 Monte Carlo-based jet calibration After the origin and pile-up corrections have been employed, a baseline jet energy scale calibration is applied to correct the reconstructed jet energy to the truth-particle jet energy. This calibration is derived in MC-simulated dijet samples follow­ing the same procedure used in previous ATLAS jet calibra­tions[5,6].Reconstructed and truth-particle jets are matched algorithm, and . is shown for different numbers of reconstructed pri­mary vertices NPV in events with average number of pp interactions in the range 20 . µ< 21 and required to fulfl the isolation criteria as described in Sect. 4.2. The jets are then subdivided into narrow bins of .det of the reconstructed jet and energy of the truth­particle jet Etruth, and RE is determined for each such bin from the mean of a Gaussian ft (Sect. 4.2). The average reconstructed jet energy Ereco (after pile-up correction) is also recorded for each such bin. A calibration function cJES,1(Ereco) = 1/R1(Ereco)is determined for each .det bin by ftting a smooth function R1(Ereco)to a graph of RE versus Ereco measurements for all Etruth bins within the given .det bin. After applying this correction (Ereco › cJES,1 Ereco) 123 (a) (b) (c) (d) Fig. 4 Jet energy and mass responses as a function of .det for different truth-particle jet energies. The energy responses RE for anti-kt jets with R =0.4atthe a EM scale and the b LCW scale and c for trimmed anti-kt R =1.0 jets are presented. Also, d the jet mass response Rm for the latter kind of jets is given and repeating the derivation of the calibration factor, the jet response does not close perfectly. The derived calibration fac-tor from the second iteration cJES,2 is close to but not equal to unity. The calibration improves after applying three such iterative residual corrections cJES,i (i .{2,3,4}) such that the fnal correction factor cJES = 41 cJES,i achieves a jet i=response close to unity for each (Etruth,.det)bin. For the large-R jets (trimmed anti-kt R = 1.0), a sub­sequent jet mass calibration is also applied, derived analo­gously to the energy calibration. Figure 4 shows the energy and jet mass responses for jets with R =0.4 and R =1.0. Jets reconstructed from LCW-calibrated topo-clusters have a response closer to unity than jets built from EM-scale topo­clusters. Figure 5 shows the jet E, pT, and m response plots after the application of the MC-based jet calibration. Good closure is demonstrated across the pseudorapidity range, but there is some small non-closure for low-pT jets primarily due to imperfect fts arising from the non-Gaussian energy response and threshold effects. A small, additive correction . is also applied to the jet pseudorapidity to account for biased reconstruction close to regions where the detector technology changes (e.g. the barrel–endcap transition region). The magnitude of this cor­rection is very similar to that of the previous calibrations (Figure 11 of Ref. [5]) and can reach values as large as 0.05 near the edge of the forward calorimeters around |.|=3, but is typically much smaller in the well-instrumented detector regions. 4.4 Defnition of the calibrated jet four momentum For small-R jets, i.e. jets built with a radius parameter of R =0.4or R =0.6, the fully calibrated jet four-momentum is specifed by  orig orig (E,.,.,m) = ccalib Eorig,.orig + .,., ccalib m, (3) where the quantities denoted “orig” are the jet four-vector after the origin correction discussed in Sect. 4.3.1, .is the 123 (a) (b) (c) (d) (e) (f) Fig. 5 Jet energy, pT, and mass response after the MC-based jet calibration has been applied for R = 0.4and R = 1.0anti-kt jets reconstructed from LCW calibrated topo-clusters MC-based pseudorapidity calibration reported in Sect. 4.3.3, Here, the pile-up correction factor is defned as and ccalib is a four-momentum scale factor that combines the pT - . A - .(NPV - 1) - ßµ other calibration steps: cPU = pT in accordance with Eq. (2)( pT › cPU pT), cJES is derived  as explained in Sect. 4.3.3, cGS is the global sequential cal­cPU · cJES · cGS · c. · cabs for data ibration that is discussed in Sect. 5, and the pseudorapidity ccalib = (4) cPU · cJES · cGS for MC simulation. intercalibration c. and the absolute in situ calibration cabs are 123 detailed in Sects. 6–9.Asgiven inEq.(4), the MC-derived calibrations cJES and cGSC correct simulated jets to the truth­particle jet scale, but jets in data need the in situ corrections c. and cabs to reach this scale. JES systematic uncertainties are evaluated for the in situ terms. The calibration procedure is slightly different for the large-R jets used in this paper (Sect. 4.1). These jets do not receive any origin correction or global sequential calibration as the precision needs of the overall scale are not the same as for R = 0.4 and R = 0.6 jets. Further, no pile-up correction is applied since the trimming algorithm detailed in Sect. 4.1 mitigates the pile-up dependence. However, large-R jets do receive a MC-derived jet mass calibration cmass. The cali­brated large-R jet four-momentum is given by  cJES Econstconst const const (E,.,., m) = ,.+ .,., cmass m. (5) By expressing the jet transverse momentum in terms of energy, mass, and pseudorapidity, it can be seen that all cal­ibration terms of Eqs. (3) and (5) affect pT, for example cJES Econst  cmass mconst E  m pT ==  , .const cosh . cosh + . where the symbol  denotes subtraction in quadrature, i.e. . a  b . a2 - b2. 5 Global sequential calibration The global sequential (GS) calibration scheme exploits the topology of the energy deposits in the calorimeter as well as tracking information to characterize fuctuations in the jet particle content of the hadronic shower development. Cor­recting for such fuctuations can improve the jet energy reso­lution and reduce response dependence on the so-called “jet favour”, meaning dependence on the underlying physics pro­cess in which the jet was produced. Jets produced in dijet events tend to have more constituent particles, a wider trans-verse profle and a lower calorimeter energy response than jets with the same pT and . produced in the decay of a W boson or in association with a photon (. +jet) or Z boson (Z +jet). This can be attributed to differences in fragmen­tation between “quark-initiated” and “gluon-initiated” jets. The GS calibration also exploits information related to the activity in the muon chamber behind uncontained calorime­ter jets, for which the reconstructed energy tends to be smaller with a degraded resolution. The calibration is applied in sequential steps, each designed to fatten the jet energy response as a function of a jet property without changing the mean jet energy. 5.1 Description of the method Any variable x that carries information about the jet response can be used for the GS calibration. A multiplicative correc­tion to the jet energy measurement is derived by inverting the jet response as a function of this variable: c(x) = k/R(x), where the constant k is chosen to ensure that the average energy is not affected by the calibration, and the average jet response R(x) is determined using MC simulation as described in Sect. 4.2. After a successful application, the jet response should no longer depend on x. As a result, the spread of reconstructed jet energy is reduced, thus improving the resolution. Each correction is performed separately in bins of .det,in order to account for changes in the jet pT response in dif­ferent detector regions and technologies. The corrections are further parameterized as a function of pT and jet property x: c( pT, x), except for the correction for uncontained calorime­ter jets, which is constructed as a function of jet energy E and the logarithm of the number of muon segments reconstructed in the muon chambers behind the jet: c(E, log Nsegments).The uncontained calorimeter jet correction is constructed using the jet E rather than the pT to better represent the probability of a jet penetrating the full depth of the calorimeter, which depends on log E. The two-dimensional calibration function is constructed using a two-dimensional Gaussian kernel [6] for which the kernel-width parameters are chosen to capture the shape of the response across .det and pT, and at the same time provide stability against statistical fuctuations. Several variables can be used sequentially to achieve the optimal resolution. The jet pT after N GS calibration steps is given by the initial jet pT multiplied by the product of the N corrections:  N pTGS = pT,0 cGS = pT,0 j=1 cj ( pT, j-1, xj ), pT,i = pT,i-1 ci ( pT,i-1, xi ), (6) where pT,0 is the jet pT prior to the GS calibration. Hence, when deriving correction j, one needs to start by calibrat­ing the jets with the previous j - 1 correction factors. This method assumes there is little to gain from non-linear corre­lations of the variables used and this has been demonstrated in simulation. 5.2 Jet observables sensitive to the jet calorimeter response The GS calibration relies on fve jet properties that were identifed empirically to have a signifcant effect on the jet energy response. This empirical study was conducted pri­marily using EM jets, while a reduced scan was performed for LCW jets given that they already exploit some of the following variables as part of the LCW procedure. Two of the variables characterize the longitudinal shower structure 123 of a jet, namely the fractions of energy deposited in the third electromagnetic calorimeter layer, fLAr32, and in the frst hadronic Tile calorimeter layer, fTile0. These fractions are defned according to  ELAr3 Ejet = ETile0 Ejet fLAr3 = EM EM, and fTile0 EM EM, (7) where the subscript EM refers to the electromagnetic scale. The next two of the fve jet properties rely on reconstructed tracks from the selected primary vertex that are matched to the calorimeter jets using ghost association (Sect. 4.2). The tracks are required to fulfl quality criteria relating to their impact parameter and the number of hits in the different inner-detector layers, and to have pT > 1 GeV and |.| < 2.5. The track-based observables are the number of tracks asso­ciated with a given jet ntrk, and the jet width Wtrk defned as Ntrk Ntrk   Wtrk = pT,i R(i, jet) pT,i , (8) i=1 i=1 where Ntrk are the number of tracks associated with the jet, pT,i is the pT of the ith track, and R(i, jet) is the R dis-tance in (., .)-space between the ith track and the calorime­ter jet axis. The jet width Wtrk quantifes the transverse struc­ture of the jet, which is sensitive to the “jet favour”. The fnal variable used in the GS calibration is Nsegments, the number of muon segments behind the jet, which quantifes the activity in the muon chambers. Muon segments are partial tracks con­structed from hits in the muon spectrometer chambers [55], and are matched to the jet of interest in two stages. Based on jets built using anti-kt with R = 0.6, Nsegments is defned by the number of matching muon segments within a cone of size R = 0.4 around the jet axis. For anti-kt R = 0.4jets, the closest R = 0.6 jet is found (fulflling R < 0.3), and Nsegments is assigned to the R = 0.4 jets according to the corresponding value for the R = 0.6jet. Figures 6 and 7 show distributions comparing data with MC simulations for fTile0, fLAr3, ntrk, Wtrk and Nsegments forjetswith |.det| < 0.6 produced in dijet events selected as described in Sect. 6.3. Predictions are provided using the default Pythia8 sample with full detector simulation from which the GS calibration is derived, and also using the AFII fast simulation, which is often used in physics anal­yses (Sect. 3). For the AFII detector simulation, there is no complete implementation of the muon segments produced behind high-energy uncontained jets. Therefore, this correc­ 2 The ATLAS calorimeters have three electromagnetic layers in the pseudorapidity interval |.| < 2.5, but only two in 2.5 < |.| < 3.2. fLAr3 includes energy deposits with |.| < 2.5inthe thirdEMlayer and contributions with 2.5 < |.| < 3.2 in the second EM layer. Energy deposits with |.| > 3.2 are not included, however a jet with |.| 3.2 will most often have topo-clusters with |.| < 3.2 that leave contribu­tions to the second EM layer. tion is not applied to AFII samples, and no AFII prediction is provided in Fig. 7e. It can be seen that the simulation predicts the general shapes of the data, although there are visible dif­ferences. Similar results are found in the other .det regions. Disagreements in the distributions of the jet properties have little impact on the GS calibration performance as long as the response dependence R(x) of the jet properties x is well described by the simulation (Sect. 5.6). 5.3 Derivation of the global sequential jet calibration The jet observables used for the GS calibration and their order of application are summarized in Table 2. The frst four corrections are determined separately in .det-bins of width 0.1 and are parameterized down to pT = 15 GeV. For jets at the LCW + JES scale, only the tracking and uncontained calorimeter jets corrections are applied since the LCW calibration already takes into account shower shape information. No further improvement in resolution is thus achieved through the use of fTile0 and fLAr3 for LCW jets. The calorimeter response for EM + JES calibrated anti­ truth kt R = 0.4 jets with pT in three representative intervals is presented as a function of the different jet property vari­ables used by the GS calibration in Fig. 8. For all properties, a strong dependence of the response as a function of the property is observed. The ntrk and Wtrk show a stronger pT dependence than the other properties and this is extensible for other pT and .det bins and jet collections. The corre­sponding distributions after the GS calibration are shown in Fig. 9. The jet response dependence on the jet properties is removed to within 2% after applying the GS calibration for all observables. Deviations from unity are expected since the correlations between the variables are not accounted for in the GS calibration procedure. 5.4 Jet transverse momentum resolution improvement in simulation Figure 10 shows the jet transverse momentum resolution as truth a function of pT in simulated Pythia8 dijet events. While the response remains unchanged, the jet resolution improves as more corrections are added. The relative improvement3 for EM + JES calibrated anti-kt R = 0.4 jets with central rapidity is found to be 10% at pT = 30 GeV, rising to 40% at 400 GeV. This is equivalent to removing an absolute uncorrelated reso­lution source . of 10% or 5%, respectively, as can be seen 3 The relative improvement in the jet pT resolution in com­parison with the baseline (no-GS) calibration is calculated as (.pT / pT)no-GS-(.pT / pT)GS , where the label no-GS refers to the jet prior to (.pT / pT)no-GS the GS calibration, i.e. directly after the MC-based calibration (Fig. 1) and GS refers to the jet after the GS calibration. 123 (a) (c) Fig. 6 Normalized distributions of fTile0, fLAr3, ntrk,and Wtrk for avg jets |.det| < 0.6 in dijet events with 80 GeV < p< 110 GeV in T data (flled circles) and Pythia8 MC simulation with both full (empty circles) and fast (empty squares) detector simulation. All jets are recon­ in the lower part of Fig. 10a. The quantity . is calculated by subtracting in quadrature the relative jet pT resolution:    (b) (d) structed with anti-kt R = 0.4 and calibrated with the EM + JES scheme. avg The quantity pT is the average pT of the leading two jets in an event, and hence represent the pT scale of the jets being probed. Nsegments is not shown since the vast majority of jets in this pT range have Nsegments = 0 explained by considering the jet resolution distributions for different values of the jet properties. As is evident in Fig. 8,  - .pT / pT  .pT / pT if .pT / pT .pT / pT no-GS GS no-GS > GS . =   (9) + .pT / pT  .pT / pT otherwise. GS no-GS The improvement observed for jets initially calibrated with the LCW + JES scheme is found to be smaller, which is expected as only tracking and non-contained jet corrections areappliedtothesejets.Forboth EM+JESand LCW+JES calibrated jets, improvements to the JER is observed across the full pT range probed (25 GeV . pT < 1200 GeV). The fact that JER reduction is observed at high jet pT means that also the constant term of the calorimeter resolution (Eq. (24)) is reduced by the GS calibration. This improvement can be the mean of these distributions have a strong dependence on the jet property, while the width of the distributions (JER) are not expected to have any such dependence at high jet pT. The GS calibration can hence be seen as aligning several similarly shaped response distributions, which each have a biased mean, towards the desired truth-particle jet scale. The conclusions from this section can generally be extended to the whole .det range, although close to the calorimeter transition regions where the detector instrumen­ 123 (a) (b) (c) (d) (e) Fig. 7 Normalized distributions of fTile0, fLAr3, ntrk, Wtrk and are reconstructed with anti-kt R = 0.4 and calibrated with the EM + JES avg avg Nsegments for jets |.det| < 0.6 in dijet events with 600 GeV < p< scheme. The quantity pis the average pT of the leading two jets in TT 800 GeV in the data (flled circles) and Pythia8 MC simulation with an event, and hence represent the pT scale of the jets being probed both full (empty circles) and fast (empty squares) simulation. All jets 123 Eur. Phys. J. C (2020) 80 :1104 Page 15 of 81 1104 Table 2 Sequence of GS corrections used to improve the |.| Region Correction 1 Correction 2 Correction 3 Correction 4 Correction 5 jet performance in each .det region. For jets at the LCW + JES scale, only the tracking and uncontained calorimeter jet corrections are applied [0, 1.7] [1.7, 2.5] [2.5, 2.7] [[2.7, 3.5] fTile0 fLAr3 fLAr3 fLAr3 fLAr3 ntrk ntrk Wtrk Wtrk Nsegments Nsegments Nsegments tation is reduced (Fig. 4), the track-based observables intro-duce an even stronger improvement. The enhancement in JER due to the GS calibration is found to be similar for dif­ferent MC generators. Only a small improvement is observed after applying the last GS correction for uncontained calorimeter jets in the inclusive jet sample since only a small fraction of energetic jets are uncontained. Figure 11 presents a measure of the improvement in jet energy resolution from applying the ffth GS correction both to inclusive jets and to jets with at least 20 associated muon segments, which are less likely to be fully contained in the calorimeters. The resolution metric is the standard deviation (RMS) of the jet response distribution divided by the arithmetic mean. This quantity is used instead of the normal resolution defnition (from the . of a Gaussian ft as described in Sect. 4.2) since it gives information about the reduction in the low response tail. While the improvement observed is small for an inclusive jet sample, the impact is sig­nifcant for uncontained jets. A relative resolution improve­ment of 10% is seen for jets with pT . 100 GeV, while the improvement is 20% for jets with pT . 1 TeV. This corre­sponds to removing an absolute resolution source of 8% or 4%, respectively. 5.5 Flavour dependence of the jet response in simulation The internal structure of a jet, and thereby also its calorime­ter response, depends on how the jet was produced. Jets pro­duced in dijet events are expected to originate from gluons more often than jets with the same pT and . produced in the decay of a W boson or in association with a photon or Z boson. The hadrons of a quark-initiated jet will tend to be of higher energy and hence penetrate further into the calorime­ter, while the less energetic hadrons in a gluon-initiated jet will bend more in the magnetic feld in the inner detector. It is desirable that such favour dependence of the calibrated jet should be as small as possible to mitigate sample-specifc systematic biases in the jet energy scale (Sect. 9.2.3 for dis­cussion of the associated uncertainty). The favour dependence of the response is studied in simulated dijet events by assigning a favour label to each calorimeter jet using an angular matching to the particles in the MC event record. If the jet matches a b-ora c-hadron, it is labelled a b-jet or c jet, respectively. If it matches both a b-and a c-hadron, it is labelled a b-jet. If it does not match any such heavy hadron, the jet is labelled “light quark” (LQ) or gluon initiated, based on the type of the highest-energy matching parton. The matching criterion used is R < R, where R is the radius parameter of the jet algorithm (0.4 or 0.6). The pT responses before and after GS calibration for jets in different favour categories are presented in Fig. 12. For each favour category, results are shown for two repre­sentative pseudorapidity regions. The response for LQ jets is larger than unity since the MC-derived baseline calibra­tion (Sect. 4.3) is derived in dijet events that contain a large fraction of gluon jets. For gluon-initiated jets the response is lower than that of LQ jets, as expected, and b-jets have a pT response between that of LQ and gluon jets. In all cases, the GS calibration brings the response closer to unity and hence reduces the favour dependence, which is important as analyses do not know the favour of each jet. The change in pT response introduced by the GS calibration for jets with pT = 80 GeV with |.| < 0.3is -4%, + 1% and -2% for LQ jets, gluon jets and b-jets, respectively. 5.6 In situ validation of the global sequential calibration The GS correction is validated in situ with dijet events using the tag-and-probe technique, using the event selection described in Sect. 6, with only one modifcation: both jets are required to be in the same |.det| region to avoid biases from any missing .-dependent calibration factors. The jet whose response dependence is studied is referred to as the probe jet, while the other is referred to as the reference jet. The choice of reference jet and probe jet is arbitrary when studying the response dependence on the jet properties, and the events are always used twice, alternating the roles of reference and probe. The response for the probe jet is measured through the dijet pT asymmetry variable A(Eq. (10) and Sect. 6.1) in bins of the average pT of the probe and the reference jet avg pT , and is studied as a function of the jet property of the probe jet. Results for all variables used in the GS calibration are shown in Fig. 13 forjetswith |.det| < 0.6 in two represen­tative pT ranges. No GS calibration is applied to either the probe or the reference jet. It can be seen that the reference Pythia8 dijet MC sample agrees with the data within 1% avg avg (4%) for 600 GeV < pT < 800 GeV (80 GeV < pT < 123 (a)(b) (c) (d) Fig. 8 Jet pT response as a function of fTile0, fLAr3, ntrk, Wtrk and Nsegments for jets with |.det| < 0.3(|.det| < 1.3for Nsegments)indif­truth ferent pT ranges. All jets are reconstructed with anti-kt R = 0.4and calibrated with the EM + JES scheme without global sequential cor­ (e) rections. The horizontal line associated with each data point indicates the bin range, and the position of the marker corresponds the centroid within this bin. The underlying distributions of the jet properties for each truth pT bin normalized to the same area are also shown as histograms at the bottom of the plots 123 (a)(b) (c) (d) Fig. 9 Jet pT response as a function of fTile0, fLAr3, ntrk, Wtrk and Nsegments for jets with |.det| < 0.3(|.det| < 1.3for Nsegments)indif­truth ferent pT ranges. All jets are reconstructed with anti-kt R = 0.4and calibrated with the EM + JES scheme including global sequential cor­ (e) rections. The horizontal line associated with each data point indicates the bin range, and the position of the marker corresponds the centroid within this bin. The underlying distributions of the jet properties for each truth pT bin normalized to the same area are also shown as histograms at the bottom of the plots 123 ( a ) truth (b) squares), with calorimeter-and track-based corrections only (green upward triangles) and including all the global sequential corrections (blue downward triangles). The lower panels show the improvement relative to the EM + JES scale without global sequential corrections obtained using subtraction in quadrature (Eq. (9)) (a) Fig. 11 Standard deviation over arithmetic mean of the jet energy response as a function of Etruth for |.det| < 1.3 before (flled circles) and after (empty circles) the ffth global sequential correction for a all jets and b calorimeter jets with Nsegments > 20 in the nominal Pythia8 dijet MC sample. All jets are reconstructed with anti-kt R = 0.4and ini­tially calibrated at the EM + JES scale. The requirement Nsegments > 20 110 GeV) for the calorimeter-based variables, and slightly better for the track-based observables. A similar level of agreement is seen in other jet pT and .det ranges. These dif­ferences impact the average jet pT weighted by the fraction of jets with corresponding values of the GS property in ques­tion; given that these differences occur in the tails of the distributions, the impact on the average jet pT is thus mini­ (b) selects a large fraction of “uncontained” jets, i.e. jets for which some of the particles produced in the hadronic shower travel into the muon spectrometers behind the calorimeters. The bottom panels show the improvement introduced by the corrections quantifed using subtrac­tion in quadrature (Eq. (9)) mal. Results using MC samples produced with the AFII fast detector simulation are also shown and demonstrate similar agreement with data, although these samples have larger sta­tistical uncertainties. The relative data–MC agreement stays the same after the GS calibration is applied for both full and fast detector simulation. 123 Fig. 12 The pT response for anti-kt R = 0.4 jets as a function of truth pT for light quark (LQ) jets (top), gluon jets (middle) and b-jets (bot­tom) with |.det| < 0.3(left)and2.1 < |.det| < 2.4 (right) regions in the Pythia8 MC sample. The pT response after the EM + JES cal­ibration without GS corrections (circles), with calorimeter-based GS corrections only (squares) and including all the GS corrections (trian­gles) are shown. The lower box of each plot shows the impact on the jet response, subtracting the response before the GS corrections (R)from the response after applying the GS corrections (R) 123 Fig. 13 Dijet in situ validation of jet response as a function of fTile0, avg fLAr3 and ntrk for jets with 80 GeV < p< 110 GeV and |.det| < 0.6 T avg (top) and for jets with 600 GeV < p< 800 GeV and |.det| < 0.6 T (middle) and the same quantity as a function of Wtrk and Nsegments 5.7 Comparison of jet resolution and favour dependence between different event generators Figure 14 presents comparisons of pT resolution and response dependence on jet favour between three MC event genera­tors, namely Pythia8, Herwig++, and Sherpa, each with a different implementation of parton showering, multiple parton–parton interactions and hadronization (Sect. 3). These quantities are shown as a function of jet pT both with and without GS calibration applied in two representative .det regions. Pythia8 tends to predict a slightly worse jet pT resolution for jets with pT < 50 GeV compared with the jet resolution in Herwig++ and Sherpa, but the improvement introduced by the GS correction is compatible between the different generators. The reduction of jet favour dependence (bottom). Each set of measurements are shown for data (flled circles) and for Pythia8 MC simulation with both full (empty circles) and fast (empty squares) detector modelling. All jets are reconstructed with anti-kt R = 0.4 and calibrated with the EM + JES scheme without any global sequential corrections is studied by taking the difference between the jet responses for LQ and gluon jets, determined as discussed in Sect. 5.5 and as used for light-quark vs gluon discrimination [56]. The overall favour dependence of the jet response is found to be smaller for Herwig than for Pythia8 and Sherpa, and in general, the LQ jet response is quite similar between the gen­erators, while the response for gluon jets varies more. For jets with pT > 40 GeV, the response difference between LQ and gluon jets is reduced by at least a factor of two after applying the GS correction. 123 truth gluon and light quark (LQ) initiated jets (bottom) as a function of pT for two representative |.det| regions. Results are shown both before (closed markers) and after (open markers) the global sequential cor­rections is applied, and separately for jets in the Pythia8 (circles), 6 Intercalibration and resolution measurement using dijet events Following the determination and application of MC-based jet calibration factors, it is important to measure the jet response and resolution in situ, quantify the level of agree­ment between data and simulation, and correct for any dis­crepancy. The frst step is to investigate the jet response dependence across the detector in terms of pseudorapidity. All results presented in this section are obtained with jets calibrated with the calibration chain up to, and including, the GS calibration (Sect. 4.4). 6.1 Techniques to determine the jet calibration and resolution using dijet asymmetry The jet energy resolution (JER) and the relative response of the calorimeter as a function of pseudorapidity are deter­mined using events with dijet topologies [6,7]. The pT bal­ance is quantifed by the dijet asymmetry probe p- pref TT A= avg , (10) p T Sherpa (squares), and Herwig++ (triangles) dijet MC samples. All jets are reconstructed with anti-kt R = 0.4. Jets are labelled LQ-or gluon-initiated, based on the highest-energy parton in the MC event record which fulfls an angular matching to the jet as further detailed in Sect. 5.5 where pTref is the transverse momentum of a jet in a well­probe calibrated reference region, pT is the transverse momen­ tum of the jet in the calorimeter region under investigation, avg probe ref and p= ( p+ p)/2. The average calorimeter TT T response relative to the reference region, 1/c, is then defned as  probe p 12 +A T ..  ref  , (11) c 2 -A pT where A is the mean of the asymmetry distribution in a given bin of pTavg and .det, and the last equality of Eq. (11) can be obtained by inserting the expectation value of a frst-order Taylor expansion of Eq. (10), giving A =  probe avg p-pref /p. T TT Two versions of the analysis are performed. In the cen­tral reference method, the calorimeter response is measured as a function of pTavg and .det relative to the region defned by |.det| < 0.8. Jets in this region are precisely calibrated using Z +jet, . + jet and multijet data (Sects. 7 and 8). In the matrix method, multiple .det regions are chosen and the calorimeter response in a given region is measured relative avg to all other regions. For a given pT bin, A is determined 123 for each of a large number of combinations of .det regions of the two jets involved. The calorimeter response relative to the central region is then obtained by solving a set of linear equa­tions based on this matrix of dijet asymmetries [6]. A con­straint is applied that sets the average response for jets with |.det|< 0.8 to unity. The advantage of the matrix method is that a much larger fraction of events can be used, since events with both jets outside |.det| < 0.8 are considered, thus reducing the statistical uncertainty of the fnal result. Statistical uncertainties in the matrix method result are esti­mated using pseudo-experiments. Each pseudo-experiment generates a new matrix of dijet asymmetries by sampling the average asymmetry A of each bin (matrix element) accord­ing to their statistical uncertainty. The intercalibration factors are then derived for each pseudo-experiment, and the statisti­cal uncertainty of the calibration is obtained from the spread. In this paper, the main results are obtained using the matrix method, and the simpler central reference method is used for validation. The asymmetry distribution also probes the jet energy res­olution. The standard deviation of the asymmetry distribution  probe avg probe . inagiven p,.bin can be expressed as A T det probe .. ref probe . pT pT .pT .pT . = =. A avg ppT pT T probe ref   .E .E =. , (12) E probe E ref probe probe where . and . ref are the standard deviations of p pT pTT and pTref, respectively. The frst two equalities of Eq. (13) follow from error propagation of Eq. (10) and from the fact probe ref avg that after calibration p=p=pin a given T TT pTavg bin. The energy and pT resolutions are approximately the same since contributions of the jet angular resolution are negligible (Fig. 2). The standard deviation of the asymmetry distribution .A is obtained from a Gaussian ft to the core of the distribution. The standard deviation of the probe jet pT is derived from Eq. (13)as .pT probe .pT =. A  , (13) pT pT probe ref where the latter term is derived from events where both jets fall in the central reference region (|.det|< 0.8). In this case, the reference region is being probed, and the frst and last  terms in Eq. (13) are hence equal, which gives .pT / pT ref =  . .A 2. When calculating the asymmetry, the jets are fully calibrated including all data-driven correction factors. The pT balance strictly holds only for 2 ›2 partonic events. In reality, the pT balance between two jets is affected on an event-by-event basis by additional quark/gluon radi­ation outside of the jets, as well as hadronization and MPI effects that cause particle losses and additions to the jets, respectively. To account for the impact of such effects, the dijet asymmetry standard deviation .A is measured sepa­rately for reconstructed and truth-particle jets, and the stan­dard deviation due to detector smearing . det is obtained A by subtracting the truth-particle quantity from the observed quantity in quadrature: det . reco truth . =.. (14) AA A  This fnal jet energy resolution measurement .pT / pT is cal­culated according to Eq. (13) after frst correcting the asym­ metry width .A according to Eq. (14). 6.2 Determining the jet resolution using the dijet bisector method The bisector method attempts to separate the desired part of the dijet pT imbalance that is due to fuctuations in the jet calorimeter response from contributions from other effects such as soft parton radiation and the underlying event. In the same way as for the central reference method, selection criteria are applied to select events with dijet topology, and at least one of the two jets is required to have |.det|< 0.8. This jet is referred to as the “reference jet”, while the other jet is labelled “probe jet”. If both jets fulfl |.det|< 0.8, the labels are assigned randomly. The pT (imbalance) of the dijet system in the transverse plane is defned as the vectorial sum jj probe of the pT vectors of the leading two jets: p =p +p ref. TT T This vector is projected onto a Cartesian coordinate system in the transverse plane (., .), where the .-axis is defned to be along the direction that bisects the angle .12 between the two jets, and the .-axis is defned to have a direction that minimizes the angle to the probe jet as illustrated in Fig. 15. Both effects from the detector (response and resolution) and from physics (e.g. radiation) are present in the . component of the pT balance that is oriented “towards” the probe jet axis, whereas detector effects should be signifcantly smaller than physics effect in the . component, oriented “away” from both the probe and the reference jet. As a result [7], the jet avg energy resolution for events in a given pT bin where both probe jets are in the reference region (|.|< 0.8) is given by det .pT .. .. = avg . , (15) pT p2 |cos .12| ref T and for events where the probe jet is outside the reference region it is given by .pT .. .. .pT = avg . . (16) pT p|cos .12| pT probe T ref The standard deviations .. and .. are evaluated as the width parameters of Gaussian fts to the pT. and pT. distributions, respectively. 123 Fig. 15 Illustration of observables used in the dijet bisector technique. The (., .)-coordinate system is defned such that the .-axis bisects the azimuthal angle .12 between the leading two jets while the .-axis minimizes the angle to the probe jet. The vectorial sum of the transverse momenta of the probe and the reference jets defne the dijet transverse momentum p T jj . Its components along the .-and .-axes (pT. and pT. ) are used to extract a measurement of the jet energy resolution Although the bisector observables in Eqs. (15) and (16) have less dependence on soft quark or gluon emission than the asymmetry-based jet resolution measurement of Eq. (13), the approach relies on the assumption that the physics effects are the same in the . and . components. Corrections to the measured .. and .. are made by subtracting the correspond­ing quantities derived using truth-particle jets in quadrature from the measured quantity, analogously to what is done for the central reference method (Eq. (14)). 6.3 Dijet selection Dijet events are selected using a combination of central (|.det| < 3.2) and forward (|.det| > 3.2) jet triggers. For avg this selection, the trigger effciency for each region of pT is greater than 99% and approximately independent of the pseudorapidity of the probe jet. The jet triggers used have different prescales, downscaling factors used to meet band­width constraints on the recording of data. Larger prescales are used for data recorded when the instantaneous luminosity is high or for triggers that require lower jet pT. Due to the different prescales for the central and forward jet triggers, the data collected by the different triggers correspond to different integrated luminosities. Each data event is assigned a trigger based on the pavg and .det of the more forward jet. The data T is hence split into different categories, and each is weighted according to the integrated luminosity of the dedicated trig­ger used following the “exclusion method” [57]. Events are selected in which there are at least two jets with pT > 25 GeV and |.det| < 4.5. To select events with a dijet topology, the azimuthal angle between the two leading jets (i.e., the refer­ence and probe jets) is required to be .12 > 2.5 and events j3 avg are rejected if they contain a third jet with pT > 0.4 pT. The jets are also required to fulfl the preselection described in Sect. 4.1. 6.4 Method for evaluating in situ systematic uncertainties The in situ techniques rely on assumptions that are only approximately fulflled, and simulation is used to account for these approximations. For example, the momentum balance between the jet and the reference object is altered to varying degrees by the presence of additional radiation. The impact from such radiation is reduced by event topology selection criteria. Since the choice of the exact threshold values is arbi­trary, systematic uncertainties are evaluated by rederiving the fnal result, which is a data-to-MC ratio, after varying these selection criteria. Other systematic uncertainties are evalu­ated by altering choices used by the method, such as a param-eter used in a ft or changing the MC generator. In the case of the . +jet, Z + jet, and multijet techniques (Sects. 7 and 8), uncertainties are also established by adjusting the kinematic properties (energy, pT, etc.) of the reference object accord­ing to their associated uncertainties. These variations test the ability of the MC simulation to model the physics effects since they either reduce or amplify their importance. Many potential effects are considered as systematic uncer­tainty sources. As explained above, each of these is evaluated by introducing a variation to the analysis. However, due to limited statistics in both the data and MC samples, these variations have an associated statistical uncertainty (i.e. an “uncertainty on the uncertainty”). For example, an introduced variation that has no impact on the measured calibration fac-tor (or resolution) still produces changes consistent with sta­tistical fuctuations. Thus, it is important to only include sta­tistically signifcant variations as systematic uncertainties. This is achieved with a two-step procedure outlined below. In the frst step, the statistical uncertainty of the system­atic variations is evaluated in each pT bin using pseudo­experiments, following the “bootstrapping” method [58]. Each such pseudo-experiment is constructed by altering the data and MC samples. Each event is counted n times, where n is sampled from a Poisson distribution with a mean of unity. For each pseudo-experiment i, both the nominal cnom,i and varied cvar,i results are extracted, and the uncer­tainty is evaluated as the difference between these results cvar,i = cvar,i - cnom,i . If the variation is a change in the selection criteria or a change of the calibration or resolution smearing of any of the objects, the random fuctuations of the events that stay in the same bin are the same between the nominal and varied samples, while the events that migrate between bins will have independent fuctuations. The statis­tical uncertainty of the systematic uncertainty amplitude is evaluated as the standard deviation of the systematic uncer­tainty (difference between varied and nominal result) of the pseudo-experiments. 123 In a second step, adjacent pT bins might iteratively be combined until the observed variation is statistically signif­icant. If the variation already is signifcant with the original binning, it is recorded as a systematic uncertainty. Otherwise, neighbouring bins are merged, which results in improved sta­tistical precision. After each bin-merging, it is checked if the systematic variation is signifcant, and if so, it is recorded as a systematic uncertainty. If after all bins are merged, the varia­tion is still not signifcant, the systematic effect is considered consistent with zero and is discarded. For some systematic variations, there are physics reasons for the response to depend on pT, such as the out-of-cone effects being relatively larger at low pT. In such cases, the bin merging step is not performed for the nominal uncertainty evaluation, but it is considered within alternative uncertainty scenarios (Sect. 9.4). The use of the pseudo-experiments and the bin merging procedure strongly reduces the effect of statistical fuctua­tions when evaluating systematic uncertainties. This proce­dure is used for all the in situ methods discussed in this paper. 6.5 Relative jet energy scale calibration using dijet events The following sections detail the determination of the inter­calibration aimed at achieving a uniform scale for jets as a function of pseudorapidity. 6.5.1 Comparison of matrix and central reference methods Figure 16 compares the relative jet response calculated using the matrix method with that obtained from the central refer­ence method. The relative response obtained from the matrix method differs slightly from that from the central refer­ence method, most notably in the forward regions where the difference is up to 4%. This is not surprising since the matrix method uses a signifcantly larger pool of events that have different kinematics (smaller rapidity separation) than the ones used by the central reference method. The same shift appears in both data and MC simulation, resulting in consistent data-to-MC ratios between the two methods. For 25 GeV . pavg < 40 GeV the statistical precision of the T matrix method generally exhibits a 40% improvement com­pared with the precision of the central reference method. The level of improvement decreases with increasing pTavg and is typically less than 10% for pavg > 400 GeV. Since the fnal T . intercalibration is derived using data-to-MC ratios that are found to be consistent between the methods and the matrix method gives signifcantly smaller uncertainties, the matrix method is chosen, and hereafter all . intercalibration results presented are derived using this method. 6.5.2 Comparison of data with simulation Figure 17 shows the relative response as a function of .det for data and the MC simulations for four pTavg regions. Fig­ure 18 shows the relative response as a function of pTavg for two representative .det bins, namely -1.5 . .det < -1.2 and 2.1 . .det < 2.4. The general features of the response in data are reproduced reasonably well by the Sherpa and Powheg+Pythia8 predictions. Furthermore, the theoreti­cal predictions are in good agreement with each other, with a much smaller spread than that observed in the previous studies using Pythia8 and Herwig++ [6], because the new theoretical predictions are accurate to leading order in pertur­bative QCD for variables sensitive to the third jet’s activity, such as the dijet balance, whereas the Pythia8 and Her-wig++ predictions rely on the leading-logarithm accuracy of the parton shower algorithms. 6.5.3 Derivation of residual jet energy scale correction The residual calibration factor c. is derived from the ratio of data and Sherpa .-intercalibration factors, i.e. c.,i = data Sherpa avg c/c. The calibration factors from many bins of p ii T and .det are combined into a smooth function using a two­dimensional Gaussian kernel [6]. The kernel-width parame­ters of this function are chosen to capture the shape of the MC-to-data ratio across pT and .det, and at the same time provide stability against statistical fuctuations. The resulting residual correction c. is shown as a black line in the lower panels of Figs. 17 and 18. In these panels, it can also be seen that the calibration function is fxed for .det and pT regions that extend beyond the data measurements. The same freez­ing of the calibration is also done for |.det| > 2.7 since the generator dependence becomes larger in this region. Mea­surements in these forward regions are not used to derive the intercalibration but are used when assessing the uncertainty. 6.5.4 Systematic uncertainties All intercalibration systematic uncertainties are derived as a function of pT and |.det| with no uncertainty assigned in the reference region (|.det| < 0.8). No statistically signifcant difference is observed for positive and negative .det for any of the uncertainties, justifying the parameterization versus |.det|, which increases the statistical power in the uncertainty evaluation. The difference between Sherpa and Powheg+Pythia8 is used to assess the physics modelling uncertainty. Both of these generators are accurate to leading order in QCD for variables sensitive to the modelling of the third jet (such as the dijet balance). Since there is no a priori reason to trust one generator over the other, the difference between the two 123 Fig. 16 Relative jet response measured using the matrix and central for data (circles) and Sherpa (triangles) using the central reference reference methods for anti-kt jets with R = 0.4 calibrated with the method (empty symbols) and the matrix method (flled symbols). Only EM + JES scheme as a function of the probe jet pseudorapidity. Results statistical uncertainties are shown. The dashed lines in the lower panels avg avg are presented for 65GeV.pT < 85 GeV and 270GeV.pT < 330GeV indicate 1 ± 0.02 and 1 ± 0.05 Fig. 17 Relative jet response, 1/c, as a function of the jet pseu­dorapidity for anti-kt jets with R = 0.4 calibrated with the EM + JES scheme, for data (black circles), Sherpa (blue triangles) and Powheg+Pythia8 (red squares). Results are shown separately avg avg for 25 GeV < pT < 40 GeV, 85 GeV < pT < 115 GeV, avg avg 220 GeV < pT < 270 GeV and 760 GeV < pT < 1200 GeV with associated statistical uncertainties. The lower part of each fgure shows the ratio of relative response in MC simulation to that in data, while the thick line indicates the resulting residual correction. The dashed part of this line represents the extrapolation of the ratio into regions which are either statistically limited or probe |.det| > 2.7. These measurements are performed using the matrix method. The dashed lines in the lower panels indicate 1 ± 0.02 and1 ± 0.05 123 predictions is used to estimate the modelling uncertainty. For 0.8 .|.det|< 2.7, where data are corrected to the Sherpa predictions, the full difference between Powheg+Pythia8 and Sherpa is taken as the uncertainty.4 For |.det|.2.7, where the calibration is frozen, the uncertainty is taken as the maximum difference between the extrapolated calibra­tion and the prediction from either Powheg+Pythia8 or Sherpa. The use of these event generators results in a sub­stantial improvement in the agreement between the theoret­ical predictions, thus reducing the modelling-based uncer­tainty by a factor of approximately two relative to the pre­vious result [6]. Despite the improvement, this modelling uncertainty remains the largest systematic uncertainty in the measurement. The physics modelling uncertainty in the relative response is cross-checked using truth-particle jets by varying the Powheg+Pythia8 predictions. The QCD renormalization and factorization scales in the Powheg Box are each varied by factors of 0.5 and 2.0, which has a signifcantly smaller impact on the relative response than the difference between the Powheg+Pythia8 and Sherpa predictions. A compar­ison of the relative response between the Powheg+Herwig sample and the Powheg+Pythia8 sample is also per­formed and is similar to the truth-particle jet relative response between Powheg+Pythia8 and Sherpa.The assigned uncertainty from the difference between Sherpa and Powheg+Pythia8 is a good refection of the underly­ing physics modelling uncertainty. 4 The full difference between the generators is considered the uncer­tainty amplitude of a two-sided systematic uncertainty. All uncertainty components discussed in this paper are treated as two-sided uncertain­ties. relative response, while the thick line indicates the resulting residual correction. The dashed part of this line represents the extrapolation of the ratio into regions which are statistically limited. The dashed lines in the lower panels indicate 1 ±0.02 and 1 ±0.05 The event topology selection requires .12 > 2.5 and j3 avg pT < 0.4 pT . To assess the infuence of these selection criteria on the MC modelling of the pT balance, the resid­ual calibration is rederived after shifting the .12 selection by ±0.3 radians and the radiation criteria based on the frac­tional pT of a potential third jet by ±0.1. The maximum difference between the rederived calibration after the up and down shifts to the nominal is taken as uncertainty. To assess the impact of pile-up, the calibration is rederived in sub­sets split into high and low µ (µ< 14 and µ .17), and high and low NPV subsets (NPV < 9 and NPV .11). The uncertainty due to pile-up effects is taken to be the maximum fractional difference between the varied and nominal calibra­tions. Similarly, an uncertainty due to the JVF requirement is derived by redoing the calibration after tightening and loos­ening the JVF criteria following the procedure defned in Ref. [51]. These variations account for the extent to which JVF is mis-modelled for jets originating from the primary inter-action vertex. An uncertainty due to imperfect modelling of the jet energy resolution is also assigned by smearing the jet four-momenta in MC simulation using Gaussian random sampling with a standard deviation calculated from the JER data-to-MC difference. The difference between the calibra­tions obtained with nominal and smeared simulation is taken as the uncertainty due to JER effects. The total systematic uncertainty is the sum in quadrature of the various components mentioned. Figure 19 presents a summary of the uncertainties as a function of |.det|for two representative values of jet transverse momentum, namely pT =35 GeV and pT =300 GeV. The uncertainties have a strong pseudorapidity dependence, increasing with .det, and have a weaker pT-dependence, decreasing with increasing jet pT. 123 6.6 Jet energy resolution determination using dijet events Figure 20 shows the measured relative jet energy resolution avg as a function of pT forEM+JEScalibratedjetsindifferent .det regions of the calorimeter. The results are presented for both the dijet balance and bisector methods, and there is good agreement between the methods for all values of pavg and T |.det|. The jet energy resolution in simulated events, deter­mined as described in Sect. 4.2, is also shown as a dotted line and is in agreement with the measured JER in data. 6.6.1 Systematic uncertainties The JER is determined in data by subtracting the truth­particle jet asymmetry from the measured asymmetry as discussed in Sect. 6.1. The truth-particle jet asymmetry is defned as the weighted average of the truth-particle jet asym­metries obtained for each of the Sherpa, Powheg+Pythia8, Pythia8, and Herwig++ event samples. The uncertainty in this weighted average is taken to be the RMS deviation of the truth-particle jet asymmetries obtained from the four event generators. This source of uncertainty is typically 0.02 at low pTavg for both methods, falling to less than 0.01 at the highest avg p. T Non-closure is defned as the difference between the jet resolution measured by the in situ method and the truth­particle jet resolution obtained by matching truth-particle and calorimeter jets (Sect. 4.2). This is treated as a sys­ tematic uncertainty in the method. The weighted average of the truth-particle jet asymmetries predicted by Sherpa, Powheg+Pythia8, Pythia8, and Herwig++ is subtracted in quadrature from the weighted average of the asymmetries evaluated for reconstructed calorimeter jets. The non-closure is typically about 10–15% for the bisector method, but it is larger for the dijet balance method, reaching 25% in some regions. The individual components are added in quadrature to obtain the total uncertainty. The MC modelling uncertainty is the dominant component for jets with |.det| > 1.5 Finally, there are a number of systematic uncertainties that arise from experimental sources. The uncertainty in the JES calibration is investigated by shifting the energy of the jets by the ±1. uncertainty, with a typical effect between 5% and 10% at low pavg . The uncertainty due to the choice of T JVF selection has a less than 2% effect for both methods. The uncertainty due to the criterion on the azimuthal angle between the jets is investigated by changing the requirement by ±0.3, with a negligible effect at high pavg for both meth- T ods, a small (< 4%) effect on the dijet balance results at low pTavg and a larger effect (5–15%) on the bisector results at low pavg . The impact of the veto on the third jet is investigated by T changing the selection criteria by ±4 GeV, and is found to have a 10–15% effect at low pavg for both methods, falling T to a few percent at higher pTavg values. The total systematic uncertainty, which is taken as the sum in quadrature of all sources discussed above, is shown as a dashed band around the points in Fig. 20. 7 Calibration and resolution measurement using . +jet and Z + jet events This section describes the determination of the fnal jet cal­ibration that corrects the absolute energy scale of the jets to achieve a data-to-MC agreement within the associated uncertainties. The jet calibration is based on measurements conducted by in situ techniques that exploit the transverse momentum balance between a well-calibrated object and the hadronic recoil (jet). The well-calibrated object is either a photon or a Z boson that decays leptonically, either Z›ee or Z›µµ. Three separate datasets are used: (Z›ee) + jet, (Z›µµ) + jet and . + jet, and two different in situ tech­niques are used for each dataset, namely the direct balance technique (DB) and the missing projection fraction method (MPF). The three independent datasets and the two analy­ 123 Fig. 20 Relative jet energy resolution obtained for EM + JES cali­brated jets using the bisector (flled circles) and dijet balance (flled squares) methods, respectively. The MC simulated resolution derived from matching truth-particle jets with calorimeter jets is presented by the open triangles connected by dashed lines. The error bars refect the sis methods provide six separate measurements of the jet calorimeter response that can be cross-checked with each other, allowing detailed studies of systematic uncertainties. For each dataset, the method that gives the smallest overall uncertainty is chosen and is used as input to the fnal combi­nation of the absolute jet calibration (Sect. 9). Due to the steeply falling Z boson pT spectrum, the Z +jet data provide suffcient statistics to calibrate jets at lower pT and are used in the range 17 GeV . pT < 250 GeV. The Z boson four-momentum is reconstructed by four-vector addition of its decay products (leptons). The . + jet pro­cess has a higher cross section and covers the jet pT range 25 GeV . pT < 800 GeV. However, at low pT the photon sample has a large contamination from events that do not con­tain any true prompt photon and hence a sizeable systematic uncertainty. As discussed in Sect. 9.1, a combination of both the Z + jet and . + jet channels covers the full momentum range 17 GeV .pT < 800 GeV. statistical uncertainty while the hashed band indicates the total system­atic uncertainty. Results are shown as a function of the jet pT in four regions of detector pseudorapidity: |.det|< 0.8, 0.8 .|.det|< 1.2, 1.2 .|.det|< 2.1, and 2.1 .|.det|< 2.8. The lower panels show the data-to-MC ratio, and the thin dashed lines indicate 1 ±0.2and 1 ±0.4 7.1 The direct balance and missing projection fraction methods Both the DB and MPF methods exploit the momentum bal­ance in events with . + jet or Z + jet topology to study the jet calorimeter response. Both methods beneft from accurate knowledge of the energy scale and resolution of the boson (i.e. the photon or the dilepton system). The calibration of electrons and photons is accurately known through measure­ments using Z ›ee data and other fnal states [44], while the muon reconstruction is determined to high precision through studies of J/ ›µµ, Z ›µµ, and . ›µµ [59]. The DB response RDB is  j1 ref Z/. RDB = pT / pT , where pTref =p T |cos .|, (17) j1 where pT is the pT of the leading jet being probed and . is the azimuthal angle between this jet and the boson (Z or . ). If the jet includes all the particles that recoil against the Z boson or . and all particles are perfectly measured, then pTj1 / pref =1 and cos . =cos . =-1. In reality, there T is always additional QCD radiation not captured by the jet, 123 which skews the balance. This radiation, referred to as out­of-cone radiation (OOC), tends to be in the same hemisphere as the jet and hence biases the DB to values below unity. The reference transverse momentum pTref used in the denomina­tor of RDB is the boson momentum projected onto the jet axis in the transverse plane in order to attempt to at least partially reduce OOC effects. The DB is also affected by uncertainties in the reconstructed photon, electron, or muon momenta, as well as contributions from pile-up and multiple parton–parton interactions (the underlying event). The MPF method [5,60] is an alternative to the DB tech­nique. Rather than balancing the jet object itself against the well-measured boson, the whole hadronic recoil is used. The MPF measures the response for the full hadronic recoil, which is signifcantly less sensitive to OOC radiation and effects due to pile-up and the underlying event. The logic of the MPF method is detailed below for . + jet events. The case of Z +jet is the same with the Z boson replacing the photon. From conservation of transverse momentum, the pT vec­tor of the system of all hadrons produced in a . + jet event, . recoil p T , will perfectly balance the photon p T at the truth­ recoil particle level. In a perfect 2 ›2 process, p T would be equal to the pT of the parton, which in turn is that of the jet. At reconstruction level, the pT of the photon (or Z boson) is well calibrated and hence accurately reconstructed, while the hadronic response is low prior to calibration, primarily due to the non-compensating nature of the ATLAS calorimeters.5. There is hence a momentum imbalance, which defnes the missing transverse momentum E miss: T . recoil p =0 (truth-particle level) T,truth + p T,truth . recoil + E miss p +p =0 (detector level). (18) TT T Projecting the vector quantities of Eq. (18) onto the direction . of the photon n^. and dividing the result by p T gives the MPF observable rMPF, whose mean is the MPF response RMPF, where recoil ·E miss n^. ·p T n^. T rMPF =- . =1 + . and pp TT ¢ ·E miss n^. T RMPF = 1 + .. (19) p T The Emiss T defnition used in Eqs. (18) and (19) is based on the calibrated momentum of the photon (or dilepton system for Z + jet data) using topo-clusters at the constituent scale, either at the EM-scale when studying the EM+JES calibration or at the LCW-scale for the LCW+JES calibration. Details of the ATLAS Emiss reconstruction are in Ref. [61]. T 5 The hadronic recoil is reconstructed at the constituent scale, for which the calorimeter response can have a signifcant energy dependance as can be seen in Fig. 4. The MPF response RMPF provides a measure of the pT response of the calorimeter to the hadronic recoil for a given . p T. A feature of this method is that it is almost independent of the jet algorithm as the jet defnition enters only in the event selection criteria applied (Sect. 7.2). Except for two relatively small corrections known as the topology and showering cor­rections (Sect. 7.3.4.2), the RMPF determined in . + jet or Z + jet events can be used as an estimator of the calorime­ter jet response at pile-up-subtracted scale (Sect. 4.3.2). This is because pile-up is independent of both the hard interac­ ·Emiss tion and the azimuth ., and so its contribution to n^. T will be zero on average, meaning that RMPF already effec­tively subtracts the pile-up as is done for jets using Eq. (2). Since RMPF is an approximation of the pile-up-subtracted jet response, it can be compared with the corresponding quantity of the MC-derived calibration in Fig. 4 that defnes 1/cJES. The RDB and RMPF parameters are determined in bins of pTref (Eq. (17)) from the mean parameter extracted from j1 ref fts to the balance distributions (pT / pand rMPF)usinga T Modi.ed Poisson distribution, which was also used in the previous ATLAS jet calibration [6]. This distribution starts from a standard Poisson distribution fP(n;.) and is extended to non-integer values using a Gamma function (n + 1), followed by the introduction of a new parameter s used to redefne the argument using x = s2 n and defning µ . E[x]=s2 .,giving 22 2)x/s-µ/s (µ/se fMP(x;µ, s) = . (20) (x/s2 +1) s2 This distribution has the same shape as a “smoothed” Poisson distribution with . = µ/s2 and has mean µ and standard deviation . µ s. For larger values of µ/s2(15), it is very similar to a Gaussian distribution, while for lower values (µ/s2 5) the longer upper tail of a Poisson distribution is prominent. The Modifed Poisson function better describes the balance distributions and is motivated by the Poisson nature of sampling calorimeters. The MPF and DB methods probe the calorimeter response to jets in a different way and are sensitive to different system­atic effects. They therefore provide complementary measure­ments of the jet-energy scale. The explicit use of jets in the measurement of the jet response from DB makes this tech­nique dependent on the jet reconstruction algorithm while the MPF technique is mostly independent of the jet algorithm, as explained above. Thus, in the following, when presenting MPF results, no jet algorithm is explicitly mentioned. 7.2 Event and object selection This section outlines the event selection used for the DB and MPF analyses separately for the . + jet and Z + jet datasets. The two methods have similar selections, but the restriction 123 on the subleading jet pT (Sect. 7.2.3) is less stringent for the MPF method because it is less sensitive to QCD radiation. 7.2.1 Photon selection The . +jet data was collected using six different single­photon triggers, each with a different associated photon pT threshold. The fve lower-threshold triggers were prescaled, while only the highest-threshold trigger was not prescaled. Agiven . + jet event was assigned to one of these triggers, based on the pT of the leading photon reconstructed by the algorithm used in the high-level trigger. This mapping was created such that the trigger effciency for each pT range was at least 99%. The lowest-threshold trigger data has the largest associated prescale factor and is used for photons between 20 and 40 GeV, while the highest-threshold trigger, which was not prescaled, is used for pT > 120 GeV. Reconstructed photons are required to satisfy strict iden­tifcation criteria ensuring that the pattern of energy depo­sition in the calorimeter is consistent with that expected for a photon [62]. Photons are calibrated following the proce­dure in Ref. [44] and are required to have pT > 25 GeV and |.| < 1.37 such that they are fully contained within the elec­tromagnetic barrel calorimeter. In order to suppress back­grounds from calorimeter signatures of hadrons misidenti­fed as photons, an isolation criterion is further applied to all photons. The isolation transverse energy of a photon Eiso is T calculated from calorimeter energy deposits in a cone of size R = 0.4 around the photon, excluding the photon itself and the expected contribution from pile-up [62]. Photons are ini­tially required to fulfl Eiso < 3.0 GeV. However, for events T where the leading photon has pT below 85 GeV, the contam­ination from misidentifed photons is still large. Hence, more stringent criteria are applied as follows: Eiso < 0.5GeVif T .. p T < 45 GeV, or else Eiso < 1.0GeV if p T < 65 GeV, and T . otherwise Eiso < 2.0GeV if p < 85 GeV. Each event is TT required to have at least one photon fulflling these criteria. In the very rare case of two such photons, the leading one is used. 7.2.2 Z boson selection A typical Z boson selection is applied, starting by requiring dilepton triggers that were not prescaled during the data­taking period. For the Z›ee channel, the dielectron triggers requires two “loose” electrons, defned in Ref. [63], with ET > 12 GeV and |.| < 2.5. For the Z›µµ channel, the trigger requires one “tight” and one “loose” muon, defned in Ref. [64], with pT > 18 GeV and pT > 8GeV, respectively. The reconstructed electrons are required to ful-fl “medium” quality requirements [65] and are calibrated as detailed in Ref. [44]. Electrons are required to have pT > 20 GeV and |.| < 2.37, excluding the barrel–endcap tran­sition region 1.37 < |.| < 1.52. Muons are reconstructed through the combination of trajectories and energy-loss infor­mation in several detector systems [59] and are required to have |.| < 2.5 and pT > 20 GeV. Each event is required to have exactly two reconstructed electrons or two muons with opposite charge. The invariant mass of the dilepton system m must then fulfl 80 GeV < m < 116 GeV, ensuring high Z ›  purity. 7.2.3 Jet and boson+jet topology selection Jets are reconstructed and a preselection is applied, includ­ing standard JVF requirements, as described in Sect. 4.1. They are calibrated with all steps prior to the absolute in situ correction (Sect. 4.3). To avoid double counting of energy depositions, jets are required to be R > 0.35 from a pho­ton for the . +jet analysis or from any of the leptons in the Z + jet analysis for jets reconstructed with R = 0.4. The corresponding criterion is R > 0.5for R = 0.6jets. The leading jet is required to have |.det| < 0.8 and pT greater than 10 GeV for the Z +jet analysis and 12 GeV for the . + jet analysis. To enforce a “boson + jet” topology and hence suppress additional QCD radiation, criteria are imposed on the azimuthal angle .(Z/., j1) between the Z boson or photon and the leading jet and on the sublead­ j2 ing jet transverse momentum pT , if such a jet is present. j2 The DB analysis requires .(Z/., j1)> 2.8 and pT < max(8GeV, 0.1 pref ) while the MPF analysis uses the cri- T teria .(Z/., j1)> 2.9 and pj2 < max(8GeV, 0.3 pref ). TT The subleading jet pT is always defned using the jet collec­ tion reconstructed using R = 0.4, even when studying jets built using R = 0.6or R = 1.0. For jets built using R = 1.0, j2 pT is defned as the pT of the leading R = 0.4 jet that fulfls R(j1, j2)> 0.8, where “j1” refers to the leading R = 1.0 jet, i.e. the jet that is being probed. This ensures that the “j2” jet will have a signifcant proportion of its energy depositions outside of the large-R jet. 7.3 Jet response measurements using Z +jet and . + jet data Measurements of RDB and RMPF using both of the individ­ual Z ›  datasets and the . + jet dataset are discussed below. The subsequent combination of the Z ›  and . + jet results into the fnal in situ calibration is detailed in Sect. 9.1. The Z›ee and Z›µµ analyses probe jets over the same kinematic space and use exactly the same pTref binning. Within each bin, the balance distributions pj1 ref T / pT and rMPF agree between the channels for both the cores of the distribu­tions (including their means) and their tails (including their standard deviations). The two datasets are combined into a Z ›  channel, which increases the statistical power of the 123 (b) (a) (c) j1 ref ref TT ref ref b 60 GeV . pT < 80 GeV, c 160 GeV . pT < 210 GeV, and ref d 500 GeV . pT < 600 GeV using anti-kt jets with R = 0.4 cali­brated with the EM + JES scheme in data from the a, b Z + jet and c, d . + jet analyses. The dashed lines in a, b show the ftted Modifed measurement. This combination is done consistently for data and MC simulation, and also for systematic variations. 7.3.1 Direct balance results j1 ref Figure 21 presents four DB pT / pdistributions in rep- T resentative pref bins from the Z + jet and . + jet analyses T using anti-kt jets with R = 0.4 calibrated with the EM + JES scheme. Good ft quality using the Modifed Poisson param­eterization of Eq. (20) is observed. This is true for the other pref bins considered, both for data and for all MC samples T considered. The value of RDB is extracted for each pref bin for both T data and simulation. Figure 22 shows the measurements of RDB in data compared with predictions from the different MC generators as a function of pTref for anti-kt R = 0.4 jets calibrated with the EM + JES scheme. The different MC (d) Poisson distributions of Eq. (20), from which the means are taken as the DB response measurements RDB. The solid lines indicate the ft­ting ranges. The lack of data at low pTj1 / pref visible in a is due to the T j1 pT > 10 GeV criterion. The markers are the data counts with error bars corresponding to the statistical uncertainties generators agree with data within 1% for pT > 40 GeV with slightly worse agreement at lower pT. The worst data-to-MC agreement is for EM + JES calibrated R = 0.4jetsin the 17 GeV . pTref < 20 GeV bin (Fig. 22a), for which the Powheg MC sample predicts ~5% higher RDB than what is observed in data. For LCW + JES calibrated R = 0.4 jets and R = 0.6 jets using both calibration schemes, the data-to-MC agreement is within 3% across the full pTref range probed. For the . + jet analysis, the measured responses agree within 1% with the MC predictions for pTref < 100 GeV for both R = 0.4 and R = 0.6 jets using both calibration schemes. For jets with pref > 100 GeV, the MC simulation T systematically tends to overestimate the measured response by approximately 1%. 123 (a) (b) 7.3.2 Validation of intercalibration of forward jets using Z +jet data The derived intercalibration in Sect. 6 corrects jets with for­ward rapidities |.det|> 0.8 by about 1-3% (Fig. 17). The total uncertainty in this calibration is presented in Fig. 19 and is typically below 1% for jets with |.det|< 3, increasing to about 3.5% for low-pT jets with |.det|> 4. To validate this calibration, the DB analysis is repeated for the jets with 0.8 .|.det|< 4.5using Z +jet events. As in the standard analysis (Sect. 7.2.3), the intercalibration is applied to the jets, and hence the data-to-MC ratio of RDB is expected to be uniform versus .det within the uncertainty assigned to the intercalibration. Results of this analysis for EM+JES calibrated anti-kt R =0.4 jets are presented in Fig. 23.The prediction of both MC generators agree with the data within the assigned uncertainties for jets with 0.8 .|.det|< 2.8. For the region |.det|> 2.8, differences can be up to 7% as shown in Fig. 23; however, the statistical uncertainties of the Z › measurements are of similar magnitude. Hence, the results validate the derived dijet intercalibration. 7.3.3 MPF results Figure 24 presents RMPF calculated at both the EM and LCW scales as a function of pTref extracted using both the Z + jet and . + jet events. As mentioned in Sect. 7.1, RMPF is a measure­ment of the hadronic response of the calorimeter and does not include the MC-derived calibration cJES nor the GS calibra­tion cGS (see Sects. 7.3.4.2 and 7.3.4.6 for further discussion on this). The “upturn” of RMPF at low values of pTref visible in Fig. 24 is an expected artefact of the jet reconstruction threshold. Since a jet is required to be present in the event (Sect. 7.2.3), when this jet’s pT fuctuates low the event might fail the selection. For such an event, rMPF will also tend to be low. And similarly, events with jets that fuctuate high in pT will have high rMPF and will pass the selection. For the Z +jet analysis, the RMPF measured in data is sys­tematically about 1% below the prediction of Powheg+Pythia8, considered the reference MC sample. For the . + jet analysis, the predictions of RMPF from both MC simulations agree across the full pTref range within the statistical precision. Both simulations systematically over­estimate the RMPF value measured in data by about 1% for pTref > 85 GeV at the EM scale and by about 1% for pTref > 50 GeV at the LCW scale. 7.3.4 Systematic uncertainties The fnal JES calibration that is described in Sect. 9 is based on the data-to-MC ratio of the response measurements. As explained in detail in Sect. 6.4, systematic uncertainties in this quantity are evaluated by introducing variations to the analysis. The following seven sections present the evaluation of in total 17 uncertainty sources that affect the data-to-MC ratio of RDB and RMPF. These uncertainties assess various effects that can affect the response measurement, such as impact of additional QCD radiation, choice of MC genera­tor, effects from out-of-cone radiation and pile-up, and the precision of the pT scale of the reference objects (photons, electrons, or muons). 7.3.4.1 Suppression of additional radiation As explained in Sect.7.2.3, a“boson+jet” topologyisselected byimposing constraints on the azimuthal angle . between the boson and the jet and by restricting the pT of any subleading jet. These criteria reduce the impact from additional QCD radia­tion on the momentum balance between the jet and the boson. Systematic uncertainties from two sources are evaluated, one through varying the . requirement and one through varia­ 123 (a) (b) ref ref Powheg+Pythia8 (blue) simulation, for a 45 GeV . pT < 65 GeV and b 110 GeV . pT < 160 GeV. Only statistical uncertainties are shown j2 tions of the pT selection. Constructing a single uncertainty component from variation in simulations of the two criteria is also considered (as was done previously [5]); however, the two-component approach is suffcient. The . selection is varied by ±0.1 around the nominal values of 2.9 for MPF and 2.8 for DB (Sect. 7.2.3). The j2 pT requirement for the DB analysis is similarly tightened to ref ref max(7GeV, 0.05 pT ) and loosened to max(9GeV, 0.15 pT ). The MPF selection is varied by similar amounts around the nominal selection. The resulting uncertainty from the . variation is generally negligible. The uncertainty due to the pTj2 requirement is 0.4% or smaller for pref < 50 GeV and is T negligible above this value. 7.3.4.2 Systematic uncertainties due to out-of-cone radia­tion For the DB method, the pT of a jet, even if perfectly calibrated, will always tend to be smaller than that of the photon or Z boson due to the out-of-cone radiation (Fig. 21). The impact of the out-of-cone radiation on RDB is studied in both data and simulation by measuring the average pT density of tracks as a function of the angular distance (R) between the track direction and the leading jet axis. Based on this pT profle, the fraction of the radiation outside the jet cone is estimated (see Section 9.4 of Ref. [6] for details), and an out-of-cone systematic uncertainty is evaluated on the basis of the simulation’s ability to model the measured value of this quantity. The resulting uncertainty is as large as 2% ref ref at pT = 40 GeV and is smaller at higher pT. In principle, the MPF technique does not depend on the OOC correction because the calorimeter response is inte­grated over the whole detector. However, two effects related to the OOC contribution must be considered. The “showering correction” quantifes the migration of energy across the jet boundary of the calorimeter jet relative to the truth-particle jet and is diffcult to measure with data. This effect is included in the DB analysis by design since it is based on reconstructed jets but is not included for the MPF method since it measures the entire hadronic recoil. In addition, the hadronic response in the periphery of the jet is different than in the core because of the different energy densities and particle compositions. This “topology correction” is also diffcult to extract from data but is expected to be small since the average pT den-sity around the jet axis decreases fairly rapidly, and only a small fraction of the pT is outside the jet radius. MC studies have shown that the uncertainty in each of these corrections is signifcantly smaller than the DB OOC uncertainty. As a conservative approach, the OOC uncertainty measured in data for the DB case is used to estimate the contributions from showering and jet topology to the uncertainty in the JES determined using the MPF technique. The use of this larger uncertainty does not signifcantly affect the total sys­tematic uncertainty in the JES from this analysis over most of the pT range. 7.3.4.3 Impact of the Monte Carlo generator For each fnal state, predictions of the response observables (RDB and RMPF) are produced with two different MC generators: Pow­heg and Sherpa for Z + jet and Pythia8 and Herwig++ for . + jet. As detailed in Sect. 3, these generators use different modelling of the parton shower, jet fragmentation, and mul­tiple parton interactions. The difference in the data-to-MC ratio of the response between the generators is taken as a “generator” systematic uncertainty source. This is a reason­able estimate of the dependence of the pp collision modelling on RDB and RMPF, but a possible compensation by competing modelling effects cannot be excluded. This generator mod­elling constitutes the largest systematic uncertainty source ref for Z +jet for pT  50 GeV, where it can be as large as 2.5%. 7.3.4.4 Uncertainties associated with the reference objects The defnitions of RDB and RMPF both have the pT of the ref­erence object in the denominator and are hence sensitive to 123 (a) (b) (c) (d) knowledge of its energy scale and resolution. For the Z +jet analyses, uncertainties in pref arise from the precision of T the electron energy scale (EES) and energy resolution (EER) and from the muon momentum scale (MMS) and resolution (MMR), while for . + jet, uncertainties arise from the preci­sion of the photon energy scale (PES) and energy resolution (PER). The EES is measured in data [44] and has three uncer­tainty components: MC modelling of the Z › ee decay; the material description in simulation; and the response of the calorimeter’s presampler. These are treated statistically independent of each other. The EER uncertainty is param­eterized by a single component. The MMS and MMR are determined in data [59] and have one and two associated uncertainty components, respectively. Finally, the PES and PER are evaluated using extrapolation of EES and EER, and are hence affected by the same uncertainty sources. Hence, they have the same four uncertainty sources, but these affect photons and electrons quite differently. Each of the 11 uncertainty sources are propagated to the simulated samples by adjusting the four-momenta of the reconstructed electron, muon, or photon. The uncertainties in RDB and RMPF are then evaluated following the proce­dure described in Sect. 6.4. For all objects, the resolution uncertainties are found to be negligible (0.1% or less). For . + jet, the PES uncertainties are reasonably independent of pref and their sum in quadrature amounts to 0.5–0.6%. The T magnitudes of the EES and MMS uncertainties are less than 0.3%. 123 7.3.4.5 Impact of additional pile-up interactions Jets produced in additional pile-up interactions are present in both data and simulation and might impact the response measurements. To study this effect, the JVF criterion is varied around its nominal value of 0.25 (Sect. 4.1). The JVF criteria used for this variation are based on studies presented in Ref. [51] and are 0.24 and 0.27 for EM + JES calibrated jets and are 0.21 and 0.28 for jets calibrated using LCW + JES. Studies of the dependence of RDB and RMPF on the num­ber of primary vertices NPV in the event and on the average number of interactions per beam bunch crossing µ were also performed. Figure 25 presents results from these studies for the MPF method for a representative selection of pTref bins. The data-to-MC ratio of RMPF is found to be independent of both NPV and µ for all pref bins. The same conclusion is T reached for the DB analysis. Hence, only one pile-up uncer­tainty component is assigned, due to the pile-up mitigation using the JVF criterion. 7.3.4.6 Impact of lack of GS correction for the MPF method The GS correction (Sect. 5) is based on the properties of jets. Since the MPF does not use jets directly, applying the GS correction in the standard way will have no impact on RMPF. Instead, the GS correction factor cGSC is extracted from the leading jet in each event and is used to adjust RMPF. Two methods were tested: simply scaling RMPF with cGSC and recalculating RMPF after adjusting Emiss by adding the T change of the jet momentum vector due to the GS correction j1 (cGSC -1)p T . Both methods result in a negligible change to the data-to-MC ratio of RMPF, and no uncertainty is assigned for this effect. 7.3.4.7 Impact of background in the . +jet sample The . + jet dataset suffers from non-negligible contamina­tion from dijet events where one of the jets is misrecon­structed as a photon. The purity, i.e. the fraction of actual . + jet events, after the nominal selection is estimated using a “sideband” technique based on the event yields in differ­ent control regions defned by alternative photon isolation and identifcation criteria. This technique is described in . detail in Refs. [5,62]. The purity increases with p T, being . about 80% at p T = 85 GeV and rising above 90% for . p T  200 GeV. The misreconstructed events tend to have j1 ref higher pT / pand rMPF. The difference in DB and MPF T response between true . + jet events and misreconstructed events is estimated by varying the photon identifcation cri­teria. The . + jet MC samples used have perfect purity by defnition. The uncertainty due to the contamination from dijet events in the . + jet analyses was estimated by multi­plying the fraction of misreconstructed events by the relative difference in response between . + jet and misreconstructed events. The resulting uncertainty decreases with pref.For the T DB analysis, it is ~3.5% at pTref = 35 GeV, decreasing to 1% ref ref at pT = 100 GeV and to < 0.4% for pT > 250 GeV. For MPF, this uncertainty is smaller by approximately a factor of 2. This reduction is due to the defnition of the observable, where RMPF is inherently more stable against stochastically­oriented effects (pileup, fake photons, etc) compared to RDB due to such contributions cancelling in RMPF when averaged over many events. 7.3.4.8 Summary of the systematic uncertainties Figure 26 presents the JES uncertainties from various sources, evalu­ated for both the DB and MPF methods with anti-kt R = 0.4 jets calibrated with the EM + JES using the Z + jet dataset. The total uncertainty is obtained by addition in quadrature of the uncertainties from different sources. Overall, the DB and MPF methods achieve similar levels of precision. The MC generator uncertainties dominate for pref 50 GeV and the T ref out-of-cone uncertainty is also signifcant for pT 80 GeV. The statistical uncertainty is the major uncertainty for the Z + jet analyses at pTref > 200 GeV. Figure 27 shows the uncertainties for the corresponding . + jet analyses. Here, the photon purity systematic uncer­tainty is the dominant uncertainty for the DB method for pref < 100 GeV, while it is signifcantly smaller and sub- T dominant for MPF. The other systematic uncertainties are of similar magnitude for the two methods. For the range 100 GeV . pTref < 400 GeV, the photon energy scale con­tributes the dominant uncertainty. 7.4 Calibration of large-R jets For analyses based on pre-2012 data, the JES uncertainty of large-R jets has been evaluated in situ using track jets (Sect. 4.1)[45]. This method, discussed further in Sect. 9.5, is limited to 2–7% precision due to tracking uncertainties and the uncertainty in the charged-particle component of the jet. Furthermore, this method is restricted to the central calorime­ter region |.det| < 1.2, since at more forward .det, the large-R jet will not be fully contained in the acceptance of tracking detectors. This section presents an improved large-R jet JES uncertainty evaluation using . + jet events. 7.4.1 RDB measurements using . +large-R jet events The DB analysis is performed for large-R jets using the same approach as for small-R jets. The binning in pTref and .det is different, chosen to account for the available data statistics, ref ref . and pis defned simply as p. p T instead of projecting TT onto the jet axis (Eq. (17)). Examples of pTj1 / pref distribu- T tions ftted with the Modifed Poisson function are shown in Fig. 28. 123 (c) Figure 29 presents RDB as a function of pTref for large-R jets in two .det ranges, both for data and MC simulations. The response in the central calorimeter region, |.det| < 0.8, is modelled within 1% by the simulation, with simulations tending to overestimate the response by ~0.5%. For large-R jets with 0.8 < |.det| < 1.2, this deviation grows to ~2%. Rather than using this deviation as a calibration to correct for the difference between data and MC simulation, this dif­ference is taken as an additional uncertainty. As detailed in Sect. 4.4, large-R jets do not receive any intercalibration c.. (d) ref a reference pT range of a, c 45 GeV . pT < 65 GeV and b, d 110 GeV . pref < 200 GeV. Only statistical uncertainties are shown T 7.4.2 Systematic uncertainties Most of the systematic uncertainties are evaluated in the same way as for small-R jets as detailed in Sect. 7.3.4. Additional uncertainties specifc to large-R jets and changes to the eval­uation of some of the uncertainty sources are detailed below. • Rather than using the difference of the data-to-MC ratio of RDB from unity as a calibration, it is instead taken as an uncertainty. This allows a straightforward combination with the procedure used to derive uncertainties outside of the kinematic range for which the . + large-R jet RDB 123 (a) (b) Fig. 26 Summary of the JES statistical and systematic uncertainties in quadrature of all uncertainty sources. EES/EER denotes the electron evaluated for the Z +jet a DB and b MPF analyses for anti-kt jets energy scale/resolution, while MMS/MMR denotes the muon momen­with R = 0.4 and calibrated with the EM + JES scheme. The total tum scale/resolution uncertainty, shown as a shaded region, is obtained from the addition (a) Fig. 27 Summary of the JES statistical and systematic uncertainties evaluated for the .+jet a DB and b MPF analyses for anti-kt jets with R = 0.4 and calibrated with the EM + JES scheme. The total can be derived. This is a signifcant uncertainty source, especially for jets with 0.8 .|.det|<1.2. • The OOC uncertainty is evaluated only for large-R jets with |.det| < 0.8, since for other .det bins the large-R jets are not always fully contained within the tracking acceptance. The uncertainty derived in this central .det range is also applied to the more forward |.det|bins. Due (b) uncertainty, shown as a shaded region, is obtained from the addition in quadrature of all uncertainty sources. PES denotes the photon energy scale, while PER denotes the photon energy resolution to the large radius (R = 1.0), out-of-cone effects are very small, and the uncertainty is negligible for pT > 100 GeV. • As mentioned in Sect. 7.2.3, the subleading jet (labelled “j2”) that is used to suppress additional QCD radiation is required to have an angular separation of R(j1,j2)> 0.8 from the large-R jet (“j1”). Since the leading jet has 123 (a) (b) j1 ref ref Fig. 28 pT / pdistributions for events with a 85 GeV . p< present fts to the data of a Modifed Poisson function (Eq. (20)). The TT 110 GeV and b 260 GeV . p< 310 GeV for trimmed anti-kt jets markers show data with error bars corresponding to the statistical uncer­ ref T with R =1.0 calibrated with the LCW + JES scheme in data. The lines tainties (a) (b) Fig. 29 RDB for trimmed anti-kt jets with R =1.0 calibrated with the LCW + JES scheme for a |.det|< 0.8and b 0.8 .|.det|< 1.2 for both data (flled circles) and MC simulation (empty circles), as a function of the pTref. Only statistical uncertainties are shown R =1.0 while the subleading jet has R =0.4, this means that there is a signifcant overlap in terms of solid angle, but since the pT profle of jets tend to be narrow (see the Wtrk distribution of Figs. 6 and 7), the amount of energy sharing is still expected to be small. The assigned uncertainty component is evaluated by changing the R requirement from 0.8 to 1.4 to ensure that there is strictly no overlap between the two jets. • Since the small-R jets are reconstructed independently of the large-R jets using the same topo-clusters as input, a large-R jet will sometimes contain two small-R jets close to the large-R jet axis. It is possible that events with such topologies have additional uncertainties due to the QCD modelling. To assess this effect, an alternative subleading jet selection was applied in which “j2” is defned simply as the subleading R = 0.4 jet, without any restriction based on the angle to the large-R jet. This means that “j2” will sometimes be within the large-R jet and sometimes not (the leading R = 0.4 jet tends to be aligned very close to the large-R jet axis). With this defnition, the 123 j2 ref event selection pT < 0.1 pT was applied in place of j2 the standard pT selection, and an uncertainty component was derived from the impact of this variation. • An additional dependence of the jet response for large-R jets on the ratio of the jet mass to the pT, m/ pT,is observed, particularly for large |.det|. A systematic uncer­tainty is assigned to account for this dependence, derived as a triple ratio. The data/MC ratios of the RDB ratios are evaluated in the two m/ pT ranges shown in Fig. 30, corresponding to m/ pT < 0.15 and m/ pT > 0.15. The systematic uncertainty is given by the ratio of the double ratios obtained for the two m/ pT ranges. 7.4.3 Pile-up uncertainty for large-R jets As discussed in Sect. 4.1, large-R jets do not receive any pile-up correction. Due to the trimming algorithm applied, large-R jets are signifcantly less sensitive to pile-up than standard small-R jets. To study the impact of pile-up on the large-R jet pT, it is measured as a function of NPV and µ in bins of pT of track jets that are matched to the large-R jets being probed. Track jets are resilient to pile-up since they are built from inner-detector tracks that are matched only to the primary vertex, and do not contain contributions (tracks) from pile-up vertices (in most cases). The track jets are reconstructed using the same algorithm as the calorimeter large-R jets (trimmed anti-kt R = 1.0). Within a given track jet pT bin, the large-R jets are expected to have a similar truth-particle jet pT. The recon­structed pT is studied as a function of NPV and µ. The results for a representative track jet pT bin is presented in Fig. 31.As expected (Eq. (2) and Ref. [6]) there is a linear dependence of the jet pT on both NPV and µ. For each track jet pT bin, the “gradients” . pT/. NPV and .pT/.µ are extracted from the slopes of a linear fts of pT vs NPV and pT vs µ (Fig. 31). Figure 32 shows these gradients as a function of the aver­age pT of the large-R jets. Both of these graphs are well described with a function of the form a + b log ( pT/ pT,0), where the parameters a and b are extracted from a ft and pT,0 is a constant chosen to be 50 GeV. Basedonthe pT parameterization of the gradients from the fts to data described in the previous paragraph (Fig. 32), two uncertainty components are derived that have the following impact on the jet pT  NPV - Nref = (. pT/. NPV) and NPV PV µ = (. pT/.µ)(µ - µref), (21) where . pT/. NPV and . pT/.µ are the gradients parameter­ized as a function of large-R jet pT according to the ftted functions, µ is the average number of interaction per bunch crossing, and NPV is the number of primary vertices of the event, and µref = 20.7 and N ref = 11.8 are the average PV values for the full 2012 . + jet dataset. As can be seen from Eq. (21), the impact on the jet pT from the two uncertainty components can change sign depending on the amount of pile-up, and become zero for jets produced in events with pile-up conditions matching the 2012 average values. The resulting fractional pT uncertainties are presented for two values of large-R jet pT in Fig. 33. 7.4.3.1 Summary of systematic uncertainties Figure 34 presents a summary of the statistical and systematic uncer­tainties in the large-R jet pT from the DB analysis, including a detailed breakdown of the uncertainty components that are in common with the small-R jet . + jet measurements pre­sented in Sect. 7.3.4, while the additional uncertainty sources specifc to large-R jets are presented in Sect. 7.4.2. The total uncertainty for |.| < 0.8 is found to be ~1% above 150 GeV, rising to ~2% at 1 TeV. At larger |.|, the uncertainty increases to ~2% at low pref, rising to ~3% at 1 TeV. The uncertain- T ties are dominated by the photon energy scale uncertainty, the uncertainty coming from the large-R jet response depen­dence on the ratio of m/ pT, and the difference of the data-to-MC RDB from unity. The generator systematic uncertainty becomes dominant for |.| > 1.2. 7.5 Measurement of the jet energy resolution using the DB method The width of the DB distribution in a given pref binisusedto T probe the JER. The detector resolution of the reference object is negligible compared with that of the jet, so the method to measure the JER using Z + jet and . + jet events is signif­cantly simpler than that for dijets described in Sect. 6.The event selection and binning is the same as for the RDB mea­surements, but instead of determining the mean RDB of the j1 ref ref pT / pdistribution within each pbin, the width . reco T TDB is extracted as the standard deviation of the same Modifed Poisson ft. The relative JER .E /E is then estimated using .E .pT = . reco truth = ., (22) DB DB EpT where the frst equality holds to a good approximation since the contribution from the angular resolution is negligible, and the second relation follows from the same reasoning as for Eq. (14) (Sect. 6.1). The parameter . truth is obtained using DB truth ref afttothe pT / pT distribution extracted using MC simu­lation with same selection (applied to reconstructed jets) as truth for the DB measurement. For each simulated event, pT is defned from the truth-particle jet that is ghost-matched (Sect. 4.2) to the leading reconstructed jet. The simulated JER truth is also extracted from the MC samples with fts to pTreco / pT (Sect. 4.2). Figure 35 presents a MC-based comparison between the relative JER obtained using the in situ technique applied to the simulated events (Eq. (22)) and the relative JER extracted 123 (a) ref Fig. 30 RDB as a function of pT measured for trimmed anti-kt jets with R = 1.0in .+ jet events shown separately for jets with a |.det|< 0.8and b 0.8 .|.det|< 1.2. Separate results are shown for jets with m/pT <0.15 and m/pT >0.15, displayed with circles and triangles, respectively. Measurements in data are shown as flled (b) markers and MC predictions as open makers. Statistical uncertainties are shown for each point. The lower parts of the fgures show the sys­tematic uncertainty evaluated as the data-to-MC ratio of the ratios of RDB extracted in the two m/pT ranges (a) Fig. 31 Large-R jet pT as a function of a NPV in .+ jet events with 20 <µ<22, and as a function of b µin events with 10 800 GeV. 8.1 Event selection Multijet events were obtained using single-jet triggers that recoil are fully effcient for a given bin of pT . The triggers used recoil for 300 GeV < pT < 600 GeV were prescaled, whereas recoil a non-prescaled jet trigger was used for pT > 600 GeV. Events are required to contain at least three jets with pT > 25 GeV. The leading jet is required to have |.det| < 1.2, and the subleading jets that constitute the recoil system are required to have |.det| < 2.8. To select non-dijet events, the j2 leading jet in the recoil system pT is required to have less than j2 recoil 80% of the total pT of the recoil system (pT / p< 0.8). T Furthermore, the angle . in the azimuthal plane between the leading jet three-momentum and the vector defning the recoil system is required to satisfy |. - .| < 0.3 radians, and the angle ß in the azimuthal plane between the leading jet and the nearest jet from the recoil system is required to be greater than 1 radian. 8.2 Results Figure 37 shows RMJB for data and MC simulation using the EM + JES calibration scheme. The MJB method provides 123 inputs for the in situ jet calibration in the pT range between 300 GeV and 1900 GeV. The data and MC simulation agree to within 1% across the pT range probed, a feature that is reproduced by the Z/. + jet analyses (Sect. 7). 8.3 Systematic uncertainties Since the jets entering RMJB have been calibrated using the other in situ approaches, the uncertainty in the energy scale of the jets in the recoil system is defned by the system­atic and statistical uncertainties of each in situ procedure. To propagate the uncertainty to RMJB, all input components are individually varied by ±1. and the full iterative analysis pro­cedure is repeated for each such variation. Changes in RMJB due to the statistical uncertainties of the . +jet and Z +jet calibrations are typically much smaller than 1%. Also, the event selection criteria and the modelling in the event generators affect the pT balance RMJB. The impact of the event selection is investigated by shifting each selection criterion up and down by a specifed amount and observing the change in RMJB.The pT threshold for jets is shifted by j2 recoil ±5 GeV, the requirement on the ratio pT / pis shifted T by ±0.1, the angle . by ±0.1, and the angle ß by ±0.5. The uncertainty due to MC modelling of multijet events is estimated from the symmeterized envelope of MJB correc­tions obtained by comparing the nominal results obtained from Sherpa with those obtained from Powheg+Pythia8, Pythia8, and Herwig++. The unknown favour of each jet is also a source of system­atic uncertainty. The uncertainty in RMJB due to the jet favour response is evaluated using a correlated propagation of the jet favour response uncertainties, i.e. all jets in the recoil sys­tem are shifted simultaneously. The jet favour composition uncertainty is propagated to RMJB for the frst, second, and third recoil jets independently, with the fnal composition uncertainty obtained from the quadrature sum of the three variations. The total uncertainty due to the unknown par­ton favour is taken as the sum in quadrature of the favour response and composition uncertainties. Examples of the impact of systematic uncertainties are showninFig. 37b for anti-kt R = 0.4 jets using the EM +JES calibration scheme. The uncertainties are grouped together into in situ, event topology, physics modelling, and jet favour categories. Uncertainties for anti-kt R = 0.6jetsorthe LCW + JES scheme are comparable. The uncertainty accounting for the difference of the jet energy resolution between data and simulation was not prop­agated to the recoil system of the multi-jet balance as the scale was derived before the resolution. However, the impact of this effect on the multi-jet balance was checked after the resolution was derived, and was found to introduce per-mille level differences on the extraction of the scale. This effect is therefore negligible compared to the existing uncertainties on the multi-jet balance shown in Fig. 37b. 9 Final jet energy calibration and its uncertainty As detailed in Sects. 7 and 8, response observables that are directly proportional to the JES are constructed using in situ techniques by exploiting the transverse momentum balance in . +jet, Z + jet, and multijet events. These response observ­ables are determined in both data and MC simulations. The fnal residual jet calibration cabs, which accounts for effects not captured by the MC calibration, is defned through the ratio of the responses measured in data and MC simulation by 1 Rdata = . (23) cabs RMC As explained in Sect. 4.3, the absolute in situ correction cabs is applied last in the calibration chain following the ori­gin, pile-up, MC-based, and dijet in situ calibrations. Just as for the dijet intercalibration (Sect. 6), the absolute correction is applied only to data to remove any residual differences in the jet response following the MC calibration. The dijet . intercalibration is referred to as a relative in situ calibration, as it quantifes the balance between a pair of jets in differ­ent detector regions without evaluating the absolute scale of either jet. The absolute calibration is done for the Z +jet, . + jet, and MJB techniques, which all balance the probe jet against a well-known reference quantity, thus providing a measure of the absolute scale of the jet and are known as absolute in situ calibrations. Figure 38 summarizes the results of the Z +jet, . + jet, and multijet balance analyses, showing the ratio of jet response in data to jet response in MC simulations. In the pT range 20-2000 GeV, the response agrees between MC simulations and data at the 1% level. The deviation of the response from unity defnes the absolute in situ calibration which is applied to jets in data. There is good agreement and little tension between the three different in situ methods in the regions of phase space where they overlap. 9.1 Combination of absolute in situ measurements The separate measurements from Z +jet, . + jet, and multijet balance are combined using the procedure outlined in Ref. [6]. For the Z + jet and . +jet measurements, the method giving the smallest overall uncertainty is used, corresponding to the DB approach for Z + jet and the MPF approach for . + jet (see Sect. 7 for details on the methods). The choice of DB for Z + jet is a compromise between the precision of the R = 0.4 and R = 0.6 jet calibrations in the low pT regime where the Z +jet fnal state is most relevant: it was found 123 (a) (b) Fig. 37 a Multijet balance RMJB in data (circles) and MC simula­ in situ, event selection (topology), physics modelling, and jet favour tion (triangles) for anti-kt R = 0.4 jets calibrated with the EM + JES systematic uncertainties on RMJB. The error bars on the RMJB measure­ scheme. The bottom frame compares RMC MJB/Rdata MJB (triangles) with the ments only show statistical uncertainties corresponding . /Z + jet results (magenta solid line). b The impact of (a) Fig. 38 Ratio of response measured in data to response measured in MC samples for Z + jet (empty squares), . + jet (flled triangles) and multijet balance (empty triangles) in situ analyses. The method giv­ing the smallest overall uncertainty is used, corresponding to the DB approach for Z + jet and the MPF approach for . + jet. Each measure­ that the DB and MPF techniques give similar uncertainties for R = 0.4 jets, while the DB technique provides improved precision for R = 0.6 jets. In contrast, the MPF technique is used for . + jet events as it is found to generally provide better uncertainties across its kinematic range of relevance. This combination uses the compatibility of the three in situ measurements and their associated systematic uncertainties to produce a combined measurement of the response ratio with associated uncertainties. Table 3 presents the 26 systematic uncertainty sources that affect cabs. These are evaluated as detailed in Sects. 7.3.4 and 8.3. The electron and photon energy scale uncertainties are each split into four sources that are fully correlated. These are treated as four e/. energy scale sources, yielding a list of (b) ment has two error bars: the smaller interval corresponds to the sta­tistical uncertainty, while the outer error interval corresponds to the total uncertainty. Also shown is the combined correction (line) with its associated total uncertainty (wider band) and statistical uncertainty (narrower band) as discussed in Sect. 9.1 22 systematic uncertainty components. Each source is further classifed into one of the following four categories: • detector description (det.), • physics modelling (model), • statistics and method (stat./meth.), and • mixed detector and modelling (mixed). The combination is carried out using the absolute in situ measurements (Eq. (23)) in bins of pTref and evaluated at ref ref pT . The data-to-MC response ratio is defned in fne pT bins for each method using interpolating second-order poly­nomial splines. The combination is then carried out using a weighted average of the absolute in situ measurements based 123 Table 3 Summary of the uncertainty components propagated through to the combination of absolute in situ jet energy scale measurements from Z+jet, . + jet, and multijet balance studies. These are discussed in more detail in Sects. 6 and 7 Name Description Category Z+jet eE-scale material Material uncertainty in electron energy scale Det. eE-scale presampler Presampler uncertainty in electron energy scale Det. eE-scale baseline Baseline uncertainty in electron energy scale Mixed eE-scale smearing Uncertainty in electron energy smearing Mixed µ E-scale baseline Baseline uncertainty in muon energy scale Det. µ E-scale smearing ID Uncertainty in muon ID momentum smearing Det. µ E-scale smearing MS Uncertainty in muon MS momentum smearing Det. MC generator Difference between MC generators Model JVF JVF choice Mixed . Extrapolation in . Model Out-of-cone Contribution of particles outside the jet cone Model Subleading jet veto Variation in subleading jet veto Model Statistical components Statistical uncertainty Stat./meth. . +jet . E-scale material Material uncertainty in photon energy scale Det. . E-scale presampler Presampler uncertainty in photon energy scale Det. . E-scale baseline Baseline uncertainty in photon energy scale Det. . E-scale smearing Uncertainty in photon energy smearing Det. MC generator Difference between MC generators Model . Extrapolation in . Model Out-of-cone Contribution of particles outside the jet cone Model Subleading jet veto Variation in subleading jet veto Model Photon purity Purity of sample in . + jets Det. Statistical components Statistical uncertainty Stat./meth. Multijet balance . selection Angle between leading jet and recoil system Model ß selection Angle between leading et and closest subleading jet Model MC generator Difference between MC generators (fragmentation) Mixed pT asymmetry selection Asymmetry selection between leading and subleading jet Model Jet pT threshold Jet pT threshold Mixed Statistical components Statistical uncertainty Stat./meth. on a .2-minimization. This local . 2 is used to defne the level of agreement between measurements. Each uncertainty source in the combination is treated as being fully correlated across pT and . and independent of one another. All the uncertainty components are propagated to the combined results using pseudo-experiments [5]. To deter­mine the correlations between different phase-space regions, it is necessary to understand the contribution of each uncer­tainty component to the fnal uncertainty. Therefore, each individual source is propagated separately to the combined result by coherently shifting all the correction factors by one standard deviation. Comparison of this shifted combination result with the nominal result provides an estimate of the propagated systematic uncertainty. One exception is the jet favour uncertainty of the recoil in the multijet balance method (Sect. 8). It is correlated in a non­ trivial way with the additional uncertainties due to favour composition and response considered in analyses. Including this uncertainty does not change the overall absolute in situ uncertainty by a signifcant amount after combination with the other in situ methods, so it is dropped. To take tensions between measurements into account, each uncertainty source is increased by rescaling it by .2/ndof if .2/ndof is larger than unity [66], where ndof is the number of degrees of freedom. The number of degrees of freedom 123 varies with pT and corresponds to the number of in situ meth­ods nin-situ that contribute to the combination minus one, i.e. ndof = nin-situ - 1. The local .2/ndof of the fnal com­bination (Fig. 39) for both jet collections is below unity for most of the pT range and barely exceeds 2 anywhere. The combined in situ factor is the fnal calibration factor to be applied to data after reducing statistical fuctuations using a sliding Gaussian kernel. Figure 40 shows the uncertainty sources for the three abso­lute in situ analyses used in the combination as a function of pT. In the combination, the Z + jet measurement is most important at low pT,the . + jet measurement at medium pT, and the multijet balance at high pT. The combined jet response, shown as a line in Fig. 38,is observed to have a general offset of 0.5% between data and MC simulation (with data below the MC prediction). The total uncertainty from the combination of absolute in situ techniques is shown as the wider band around the measured response and is about 3.5% (2.5%) for jets with pT . 25 GeV for EM (LCW) jets and decreases to about 1% (1%) for pT above 200 GeV. As mentioned a spline-based combination procedure, with a local averaging within fne pT intervals followed by a global smoothing, is used for the in-situ JES combination. This method avoids assumptions on the jet energy response dependence that are implicitly present in procedures based on global fts using a functional form, which can further reduce the uncertainties (see e.g. Ref. [67]). 9.2 Jet energy scale uncertainties In addition to the uncertainties coming from the combi­nation of in situ methods detailed above, there are sev­eral other uncertainties that account for other potential sys­tematic effects or expand the kinematic reach. These addi­tional uncertainties are described below, and summarized in Sect. 9.2.4 9.2.1 Single-hadron response The jet energy response measured by the in situ methods can also be compared with results from a method where the jet energy scale is estimated from the calorimeter response to single hadrons measured in test beam studies. This provides a cross-check of the direct balance in situ methods, albeit with a larger uncertainty, and also allows the extension of the in situ measurements of the jet energy scale to higher energies beyond the reach of balance methods due to lim­ited data. In this “single hadron” method, jets are treated as a superposition of the individual energy deposits of their con­stituent particles [68]. In some cases, highly energetic jets contain constituents beyond test-beam energies. When this occurs, a constant 10% uncertainty is applied to each of these constituents. In the previous jet energy scale measurements based on data taken in 2011 [6], the absolute in situ methods and the single-hadron response studies gave consistent results, indi­cating that MC simulation overestimated the jet response in data by approximately 2%. However, since the in situ meth­ods are more precise (approximately 2% uncertainty com­pared to 5%) the single-particle response method is only used at high pT(> 1500 GeV) where the statistical power of in situ methods becomes limited. The single-hadron response measurements from the 2011 data [6] are propagated to high pT jets to provide an uncertainty where it is beyond the reach of the absolute in situ analyses. 9.2.2 Pile-up uncertainties There are four uncertainties sources associated with the mit­igation of the pile-up contributions to the jet momentum (Eq. (2)) that are evaluated by comparing data with simu­ lation using in situ techniques. Two of the uncertainties are in the values of the slope parameters . and ß that determine the dependence on the number of reconstructed pile-up ver­tices and the average interactions per crossing, respectively. The third uncertainty accounts for jet pT dependence of the . and ß parameters. These uncertainties are evaluated using momentum balance in Z + jet events. The fourth uncertainty is associated with a topology dependence of the event pT­density .. It is evaluated as the largest difference in mea­sured average pT density . at a given pile-up condition µ between dijet, . + jet, and Z + jet events. As shown in Eq. (2), this uncertainty is directly proportional to the jet area and is larger by approximately a factor of 0.62/0.42 = 2.25 for R = 0.6 jets compared with R = 0.4jets. For R = 0.6jets, this tends to be the dominant uncertainty component with a typical magnitude of 2% for jets with pT around 40 GeV. For R = 0.4 jets in events with moderate pile-up, the NPV-dependent uncertainty component tends to be largest for jets in the central calorimeter region while the µ component is largest in the forward calorimeter region (|.det| > 2.8). 9.2.3 Flavour-based uncertainties The in situ methods used to derive fnal corrections and uncer­tainties of the jet energy scale make use of event samples with particular fractions of jets initiated by quarks and gluons. The event samples in physics analyses may have jet favour com­positions which differ from that of the calibration sample. The response for quark-initiated jets is considerably higher than that for gluon-initiated jets (Sect. 5.5). Therefore, if the favour composition of fnal states in a given analysis is unknown, it has an impact on the JES uncertainty. The degree to which the favour of jets is known in an analysis 123 (a) (b) can be specifed in order to evaluate the corresponding uncer­tainty. Alternatively, analyses can be conservative and use a completely unknown favour composition. While the response for light-quark-initiated jets is found to be in good agreement between different generators, shifts are seen in the gluon jet response for different generators due to differences in the jet fragmentation. There is there­fore an additional uncertainty for gluon-initiated jets, which is subdominant in the Z + jet and . + jet regions used to con­strain the uncertainty, as defned by the difference between the gluon jet response in Pythia8 and Herwig++. These dif­ferences are typically reduced using LCW topo-clusters as inputs, and this is visible in the central region of the detector when comparing to jets built using EM topo-clusters. How­ever, this is less true in the forward region of the detector where the LCW correction is less robust due to the different properties of the more forward calorimeters. Further details of this uncertainty are given in Ref. [6], and additional discussion of how the GS correction reduces the jet favour uncertainties are presented in Sects. 5.5 and 5.7. 9.2.4 Summary of jet energy scale uncertainties The total jet energy scale uncertainty is compiled from mul­tiple sources: • 22 systematic sources from absolute in situ methods, • 34 statistical sources from absolute in situ methods, • a single-hadron response uncertainty which only affects the highest-pT jets beyond the reach of in situ techniques (Sect. 9.2.1), ndof is equal to one. For a small pT range near 300 GeV, only one measurement (. + jet) contributes, and there is a gap (ndof = 0). The points where the curve touches zero correspond to where the two in situ calibrations cross • two .-intercalibration uncertainties (one systematic, one statistical), • four sources from uncertainties associated with the pile-up corrections: – µ-dependent uncertainty in the pile-up correction, – NPV-dependent uncertainty in the pile-up correction, – pT dependence of pile-up corrections, and – . topology dependence, as outlined in Ref. [51] (Sect. 9.2.2), and • two sources due to jet favour (Sect. 9.2.3). The last two terms are assumed to be independent, resulting in a jet energy scale uncertainty defned in terms of 65 com­ponents (nuisance parameters). The resulting, total jet energy scale uncertainty is shown as a function of jet pT in Fig. 41 and versus jet . in Fig. 42. 9.2.5 Uncertainties in fast simulation All uncertainties discussed in the previous section apply to MC samples produced using either the full or fast simula­tion. However, a small non-closure of the jet calibration was observed in fast simulation compared with full simulation. To account for this, an additional systematic uncertainty must be included in analyses using fast simulation since relative and absolute in situ methods are not used to validate this simulation. The size of this uncertainty compared with other systematic uncertainties is generally small for R = 0.4jets (Fig. 43). However, as shown in Fig. 44, this uncertainty becomes sizeable for R = 0.6jets. 123 (a) (b) (c) (d) (e) (f) Fig. 40 Individual uncertainty sources used in the combination for the three absolute in situ calibration methods. The systematic uncertainties displayed correspond to those in Table 3 9.3 Simplifed description of uncertainty correlations lations using a reduced set of uncertainty components (nui­ sance parameters). The list of uncertainties described in Sect. 9.2.4 requires an As detailed in Ref. [6], the total covariance matrix of the analysis to propagate a total of 65 JES uncertainty terms to JES correction factors including all the in situ sources can be correctly account for all correlations in the jet calibration. diagonalized, and then a new set of independent uncertainty For many analyses it is preferable to describe such corre-sources can be derived from the eigenvectors and eigen­ values. A good approximation of the covariance matrix is 123 (a) (c) Fig. 41 The total jet energy scale uncertainty as a function of pT for central jets. Two favour compositions are shown, one for dijet events, where the quark/gluon composition is taken from MC simulations and an associated uncertainty from generator comparisons, and one for an unknown favour composition (assuming 50:50 quark:gluon jets with a 100% uncertainty). “Absolute in situ JES” refers to the uncertainty aris­ then obtained by selecting a subset of the new uncertainty sources (those with the largest eigenvalues) and combining the remaining nuisance parameters into a residual term. Fig­ure 45 demonstrates this procedure, showing the nominal correlation matrix and the difference between this and a sim­ilar matrix derived from a reduced set of nuisance parameters. Only uncertainties depending on a single parameter (in this case pT) are combined in this way and any uncertainties with dependencies on other parameters are left separate. Includ­ing such uncertainty components with additional parameter dependencies in the combination would not result in any sig­nifcant reduction of the correlation information into fewer nuisance parameters, as such components require additional dimensions to represent their correlations. Two reduction schemes are provided. The frst scheme reduces the number of central absolute in situ nuisance parameters, those shown in Fig. 40 and the statistical com­ (b) (d) ing from Z +jet, . + jet, and multijet measurements, including also the single-hadron response uncertainty at high pT. “Relative in situ JES” refers to the uncertainty arising from the dijet . intercalibration. “Punch­through” refers to the uncertainty in the fnal (muon-based) stage of the global sequential correction ponents of the . + jet, Z + jet, and multijet balance, from 56 to 6 (“standard”). To preserve some knowledge of the uncer­tainty source in this procedure, a second scheme is provided where the reduction is done within categories (statistical, detector, modelling, or mixed). This “category based” reduc­tion reduces the number of central absolute in situ parameters from 56 to 15. Retaining the separation of detector, statistical, and modelling components allows the correlation between experiments and different data-taking years to be assessed in combinations of measurements. No reduction is done for the other terms, and in addition to the 6 (15) nuisance parame­ters, nine additional parameters are required, resulting in 15 (24) parameters. This procedure gives a simpler propagation of the correlations and uncertainties associated with the jet energy scale with very little loss of information about the correlations. 123 (a) (c) Fig. 42 The total jet energy scale uncertainty as a function of |.| for pT = 40 GeV jets. Two favour compositions are shown, one for dijet events, where the quark/gluon composition is taken from MC simula­tions and an associated uncertainty from generator comparisons, and one for an unknown favour composition (assuming 50:50 quark:gluon (b) (d) jets with a 100% uncertainty). “Absolute in situ JES” refers to the uncer­tainty arising from Z +jet, . + jet, and multijet measurements. “Relative in situ JES” refers to the uncertainty arising from the dijet . intercalibra­tion. “Punch-through” refers to the uncertainty in the fnal (muon-based) stage of the global sequential correction (a) (b) Fig. 43 Total uncertainty in the calibration of anti-kt , R = 0.4jets the dijet . intercalibration. “MC non-closure, fast simulation” refers to in fast simulation as a function of pT and .. “Absolute in situ JES” the additional non-closure observed in fast simulation when comparing refers to the uncertainty arising from Z +jet, . + jet, and multijet mea-with full simulation surements. “Relative in situ JES” refers to the uncertainty arising from 123 (a) (b) Fig. 44 Total uncertainty in the calibration of anti-kt , R = 0.6jetsin ulation. “Absolute in situ JES” refers to the uncertainty arising from fast simulation as a function of pT and .. The large “MC non-closure” Z +jet, . + jet, and multijet measurements. “Relative in situ JES” refers term demonstrates the limitations of using R = 0.6jetsinfastsim­ to the uncertainty arising from the dijet . intercalibration (a) (b) (c) (d) Fig. 45 The a, c JES correlation matrix and b, d difference between the full correlation matrix and that derived from a reduced number (6) of absolute in situ uncertainty components for anti-kt R = 0.4 jets calibrated with the a, b EM+JES and c, d LCW + JES schemes 123 A method has been developed for evaluating the correla­tions between the full set of 56 in situ JES uncertainty terms and a reduced set. This is especially useful for evaluating the correlations between the uncertainties obtained for two physics analyses that use different uncertainty confgurations (e.g. the full set and a reduced set of JES uncertainty terms). In this method, each JES uncertainty term in the full set is projected, in the space of uncertainties, onto the direction of each uncertainty term in the reduced set. The corresponding projection coeffcients allow expression of the uncertainties propagated by one analysis using a given confguration in terms of the components corresponding to another confg­uration. Therefore, this allows correlations to be assessed between analyses using different uncertainty confgurations. 9.4 Alternative uncertainty confgurations Many physics analyses use “profling” of uncertainties in the statistical analysis, such as the profle log-likelihood method, which improves the precision of the associated physics results. These methods may make signifcant use of the uncertainty amplitudes and correlation in different kine­matic regions, and the exact parameterization of the JES sys­tematic uncertainties might impact the result. Since the cor­relation between uncertainty sources often is unknown, the nominal uncertainty parameterization discussed in the previ­ous sections corresponds to a “best guess”. Certain analyses could erroneously beneft from somewhat arbitrary choices made during the construction of this uncertainty scheme. To allow analyses to test if their results depend on these choices, two alternative uncertainty parameterizations are provided, one that results in stronger JES uncertainty cor­relations and one that gives weaker correlations. These are constructed by making alternative assumptions about the cor­relation between different effects and by employing a differ­ent rebinning prescription when propagating absolute in situ derived uncertainties to the combination. In both the strong and weak correlation scenarios, a change is made in the rebinning procedure described in Sect. 6.4. The condition for stopping the merging of bins is altered such that the stronger (weaker) correlation scenario has more (less) bins merged. The effect of this procedure is particu­larly noticeable at low pT and results in a reduction of the absolute in situ uncertainties for the stronger correlation sce­nario. In addition, both alternatives use a slower turn-on of the interpolation between multijet balance and single-particle uncertainties at pT . 1.7TeV (Fig. 41). For the strong correlations alternative, certain uncertainty components that are treated as being uncorrelated with each other in the nominal parametrization are combined into a cor­related component. This is only done for components that are suspected to have some correlation. The favour composition uncertainty is also switched from using Pythia8 to derive the quark/gluon response to using Herwig++ to fully encompass generator dependence. For the weak correlation alternative, several “2-point” sys­tematic uncertainties are split into two subcomponents [69]. The term 2-point systematic uncertainties refers to uncertain­ties evaluated by comparison of the nominal result with only one alternative, e.g. a comparison between the predictions from two MC generators. The two constructed uncertainty components are defned such that their sum in quadrature equals the original component, thus the total uncertainty is retained. The split is performed by multiplying the origi­nal component by a factor varying linearly from 0 to 1 in either |.| or log pT, forming the frst subcomponent, while the second subcomponent is formed as the quadrature com­plement. Components treated this way in the alternative con­fgurations include the .-intercalibration modelling term and favour components. 9.5 Large-R jet uncertainties Uncertainties in the large-R jet calibration are determined using in situ methods with the same principle as for R = 0.4 and R = 0.6 jets. Jet energy scale uncertainties are derived by combining direct balance measurements (Eq. (17)) per­ formed in . + jet events and are combined with uncertain­ties with track jets as reference objects. Uncertainties for the jet mass scale are derived only using track jets as reference objects. The track jet double-ratio method is discussed below along with an additional topological uncertainty similar to the favour composition uncertainty in small-R jets. The . +jet studies and uncertainties are discussed in Sect. 7. Track jet double-ratio method In the double-ratio method, track jets are used as reference objects since charged-particle tracks are both well measured and independent of the calorimeter and are associated with calorimeter jets using a geometrical matching in the .–. plane. This method assumes that energy fuctuations mea­sured using the calorimeter are independent of the charge-to­neutral fraction of the particle-level jet’s constituents. This is only approximately true because the calorimeter response is different for charged and neutral particles. The precision of the method requires that the track jet momentum resolution is much smaller than the calorimeter jet energy resolution, an excellent approximation for calorimeter jet momenta up to several hundred GeV. This approach was widely used in the measurement of the jet mass and substructure properties of jets in the 2011 data [45]. Performance studies [70] have shown that there is excellent agreement between the measured positions of clusters and tracks in data, indicating no systematic mis­alignment between the calorimeter and the inner detector. 123 However, the use of track jets as reference objects is lim­ited to a precision in the jet mass scale of around 3–7% in the central detector region due to systematic uncertainties arising from the inner-detector tracking effciency [71] and confdence in MC modelling of the charged and neutral com­ponents of jets. The track jet double ratio is compared for two different MC generators: Pythia8 and Herwig++, and the larger disagreement between data and MC prediction is taken as the uncertainty. Figure 46 shows the jet mass scale uncer­tainty for anti-kt R = 1.0 trimmed jets in different detector regions. The uncertainties are derived in bins of pT, |.|, and m/ pT, and two examples are shown. Topological uncertainty Similarly to the jet favour composition uncertainty for small-R jets, an uncertainty in the jet energy response for different mixtures of quark/gluon jets, boosted top jets, and W jets is derived for large-R jets. Simulated tt— events are used to account for the different hard substructure and energy distri­butions within the W or top jets compared with quark/gluons jets which are taken from W +jet samples requiring exactly one lepton. The uncertainties are derived for anti-kt R = 1.0 trimmed jets. Figure 47 shows the pT dependance of the jet response in three . regions for four different kinds of jets: “full top” jets have the three quarks from the top decay con­tained within R = 0.8 of the jet axis; “W -only” jets have the quarks from the W decay within R = 0.8 of the jet axis but any b-quark must have R > 1.2; “non-top” jets have the top quark separated from the jet axis by R > 2.0; and, “QCD jets” are jets from a leptonically decaying W +jets sample. The topological uncertainty (Fig. 47) is determined by the envelope of the responses of these different types of jets. Combination The jet pT scale uncertainties are available within |.| < 2.0 but the available data at high pT(pT > 800 GeV) is limited for the direct . +jet pT balance method. By con­trast, the uncertainties from the track jet double ratios cover pT > 800 GeV. To beneft from the drastically reduced pT scale uncertainties derived with . + jet events, a linear inter­polation is performed around pT = 800 GeV between the two methods. The uncertainty arising from the topological composition of the jet is added in quadrature to form the total uncertainty. This total uncertainty and its components are shown as a function of pT in Fig. 48. 10 Final jet energy resolution and its uncertainty The measurement of the jet energy resolution (JER) in data is a multi-step process. As detailed in Sects. 6 and 7, the analy­ ses employed to measure the JER are essentially the same as for the jet calibration, but the observable of interest is not the mean of the response observable but is its width. For the cen­tral rapidity region, the JER is measured with good precision using . +jet and Z + jet events. In the forward pseudorapidity region and for high pT, dijet events provide the most precise determination of the JER. For very low pT jets there is a sig­nifcant contribution to the jet energy resolution from pile-up particles and electronic noise. Using the data taken in 2012, new methods have been developed to measure the pile-up component. The jet energy resolution is parameterized as a function of three terms [7], .pT NS = ... C , (24) pT pT pT where N parameterizes the effect of noise (electronic and pile-up), S parameterizes the stochastic effect arising from the sampling nature of the calorimeters, and C is a pT­independent constant term. It is the determination of these terms in data that is the subject of this section. In Sect. 10.1, the MC simulated jet energy resolution is discussed, followed by the determination of the noise term in data in Sect. 10.2. The combination of the measurements of the noise term and the Z +jet, . + jet, and dijet measure­ments, described in Sects. 7 and 6, respectively, is detailed in Sect. 10.3. The uncertainty in the measurement of the jet energy resolution arising from the various in situ methods is propagated through the ft to the pT dependence of the jet energy resolution. 10.1 JER in simulation The jet energy resolution is measured in simulated event sam­ples as described in Sect. 4.2, i.e. it is defned as the width parameter . of a Gaussian ft to the jet energy response dis­tribution restricted to the range ±1.5 . around the mean. Figure 49 shows the resolution determined using Pythia8 dijet MC samples both with full Geant4 detector simula­tion and with fast simulation. The two simulations generally agree very well, although there are some discrepancies in the very forward regions. The distribution is shown both with and without the GS correction, which signifcantly improves the resolution (decreasing the resolution of R = 0.4EM+JES jets from 10% to 7% at 100 GeV), particularly for jets built from EM-scale clusters. The resolution is shown as func­ truth tions of pand |.det|. As expected, the resolution improves T truth quickly with increasing pT . The resolution for a fxed value 123 (a) (b) (a) (b) (c) truth - preco truth Fig. 47 One minus the jet pT response (p/ p= T TT 1 - RpT )for anti-kt R = 1.0 trimmed jets with different favour com-position for a 0.0 < |.| < 0.8, b 0.8 < |.| < 1.2, c 1.2 < |.| < 2.0. The categories in the plot are defned by (1) “tt —full top” jets (circles) that represent jets for which the three quarks from a hadronic top quark decay are contained within R = 0.8 of the jet axis; (2) “tt —W-only” jets (squares), for which the quarks from the W boson decay are within R = 0.8 of the jet axis while the b-quark fulfls R > 1.2; (3) “tt —non-top” jets (lower triangles) that represent jets for which the top quark is R > 2.0 from the jet; and, (4) “Wjets QCD” jets (upper triangles) representing jets from a leptonically decaying W boson in a W +jets MC sample. These are plotted as a function of reconstructed jet pT ( preco T ), but due to the large bin size compared with the pT resolution, truth the choice of plotting pTreco or pT is of little signifcance 123 (a) of pT gets better towards more forward regions (this is not the case for constant jet energy). 10.2 Determination of the noise term in data Noise, both from the calorimeter electronics and from pile-up, forms a signifcant component of the JER at low pT. The noise term is not evaluated for R =1.0 trimmed jets, as they are only used for pT > 200 GeV at which point the noise term is negligible. It is quite challenging to measure the JER at low pT with in situ techniques (Sect. 10.3) as uncertain­ ties increase at low pT and the stochastic and noise terms are correlated at intermediate pT. Two alternative methods have hence been developed to target the noise term. These attempt to extract the noise at the constituent scale (the scale of the input topo-clusters) as explained in Sects. 10.2.1 and 10.2.2. They are translated into the effect on the jet resolution at the calibrated scale in Sect. 10.2.3. Good agreement is found between the methods, and a closure test is performed using MC simulations in Sect. 10.2.4, leading to a fnal value for the noise term in the jet energy resolution. The JER noise term receives contributions from the cells inside the topo-clusters created by the actual truth-particle jet as well as from pile-up. The noise term is signifcantly affected by the topo-cluster formation threshold as jets will contain a varying fraction of particles that have enough energy to form a topo-cluster. The noise term in data with­out pile-up is denoted N µ=0. As just mentioned, this term will be affected by a contribution corresponding to the num­ber of constituent particles produced without enough energy to produce topo-clusters or that have been swept out of the cone by the magnetic feld, and also by the electronic noise from the cells inside the topo-clusters. Pile-up particles can result in increased noise of topo-clusters seeded by the truth­particle jet particles, and also create new topo-clusters that are included in the jet. The latter effects is assumed to dominate, (b) R =1.0 trimmed jets for |.|=0 and two values of m/ pT: a m/ pT =0.20 and its contribution to the JER noise term is denoted NPU. A third source of noise are topo-clusters created solely from electronic noise in the entire calorimeter. This is assumed to be a negligible effect as the topo-clusters require a calorime­ter cell with 4 . energy over noise, which is also confrmed in data from events without collisions. The following sections present two different measurements of N PU. 10.2.1 Pile-up noise measured using random cones in zero-bias data In the random cone method, a cone of given size is formed at a random values of . and . in zero-bias data, and the energies of all clusters (at either EM or LCW scale) that fall within this cone are combined. The data was collected using a zero-bias trigger that records events occurring one LHC revolution after an event is accepted by a L1 electron/photon trigger. The total pT of a random cone is hence expected to only capture contributions from pile-up interactions. Since jets formed with the anti-kt algorithm tend to be circular (Fig. 3a), fuctuations of the pT in a random cone can be considered a measure of the expected pile-up fuctuations that are captured by an anti-kt jet with a radius parameter equal to the cone size. The . of the cone is randomly sampled within the range for which the noise is being probed, and the random cone method proceeds by forming a second cone at . +. (“back­to-back” in azimuth to the frst cone) but at a new random ., also restricted to the . range probed. The effect of the noise in these cones is expected to be the same on average6, and the difference in the random cone pT, pT, is plotted. The difference between two cones is used to remove any absolute offset present as the jet calibration would remove any abso­ 6 The noise is . dependent, but since both . values are sampled ran­domly within the probe region, the noise will be the same on average. 123 (a) (b) (c) tion of pT for a EM + JES and b LCW + JES jets (flled markers). The resolution in both events simulated with the full Geant4 toolkit (cir­cles) and with fast simulation (squares) are shown. Additionally the lute bias affecting the jets. The noise is studied as a function of . by restricting the |.| values that can be chosen for the ran­dom cones as previously mentioned. Since the topo-clusters that enter the random cone have no origin correction applied (Sect. 4.3.1), the . of the random cone corresponds to .det of a jet. An example of the distribution of this noise in data isshowninFig. 50. Due to the random nature of the pile-up energy deposits with signifcant energy over noise, the pT distribution is not expected to be Gaussian. The 68% con­fdence interval of this distribution is defned as the width. Since pT gives the fuctuations of two cones, this value is . divided by 2 to give an estimate of the noise term due to pile-up N PU at the constituent scale for a given jet. The growth of this noise term at the constituent scale as a function of the average number of interactions per bunch crossing is shown in Fig. 51 separately for |.| < 0.8 and 3.2 < |.| < 4.5. From these results, it is clear that the MC simulations overestimate the infuence of pile-up events, and this effect is increased in the forward region. Also, the noise term at constituent scale is larger for LCW than EM topo­clusters, because the LCW weighting acts to increase the (d) improvement from the global sequential correction is shown (empty markers). Figures c and d show the dependence of the resolution on |.det| for low-pT (20–25 GeV) jets and the level of agreement between full simulation (circles) and fast simulation (squares) energy scale of the topo-clusters, which also increases the constituent-level noise term. The EM-and LCW-scale noise terms can only be fairly compared after applying the jet cal­ibration factor, which is done later in Sect. 10.2.3. Figure 52 shows the average pile-up noise fuctuations expected in dif­ferent jets in 2012 for the different |.| regions. The data–MC agreement deteriorates in the more forward regions of the detector. This is likely to arise from poor modelling of the pile-up being exacerbated in this region due to the change in detector granularity and noise thresholds. To extract the pile-up noise term for average 2012 condi­tions, the noise term in random cones is extracted from the total 2012 zero-bias dataset. To ensure that the µ distribution used in other in situ measurements (dijet, Z + jet, and . +jet) is identical to that in the zero-bias dataset, a reweighting is applied dependent on the µ distribution. This reweighting has a very small effect as the zero-bias trigger and prescales are designed to produce a dataset which mimics the µ distribu­tion of the full dataset used for physics. In addition, to enable a direct comparison between data and MC simulations, the simulated µ distribution is reweighted to that of the data. 123 (a) (b) 12 (a) 10.2.2 Pile-up noise term measurements using the soft jet momentum method As explained in Sect. 4.3.2, the event pT-density . is obtained by reconstructing jets using the kt algorithm without applying any jet pT threshold and defning . to be the median of the (b) both the EM and LCW scales probing two calorimeter |.| regions, one central (|.| < 0.8) and one forward (3.2 < |.| < 3.6). A scale factor of 1.09 has been applied to µ in the MC simulations to correct for extra activity observed in the minimum-bias tune jet pT-density pT/ A, where A is the area of the jet. Starting from this quantity, the noise term of the JER due to pile-up N PU is extracted by defning a new observable .. that is a measure of the fuctuations in pT per unit area assuming a stochastic model of noise. Due to using the median (rather than the mean) in its defnition, . is to frst order insensitive 123 to the hard process. Any type of data can in principle be used for the measurement. The results presented in this section are based on Z › µµ data. The following steps are performed: • Jets are reconstructed using the Cambridge–Aachen algo­rithm [72] with R = 0.6 and required to have |.| < 2.1. No pT threshold is applied, and the jet pT extends down to zero. . • For each jet, the quantity r = ( pT - . A)/ A is calcu­lated, where A is the jet area defned using the Voronoi procedure [54]. Since no jet pT threshold is applied, many jets will be built from noise only. The distribution of r is expected to be centred at zero since after subtracting . A there should be as many jets above the pT density as below. • The observable .. is defned event-by-event from the width of the r distribution of all jets in the event. To avoid complications of non-Gaussianity and the hard­scatter event biasing the upper side tail, .. is defned by half the difference between the 84% and 16% quantile points. The size of the expected fuctuations at the constituent . scale of a given jet is given by .. A. The distributions of .. for EM-scale and LCW-scale clusters in Z › µµ data and Pythia8 samples are shown in Fig. 53. Z › µµ events are used to select an unbiased set of events for data-to-MC comparison, thus avoiding the use of any jet-based trigger which would bias the jet distributions. As in the random cone method (Fig. 51), the pile-up noise is overestimated in the MC simulations. An estimate of the noise term due to pile-up is obtained by scaling the mean value of the .. distribution by . . R2. 10.2.3 Comparison of methods and construction of the noise term As described in the previous two sections, the random cone and the soft jet momentum methods can both be used to measure the noise term of the jet energy resolution. It is useful to compare their results and to contrast the two methods. As well as using different data samples, these methods make quite different assumptions about the underlying physics: • The soft jet momentum method implicitly assumes the . pile-up noise is stochastic (such that it grows with A). • The random cone method measures the noise in several .-bins, while the soft jet momentum method does not consider any .-dependence of the noise within the probed detector region |.| < 2.1. • The symmetry assumption of the two cones back-to-back in azimuth in the zero bias events is not required by the soft jet momentum method. Further, while the soft jet momentum method gives an esti­mate of the noise term in each event (as is done for the cal­culation of .), the random cone method gives the noise term over an event sample. Table 4 compares the measured noise term at the constituent scale using the two methods. The two sets of measurements agree at the level of 20%. 10.2.4 Closure test of the pile-up noise measurement in MC simulation A closure test is performed on the pile-up noise measure­ments by comparing the random cone result with the pile-up noise extracted using truth-particle jets in MC simulation. The pile-up noise in MC simulations is extracted by measur­ing the MC JER (Sect. 4.2)intwo Pythia8 dijet samples: one without pile-up and one sample with 2012 pile-up condi­tions. By subtracting the JER measured in the sample without pile-up from the JER measured in the sample with pile-up, the contribution from the pile-up noise is isolated and can be compared with the measurement of the noise term using the random cone method. However, this comparison cannot be done directly since the random cone measures the noise at constituent scale (EM or LCW), while the JER is measured at the fully calibrated scale (EM+JES or LCW+JES). To account for this mismatch in scale, the random cone mea­surements are scaled by the average MC calibration fac-tor cJES evaluated for the jets in the kinematic region of interest. The results of these tests are shown in Fig. 54 as a function of pT for both EM and LCW jets. The relevant comparison is that of the estimated noise term N PU and the quadrature difference of the MC JER measurements with and without pile-up. In the central region |.| < 0.8, good closure is observed, both for EM+JES and LCW+JES. In 123 . Table 4 Measurements of .. and .. A ,where .. is the mean ment from the soft jet momentum method, is extracted using the region of the .. distribution, and the random cone results, both using data |.| < 2.1 while the noise term measurement using the random cone and MC simulations. The area is defned by A = . R2,where R is the method is extracted for jet |.| < 0.8. Statistical uncertainties of both . radius parameter. The .. A results, which is a noise term measure-measurements are negligible EM LCW EM LCW R = 0.4 R = 0.4 R = 0.6 R = 0.6 .. (Z › µµ, data) (GeV) 1.81 3.25 1.81 3.25 .. (Z › µµ, MC) (GeV) . 2.09 3.72 2.09 3.72 .. A (Z › µµ, data) (GeV) 1.28 2.30 1.92 3.46 Random cone, data (GeV) 1.52 2.61 2.42 4.19 Difference (%) . 16 12 21 17 .. A (Z › µµ, MC) (GeV) 1.48 2.64 2.22 3.96 Random cone, MC (GeV) 1.60 2.73 2.61 4.49 Difference (%) 7.5 4.4 15 12 this region, the calorimeters have high granularity, and as a consequence energy clusters from pile-up and from the hard-scatter signal tend to form separately with little over­lap. Slightly larger non-closure is observed towards the more forward regions, which is expected due to the coarser angu­lar granularity and higher noise thresholds, which result in a larger overlap between energy deposits from pile-up and the hard scatter. The same closure test was performed for the N PU mea­sured with the soft jet momentum method, and the difference between the results is taken as a systematic uncertainty due to the arbitrariness of the selection of method. Additionally, the degree of non-closure of the method is taken as a systematic uncertainty. 10.2.5 Noise term in the no pile-up scenario The random cone and soft jet momentum methods provide measurements of the part of the noise term arising from pile-up activity N PU. In the dijet MC sample without pile-up, for which µ = 0, the noise term does not have any pile-up contribution but does include other effects such as electronic noise on the signal clusters and threshold effects. To get a handle on the additional noise terms not included in the ran­dom cone or soft jet methods, the µ = 0 MC simulated resolution is ftted with the standard N , S and C parameteri­zation of Eq. (24) to extract the no pile-up noise term Nµ=0. The result of such fts are presented in Table 5. The total jet energy resolution (Eq. (24)) was measured in 2010 and agreed between data and MC simulations within 10% for jet pT in the range 30 GeV < pT < 500 GeV [7]. For pT = 30 GeV in the central region, the noise term is responsible for more than half of the total resolution. Given that the dominant resolution source leads to a total resolution modelled to the level of 10%, this implies that the noise term itself agrees between data and MC simulation to the level of 20% in simulated samples without pile-up. This conclu­sion is also supported by single-particle measurements [68]. 123 Fig. 54 Comparison between the pile-up noise term NPU extracted using the random cone method (upward triangles) with the expecta­tion from MC simulation (downward triangles). Results are shown for jets built from EM (left) and LC (right) topo-clusters, for jets with |.det| < 0.8(top) and1.2 < |.det| < 2.1 (bottom). The expected NPU is obtained by quadrature subtraction of the JER obtained from MC simulation of events with nominal pile-up (circles) from that of events with no pile-up (squares). Fits performed to the measured and expected pile-up noise data are displayed as dotted curves. Quadrature differ­ences corresponding to points where, due to statistical fuctuations, the resolution is worse in the no pile-up scenario are not displayed Table 5 The noise term Nµ=0 in GeV extracted in a dijet MC sample without pile-up. The values and uncertainties are extracted from a ft. For data, an additional 20% uncertainty is assigned, based on the 2010 measurements [7] EM+JES R= 0.4 LCW+JES R= 0.4 EM+JESR= 0.6 LCW+JES R= 0.6 |.| < 0.82.28 ± 0.13 2.66 ± 0.09 0.8 < |.| < 1.21.95 ± 0.25 2.14 ± 0.17 1.2 < |.| < 2.12.52 ± 0.18 2.99 ± 0.09 2.1 < |.| < 2.82.25 ± 0.30 2.19 ± 0.13 This extrapolation includes some additional assumptions in the MC modelling of the detector as several settings changed between 2010 and 2012, most notably the topo-cluster noise thresholds; however, 20% is considered a conservative esti­mate of the uncertainty in this component. The total JER noise term N is defned by combining the noise term extracted in the no pile-up sample with that origi­nating from pile-up (measured above) using a sum in quadra­ = NPU . N µ=0 ture, i.e. N . 1.83 ± 0.12 2.54 ± 0.09 1.29 ± 0.25 2.34 ± 0.15 0.90 ± 0.28 2.94 ± 0.09 0 ± 0.95 2.24 ± 0.11 10.3 Combined in situ jet energy resolution measurement The JER measurements based on the bisector method in dijet events reported in Sect. 6.6 and the vector boson plus jet bal­ance reported in Sect. 7.5 are statistically combined using a chi-squared minimization of the function in Eq. (24). In this ft, the noise term is held at the central value found in the previous section, while measurements of the S and C terms are extracted. The uncertainties in each term are evaluated in the same way they were in the JES determination in Sect. 9.1, 123 (a) (b) (a) (b) (c) (d) i.e. by re-evaluating the JER measurement after a 1. shifts of range demonstrates that the in situ methods agree well. As each individual uncertainty source. The degree of agreement expected, there is a large anti-correlation between the S and between the three in situ measurements is in Fig. 55, which C parameters of -0.25 (-0.44) for EM + JES (LCW + JES) shows the .2 per degree of freedom as a function of pT.The calibrated jets, and the .2 per degree of freedom for the ft low values of the . 2 per degree of freedom across the pT to fnd N , S and C is 8/35 (15/35) when correlations are not 123 considered, and 71/35 (58/35) when correlations are consid­ered. The relatively large size of the . 2 per degree of freedom when correlations are considered indicates a limitation in the ftting function used. It is a possible indication of the need for higher-order terms in the series to better describe the resolu­tion dependence on pT. A similar effect is seen when looking at the ft to these three parameters in MC simulations. When propagating the uncertainty in the noise term to the ft the resulting changes in the ftted values of N, S and C + 0.63 for anti-kt R = 0.4 EM+JES (LCW+JES) jets are -0.63 , -0.038 + 0.001 + 0.74 -0.048 + 0.002  . Again, correla­ + 0.030 , -0.001 -0.74 , + 0.039, -0.002 tions between the different components are observed, namely increasing N results in a reduced S and increased C. To reduce the number of parameters which need to be propagated, the full set of eigenvectors is built according to the total effect on the JER measurement of each uncer­tainty component (rather than the effect of each component on the N , S and C terms individually). These uncertainty sources can then be reduced in number by using an eigenvec­tor decomposition (diagonalization) as was done for the JES. This allows the full correlations to be retained and propagated to analyses. Figure 56 shows the three eigenvectors after this diagonalization. Combining in quadrature the results from balance (empty triangles) are shown displaying the compatibility of the measurements. The fnal ft using the function in Eq. (24) is included with its associated statistical and total uncertainty varying N and propagating the in situ uncertainties gives N = 3.33±0.63 (4.12±0.74) GeV, S = 0.71±0.07 (0.74± . 0.10) GeV, and C = 0.030 ± 0.003 (0.023 ± 0.003) for anti-kt R = 0.4 EM+ JES (LCW+ JES) jets. Figure 57 shows the individual measurements of the resolution in the cen­tral region, the result of the combination, and the associated uncertainty. The uncertainty in the jet energy resolution for anti-kt R = 0.4 jets is less than 0.03 at 20 GeV and below 0.01 above 100 GeV. When considering the more forward |.| bins, the large statistical uncertainty in Z + jet and . + jet events means that only dijet measurements are useful. These are combined with the measured noise term in data in the same way as in the cen­tral region. For LCW + JES anti-kt R = 0.4 jets all the differ­ent regions are shown in Fig. 58 and the extracted N, S, and C parameters for all jet collections are shown in Tables 6 and 7. Finally, to account for correlations between the measure­ments at different |.| a correlation matrix as a function of pT and |.| is built. The systematic uncertainties of the noise term and dijet balance results are assumed to be correlated between |.| regions. The eigenvector reduction is performed, which results in, at most, 12 uncertainty components required 123 Table 6 Extracted values of the N, S,and C terms from a combined ft to the jet energy resolution measurements for R = 0.4and R = 0.6jets, both calibrated with the EM + JES scheme. The quoted uncertainties of the N, S,and C terms are highly correlated with each other |.| Range EM + JES, R = 0.4 N (GeV) S (GeV0.5) C EM + JES, R = 0.6 N (GeV) S (GeV0.5) C (0, 0.8) (0.8, 1.2) (1.2, 2.1) (2.1, 2.8) 3.33 ± 0.63 3.04 ± 0.70 3.34 ± 0.80 2.9 ± 1.0 0.71 ± 0.07 0.69 ± 0.13 0.61 ± 0.16 0.46 ± 0.30 0.030 ± 0.003 0.036 ± 0.003 0.044 ± 0.008 0.053 ± 0.011 4.34 ± 0.93 4.06 ± 0.93 3.96 ± 0.91 3.41 ± 0.84 0.67 ± 0.08 0.76 ± 0.10 0.56 ± 0.14 0.48 ± 0.27 0.030 ± 0.003 0.031 ± 0.003 0.042 ± 0.007 0.049 ± 0.012 Table 7 Extracted values of the N, S,and C terms from a combined ft to the jet energy resolution measurements for R = 0.4and R = 0.6jets, both calibrated with the LCW + JES scheme. The uncertainties shown are highly correlated between the N , S,and C terms |.| Range LCW + JES, R = 0.4 N (GeV) S (GeV0.5) C LCW+JES, R = 0.6 N (GeV) S (GeV0.5) C (0, 0.8) 4.12 ± 0.74 0.74 ± 0.10 0.023 ± 0.003 5.50 ± 0.99 0.66 ± 0.12 0.026 ± 0.004 (0.8, 1.2) 3.66 ± 0.75 0.64 ± 0.13 0.039 ± 0.009 5.40 ± 0.98 0.78 ± 0.15 0.032 ± 0.005 (1.2, 2.1) 4.27 ± 0.75 0.58 ± 0.15 0.034 ± 0.007 5.7 ± 1.0 0.62 ± 0.16 0.031 ± 0.006 (2.1, 2.8) 3.38 ± 0.65 0.26 ± 0.36 0.050 ± 0.010 5.2 ± 1.0 0.51 ± 0.38 0.028 ± 0.019 123 to capture all the correlations between the pT and |.|regions covered by the in situ studies. 11 Conclusions This article describes the determination of the jet energy scale (JES) and jet energy resolution (JER) for data recorded by . the ATLAS experiment in 2012 at s =8TeV. The calibration scheme used for anti-kt jets reconstructed using radius parameter R = 0.4or R = 0.6 corrects for pile-up and the location of the primary interaction point before performing a calibration based on MC simulation. These initial steps in the calibration provide stability of the calibration as a function of pile-up and improve the angu­lar resolution of jets. Following the MC-simulation-derived baseline calibration, a global sequential correction is per­formed. It is also derived from MC simulations using infor­mation about how the jet deposits energy in the calorimeter, the tracks associated with the jet, and the activity in the muon chambers behind the jet (particularly important for high-pT jets). This improves the resolution of jets and reduces the dif­ference in energy scale between quark-and gluon-initiated jets. Following these MC-based calibration steps, the data taken in 2012 are used to perform a residual calibration that constrains the uncertainties. This is performed for anti-kt jets with R =0.4 and R =0.6 calibrated with both the EM + JES and LCW+JES schemes. Dijet events are used to calibrate jets in the forward region relative to the central region as a function of jet transverse momentum and pseudorapidity. The uncertainties of this calibration step have been signifcantly reduced compared with previous results primarily though the use of event generators with improved modelling of multijet production. The total uncertainties are typically below 1% for central jets, rising to 3.5% for low-pT jets at high abso­lute pseudorapidity. Central jets are calibrated by exploiting the balance between jets recoiling against either a photon or a Z boson. In the pseudorapidity region 0.8 .|.det|< 2.8, the jet energy scale is validated with Z + jet events using the direct pT balance technique. The jet energy scale calibra­tion for central jets with high pT is determined using events in which an isolated high-pT jet recoils against a system of lower-pT jets. The fnal calibration is obtained through a statistical combination of the different measurements. This results in a correction at the level of 0.5% to the JES in data with an associated uncertainty of less than 1% for cen­tral anti-kt R =0.4 jets with 100 < pT < 1500 GeV. At higher pT, the uncertainty is about 3% as in situ measure­ments become statistically limited, and instead the calibration relies on single-hadron response studies. The jet energy scale of trimmed anti-kt jets with R =1.0is derived using MC simulation in the same way as for R =0.4 and R =0.6 jets, thus calibrating the jets to the LCW+JES scale. In an additional step, a dedicated calibration of the jet mass for the R =1.0 jets is derived. The MC-derived cali­bration is tested in situ using the direct balance method with . + jet events. These studies are used to evaluate uncertain­ties in the calibration. The total uncertainty for |.det|< 0.8 is found to be around 3% for jets with low pT, falling to about 1% for jets with pT .150 GeV. At larger |.det|,the uncertainty increases to 4-5% at low jet pT, decreasing to 1-2% for pT > 150 GeV. The JER is measured in 2012 data using several in situ methods. The JER pile-up noise term is determined using novel techniques that exploit the increased level of pile-up interactions in the 2012 data. Three measurements of the JER as a function of jet pT and .det are performed using . +jet, Z + jet and dijet data. A fnal measurement of the JER is obtained using a statistical combination of these measure­ments, using a methodology similar to that used for the JES calibration. The different in situ inputs are found to be consis­tent with each other over the kinematic regions where they overlap. For anti-kt R = 0.4 jets in the central calorime­ter region |.| < 0.8 calibrated with the EM + JES calibra­tion scheme, the JER resolution parameters are measured . to be N = 3.33 ±0.63 GeV, S = 0.71 ±0.07 GeV, and C = 0.030 ±0.003, which corresponds to a rela­tive JER of .pT / pT = (23 ±2)%for pT = 20 GeV and .pT / pT =(8.4 ±0.6)%for pT =100 GeV. The jet energy resolution in data is generally well reproduced by the MC simulation. In certain kinematic regions, the simulated jets have a slightly smaller resolution than jets in data. In physics analyses, the pT of the simulated jets is corrected by ran­dom smearing to match the resolution observed in data. The required amount of smearing is of similar order of magnitude as the jet energy resolution uncertainties. Acknowledgements We thank CERN for the very successful oper­ation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated effciently. We acknowl­edge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIEN­CIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRT, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portu­gal; MNE/IFA, Romania; MES of Russia and NRC KI, Russia Fed­eration; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wal­lenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, Compute Canada and CRC, Canada; ERC, ERDF, Horizon 2020, Marie Sk³odowska-Curie Actions and COST, European Union; 123 Investissements d’Avenir Labex, Investissements d’Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-fnanced by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya and PROMETEO Programme Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Lever­hulme Trust, United Kingdom. The crucial computing support from all WLCG partners is acknowl­edged gratefully, in particular from CERN, the ATLAS Tier-1 facili­ties at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC­IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL­T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [73]. Data Availability Statement This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All ATLAS sci­entifc output is published in journals, and preliminary results are made available in Conference Notes. All are openly available, without restric­tion on use by external parties beyond copyright law and the standard conditions agreed by CERN. Data associated with journal publications are also made available: tables and data from plots (e.g. cross section values, likelihood profles, selection effciencies, cross section limits, ...) are stored in appropriate repositories such as HEPDATA (http:// hepdata.cedar.ac.uk/). ATLAS also strives to make additional material related to the paper available that allows a reinterpretation of the data in the context of new theoretical models. For example, an extended encapsulation of the analysis is often provided for measurements in the framework of RIVET (http://rivet.hepforge.org/).” This information is taken from the ATLAS Data Access Policy, which is a public docu­ment that can be downloaded from http://opendata.cern.ch/record/413 [opendata.cern.ch]. 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Winter24, M. Wittgen152, M. Wobisch95,A. Wolf99, T.M.H.Wolf119,R. Wolff101, M.W.Wolter84, H. Wolters139a,139c, V. W. S. Wong175, N. L. Woods145, S.D.Worm21,B. K. Wosiek84, K.W.Wo´zniak84, K. Wraight56,M. Wu37,S. L. Wu181, X. Wu53,Y. Wu59a, T. R. Wyatt100, B. M. Wynne49, S. Xella40,Z. Xi105,L. Xia15b,D. Xu15a,H. Xu59a,d,L. Xu29,T. Xu144, W. Xu105, B. Yabsley156, S. Yacoob33a, K. Yajima132, D. P. Yallup94, D. Yamaguchi165, Y. Yamaguchi165, A. Yamamoto81, T. Yamanaka163, F. Yamane82, M. Yamatani163, T. Yamazaki163, Y. Yamazaki82,Z. Yan25, H. J. Yang59c,59d, H. T. Yang18, S. Yang77, Y. Yang163, Y. Yang157, Z. Yang17,W-M. Yao18,Y. C. Yap45,Y. Yasu81, E. Yatsenko5, K. H. Yau Wong24, J. Ye42,S. Ye29, I. Yeletskikh79, E. Yigitbasi25, E. Yildirim99, K. Yorita179, K. Yoshihara136, C. J. S. Young36, C. Young152, J. Yu78,J. Yu8,X. Yue60a, S.P.Y.Yuen24, I. Yusuff32, B. Zabinski84, G. Zacharis10, R. Zaidan14, A.M.Zaitsev122,an, N. Zakharchuk45, J. Zalieckas17, S. Zambito58, D. Zanzi36, C. Zeitnitz182, G. Zemaityte134, J.C.Zeng173, Q. Zeng152, 134 O. Zenin122, T. Ženiš28a,D. Zerwas64, M. Zgubic, D. F. Zhang59b, D. Zhang105, F. Zhang181, G. Zhang59a,ah, H. Zhang15c, J. Zhang6, L. Zhang51, L. Zhang59a, M. Zhang173, P. Zhang15c, R. Zhang59a,d, R. Zhang24, X. Zhang59b, Y. Zhang15a,15d, Z. Zhang64, X. Zhao42, Y. Zhao59b,64,ab, Z. Zhao59a, A. Zhemchugov79, B. Zhou105, C. Zhou181, L. Zhou42, M. S. Zhou15a,15d, M. Zhou154, N. Zhou59c, Y. Zhou7, C.G.Zhu59b,H. L. Zhu59a,H. Zhu15a,J. Zhu105,Y. Zhu59a, X. Zhuang15a, K. Zhukov110, V. Zhulanov121a,121b, A. Zibell177, D. Zieminska65, N. I. Zimine79, S. Zimmermann51, Z. Zinonos114,M. Zinser99,M. Ziolkowski150,L. Živkovi´c16,G. Zobernig181,A. Zoccoli23b,23a,K. Zoch52,T. G. Zorbas148, R. Zou37, M. Zur Nedden19, L. Zwalinski36 1 Department of Physics, University of Adelaide, Adelaide, Australia 2 Physics Department, SUNY Albany, Albany, NY, USA 3 Department of Physics, University of Alberta, Edmonton, AB, Canada 4 (a)Department of Physics, Ankara University, Ankara, Turkey; (b)Istanbul Aydin University, Istanbul, Turkey; (c)Division of Physics, TOBB University of Economics and Technology, Ankara, Turkey 5 LAPP, Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France 6 High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA 7 Department of Physics, University of Arizona, Tucson, AZ, USA 8 Department of Physics, University of Texas at Arlington, Arlington, TX, USA 9 Physics Department, National and Kapodistrian University of Athens, Athens, Greece 10 Physics Department, National Technical University of Athens, Zografou, Greece 11 Department of Physics, University of Texas at Austin, Austin, TX, USA 12 (a)Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey; (b)Istanbul Bilgi University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey; (c)Department of Physics, Bogazici University, Istanbul, Turkey; (d)Department of Physics Engineering, Gaziantep University, Gaziantep, Turkey 13 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan 14 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain 15 (a)Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China; (b)Physics Department, Tsinghua University, Beijing, China; (c)Department of Physics, Nanjing University, Nanjing, China; (d)University of Chinese Academy of Science (UCAS), Beijing, China 16 Institute of Physics, University of Belgrade, Belgrade, Serbia 123 17 Department for Physics and Technology, University of Bergen, Bergen, Norway 18 Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley, CA, USA 19 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany 20 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland 21 School of Physics and Astronomy, University of Birmingham, Birmingham, UK 22 Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Narino, Bogota, Colombia 23 (a)Dipartimento di Fisica, INFN Bologna and Universita’ di Bologna, Bologna, Italy; (b)INFN Sezione di Bologna, Bologna, Italy 24 Physikalisches Institut, Universität Bonn, Bonn, Germany 25 Department of Physics, Boston University, Boston, MA, USA 26 Department of Physics, Brandeis University, Waltham, MA, USA 27 (a)Transilvania University of Brasov, Brasov, Romania; (b)Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania; (c)Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania; (d)National Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj-Napoca, Romania; (e)University Politehnica Bucharest, Bucharest, Romania; (f)West University in Timisoara, Timisoara, Romania 28 (a)Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia; (b)Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 29 Physics Department, Brookhaven National Laboratory, Upton, NY, USA 30 Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina 31 California State University, Long Beach, CA, USA 32 Cavendish Laboratory, University of Cambridge, Cambridge, UK 33 (a)Department of Physics, University of Cape Town, Cape Town, South Africa; (b)iThemba Labs, Western Cape, South Africa; (c)Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa; (d)University of South Africa, Department of Physics, Pretoria, South Africa; (e)School of Physics, University of the Witwatersrand, Johannesburg, South Africa 34 Department of Physics, Carleton University, Ottawa, ON, Canada 35 (a)Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies, Université Hassan II, Casablanca, Morocco; (b)Faculté des Sciences, Université Ibn-Tofail, Kénitra, Morocco; (c)Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA, Marrakech, Morocco; (d)Faculté des Sciences, Université Mohamed Premier and LPTPM, Oujda, Morocco; (e)Faculté des sciences, Université Mohammed V, Rabat, Morocco 36 CERN, Geneva, Switzerland 37 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA 38 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France 39 Nevis Laboratory, Columbia University, Irvington, NY, USA 40 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 41 (a)Dipartimento di Fisica, Universita della Calabria, Rende, Italy; (b)INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Frascati, Italy 42 Physics Department, Southern Methodist University, Dallas, TX, USA 43 Physics Department, University of Texas at Dallas, Richardson, TX, USA 44 (a)Department of Physics, Stockholm University, Sweden; (b)Oskar Klein Centre, Stockholm, Sweden 45 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany 46 Lehrstuhl für Experimentelle Physik IV, Technische Universität Dortmund, Dortmund, Germany 47 Institut für Kern-und Teilchenphysik, Technische Universität Dresden, Dresden, Germany 48 Department of Physics, Duke University, Durham, NC, USA 49 SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK 50 INFN e Laboratori Nazionali di Frascati, Frascati, Italy 51 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany 52 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 53 Département de Physique Nucléaire et Corpusculaire, Université de Geneve, Geneve, Switzerland 54 (a)Dipartimento di Fisica, Universita di Genova, Genoa, Italy; (b)INFN Sezione di Genova, Genoa, Italy 55 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 123 56 SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, UK 57 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France 58 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA 59 (a)Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China; (b)Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China; (c)School of Physics and Astronomy, Shanghai Jiao Tong University, KLPPAC-MoE, SKLPPC, Shanghai, China; (d)Tsung-Dao Lee Institute, Shanghai, China 60 (a)Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany; (b)Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 61 Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan 62 (a)Department of Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong; (b)Department of Physics, University of Hong Kong, Hong Kong, China; (c)Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong 63 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 64 IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405 Orsay, France 65 Department of Physics, Indiana University, Bloomington, IN, USA 66 (a)INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy; (b)ICTP, Trieste, Italy; (c)Dipartimento Politecnico di Ingegneria e Architettura, Universita di Udine, Udine, Italy 67 (a)INFN Sezione di Lecce, Lecce, Italy; (b)Dipartimento di Matematica e Fisica, Universita del Salento, Lecce, Italy 68 (a)INFN Sezione di Milano, Milan, Italy; (b)Dipartimento di Fisica, Universita di Milano, Milan, Italy 69 (a)INFN Sezione di Napoli, Naples, Italy; (b)Dipartimento di Fisica, Universita di Napoli, Naples, Italy 70 (a)INFN Sezione di Pavia, Pavia, Italy; (b)Dipartimento di Fisica, Universita di Pavia, Pavia, Italy 71 (a)INFN Sezione di Pisa, Pisa, Italy; (b)Dipartimento di Fisica E. Fermi, Universita di Pisa, Pisa, Italy 72 (a)INFN Sezione di Roma, Rome, Italy; (b)Dipartimento di Fisica, Sapienza Universita di Roma, Rome, Italy 73 (a)INFN Sezione di Roma Tor Vergata, Rome, Italy; (b)Dipartimento di Fisica, Universita di Roma Tor Vergata, Rome, Italy 74 (a)INFN Sezione di Roma Tre, Rome, Italy; (b)Dipartimento di Matematica e Fisica, Universita Roma Tre, Rome, Italy 75 (a)INFN-TIFPA, Trento, Italy; (b)Universita degli Studi di Trento, Trento, Italy 76 Institut für Astro-und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria 77 University of Iowa, Iowa City, IA, USA 78 Department of Physics and Astronomy, Iowa State University, Ames, IA, USA 79 Joint Institute for Nuclear Research, Dubna, Russia 80 (a)Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil; (b)Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil; (c)Universidade Federal de Sao Joao del Rei (UFSJ), Sao Joao del Rei, Brazil; (d)Instituto de Física, Universidade de Sao Paulo, Sao Paulo, Brazil 81 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 82 Graduate School of Science, Kobe University, Kobe, Japan 83 (a)AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland; (b)Marian Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland 84 Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland 85 Faculty of Science, Kyoto University, Kyoto, Japan 86 Kyoto University of Education, Kyoto, Japan 87 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan 88 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 89 Physics Department, Lancaster University, Lancaster, UK 90 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK 91 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia 92 School of Physics and Astronomy, Queen Mary University of London, London, UK 93 Department of Physics, Royal Holloway University of London, Egham, UK 94 Department of Physics and Astronomy, University College London, London, UK 95 Louisiana Tech University, Ruston, LA, USA 123 96 Fysiska institutionen, Lunds universitet, Lund, Sweden 97 Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules (IN2P3), Villeurbanne, France 98 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain 99 Institut für Physik, Universität Mainz, Mainz, Germany 100 School of Physics and Astronomy, University of Manchester, Manchester, UK 101 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France 102 Department of Physics, University of Massachusetts, Amherst, MA, USA 103 Department of Physics, McGill University, Montreal, QC, Canada 104 School of Physics, University of Melbourne, Parkville, VIC, Australia 105 Department of Physics, University of Michigan, Ann Arbor, MI, USA 106 Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA 107 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus 108 Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Belarus 109 Group of Particle Physics, University of Montreal, Montreal, QC, Canada 110 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia 111 National Research Nuclear University MEPhI, Moscow, Russia 112 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia 113 Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany 114 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany 115 Nagasaki Institute of Applied Science, Nagasaki, Japan 116 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 117 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA 118 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, Netherlands 119 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands 120 Department of Physics, Northern Illinois University, DeKalb, IL, USA 121 (a)Budker Institute of Nuclear Physics and NSU, SB RAS, Novosibirsk, Russia; (b)Novosibirsk State University Novosibirsk, Novosibirsk, Russia 122 Institute for High Energy Physics of the National Research Centre Kurchatov Institute, Protvino, Russia 123 Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre “Kurchatov Institute”, Moscow, Russia 124 Department of Physics, New York University, New York, NY, USA 125 Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan 126 Ohio State University, Columbus, OH, USA 127 Faculty of Science, Okayama University, Okayama, Japan 128 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA 129 Department of Physics, Oklahoma State University, Stillwater, OK, USA 130 Palacký University, RCPTM, Joint Laboratory of Optics, Olomouc, Czech Republic 131 Center for High Energy Physics, University of Oregon, Eugene, OR, USA 132 Graduate School of Science, Osaka University, Osaka, Japan 133 Department of Physics, University of Oslo, Oslo, Norway 134 Department of Physics, Oxford University, Oxford, UK 135 LPNHE, Sorbonne Université, Université de Paris, CNRS/IN2P3, Paris, France 136 Department of Physics, University of Pennsylvania, Philadelphia, PA, USA 137 Konstantinov Nuclear Physics Institute of National Research Centre “Kurchatov Institute”, PNPI, St. Petersburg, Russia 138 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA 139 (a)Laboratório de Instrumentaçao e Física Experimental de Partículas, LIP, Lisbon, Portugal; (b)Departamento de Física, Faculdade de Ciencias, Universidade de Lisboa, Lisbon, Portugal; (c)Departamento de Física, Universidade de Coimbra, Coimbra, Portugal; (d)Centro de Física Nuclear da Universidade de Lisboa, Lisbon, Portugal; (e)Departamento de Física, Universidade do Minho, Braga, Portugal; (f)Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, Spain; (g)Dep Física and CEFITEC of Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal; (h)Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal 123 140 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 141 Czech Technical University in Prague, Prague, Czech Republic 142 Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 143 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK 144 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France 145 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA 146 (a)Departamento de Física, Pontifcia Universidad Católica de Chile, Santiago, Chile; (b)Universidad Andres Bello, Department of Physics, Santiago, Chile; (c)Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile 147 Department of Physics, University of Washington, Seattle, WA, USA 148 Department of Physics and Astronomy, University of Sheffeld, Sheffeld, UK 149 Department of Physics, Shinshu University, Nagano, Japan 150 Department Physik, Universität Siegen, Siegen, Germany 151 Department of Physics, Simon Fraser University, Burnaby, BC, Canada 152 SLAC National Accelerator Laboratory, Stanford, CA, USA 153 Physics Department, Royal Institute of Technology, Stockholm, Sweden 154 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA 155 Department of Physics and Astronomy, University of Sussex, Brighton, UK 156 School of Physics, University of Sydney, Sydney, Australia 157 Institute of Physics, Academia Sinica, Taipei, Taiwan 158 Academia Sinica Grid Computing, Institute of Physics, Academia Sinica, Taipei, Taiwan 159 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia; (b)High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 160 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel 161 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 162 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece 163 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan 164 Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan 165 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 166 Tomsk State University, Tomsk, Russia 167 Department of Physics, University of Toronto, Toronto, ON, Canada 168 (a)TRIUMF, Vancouver, BC, Canada; (b)Department of Physics and Astronomy, York University, Toronto, ON, Canada 169 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan 170 Department of Physics and Astronomy, Tufts University, Medford, MA, USA 171 Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA 172 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden 173 Department of Physics, University of Illinois, Urbana, IL, USA 174 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia -CSIC, Valencia, Spain 175 Department of Physics, University of British Columbia, Vancouver, BC, Canada 176 Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada 177 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany 178 Department of Physics, University of Warwick, Coventry, UK 179 Waseda University, Tokyo, Japan 180 Department of Particle Physics, Weizmann Institute of Science, Rehovot, Israel 181 Department of Physics, University of Wisconsin, Madison, WI, USA 182 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany 183 Department of Physics, Yale University, New Haven, CT, USA 184 Yerevan Physics Institute, Yerevan, Armenia a Also at Borough of Manhattan Community College, City University of New York, New York, NY, USA b Also at Centre for High Performance Computing, CSIR Campus, Rosebank, Cape Town; South Africa 123 c Also at CERN, Geneva, Switzerland d Also at CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France e Also at Département de Physique Nucléaire et Corpusculaire, Université de Geneve, Geneve, Switzerland f Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain g Also at Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, Spain h Also at Department of Applied Physics and Astronomy, University of Sharjah, Sharjah, United Arab Emirates i Also at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece j Also at Department of Physics and Astronomy, University of Louisville, Louisville, KY, USA k Also at Department of Physics and Astronomy, University of Sheffeld, Sheffeld, UK l Also at Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel m Also at Department of Physics, California State University, East Bay, USA n Also at Department of Physics, California State University, Fresno, USA o Also at Department of Physics, California State University, Sacramento, USA p Also at Department of Physics, King’s College London, London, UK q Also at Department of Physics, Nanjing University, Nanjing, China r Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia s Also at Department of Physics, University of Fribourg, Fribourg, Switzerland t Also at Department of Physics, University of Michigan, Ann Arbor, MI, USA u Also at Dipartimento di Fisica E. Fermi, Universita di Pisa, Pisa, Italy v Also at Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia w Also at Giresun University, Faculty of Engineering, Giresun, Turkey x Also at Graduate School of Science, Osaka University, Osaka, Japan y Also at Hellenic Open University, Patras, Greece z Also at Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania aa Also at II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany ab Also at IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405, Orsay, France ac Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain ad Also at Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain ae Also at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, The Netherlands af Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary ag Also at Institute of Particle Physics (IPP), Vancouver, Canada ah Also at Institute of Physics, Academia Sinica, Taipei, Taiwan ai Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan aj Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia ak Also at Louisiana Tech University, Ruston, LA, USA al Also at LPNHE, Sorbonne Université, Université de Paris, CNRS/IN2P3, Paris, France am Also at Manhattan College, New York, NY, USA an Also at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia ao Also at National Research Nuclear University MEPhI, Moscow, Russia ap Also at Near East University, Nicosia, North Cyprus, Mersin, Turkey aq Also at Ochadai Academic Production, Ochanomizu University, Tokyo, Japan ar Also at Physics Department, An-Najah National University, Nablus, Palestine as Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany at Also at School of Physics, Sun Yat-sen University, Guangzhou, China au Also at The City College of New York, New York, NY, USA 123 av Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China aw Also at Tomsk State University, Tomsk, and Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia. ax Also at TRIUMF, Vancouver, BC, Canada ay Also at Universita di Napoli Parthenope, Naples, Italy. *Deceased 123