Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV

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1 Journal of Instrumentation OPEN ACCESS Jet energy scale and resolution in the exeriment in collisions at 8 ev o cite this article: V. Khachatryan et al View the article online for udates and enhancements. Related content - Determination of jet energy calibration and transverse momentum resolution in he collaboration - Identification of heavy-flavour jets with the detector in collisions at 3 ev A.M. Sirunyan, A. umasyan, W. Adam et al. - Missing transverse energy erformance of the detector he collaboration Recent citations - Search for air-roduced resonances decaying to quark airs in roton-roton collisions at s=3 ev A. M. Sirunyan et al - Observation of Medium-Induced Modifications of Jet Fragmentation in Pb- Pb Collisions at snn=5.02 ev Using Isolated Photon-agged Jets A. M. Sirunyan et al - he exerimental status of direct searches for exotic hysics beyond the standard model at the Large Hadron Collider Salvatore Raoccio his content was downloaded from IP address on 6/0/209 at 6:07

2 Published by IOP Publishing for Sissa Medialab Received: July 3, 206 Revised: January 22, 207 Acceted: January 29, 207 Published: February 22, 207 Jet energy scale and resolution in the exeriment in collisions at 8 ev he collaboration cms-ublication-committee-chair@cern.ch Abstract: Imroved jet energy scale corrections, based on a data samle corresonding to an integrated luminosity of 9.7 fb collected by the exeriment in roton-roton collisions at a center-of-mass energy of 8 ev, are resented. he corrections as a function of seudoraidity η and transverse momentum are extracted from data and simulated events combining several channels and methods. hey account successively for the effects of ileu, uniformity of the detector resonse, and residual data-simulation jet energy scale differences. Further corrections, deending on the jet flavor and distance arameter (jet size) R, are also resented. he jet energy resolution is measured in data and simulated events and is studied as a function of ileu, jet size, and jet flavor. yical jet energy resolutions at the central raidities are 5 20% at 30 GeV, about 0% at 00 GeV, and 5% at ev. he studies exloit events with dijet toology, as well as hoton+jet, Z+jet and multijet events. Several new techniques are used to account for the various sources of jet energy scale corrections, and a full set of uncertainties, and their correlations, are rovided.he final uncertainties on the jet energy scale are below 3% across the hase sace considered by most analyses ( > 30 GeV and η < 5.0). In the barrel region ( η <.3) an uncertainty below % for > 30 GeV is reached, when excluding the jet flavor uncertainties, which are rovided searately for different jet flavors. A new benchmark for jet energy scale determination at hadron colliders is achieved with 0.32% uncertainty for jets with of the order of GeV, and η < 0.8. Keywords: Large detector-systems erformance; Performance of High Energy Physics Detectors ArXiv eprint: CERN 207 for the benefit of the collaboration, ublished under the terms of the Creative Commons Attribution 3.0 License by IOP Publishing Ltd and Sissa Medialab srl. Any further distribution of this work must maintain attribution to the author(s) and the ublished article s title, journal citation and DOI. doi:0.088/ /2/02/p0204

3 Contents Introduction 2 he detector and event reconstruction 4 2. Jet reconstruction 5 3 Event samles and selection criteria 6 3. Simulated samles Data sets and event selection 6 4 Pileu offset corrections 8 4. Pileu observables Pileu mitigation Hybrid jet area method Pileu offset correction uncertainties Summary of ileu offset corrections 8 5 Simulated resonse corrections Corrections versus η and Deendence on the jet size Detector simulation uncertainties Jet energy corrections roagation to missing transverse momentum Summary of simulated resonse corrections 24 6 Residual corrections for data Relative η-deendent corrections Relative correction uncertainties Absolute corrections Global fit of absolute corrections Absolute correction uncertainties Summary of residual corrections 42 7 Jet flavor corrections Jet flavor definitions Simulated flavor corrections Flavor uncertainties Z+b balance 49 8 Jet resolution Methods Simulated article-level resolution Dijet asymmetry 54 i

4 8.4 he γ+jet balance 58 9 Systematic uncertainties Uncertainties in 7 ev analyses 65 0 he PF jet comosition 66 Conclusions 69 he collaboration 75 Introduction he state-of-the-art techniques used in the exeriment at the CERN LHC for jet energy scale (JES) and jet energy resolution (JER) calibration are resented, based on a data samle corresonding to an integrated luminosity of 9.7 fb collected in roton-roton collisions at a center-of-mass energy of 8 ev. Jets are the exerimental signatures of energetic quarks and gluons roduced in high-energy rocesses. Like all exerimentally-reconstructed objects, jets need to be calibrated in order to have the correct energy scale: this is the aim of the jet energy corrections (JEC). he detailed understanding of both the energy scale and the transverse momentum resolution of the jets is of crucial imortance for many hysics analyses, and a leading comonent of their associated systematic uncertainties. Imrovements made in understanding the JES in the recent years have resulted in very recise measurements of, e.g., the inclusive jet cross section [ 5], and the to quark mass [6 9]. he JES uncertainties resented here roagate to uncertainties of 2 4% in the jet cross sections in the central region, and of ±0.35 GeV in the to-quark mass determination. he results in this aer are reorted for jets reconstructed with the article-flow (PF) method [0, ] using the anti-k algorithm [2] with distance arameter R = 0.5. he jet energy corrections are calculated using a detailed Monte Carlo (MC) simulation of the detector, and are then adjusted for data using a combination of several channels and data-driven methods. he JEC successively correct for the offset energy coming from multile roton-roton collisions in the same and adjacent beam crossings (ileu), the detector resonse to hadrons, and residual differences between data and MC simulation as a function of the jet seudoraidity η and transverse momentum. he jet is corrected u to the so-called article-level jets clustered from stable (decay length cτ > cm) and visible (excluding neutrinos) final-state articles. Corrections deending on jet flavor (for quarks: u and d, s, c and b; and for gluons) and jet distance arameter R are also resented. he uncertainties affecting the JES determination are discussed, and a full set of uncertainties and their correlations are rovided. Figure shows the jet resonse at the various stages of JEC for jets (roduced in quantum chromodynamics (QCD) hard-scattering rocesses) measured at central seudoraidities ( η <.3): for each bin in, tcl, the jet resonse is defined as the average value of the ratio of measured jet to article-level jet, tcl. he resonse is shown before any correction, after correcting for the effect of ileu, and after all stages of corrections, that will be detailed in the following. Distributions corresonding

5 Resonse Simulation (8 ev) QCD Monte Carlo Anti-k R=0.5, PF+CHS η <.3 No ileu (µ = 0) 0 < µ < 0 0 < µ < < µ < < µ < (GeV), tcl Pileu-corrected resonse Simulation (8 ev) QCD Monte Carlo Anti-k R=0.5, PF+CHS η <.3 No ileu (µ = 0) 0 < µ < 0 0 < µ < < µ < < µ < (GeV), tcl Corrected resonse Simulation (8 ev) QCD Monte Carlo Anti-k R=0.5, PF+CHS η <.3 No ileu (µ = 0) 0 < µ < 0 0 < µ < < µ < < µ < (GeV), tcl Figure. Average value of the ratio of measured jet to article-level jet, tcl in QCD MC simulation, in bins of, tcl, at various stages of JEC: before any corrections (left), after ileu offset corrections (middle), after all JEC (right). Here µ is the average number of ileu interactions er bunch crossing. to different average numbers of ileu interactions er bunch crossing (µ) are shown searately, to dislay the deendence of the resonse on the ileu. he jet resolution, measured after alying JEC, is extracted in data and simulated events. It is studied as a function of ileu, jet size R, and jet flavor. he effect of the resence of neutrinos in the jets is also studied. he tyical JER is 5 20% at 30 GeV, about 0% at 00 GeV, and 5% at ev at central raidities. he general rinciles behind the methods of extraction of the JES, and the reasons why the JES obtained with the PF algorithm is different from unity, are discussed. he results and methods are comared to revious studies done for 7 ev roton-roton collisions [3]. Several new techniques are introduced in this aer to account for -deendent ileu offset, out-of-time (OO) ileu, initial- and final-state radiation (ISR+FSR), and b-quark jet (b-jet) flavor resonse. We also add the information from multijet balancing [4] and introduce a new technique that uses it as art of a global -deendent fit which constrains the uncertainties by using their correlations between channels and methods. Pileu collisions result in unwanted calorimetric energy deositions and extra tracks. he charged-hadron subtraction (CHS, section 4.2) reduces these effects by removing tracks identified as originating from ileu vertices. he results in this aer are reorted for jets reconstructed with and without CHS. he JEC are extracted for jets with > 0 GeV and η < 5.2, with uncertainties less than or about 3% over the whole hase sace. he minimum JES uncertainty of 0.32% for jets with 65 < < 330 GeV and η < 0.8, when excluding samle-deendent uncertainties due to jetflavor resonse and time-deendent detector resonse variations, surasses the recision of revious JES measurements at the evatron [5, 6] and the LHC [3, 7]. Outline of the aer and overview of the corrections he detector and reconstruction algorithms are briefly described in section 2. he data and MC samles used throughout this document, together with the different selection criteria, are detailed in section 3. 2

6 Alied to data Reconstructed Jets Pileu MC + RC MC Resonse (, η) MC Residuals(η) dijets Residuals( ) γ/z+jet, MJB Flavor MC Calibrated Jets Alied to simulation Figure 2. Consecutive stages of JEC, for data and MC simulation. All corrections marked with MC are derived from simulation studies, RC stands for random cone, and MJB refers to the analysis of multijet events. he ileu offset corrections, discussed in section 4, are determined from the simulation of a samle of dijet events rocessed with and without ileu overlay. hey are arameterized as a function of offset energy density ρ, jet area A, jet seudoraidity η, and jet transverse momentum. Corrections for residual differences between data and detector simulation as a function of η are determined using the random cone (RC, section 4.3) method in zero-bias events (section 3.2). he ileu offset corrections are determined both before and after CHS, which removes tracks identified as originating from ileu vertices. he simulated jet resonse corrections are determined with a detector simulation based on Geant4 [8] combined with the ythia 6.4 [9] tune Z2* [20], as discussed in section 5. he corrections are determined for various jet sizes. he default corrections are rovided for the QCD dijet flavor mixture as a function of and η. Uncertainties arising from the modeling of jet fragmentation are evaluated with herwig [2] tune EE3C [22], and uncertainties from the detector simulation are evaluated with the fast simulation [23]. he residual corrections for data are discussed in section 6. he η-deendent corrections are determined with dijet events, relative to a jet of similar in the barrel reference region η <.3. hese corrections include a deendence of the JES relative to the JES of the barrel jet for > 62 GeV and u to about ev, the limit of available dijet data. he absolute scale, together with its deendence within η <.3 for 30 < < 800 GeV, is measured combining hoton+jet, Z( µµ)+jet and Z( ee)+jet events. he deendence at > 800 GeV is constrained with multijet events. Detailed studies are erformed to correct for biases in the data-based methods due to differences with resect to the MC simulation in ISR+FSR as well as in jet resolution. he otional jet-flavor corrections derived from MC simulation are discussed in section 7 together with the JEC flavor uncertainty estimates based on comaring ythia 6.4 and herwig redictions. hese uncertainties are alicable to data vs. simulation comarisons regardless of whether or not the jet-flavor corrections are alied. he flavor corrections and their uncertainties for b-quark jets are checked in data with Z+b events. he consecutive stes of the JEC are illustrated in figure 2. he jet resolutions are determined with both dijet and hoton+jet events, as discussed in section 8. he reference resolutions obtained from simulation are arameterized as a function of article-level jet, tcl (defined in section 2) and average number µ of ileu interactions in bins of jet η. Corrections for differences between data and MC simulation are alied as η-binned scale factors. 3

7 he JES uncertainties, discussed in section 9, are rovided in the form of a limited set of sources that allow a detailed statistical analysis of uncertainty correlations. he final uncertainties are below % across much of the hase sace covered by these corrections at > 0 GeV and η < 5.2. his sets a new benchmark for jet energy scale at hadron colliders. In section 0 we describe additional studies made by investigating the article comosition of reconstructed PF jets. hese suort the overall conclusions drawn from the determination of residual jet energy corrections to be alied on data. 2 he detector and event reconstruction he central feature of the aaratus is a 3.8 suerconducting solenoid of 6 m internal diameter. Within the field volume are the silicon tracker, the crystal electromagnetic calorimeter (ECAL), and the brass and scintillator hadron calorimeter (HCAL). he muon system is installed outside the solenoid and embedded in the steel flux-return yoke. uses a right-handed coordinate system, with the origin at the nominal interaction oint, the z axis ointing along the direction of the counterclockwise beam, the y axis ointing u (erendicular to the lane of the LHC ring), and the x axis chosen to make a right-handed coordinate system. he olar angle θ is measured from the ositive z axis, and the azimuthal angle φ is measured in the x-y lane in radians. he tracker consists of 440 silicon ixel and 5 48 silicon stri detector modules, with full azimuthal coverage within η < 2.5. he ECAL consists of lead tungstate crystals, which rovide coverage in seudoraidity η <.479 in the central barrel region and.479 < η < in the two forward endca regions. he HCAL is a samling calorimeter using alternating layers of brass or steel as absorber and lastic scintillator as active material, it rovides a coverage of η <.3 in the central region and.3 < η < 3.0 in the endca regions. In the forward region (3.0 < η < 5.0), a different calorimeter technology is emloyed in the hadron forward (HF) detector, which uses the Cherenkov light signals collected by short and long quartz readout fibers to aid the searation of electromagnetic (EM) and hadronic signals. he muon system includes barrel drift tubes covering the seudoraidity range η <.2, endca cathode stri chambers (0.9 < η < 2.5), and resistivelate chambers ( η <.6). A detailed descrition of the detector can be found in ref. [24]. Events in are reconstructed using the PF technique [0, ], which reconstructs and identifies single articles with an otimized combination of all subdetector information. o suress noise in the calorimeters, only cells with energies above a given threshold are considered, this rocedure is referred to as zero suression. he energy of hotons is obtained directly from the ECAL measurement, corrected for zero-suression effects. he energy of electrons is determined from a combination of the track momentum at the main interaction vertex, the corresonding ECAL cluster energy, and the energy sum of all bremsstrahlung hotons associated with the track. he energy of muons is obtained from the corresonding track momentum. he energy of charged hadrons is determined from a combination of the track momentum and the corresonding ECAL and HCAL energies, corrected for zero-suression effects, and calibrated for the nonlinear resonse of the calorimeters. Finally, the energy of neutral hadrons is obtained from the corresonding calibrated ECAL and HCAL energies. In the forward region, energy deosits collected by the HF are considered as electromagnetic or hadronic, deending on the resective energy collected by long and short fibers. he articles reconstructed with the PF algorithm are jointly referred to as PF candidates. 4

8 Jets are reconstructed by clustering the PF candidates, and the missing transverse momentum miss is the negative vectorial sum of the transverse momenta of all PF candidates reconstructed in an event. Interaction vertices are reconstructed using track information only, and the rimary interaction vertex is defined as the vertex with the highest sum of the squared transverse momenta of the tracks associated with it. he first level (L) of the trigger system, comosed of custom hardware rocessors, uses information from the calorimeters and muon detectors to select the most interesting events in a fixed time interval of less than 4 µs. he high-level trigger (HL) rocessor farm further decreases the event rate from around 00 khz to less than khz before data storage. 2. Jet reconstruction Jets considered in this aer are reconstructed with the anti-k clustering algorithm [2]. he nominal results are obtained for a jet distance arameter, R = 0.5, which was used in most analyses of 7 and 8 ev data. Both the JES and JER are also studied for different values of the R arameter, on simulated events. he simulated article-level jets are built by alying the clustering rocedure to all stable (lifetime cτ > cm) articles excluding neutrinos. he lifetime of heavy hadrons (containing c and b quarks) is shorter than cτ = cm, so their decay roducts are the articles considered for jet clustering. he exclusion of neutrinos is a convention adoted by, but it is not universally adoted by all exeriments in high-energy hysics. Indeed, neutrinos are often included at the article level, but the resonse is measured from samles with negligible neutrino content, leading to ractically no difference for inclusive JEC. he convention allows us to define resonse in a way that is exerimentally accessible and significantly reduces resonse differences between heavyflavor (c, b) and light-quark (u, d, s) or gluon jets, caused by neutrinos roduced in semiletonic decays of heavy-flavor hadrons. It should be noted that the neutrino fraction leads to an additional systematic uncertainty in the heavy hadrons fragmentation relative to the original b and c quarks that is not included in JEC systematics, but should be considered in, e.g., measurements of the inclusive b-jet cross section or of the to quark mass. he erformance of the corrections for b jets is discussed in section 7.4. he variables referring to article-level jets are labeled tcl" in this document. We consider two tyes of reconstructed jets, deending on how the subdetector information is used: calorimeter jets and PF jets. he calorimeter (CALO) jets are reconstructed from energy deosits in the calorimeter towers alone. A calorimeter tower consists of one or more HCAL cells and the geometrically corresonding ECAL crystals. In the barrel region of the calorimeters, the unweighted sum of one single HCAL cell and 5 5 ECAL crystals form a rojective calorimeter tower. he association between HCAL cells and ECAL crystals is more comlex in the endca regions. A four-momentum is associated with each tower deosit above a certain threshold, assuming zero mass, and taking the direction of the tower osition as seen from the interaction oint. he PF jets are reconstructed by clustering the four-momentum vectors of PF candidates. he PF jet momentum and satial resolutions are greatly imroved with resect to calorimeter jets, as the use of the tracking detectors and high granularity of the ECAL imroves the energy resolution through the indeendent measurements of charged hadrons and hotons inside a jet, which together 5

9 constitute 85% of the average jet energy. In reconstructing the PF candidate four-momentum, hotons are assumed massless and charged hadrons are assigned the charged ion mass. Calorimeter jets result from a relatively simlistic yet robust aroach and were widely used in the early ublications. With the imrovement of the understanding of the detector and the commissioning of the reconstruction with data, the erformance of the PF reconstruction has roven to be outstanding and reliable. he event descrition and reconstruction is more comlete and consistent, and for these reasons, we focus here on the PF jets used in the majority of recent analyses. 3 Event samles and selection criteria 3. Simulated samles Simulated samles are generated for QCD dijet and multijet, Z+jet, and γ+jet rocesses. A samle with single-neutrino roduction is simulated as well, to reroduce emty events that only contain ileu and detector noise. he dijet, γ+jet and single-neutrino samles are generated with ythia 6.4 [9], using the tune Z2* [20]. he Z+jet and multijet samles are generated with the Mad- Grah 4 [25] rogram matched with arton showers simulated by ythia 6.4 tune Z2*. Additional samles for systematic uncertainty studies are available for QCD dijet and Z+jet rocesses, both generated with herwig [2], tune EE3C [22]. he single-neutrino samle is comared to zero-bias data (section 4.3). he dijet samle is used to simulate the jet resonse (section 5) and also in comarison to data in the dijet balance analysis (section 6.). he Z+jet and γ+jet simulated samles are used in comarisons of measured resonse with the corresonding selected samles of data (section 6.3). he multijet samle is used in the multijet balance analysis (section 6.3). Additional samles are used for the analysis of events with a Z boson and a b jet (section 7.4): the MadGrah 4 rogram, together with ythia 6.4 for the hadronization, is used to simulate to quark air, W+jets and Drell-Yan+jets (DY+jets) roduction; and the owheg [26] rogram, together with ythia 6.4 for the hadronization, is used for single to quark samles. A DY+jets samle roduced with herwig is also used for studies of systematic uncertainties. All generated samles are rocessed through the detector simulation, based on Geant4 [8]. Minimum bias events, generated with ythia 6.4 and tune Z2*, are overlayed to all above samles to simulate the ileu. As will be detailed in section 4, the MC simulation is reweighted to match the distribution of the average number of ileu interactions in data. 3.2 Data sets and event selection he studies resented in this document use the data collected by the exeriment in rotonroton collisions at a center-of-mass energy of 8 ev, during the year 202, corresonding to an integrated luminosity of 9.7 fb. In this section we describe the selection criteria used in the different analyses resented in this aer. Only data collected during stable-conditions collisions with a fully-functioning detector are considered. Aart from the zero-bias samle, all data samles are required to fulfill some basic event reselection criteria. he resence of at least one wellreconstructed rimary vertex (PV) is required [27], with at least four tracks considered in the vertex fit, and with z(pv) < 24 cm, where z(pv) reresents the osition of the PV along the beam axis. he radial osition of the rimary vertex, r xy (PV), has to satisfy the condition r xy (PV) < 2 6

10 cm. Finally, the jets used in the analyses are required to satisfy basic identification criteria ( Jet ID ) [28], which on simulation are found to retain more than 99% of genuine jets, while rejecting most of the misreconstructed jets arising from detector noise or cosmic muons. Zero-bias samle. he zero-bias samle is collected using a random trigger in the resence of a beam crossing with filled bunches, active during the whole data-taking eriod with stable collisions conditions and a fully-functioning detector. As these events are not triggered by any secific energy deosit, they generally do not contain any contribution from hard-scattering rocesses. he main sources of energy deosits in zero-bias events are detector noise and ileu. he events in the dataset are weighted, according to the luminosity evolution during the running eriod, in order to be reresentative of the average ileu conditions of the datasets used in the analyses resented in this aer. Dijet samle. he dijet samle, comosed of events with at least two jets in the final state, is collected using dedicated HLs, which accet the events deending on the value of the average (,ave = (, st jet +, 2nd jet )/2) of the two highest- jets in the event, to ensure an unbiased data set. he HL uses a PF reconstruction algorithm with simlified tracking, and the jet is corrected for nonuniformity of the energy resonse as a function of the jet η and. Several,ave thresholds are available, with different rescale factors. Deending on the value of the highest jet in the event, only the least rescaled fully efficient HL is used for the decision of keeing or rejecting the event for further analysis. Events selected with single-jet triggers are also used for the studies of jet comosition shown in section 0. he event selection requires at least one of the two leading jets to have η <.3 and the angular searation between the two leading jets in the (x, y) lane to be φ st jet, 2nd jet > 2.7. Events are rejected if there is any third jet with, 3rd jet > 5 GeV not fulfilling the condition, 3rdjet /,ave = α < 0.2. As will be exlained in section 6., the results are studied as a function of the α cut from α < 0.4 to α < 0. in order to correct for biases from ISR+FSR. he Z+jet samle. he Z( µµ)+jet and Z( ee)+jet samles are collected using singleleton HLs with various thresholds. Events are required to contain either two oositesign muons or two oosite-sign electrons, fulfilling standard tight isolation and identification requirements [29, 30], with η < 2.3 and > 20 GeV. he dileton (ll) system is required to have,ll > 30 GeV and m ll m Z < 20 GeV, where m Z is the mass of the Z boson. he leading jet in the event is required to have η <.3 and > 2 GeV, and to have a large angular searation in the (x, y) lane with resect to the dileton system, φ(z, st jet) > 2.8. Events are rejected if there is any second jet with, 2nd jet > 5 GeV not fulfilling the condition,2nd jet /,Z = α < 0.3. he value of the cut on φ(z, st jet) is such that it does not bias the distribution of α for α < 0.3. As will be exlained in section 6.3, the requirement on α is tightened from the nominal value of 0.3 and the results are studied as a function of its value. In the Z( ee)+jet analysis an additional requirement is enforced that no electron in the event lie within R = ( φ) 2 + ( η) 2 = 0.5 of a jet. he Z+jet selection is also used in section 7.4, with the additional requirement that the jet is tagged as coming from a b quark using the combined secondary vertex tagger [3], with a tyical tagging efficiency of 70% and a misidentification robability for light-flavor jets of %. 7

11 he γ+jet samle. he γ+jet samle is collected with single-hoton HLs with various thresholds and different rescale factors. Deending on the value of the highest hoton in the event, only the least rescaled fully efficient HL is used for the decision of keeing or rejecting the event for further analysis. Events are required to contain one, and only one, hoton with > 40 GeV and η <.3 that fulfills the standard tight cut-based hoton identification and isolation criteria [32]. he leading jet in the event is required to have η <.3 and > 2 GeV and to have a significant angular searation in the (x, y) lane with resect to the hoton, φ(γ, st jet) > 2.8. Events are rejected if there is any second jet with, 2nd jet > 5 GeV not fulfilling the condition,2nd jet /,γ = α < 0.3. As will be exlained in section 6.3, the requirement on α is tightened from the nominal value of 0.3 and the results are studied as a function of its value. Multijet samle. he multijet samle is collected with single-jet HLs with various thresholds and different rescale factors. Deending on the value of the highest jet in the event, only the least rescaled fully efficient HL is used for the decision of keeing or rejecting the event for further analysis. he event selection is insired by the analysis described in ref. [4]. Events containing isolated letons or hotons assing standard identification criteria are rejected. he events are required to have a > 250 GeV jet in η <.3 balanced by a recoil system, comosed of two or more low- jets with 25 < < 750 GeV, which is within the range calibrated by the Z/γ+jet events, and satisfying the condition, 2nd jet /,recoil < 0.6. he events are also required to have the recoil jets at least φ(st jet, recoil jet) > radians away from the leading jet in the transverse lane, and to have the recoil system back-to-back with the leading jet with φ(st jet, recoil syst.) π < 0.3. As will be exlained in section 6.3, all jets with η < 5, > 0 GeV are considered to be art of the recoil system; the analysis is also reeated after changing to > 20 and 30 GeV the transverse momentum threshold for jets to be considered in the recoil. 4 Pileu offset corrections he high instantaneous luminosity at the LHC results in multile roton-roton collisions taking lace within a single beam crossing. Such additional collisions occurring within the same bunch-crossing as the rimary hard interaction roduce additional tracks in the tracker and deosit energy in the calorimeters. his contribution is called in-time ileu (I PU). Due to the finite signal decay time in the calorimeters, the collisions occurring in the revious and subsequent beam crossings also contribute to calorimetric energy in the same time window as the rimary hard interaction. his contribution is called out-of-time ileu (OO PU). he additional contributions to the jet energy and momentum due to ileu are referred to as the ileu offset", or offset" in this document. his offset is studied to otimize the subtraction of ileu from the data, with the corrections leading to an imroved detector resolution and a more accurate JES. he observables used for monitoring and correcting ileu are described in section 4.. he ileu subtraction then roceeds in stes. he OO PU is mitigated by calorimeter signal rocessing (section 4.2), and the I PU by identifying charged articles originating from ileu vertices and removing them with charged-hadron subtraction (section 4.2). he ileu jets are tagged with ileu jet identification (PUJetID) and removed (section 4.2). he remaining diffuse energy from neutral 8

12 articles and OO PU is estimated er event and then subtracted er jet using a calculation of the effective jet area with the extended hybrid jet area method (section 4.3). he deendence of the article-level PU offset on jet η and for this method is determined from simulation (section 4.3), and the data/simulation offset scale factor is determined from zero-bias data and neutrino gun simulation, with the random cone (RC) method (section 4.3). he uncertainties are discussed in section 4.4 and the results are summarized in section Pileu observables he amount of ileu resent in the event can be estimated by counting the number of good-quality rimary vertices N PV or by calculating the diffuse offset energy density ρ [33, 34] in the event. It can also be measured using luminosity monitors that estimate the average number of ileu interactions er crossing. he offset energy density ρ is calculated using the k clustering algorithm [35 37] with distance arameter D = 0.6 and η < 4.7. For this calculation, a large number of nonhysical articles (ghosts) with infinitesimal momenta and random direction effectively maing all the (η, φ) sace, is added to the event. When the jet clustering is run on the event, the hard articles in the event are clustered together with such ghosts: a few jets will contain high-momentum articles from the hard-scattering interaction, but most of the jets will be entirely made of ghosts, for which the main real energy contributions come from detector noise and esecially ileu. he offset energy density ρ is defined, in each event, as the median of jet momenta,i divided by their area A i, ρ = median(,i /A i ) [38]. For this calculation, no selection on the jet momenta is alied. Using the median instead of the mean makes ρ effectively insensitive to hard jets in the event, and including zero-energy jets comosed of only ghost articles reduces bias for low ileu energy densities. For Run 2, a simler aroach is used to calculate ρ, which is evaluated as the median of the energies calculated in a grid of η φ cells, and does not make use of jet clustering anymore. he number of good rimary vertices N PV includes vertices consistent with the luminous region (where the collisions haen) and with a number of degrees of freedom N dof 4, corresonding to a minimum of four tracks. he average number of ileu interactions µ is obtained by multilying the instantaneous luminosity with the effective minimum bias cross section of σ MB = 69.4 mb for 8 ev (68.0 mb for 7 ev) [39]. wo detectors are exloited for the luminosity measurement: the hadron forward (HF) calorimeter and the silicon ixel detector. he counting of ixel clusters is used for the offline recision measurement, because of its time stability and very small deendence on ileu. he HF allows for online determination of instantaneous luminosity er bunch crossing. Its results, calibrated offline er luminosity section that corresonds to 23.3 seconds of data, are used for cross-checks [40]. he agreement between data and simulation on N PV and ρ, after reweighting the simulation to match the distribution of the average number of ileu interactions (µ) in data, is shown in figure 3. he agreement for N PV is excellent, while ρ exhibits a small, mostly linear, deviation that is due to different offset densities in data and simulation in the endca and forward calorimeters. Both N PV and ρ are very nearly linearly deendent on µ over the tested range, as shown in figure 4. he ileu vertex reconstruction and identification efficiency is about 70% (while nearly 00% for hard-scattering events), and I PU contributes about 0.5 GeV to ρ er interaction. he vertex z resolution is around µm for minimum-bias vertices, imroving to tens of microns 9

13 Events er bin I fb (8 ev).0 Data MC Events er GeV I fb (8 ev) Data MC N PV ρ (GeV) Figure 3. Comarison of data (circles) and ythia 6.4 simulation (histograms) for the distributions of the number of reconstructed rimary vertices N PV (left), and of the offset energy density ρ (right). for hard-scattering events. With a luminous region of root-mean-square (RMS) of about 4 cm in the z direction, the vertex reconstruction is exected to remain linear u to vertices. he N PV versus µ exhibits a small negative quadratic term due to infrequent merging of ileu vertices, while ρ versus µ exhibits a similarly small ositive quadratic term owing to effects such as effective failed zero-suression of overlaing calorimeter deosits. hese quadratic terms account for less than 0.5 vertices in N PV and 0.5 GeV in ρ at µ = 20, resectively. he correlation between I PU and OO PU is modeled by generating the number of interactions for each bunch crossing using a Poisson distribution with the same mean µ. his is a good aroximation for 202 (8 ev) data, given that the RMS of the bunch-to-bunch variation of µ within a single luminosity section was only about 8%. he value of N PV is insensitive to OO PU, while ρ has a small (<5% of the total) OO PU comonent with 50 ns bunch crossings. he N PV variable is highly ( 94%) correlated with the number of I PU interactions in the event, while ρ is also sensitive to the amount of energy deosited by each interaction, and thus less strongly ( 85%) correlated with the interaction multilicity. 4.2 Pileu mitigation Out-of-time ileu. he amount of OO PU can be reduced by shortening the signal timeintegration window and by increasing the searation between bunches. In HCAL, 68% of the signal is contained within a 25 ns time window [4], resulting in about 5% leakage to a subsequent crossing with 50 ns bunch sacing and 50 ns time integration window. he signal decay time in ECAL is of the order of 00 ns, but the ECAL reconstruction involves three samles of 25 ns before the signal and five on the signal, to remove a varying edestal. his removes OO PU on average, but with erformance deending on the osition of the roton bunch within the bunch train, and requiring simulation of u to six receding bunch crossings ( 300 ns). 0

14 NPV I 9.7 fb (8 ev) N PV (µ) = µ µ 2 N PV (µ) = µ µ 2 ρ (GeV) I 9.7 fb (8 ev) ρ(µ) = µ µ 2 ρ(µ) = µ µ Data MC µ Data MC µ Figure 4. Mean of the number of good rimary vertices er event, N PV (left), and mean diffuse offset energy density, ρ (right), versus the average number of ileu interactions er bunch crossing, µ, for data (circles) and ythia 6.4 simulation (diamonds). he variation in the offset correction can be u to 0% in the endcas when selecting bunches in the front of bunch trains, which reresent a small fraction (< 0%) of data. he correction is evaluated on the whole dataset and hence this effect averages out. In HF, the signal is only 0 ns wide, resulting in negligible OO PU without any secial treatment of the signal. More advanced techniques are used in Run 2, exloiting the signal timing and ulse shae to fit in-time and out-of-time ulses simultaneously. Charged-hadron subtraction. he I PU from charged articles is reduced by identifying which vertex the charged PF candidates originate from, and removing those unambiguously associated with ileu vertices before clustering jets and miss. his method is referred to as charged-hadron subtraction. he leading rimary vertex is chosen based on the largest sum of squares of the tracks transverse momenta ( track 2 ) associated with the vertex. Subleading PV s, classified as ileu vertices, are required to ass further quality criteria on the comatibility with the luminous region and on their minimum number of degrees of freedom nracks N dof = w i, and w i [0, ], (4.) i= where w i is the weight assigned to the corresonding track by the adative vertex fit [27], based on its comatibility with the vertex. he minimum requirement N dof > 4 corresonds to at least four tracks. racks are matched to vertices based on their chi-squared er degree of freedom ( χ 2 /N dof ). If χ 2 /N dof < 20 for a vertex, then the track is associated with this and only this vertex. If the track from a charged hadron is associated with a ileu PV, assing the above quality requirements, it is

15 considered a ileu track, and removed in the CHS rocedure. All other tracks, including those not associated with any PV, are ket. he CHS can remove aroximately 50% of I PU within the tracker coverage, as illustrated later by the solid red comonent labeled charged hadrons in figures 6 and 7. he remaining unassociated charged hadrons are either not ointing to any reconstructed vertex, or are associated with a vertex that did not ass all the quality requirements, or have too large χ 2 /N dof for robust vertex association. he vertex reconstruction and identification inefficiency is about 30% for ileu vertices, and it is resonsible for a large roortion of the unassociated tracks from ileu. he charged hadrons from PU are tyically soft and have an exonentially decreasing distribution, with 0.5 GeV [42]. Many of the unassociated hadrons in contrast have much higher and are often coming from the leading rimary vertex, but have too high χ 2 /N dof for robust vertex association. his is articularly common for tracks that are of high and therefore very straight and have merged ixel hits within dense jet cores. For jets of several hundred GeV the tracking efficiency within the jet core can fall as low as 60%, with a corresondingly large increase of the fraction of unassociated tracks. Future imrovements of CHS aimed at removing a higher roortion of ileu tracks, e.g., with more efficient track-vertex association, must therefore maintain a very low misreconstruction rate for tracks from high- jets, or also consider the and local environment of the tracks, as done with the ileu er article ID (PUPPI) method [43]. he PU offset subtraction has been derived with and without CHS, and the later stages of JEC are ractically identical after the alication of the corresonding offset corrections. Alication of CHS imroves the jet resolution, however, as discussed in section 8. Pileu jet identification. In addition to diffuse energy, PU interactions often generate soft jets with of a few GeV. Overlaying multile PU interactions in a single beam-crossing leads to nonnegligible robability of two or more of these soft jets overlaing, resulting in hard jets of tens of GeV in, far above the average PU density. hese overlas are referred to as ileu jets, which are articularly roblematic for hysics analyses as they can ass tyical jet requirements, e.g., > 30 GeV. he ileu jets lack the relatively hard core tyically found in hard-scattering jets, and can be identified by using a multivariate analysis (MVA) of the jet shae variables and the fraction of charged articles contributed by ileu vertices. his MVA tool is called PUJetID, can be run on jets with or without CHS, and it is documented in ref. [44]. For jets in the region η < 2.5 and > 30 GeV, the PUJetID efficiency for hard-scattering jets is around 99%, at a ileu-rejection of 90 95%. Removing ileu jets can imrove the erformance of hysics analyses, but alying PUJetID has no direct imact on the JEC. PUJetID is currently not used in the JEC measurements to avoid biases arising from the occasional removal of soft jets from the hard-scattering vertex, which affects the ISR+FSR correction. Instead, CHS is used, which indirectly removes most of the jets tagged by PUJetID by significantly lowering their. 4.3 Hybrid jet area method he jet area method uses the effective area of the jets multilied by the average energy density in the event to calculate the offset energy to be subtracted from the jets. his method was introduced in ref. [33] and was first used on data in ref. [3] with slight modifications to account for the oversubtraction of the underlying event (UE) and for the η-deendence of the offset. his slightly 2

16 modified version is referred to as the hybrid jet area method, where the hybrid in the name derives from the fact that this method combines an η-deendent average offset O(η) correction versus N PV, as already used at the evatron [6], with the original η-indeendent jet area method using only offset density ρ and jet area A j. his is effectively done by relacing (N PV )O(η) in the evatron method with (ρ ρ UE )( β(η)a j ), where each of the terms N PV and ρ, and ρ UE, and O(η) and β(η) A j have the same basic meaning, which will be detailed in the following. In this aer we further extend the hybrid method by adding a logarithmic jet deendence. he revious searate UE correction is absorbed in the new η-deendent constant term. he full correction formula used as a multilicative factor for the uncorrected jet transverse momentum,uncorr at is C hybrid (, uncorr, η, A j, ρ) = [ ρ0 (η) + ρβ(η) ( + γ(η) log(, uncorr ) )] A j, uncorr. (4.2) he inut arameters are, uncorr, jet seudoraidity η, jet area A j, and the er-event offset density ρ. In this formula the arameters ρ 0 (η), β(η), and γ(η) introduce the required shaing of the offset versus η. here is no exlicit correction for the UE density ρ UE as in ref. [3], but that term is effectively absorbed into ρ 0 (η). Because ρ ρ UE and C hybrid when µ 0, we have ρ 0 (η) = ρ UE β(η) at,uncorr GeV in the ideal situation. he multilicative factor, β(η), corrects for the nonuniformity of the I and OO PU offsets versus η, and the residual correction factor, γ(η), adds their logarithmic jet deendence. he arameters ρ 0 (η), β(η), and γ(η) are determined from the simulated article-level offset, and the offset scale factor for the ρ 0 (η) and β(η) in data is determined using the random cone method in zero-bias data, as discussed in the following. he ρ 0 (η) arameter effectively contains the ρ UE for the QCD multijet samle, while β(η) and γ(η) arameterize the ythia 6.4 MinBias overlay, which matches data well. he RC method consists of reconstructing many jets in each event, clustering articles in randomly laced cones, effectively maing all the (η, φ) sace. he average of these jets is a measurement, in each event, of the average energy density that gets clustered in a jet. When the method is alied in events with no contribution from hard scattering, as it is the case for zero-bias events, the main contributions to the jet energies come from noise and ileu. Assuming the noise energy contribution to be negligible with resect to the ileu one, the average of the jets as measured from the RC method indicates the average energy offset due to ileu, for the considered jet algorithm and jet distance arameter. Simulated article-level offset. In simulation, the most direct way to calculate the articlelevel offset in jet caused by ileu is to reconstruct the same events with and without ileu overlay and match the reconstructed jets between these samles. his is done on a QCD multijet samle generated with ythia 6.4, tune Z2*. Some care needs to be taken to reroduce the same signal fluctuations as before the overlaying ileu, to avoid random smearing of jet between these two samles. All measurements are binned in µ to decoule ileu reweighting from offset measurement, and to effectively incororate the correct average amount of OO PU in the offset correction (OO and I PU are correlated through the shared Poisson mean µ). he µ bins are then maed to the average measured value of ρ for arameterizing the correction. Similarly, the deendence of the offset is measured in bins of article jet (, tcl ) to decoule the offset 3

17 (GeV),offset Simulation (8 ev) Anti-k, R=0.5 (PF+CHS) η <.3 0 µ < 0 0 µ < µ < µ < 40 0 µ < (GeV), tcl (GeV),offset Simulation (8 ev) Anti-k, R=0.5 (PF+CHS) η <.3 0 µ < 0 0 µ < µ < µ < 40 0 µ < (GeV), tcl Figure 5. Simulated article-level offset,offset tcl defined in eq. (4.3) (left), and residual offset after correcting for ileu with eq. (4.2) (right) for η <.3, versus article jet, for different values of average number of ileu interactions er bunch crossing µ. from the sectrum and JER, before maing to the average uncorrected measured,uncorr for arameterization. We define the article-level offset,offset tcl as the average difference in between matched jets in simulated samles with and without ileu overlay:,offset tcl ( ρ, [ η ],,uncorr ) =,with PU,without PU [ µ PU, η,, tcl ]. (4.3) he square brackets [ ] denote the binning variables, while the angle brackets denote the averages within those bins for the variables that are used to arameterize the corrections. his subtle distinction is made exlicit here due to its imortance for various observational biases, and due to the fact that the binning and arameterization variables are not the same. o have an unambiguous article-level reference, both reconstructed jets are required to match the same article jet within a distance less than R < R/2, where R is the jet distance arameter. he matching efficiency for jets in the without-pu samle to jets in the with-pu samle for µ = 20 is better than 80% (98%) for jets of > 0 (30) GeV. In the with-pu samle there is also a large fraction of unmatched jets with < 60 GeV that are due to ileu. he simulated article-level offset,offset tcl is arameterized as a function of offset density ρ and jet η,,uncorr and area A j to obtain the ρ 0 (η), β(η) and γ(η) used in eq. (4.2), where C hybrid =,offset tcl /,uncorr.. he article-level simulated offset versus article jet is shown in figure 5 (left) for η <.3. he relative sloe in offset is arameterized by a logarithmic deendence and is reasonably indeendent of the level of ileu in the event, while the offset versus ρ is assumed linear. he resultant level of ileu after alying the corrections is resented in figure 5 (right), showing the effect of the subtraction. he results are consistent with the absence of additional ileu energy within about 0.2 GeV for the full samle. For µ > 30, small residual offset is visible due to a small unarameterized quadratic deendence of offset on ρ. 4

18 j (GeV) / µ,offset Simulation (8 ev) Anti-k, R=0.5 (PF+CHS) η <.3 Photons Neutral hadrons Unassoc. ch. hadrons Charged hadrons (GeV),tcl ) (GeV) A / ( µ,offset η = 0.0, PF Simulation = 00 GeV,tcl = 50 GeV,tcl = 30 GeV,tcl = 0 GeV,tcl Random cone (8 ev) R Figure 6. Simulated article-level offset versus searately for each tye of PF candidate (left). Average offset density versus jet distance arameter R for various,tcl comared to a random-cone offset density versus cone radius (right). he jet or cone area A j corresonds to πr 2. Figure 6 (left) shows the deendence of the offset for each PF candidate tye. he,offset is divided by the average number of ileu interactions, hence showing the average offset er additional interaction. While the reconstruction thresholds for charged hadrons and hotons are of the order of a few hundred MeV, the effective detector reconstruction thresholds for neutral hadrons (mostly K 0 L, K0 S, and neutrons) are of the order of 3 GeV. his is far above the tyical,offset 5 GeV for a ileu article, making the neutral hadron contribution barely visible in figure 6 (left). he observed deendence comes from an interlay of several effects for overlaing articles, such as failed zero-suression in calorimeter energy, nonlinearity of PF hadron corrections, fake tracks arising from hit combinations, and misreconstructed tracks arising from ixel hit merging and tracker dynamic inefficiency at high µ. he rate of overlas is highest in the jet core, which results in the simulated offset correction deending on the jet size. Figure 6 (right) shows the average offset density within the jet versus jet distance arameter R and jet. he simulated article-level offset converges to an RC offset measurement at low, as well as for large jet size arameters. he shallow sloe in RC offset versus distance arameter is due to vector summation of PF candidate momenta, which reduces the offset relative to the offset energy by cos( R) at the cone edges. Offset scale factor. he offset data/simulation scale factor is estimated from zero-bias data and simulation using the RC method [3]. Because zero-bias data contain no energy deosition from hard interactions, and the noise contribution is small, the average transverse momentum,cone (η) of PF candidates in a randomly laced cone centered at (η, φ) can be identified with the average offset due to ileu,,offset RC (η):,offset RC (η, ρ ) =,cone [η, µ]. (4.4) As in the case of the simulated article-level offset, the arameterization variables (η, ρ ) and the binning variables [η, µ] are exlicitly marked in order to signal their imact on the observational biases. 5

19 / µ (GeV),offset R=0.5 Anti-k <µ> = fb (8 ev) Markers: Data, Histograms: MC Photons EM deosits Neutral hadrons Hadronic deosits Unassoc. charged hadrons Charged hadrons Data/MC PF PF+CHS η Figure 7. Random-cone offset measured in data (markers) and MC simulation (histograms) normalized by the average number of ileu interactions µ, searated by the tye of PF candidate. he fraction labeled charged hadrons is removed by CHS. he ratio of data over simulation, reresenting the scale factor alied for ileu offset in data, is also shown for PF and PF+CHS. For deriving the offset scale factor, the RC measurement is fitted with a quadratic function of ρ,,offset RC = 0 + ρ+ 2 ρ 2. he constant and quadratic terms are small, but are required for a good χ 2 /N dof of the fit. he constant term has usually a small ositive value, because the mean,cone can still have a small nonzero value when the median ρ is already zero. his low-pu behavior of ρ is discussed in ref. [45]. he offset scale factor for arameters ρ 0 (η) and β(η) in eq. (4.2) is defined as,offset RC data (η, ρ data),offset RC MC (η, ρ MC). (4.5) Using different ρ working oints for data and simulation is necessary due to the slight difference of about 4% in ρ between data and simulation, seen in figure 3 (right). he offsets in data and simulation are shown in figure 7 (to), searated by PF candidate tye. he offset scale factor for PF and PF+CHS is shown in figure 7 (bottom). he offset scale factor at η < 2.4 is less than 5%, but increases u to 20% outside of the tracking coverage near the inner edge of HF at η 3.2. he triangular shae is caused by smearing shar detector effects over a cone area within η < 0.5. he uncertainty from varying the ρ working oint within the 68% confidence interval of the ρ distribution is less than 2% u to η < Pileu offset correction uncertainties he ileu offset correction uncertainties come from two main sources: uncertainty in the offset scale factor used for the η deendence in data, and uncertainty in the offset jet deendence that is 6

20 derived from simulation only. he former uncertainty is evaluated by varying the ρ working oint used for deriving the offset scale factor within one standard deviation of the ρ distribution, while the latter is evaluated using the difference between the simulated article-level offset and the RC offset. Of these, the jet deendence is the dominant uncertainty across most of the hase sace. Any residual ileu offset is absorbed on average, within the constraints of their resective arameterizations, by the relative η and absolute corrections derived from dijet, Z+jet, γ+jet and multijet data. herefore the dominant -deendence uncertainty is roagated through the fit rocedure used in the data-based methods to account for this reduction and shaing of ileu offset correction uncertainties. his results in a set of five uncertainty sources: PileUEnveloe is taken as 30% of the difference between simulated article-level offset and RC offset. his is the ileu uncertainty we would have if the later calibrations did not reduce the uncertainty. It is not directly included in the JEC uncertainties, but is roagated through the relative η and absolute corrections to give the uncertainties PileUPtEta, PileUPtRef (for µ 20 data) and PileUMuZero (for µ = 0 data), described below. PileUPtEta (Eta=BB,EC,EC2,HF) results from the roagation of the PileUEnveloe uncertainty through the η-deendent correction evaluation from dijet balance. his uncertainty accounts for the residual difference between the PileUEnveloe with shae ( 0 + log( ))/ and the η-deendent correction fit in the range of dijet data at 60 < < 2000/ cosh(η) GeV with shae 0 + log( ). PileUPtRef results from the roagation of the PileUEnveloe uncertainty through the evaluation of the absolute-scale deendence from Z/γ+jet and multijet data. his uncertainty accounts for the residual difference between the PileUEnveloe and the absolute-scale fit in the range of Z/γ+jet and multijet data at 30 < < 000/ cosh(η) GeV. PileUDataMC accounts for uncertainty in the offset scale factor for data, based on variation of the ρ working oint within one standard deviation of the ρ distribution. PileUMuZero is evaluated from the nominal result of the fit for η- and -deendent databased corrections, and accounts for the bias that results from deriving them at µ 20 instead of µ 0. his uncertainty is to be used for zero-ileu data ( µ 0, e.g., in the 2.76 ev data collected in 203) and relaces PileUPtEta, PileUPtRef and PileUDataMC. he ileu offset correction uncertainties are summarized in figure 8. he dominant uncertainty is from the residual jet deendency remaining after the alication of the data-based methods. It is at the level of % for = 30 GeV, and raidly decreases to the 0 3 level in the range constrained by the data-based methods. here is a small increase in uncertainty again at high outside the range of data-based methods, where the constrained arameterizations used for data-based residuals result in a small seesaw effect. he uncertainty for µ = 0 data is in many cases similar or even larger than for µ = 20, owing to the absortion of the residual offset into relative η and absolute corrections at > 30 GeV. 7

21 JEC uncertainty (%) R=0.5 PF+CHS = 30 GeV 9.7 fb (8 ev) SubotalPileU PileUPtEta PileUPtRef PileUDataMC PileUMuZero (ot) JEC uncertainty (%) R=0.5 PF+CHS η = 0 jet 9.7 fb (8 ev) SubotalPileU PileUPtEta PileUPtRef PileUDataMC PileUMuZero (ot) JEC uncertainty (%) R=0.5 PF+CHS η = 2.7 jet η jet (GeV) 9.7 fb (8 ev) SubotalPileU PileUPtEta PileUPtRef PileUDataMC PileUMuZero (ot) JEC uncertainty (%) (GeV) R=0.5 PF+CHS η = 3.5 jet (GeV) 9.7 fb (8 ev) SubotalPileU PileUPtEta PileUPtRef PileUDataMC PileUMuZero (ot) Figure 8. Pileu offset correction uncertainties for the average 202 (8 ev) conditions for PF jets with CHS and R = 0.5 as a function of η jet for fixed = 30 GeV (to left) and as a function of jet (to right, and bottom anels). he lots are limited to a jet energy E = cosh η = 4000 GeV so as to show only uncertainties for reasonable in the considered data-taking eriod. PileUMuZero is an otional alternative uncertainty for zero-ileu ( µ 0) events, and it is therefore not included in the quadratic sum SubotalPileU. It accounts for the ileu uncertainty absorbed in the residual resonse corrections at µ 20, which is articularly rominent at.5 < η < Summary of ileu offset corrections he ileu offset corrections for the anti-k algorithm (R = 0.5) with and without charged-hadron subtraction are summarized in figure 9 for tyical 202 (8 ev) conditions of µ 20, comared to corrections for 7 ev data taken in 200 and 20. he average ileu er interaction for R = 0.5 is about 0.5 GeV, adding u to a total of about 0 GeV er jet. his results in a tyical offset correction of about 0.75 for a,corr = 30 GeV (,uncorr = 40 GeV) jet. he CHS removes aroximately half of this offset before jet clustering by matching tracks to ileu vertices, reducing the residual offset 8

22 Pileu offset correction Pileu offset correction fb (8 ev) + 36 b fb (7 ev) η = 0 µ = 20.0 R = 0.5, PF 20 fb (8 ev) 5 fb (7 ev) 36 b (7 ev) (GeV) η = 0 µ = 20.0,corr 9.7 fb (8 ev) fb (7 ev) R = 0.5, PF+CHS 20 fb (8 ev) 5 fb (7 ev) (GeV),corr Pileu offset correction Pileu offset correction fb (8 ev) + 36 b fb (7 ev) = 30 GeV,corr µ = 20.0 R = 0.5, PF 20 fb (8 ev) 5 fb (7 ev) 36 b (7 ev) η = 30 GeV,corr µ = fb (8 ev) fb (7 ev) R = 0.5, PF+CHS 20 fb (8 ev) 5 fb (7 ev) η Figure 9. Pileu offset correction C hybrid including data/mc scale factors, with systematic uncertainty band, for the average 202 (8 ev) conditions of µ = 20 for PF jets without CHS and R = 0.5 at η = 0 versus,corr (to left), and at,corr = 30 GeV versus η (to right), comared to corrections for 200 [3] and 20 [46] data at 7 ev after extraolation to similar ileu conditions. he same results are also shown for PF jets with CHS and R = 0.5 at η = 0 versus (bottom left), and at,corr = 30 GeV versus η (bottom right), comared to corrections for 20 data at 7 ev [46]. correction to about 0.85 at,corr = 30 GeV (,uncorr = 35 GeV). Roughly one third of the remaining ileu is from PF charged hadrons that have not been matched to good ileu vertices, and much of the rest is from PF hotons. he CHS algorithm was only fully commissioned at 7 ev in 20, and the 200 (7 ev) version of the offset corrections did not yet take into account the remaining unmatched ileu tracks. herefore only results without CHS are shown for 7 ev in 200. he ileu offset corrections have been relatively stable over time at 7 ev in 200 and 20, when scaled to similar ileu conditions. his is in art due to the good linearity of the offset corrections for PF and continuous develoment on the detector side to reduce OO PU in the calorimeters, and in art due to the adatability of the jet area method to the revailing ileu offset. 9

23 he largest differences are visible in the 2.5 < η < 3.0 region, where OO PU increased at 7 ev in 20, but was again brought down in ECAL at 8 ev in 202 using more advanced reconstruction algorithms. he OO PU is also artially resonsible for the differences in the endcas within tracker coverage of.5 < η < 2.5, and for differences between 200 and in the barrel at η <.5. In addition, the JEC were imroved at 7 ev in 20 to take into account the difference between the offset outside jets (RC offset) and inside jets (article-level offset). his increased the offset correction inside the tracker coverage (failed zero-suression), and lowered it outside (calorimeter resonse nonlinearity), comared to the 200 (7 ev) corrections. he ileu uncertainties have been steadily reduced desite raidly increasing ileu. his can be credited to imrovements in the correction methods, more events at high ileu to determine the trends versus ileu, and a reduction of double counting. he 202 (8 ev) corrections exlicitly take into account the additional constraints from data-based methods, which reduce the offset uncertainty in the endcas by u to 50% for PF+CHS at,corr = 30 GeV comared to 7 ev in 20. he dominant systematic uncertainty is from the deendence of the ileu offset, which is only indirectly constrained by data. 5 Simulated resonse corrections he simulated resonse corrections are derived and alied on jets that have been corrected for ileu offset. he detector simulation contains a detailed model of the detector geometry, data-based alignment and calibration of the detector elements, and emulation of the readout electronics. It is based uon the Geant4 ackage [8] that simulates the evolution of the electromagnetic (EM) and hadronic showers and their interactions with the detector material. In addition, the ythia 6.4 tune Z2* event generator is used to simulate the fragmentation of the initial quarks and gluons. ogether these two comonents rovide an accurate and detailed descrition of the jet resonse, which is used for the bulk of the JEC. Data-based methods (section 6) are needed only for small residual corrections on to of the simulated resonse and the simulated offset corrections discussed in section 4. he benefit of relying heavily on simulation to derive the jet resonse is that we are not sensitive to many of the biases inherent in the data-based methods and can cover corners of hase sace that are not easily accessible in data. his includes samles of jets with very low ( < 30 GeV) and very high ( > ev) momenta, heavy-flavor jets, and samles with articularly low (µ < 5) and high (µ > 40) ileu. Describing jet resonse in terms of variables accessible in simulation also facilitates the understanding of data-based methods, as we can better model the correlation between various samles and corrections. For the following discussion, jets are assumed to be corrected for the ileu offset as described in section 4. Samle definitions We derive the simulated resonse from a QCD multijet samle of 0 million events generated with ythia 6.4 tune Z2*. o ensure event generation with efficient coverage of the full kinematic hase sace at the LHC with small statistical uncertainty, the events are generated with a flat sectrum and reweighted by ˆ 4.5, where ˆ is the transverse momentum of the generated 2 2 hard rocess, which allows the recovery of the original sectrum in ythia 6.4 and the roduction of unbiased results for, jet > 30 GeV. he generated and simulated events are overlaid with ileu generated 20

24 by ythia 6.4 tune Z2*, with events reweighted such that the ileu distribution matches that found in data. o estimate ileu offset in jets, we simulate the same generated events also without additional ileu overlay, as was discussed in section 4. o estimate the jet resonse deendence on the fragmentation model and jet flavor, a comlementary samle is roduced with herwig tune EE3C. o estimate the jet resonse deendence on the detector calibration, we also roduce additional samles with the fast simulation. Definition of simulated article resonse A article-level jet is matched to the closest reconstructed jet if it is within half of the jet distance arameter R. For a distance arameter of R = 0.5 this corresonds to he method ensures a high matching efficiency (reaching 00% around = 30 GeV) and rovides a unique match for the anti-k jets. In the resent aer, the simulated article resonse R tcl is defined as the ratio of arithmetic means of matched reconstructed and article-level jets transverse momenta, R tcl (, η) =, tcl [, tcl, η], (5.) in bins of article-level (, tcl ) and reconstructed η (where is the transverse momentum of the reconstructed jet). As in the revious sections, the square brackets [ ] denote the binning variables, and the angle brackets indicate the averages within those bins for the variables that are used to arameterize the resonse. 5. Corrections versus η and Simulated anti-k jets, with a distance arameter R = 0.5, are used to study the detector resonse as a function of the jet. he simulated article resonse is shown in figure 0 (left) as a function of the reconstructed jet η. he simulated article resonse after JEC is shown in figure 0 (right) as a function of the article-level jet, tcl in various η regions. he results show that the resonse is corrected to within 0.5% with resect to the article-level jet, for from about 20 GeV to 2 ev. 5.2 Deendence on the jet size he deendence of the jet resonse on the jet distance arameter R has been checked in the range R = he resonse is similar after accounting for the increasing PU offset due to the larger jet area (A jet πr 2 ). Smaller effects come rimarily from two sources: he UE energy within the jet has lower resonse than the energy from the hard scattering, lowering the resonse at low for jets with large R. A larger distance arameter averages the jet resonse over a larger area, smearing shar features in the detector resonse versus η. Figure (left) shows the comarison of the JEC factor for various jet sizes at = 30 GeV. As exected from the larger fraction of UE energy, the corrections rise slightly for larger distance arameters. he very small distance arameter R = 0.3 is an excetion to this rule, because the detector granularity smears some energy out of the cone. hese differences mostly disaear 2

25 Simulated jet resonse R = 0.5, PF+CHS 202 JES: Anti-k Barrel Endca Forward BB EC EC2 HF = 0 GeV = 30 GeV = 00 GeV (8 ev) = 400 GeV = 2000 GeV Jet η Corrected resonse Simulation (8 ev) QCD Monte Carlo Anti-k R=0.5, PF+CHS η <.3.3 < η < < η < < η < (GeV), tcl Figure 0. Simulated jet resonse R tcl versus η for R = 0.5 (left). Simulated jet resonse R tcl, after JEC have been alied, versus, tcl for R = 0.5 in various η regions, and with statistical uncertainties (right). at higher for R 0.4, with the smaller jet sizes showing slightly sharer detector features. Simulated jet resonses after the alication of the JEC are shown in figure (right) as a function of jet for a range of distance arameters from 0.3 to. he resonse is consistent with unity within % for 30 GeV. During Run of the LHC, the suorted jet size arameters in collisions were R = 0.5 and R = 0.7. he full jet energy corrections and uncertainties were derived and rovided centrally only for these two jet size arameters. 5.3 Detector simulation uncertainties We evaluate several systematic uncertainties using simulation, with the uncertainties further constrained using data-based methods, as discussed later. We discuss here the uncertainties arising from the roagation of detector calibration uncertainties to the jet resonse. he effects of jet fragmentation and flavor resonse are discussed in section 7.3. Because the jet resonse is later constrained using measurements based on data, these systematics are exlicitly set to zero at certain reference oints, discussed in section 6. hey are then used to extraolate the systematics from these reference oints to regions of the hase sace not directly calibrated with data. Single-ion resonse. he jet resonse is sensitive to the underlying detector calibrations. he calorimeters have been calibrated in test beam studies, and the single-ion resonse (SPR) has subsequently been checked on roton-roton data with charged ions [47], confirming good modeling of the barrel resonse in simulation to within ±3%. Because the PF reconstruction relies heavily on tracking for low- jets, the sensitivity to the detector calibration is strongly reduced comared to the calorimeter-only reconstruction. o show this effect, the ratio of the resonse when varying the SPR with resect to the nominal resonse is shown in figure 2, for jets reconstructed with the PF algorithm and for jets reconstructed with only calorimetric energy deosits, both using the anti-k algorithm. For this study, the SPR has been roagated to the JEC using the fast simulation. 22

26 Corr. factor Ratio to R= R=0.5 R=0.7 R=.0 (8 ev) QCD Monte Carlo Simulation Anti-k (PF+CHS) = 30 GeV R=0.3 R= η Corrected resonse Simulation (8 ev) QCD Monte Carlo Anti-k (PF+CHS) η <.3 R=0.3 R=0.4 R=0.5 R=0.7 R= (GeV),tcl Figure. Jet energy correction factors for a jet with = 30 GeV, as a function of η and for various jet sizes R (left). Simulated jet energy resonse R tcl after JEC for η <.3 as a function of the article-level jet for various jet sizes R (right). At low, PF is directly sensitive to SPR only through neutral hadrons, which on average contribute 5% of the jet energy at article level, leading to a sensitivity of about 0.5% for a simultaneous change of ±3% in both ECAL and HCAL SPR. At high the PF erformance aroaches that of the calorimetric reconstruction, because the tracking efficiency dros in the dense jet core and the leading tracks become too straight for a reliable measurement. Since 25% of the jet energy is deosited as hotons (section 0), the JEC sensitivity to a ±3% change in SPR is at most 2.3%. he sensitivity to changes in SPR has been also studied searately for a 3% change in the resonse of the ECAL and HCAL, as shown in figure 3. he results are qualitatively similar to an overall change in SPR, but show larger sensitivity to the SPR in HCAL at high. his is because hadronic showers become deeer for high- articles, and deosit a larger fraction of their energy in the HCAL. 5.4 Jet energy corrections roagation to missing transverse momentum he jet energy corrections are roagated to miss by using the so-called tye-i correction:,tyei miss miss =,uncorr +,uncorr i,corr i O RC i, (5.2) i i i where,uncorr miss corrected jet, and O RC i is the uncorrected miss,,uncorr is the uncorrected jet,,corr is the fully is the average offset due to ileu, as obtained with the RC method (see section 4.3). he sum runs over all jets with,corr > 0 GeV in the event. Including the average RC offset underneath jets in the missing transverse momentum vector sum ensures that the ileu 23

27 Resonse ratio Fast simulation η <.3 Anti-k R= (GeV) (8 ev) PFJet SPR +3% PFJet SPR -3% CaloJet SPR +3% CaloJet SPR -3% Figure 2. Changes in PF jet and calorimeter jet resonse resulting from ±3% variations of single-ion resonse in arameterized fast simulation in HCAL+ECAL. Resonse ratio Fast simulation η <.3 Anti-k R= (GeV) (8 ev) PFJet ECAL +3% PFJet ECAL -3% CaloJet ECAL +3% CaloJet ECAL -3% Resonse ratio Fast simulation η <.3 Anti-k R= (GeV) (8 ev) PFJet HCAL +3% PFJet HCAL -3% CaloJet HCAL +3% CaloJet HCAL -3% Figure 3. Changes in PF jet and calorimeter jet resonse resulting from ±3% variations of single-ion resonse in arameterized fast simulation in ECAL (left), and HCAL (right). offset remains isotroic and does not bias miss. he tye-i correction is recommended for hysics analyses and is used in most results, as well as for deriving residual JEC for data. 5.5 Summary of simulated resonse corrections he simulated article resonse corrections are summarized in figure 4 for data collected at 8 ev and comared to corrections for 7 ev data taken in 200 and 20. At low, the JEC rise toward.5 due to the 5% neutral hadron energy that largely falls below calorimeter thresholds. he resonse is quite flat at > 50 GeV, where the cometing effects of increasing calorimeter 24

28 resonse and falling tracking efficiency within the jet core comensate each other. In the barrel and endca regions, the corrections rise with η, due to the increasing amount of material located in front of the calorimeters, which leads to effects such as an increased rate of nuclear interactions in the tracker. he corrections are higher around η =.3 and 3.0 due to the degradation of the resonse in the transition regions. Significant imrovements in the simulation occurred after the first year of running at 7 ev in 200, when in situ collision data became available for tuning the detector simulation. After that, the simulated article resonse corrections have been stable in desite continuous develoment of the reconstruction software, and the changes have remained within the steadily-reducing systematic uncertainties. he differences introduced by the change in s are ractically negligible. 6 Residual corrections for data he residual data/simulation scale factors for JEC are determined after correcting jets for ileu and simulated article resonse. For consistency, the variations of the jet momenta due to corrections for ileu and simulated resonse are roagated to the miss definition à la eq. (5.2). he residual corrections for data are first determined with a samle of dijet events with low statistical uncertainty, where the resonse of jets over a wide range of is corrected relative to the one of jets with η <.3, and then with a combination of Z( µµ)+jet, Z( ee)+jet, γ+jet, and multijet events for jets with η <.3 from a of around 30 GeV to ev. he basic idea, in all the considered toologies, is to exloit the transverse momentum balance, at hard-scattering level, between the jet to be calibrated and a reference object: a jet energy scale different from unity generates imbalance at the reconstructed level. he jet energy resonse is studied using the balance and MPF (missing transverse momentum rojection fraction) methods [3]. While in the -balance method the jet resonse is evaluated by comaring the reconstructed jet momentum (, jet ) directly to the momentum of the reference object (,ref ), the MPF method considers the resonse of the whole hadronic activity in the event, recoiling versus the reference object. his leads to the following definition of resonse for the two methods: R jet, =, jet,ref, (6.) R jet,mpf = + miss,ref (,ref ) 2. (6.2) he difference and comlementarity of the two resonse determinations will be studied in the following sections. Part of the transverse momentum imbalance between the jet to be calibrated and the reference object can also come from the resence of additional jets in the event; this effect deends on the studied toology and is not correlated with the jet energy resonse. For this reason, all the corrections are studied as a function of the additional jet activity in the event, quantified by the variable α. his is defined as the ratio of the most energetic jet that does not originate from the event toology under study, divided by the tyical momentum scale of the event. In other words α =, 3rd jet /,ave for dijet events and α =, 2nd jet /,γ/z for Z+jet and γ+jet events. he corrections are then extraolated to the value they would have for α = 0 in order to address only genuine jet energy resonse effects. 25

29 Simulated resonse correction Simulated resonse correction fb (8 ev) + 36 b fb (7 ev) η = 0 R = 0.5, PF+CHS 20 fb (8 ev) 5 fb (7 ev) 36 b (7 ev) (GeV),corr,corr 9.7 fb (8 ev) + 36 b fb (7 ev) = 00 GeV R = 0.5, PF+CHS 20 fb (8 ev) 5 fb (7 ev) 36 b (7 ev) η Simulated resonse correction Simulated resonse correction ,corr 9.7 fb (8 ev) + 36 b fb (7 ev) = 30 GeV R = 0.5, PF+CHS 20 fb (8 ev) 5 fb (7 ev) 36 b (7 ev) η,corr 9.7 fb (8 ev) + 36 b fb (7 ev) = 000 GeV R = 0.5, PF+CHS 20 fb (8 ev) 5 fb (7 ev) 36 b (7 ev) η Figure 4. Resonse correction factors with their systematic uncertainty band from simulation for the 202 data collected at 8 ev for PF jets with CHS and R = 0.5, comared to corrections at 7 ev corresonding to 36 b of data taken in 200 [3] and 5 fb taken in 20 [46]. he comarison is shown at η = 0 versus,corr (to left), and as a function of η at,corr = 30 GeV (to right),,corr = 00 GeV (bottom left) and,corr = 000 GeV (bottom right). he lots are limited to a jet energy E = cosh η = 3500 GeV so as to show only the correction factors for reasonable in the considered data-taking eriods. 6. Relative η-deendent corrections Residual η-deendent corrections to the jet resonse are obtained using dijet events, where the tag" jet has η <.3, and the robe" jet seudoraidity is unconstrained. In this way, the resonse for all jets is corrected relative to the resonse for central jets ( η <.3). hese residual corrections are derived from jets already corrected with the simulation-based corrections and account for any residual difference between data and simulation, as a function of both η and. For dijet events, where the reference object (barrel jet) has oor resolution, the biases from JER are minimized by binning in average jet instead of,tag :,ave = 0.5(,tag +,robe ). 26

30 his symmetric binning also cancels out to first order the relative biases from ISR+FSR. In general, y/x y / x, unless x is constant, which is generally the case only for a sufficiently narrow bin in x. o avoid biases in the ratio variables, the denominator must therefore also use,ave. his leads to the following definitions for balance and MPF in dijet events: R rel = + A, where (6.3) A R MPF rel A =, robe, tag 2, ave, and (6.4) = + B, where (6.5) B miss (, tag /, tag ) B =. (6.6) 2, ave With sufficiently fine binning in, ave, and by extraolating the additional jet activity, not coming from the leading jet, to zero with α =, 3rd jet /, ave, both variables R rel and RMPF rel reduce to R rel =, robe /, tag. Under the assumtion that, robe, tcl =, tag, tcl, which is true after correcting for the various small second-order biases from JER and ISR+FSR, this is equivalent to the ratio of the jet resonses for the tag and robe jets such that R rel = R jet, robe /R jet, tag. he residual η-deendent corrections are based on results obtained with the MPF method, the balance results are used as a crosscheck. As shown in figure 5, the relative η- and -deendent correction R rel,mc /R rel,data varies between 0.99 and.0 in the barrel at η <.3, between 0.99 and.06 at.3 < η < 2.9, and increases to.5 in HF. Some deendence is observed in the endcas relative to the barrel, with the residual corrections aroaching unity at high, where nonlinearities in calorimeter resonse are reduced. In the following we will review the corrections for ISR+FSR, JER, and jet deendence, as well as the associated uncertainties for the η-deendent corrections. Initial- and final-state radiation correction. For central-forward jet airs there is a higher robability for the ISR to be radiated oosite to the central jet, and the FSR activity may differ slightly for the jets at different η, which leads to some residual deendence of the measured value of the -balance or MPF resonse, R rel, on additional jet activity α. We evaluate this deendence in bins of η, for the linearly extraolated α 0 and α < 0.2 resectively, and comute the following data/simulation double ratio: k FSR (α = 0.2) = R data / rel (α 0) R rel data (α < 0.2) Rrel MC (α 0) Rrel MC. (6.7) (α < 0.2) he correction factor k FSR (we use the subscrit FSR instead of ISR+FSR for brevity) is determined searately for the MPF and -balance methods and for ythia 6.4 and herwig++ 2.3, as shown in figure 6, and is then arameterized versus η with the same functional form as in ref. [3]. he differences between ythia 6.4 and herwig for the -balance method are u to 6% at η < 5.2 rior to the alication of ISR+FSR corrections, as seen in figure 6 (left). Both agree well after the ISR+FSR correction, as shown in figure 6 (right), but the MPF method is much less sensitive to ISR and FSR biases than the -balance method, because the entire hadronic recoil is used for the MPF balance. 27

31 Relative correction (jet) 60 GeV 20 GeV 240 GeV 480 GeV 9.7 fb (8 ev) Anti-k R=0.5 PF+CHS η Figure 5. Relative energy scale correction for = 60, 20, 240 and 480 GeV as a function of η. he residual corrections increase toward high raidity and low, where effects from nonlinear calorimeter resonse become more imortant. he curves are limited to a jet energy E = cosh η = 4000 GeV (corresonding to η 2.8 for a jet with = 480 GeV) so as to show only the correction factors for reasonable in the considered data-taking eriod. he statistical uncertainty associated with a constant fit versus is shown for = 20 GeV (markers). Resolution correction. he MPF and -balance methods are both sensitive to the relative differences in JER between the jets. his bias is exected to cancel out for the data/mc ratio of R rel when the jets in the simulation are smeared to match the measured resolution in data using the relation: ( ),smeared = Gaussian µ =, σ = k 2 σ MC, (6.8) where k is the data/mc scale factor for JER determined in section 8 and σ MC is the JER in the MC simulation. he factor k varies between.05 and.40 deending on η. he jet is multilied by a random number drawn from a Gaussian distribution with mean µ = and width σ, such that the smeared jet has the same resolution kσ MC as the jets in data. he smearing is alied on a jet-by-jet basis to all jets in the event, such that the resolution correction is roagated to the -balance and MPF methods in a consistent way. Relative correction: deendence. he η-deendent corrections are studied in bins of average jet, where a slight deendence is observed. For this reason, the η-deendent corrections are arameterized with a log-linear -deendence, according to the formula 0 + log( ). he correction factor as a function of η, as obtained from the -deendent fit is shown in figure 7 (left), comared to the result from a constant fit. Here, the central value is obtained from evaluating the -deendent correction at the value for which the constant fit and the logarithmic fit agree,. he blue band is obtained by varying the at which the logarithmic fit is evaluated between 0.5 times and 2 times. he is tyically close to the mean of the dijet samles, and is shown in figure 7 (right). he -deendent fit is used as the central result over the whole η range, with the excetion of the HF ( η >3). For this region, to mitigate the effect of statistical fluctuations 28

32 k FSR PF+CHS MPF Pythia6 Pt Pythia6 MPF Herwig++ Pt Herwig fb (8 ev) Relative correction PF+CHS Uncertainty MPF (Pythia6) Pt (Pythia6) MPF (Herwig++) Pt (Herwig++) 9.7 fb (8 ev) 0.98 R=0.5 anti-k.05 R=0.5 anti-k 0.96 [] cosh( η ) fit: [0]+ +[2] cosh( η ) η Ratio to Pythia6 MPF Figure 6. he k FSR (α = 0.2) correction factor (defined in eq. (6.7)) lotted vs. η (left). his ratio is used for ISR+FSR corrections that are alied to dijet events with α < 0.2, for the MPF and - balance methods, and for ythia 6.4 tune Z2* and herwig tune EE3C. he oints are fitted with f (η) = 0 + cosh(η)/( + 2 cosh(η)) as in ref. [3]. Relative η corrections obtained with the MPF and balance methods and the ythia 6.4 tune Z2* and herwig tune EE3C MC generators (right). he results are shown after corrections for ISR+FSR, and comared to the central values, obtained with the MPF method and ythia 6.4 tune Z2* simulated events. Relative correction Anti-k R=0.5 PF+CHS fb (8 ev) η (GeV), ave PF+CHS jets bin edge bin center 9.7 fb (8 ev) R=0.5 anti-k η η Figure 7. Relative η correction factor at the crossover (defined as the value of where the log-linear and constant fits versus,ave agree) value, and at half and twice the values (left). he statistical uncertainty in the constant fit at each value of is also shown. Distribution of the and η bins used in the dijet balance measurement, with a oint at the average and η for each bin (right). he horizontal red lines indicate the crossover value for each bin. (visible e.g. in figure 7 (left)), the correction is taken from the constant fit and symmetrized over ositive and negative η values. 29

33 6.2 Relative correction uncertainties he largest uncertainties in the relative corrections arise from the following sources: ISR+FSR, 0.2%. he RelativeFSR uncertainty in k FSR is estimated by using herwig as data" and comaring how well the different methods reroduce the ratio of article-level simulated resonses. his uncertainty increases smoothly with increasing η, u to 0.2% in HF. Jet resolution,.4%. he RelativeJER systematic uncertainty on the JER correction is estimated by varying the data/mc scale factor k in eq. (6.8) within the uncertainties determined in section 8, which are between 2% and 20%, deending on η. his uncertainty mainly affects the η bins in the HF, where JER is oorly constrained from data. Relative correction deendence,.4%. Half of the difference between the log-linear and constant fits observed in figure 7 is taken as a RelativePt systematic uncertainty to account for uncertainties coming from the choice of the log-linear shae for the fit. his is the dominant uncertainty in the barrel and endcas. Statistical uncertainty, 0.9%. he number of events available in data for the η-deendent corrections is limited in the endca and HF regions due to the large rescales alied to the dijet triggers during data taking. o estimate the imact of this on hysics analyses, the corrections are symmetrized and determined in wide bins of η. he remaining statistical uncertainty of u to 2.5% is assigned as RelativeStat systematic uncertainty. ime deendence,.0%. he imeeta systematic uncertainty is estimated as the RMS of the η-deendent correction factors for a set of about ten data-taking eriods, chosen arbitrarily in order to have comarable integrated luminosities. he variation is assumed to come from residual scale shifts remaining after the radiation damage corrections have been alied to the ECAL and HCAL, and increases toward high raidities, which suffer larger radiation damage. Uncertainty correlations versus η. he RelativeJER, RelativePt, and RelativeStat systematic uncertainties are assumed to be correlated versus η within the barrel (BB: η <.3), the region of the endca that is within tracker coverage (EC:.3 < η < 2.5), the region of the endca which is outside the tracker coverage (EC2: 2.5 < η < 3), and within the hadron forward calorimeter (HF: 3 < η < 5.2), but not between these regions. he RelativeStat uncertainty is significant only in the more forward regions, and is only rovided for the two latter regions (EC2 and HF, which are considered uncorrelated). All other systematic uncertainties relevant for η-deendent corrections (RelativeFSR, imeeta) are considered to be fully correlated versus η. Each correlated region is treated with a searate systematic source, and these are rovided searately to the users. he systematic uncertainties in the relative η-deendent corrections are summarized in figure 8, for low (30 GeV) and medium (00 GeV) versus η, and for the outer endca (η = 2.7) versus. he time-deendent uncertainties are otional for analyses that are erformed on the full 202 data and are shown searately versus η at = 30 GeV. Among the time-deendent systematic uncertainties only the imeeta is relevant. he uncertainties are small at high and for central raidities within the tracker coverage. hey increase to 2.% at high raidity mainly 30

34 JEC uncertainty (%) R=0.5 PF+CHS η = 2.7 jet 9.7 fb (8 ev) SubotalRelative RelativePt RelativeJER RelativeFSR RelativeStat JEC uncertainty (%) R=0.5 PF+CHS = 30 GeV 9.7 fb (8 ev) SubotalRelative RelativePt RelativeJER RelativeFSR RelativeStat JEC uncertainty (%) (GeV) R=0.5 PF+CHS = 00 GeV 9.7 fb (8 ev) SubotalRelative RelativePt RelativeJER RelativeFSR RelativeStat η jet JEC uncertainty (%) R=0.5 PF+CHS = 30 GeV imeeta η jet 9.7 fb (8 ev) Figure 8. Systematic uncertainties for the relative η-deendent corrections as a function of jet (to left) and as a function of jet η for jets with = 30 GeV (to right) and for jets with = 00 GeV (bottom left). ime-deendent uncertainties as a function of jet η for jets with = 30 GeV (bottom right). he lots are limited to a jet energy E = cosh η = 4000 GeV so as to show only uncertainties for reasonable in the considered data-taking eriod. SubotalRelative is the quadratic sum of RelativePt, RelativeJER, RelativeFSR and RelativeStat. η jet due to the limited number of events available in the data for deriving the JEC, JER and ISR+FSR corrections. he dominant PileUPt uncertainty is inherently asymmetric and has the largest visible differences in the HF region, where the asymmetric log-linear fit is comared to a symmetrized constant fit used for central value in HF. he uncertainty versus changes sign around 00 GeV for the negative η side while it remains same-sign for the ositive η. 3

35 6.3 Absolute corrections he absolute JES at η <.3 is determined with Z( µµ)+jet, Z( ee)+jet and γ+jet events for jet between 30 and 800 GeV by comaring the reconstructed of the jet to that of a recisely measured object (the Z boson, or the hoton). he resonse for jets with > 800 GeV is constrained using multijet events, where a high- jet in the barrel region is balanced by a recoil system, comosed of two or more lower- jets. For all these analyses, the corrections are derived by comaring the jet energy resonse (with different methods) in data and simulation, using events in the central region, where jets are already corrected with the simulation-based corrections and η-deendent residual corrections. As detailed below, the resonse is observed to be slightly lower in data than in simulation. In addition, the ratio of data over the MC rediction of the resonse shows a deendence. he two effects are factorized and addressed in successive stes. First, a rough estimate of the indeendent correction is derived from the analysis of Z( µµ)+jet events. Second, the resonse and its deendence are determined recisely from a global fit (described in section 6.4), with the individual resonse values obtained from the different channels (Z( µµ)+jet, Z( ee)+jet, γ+jet, multijet) as inut. Methods. he absolute jet resonse is measured relative to a hoton or Z boson momentum scale, using the -balance (R jet, ) and MPF (R jet,mpf ) methods [3], as defined in eqs. (6.) and (6.2), with, ref =,γ/z. he measurements are affected by biases from ISR+FSR, underlying event (UE) and out-of-cone (OOC) showering. o correct for the FSR+ISR bias, we define a k FSR correction as follows: k FSR (α) = R jet(α 0), α =,2nd jet, (6.9) R jet (α),γ/z where the jet resonse R jet is measured with the MPF or the -balance method, with searate corrections for each. As shown in figure 9, the value of k FSR (α) is linearly deendent on α for 0.05 < α < 0.3. Because the average of the Z boson decreases with α, the article-level jet resonse obtained from simulation also shows a deendence on α. Figure 9 demonstrates that the MPF method is significantly less sensitive to ISR+FSR and the modeling of these rocesses, than the -balance method: the sloe R jet / α is about 0.3 for the -balance method and for the MPF method. For the data/mc ratio these sloes are further reduced by an order of magnitude, confirming a good modeling of the OOC and UE effects. It can be shown that the ratio of MPF and -balance sloes versus α is dr jet,mpf /dα dr jet, /dα = R FSR+ISR jets R jet. (6.0) he difference in jet resonse between the leading jet and the ISR+FSR jets is tyically less than 20%, as seen in figure 4, but the sign can be either ositive or negative. he sloe of k FSR has some deendence on the jet flavor (gluons radiate more than quarks) and it deends, e.g., on the arton shower model used in the MC simulation. As shown in section 6.4, determining k FSR in narrow bins of,ref is needed in order to study the deendence of the JES. 32

36 Jet resonse I 9.7 fb (8 ev) Data / MC MPF (Data) MPF (MC) balance (Data) balance (MC), jet /, tcl MPF balance Figure 9. Jet resonse obtained with the -balance and MPF methods in Z+jet events (oints), for both data and simulation (MadGrah 4+ythia 6.4 tune Z2*), lotted as a function of α =,2nd jet /,Z (to). he resonse in data is scaled by a factor of.02, constant as a function of. A fit to a first-order olynomial (dashed lines) is shown, together with the statistical uncertainty from the fit (shaded bands). Only events with,z > 30 GeV and η jet <.3 are considered. he ratio of the jet resonse from the -balance and MPF methods in data and simulation shown in the bottom anel. he simulated jet resonse,jet /, tcl is higher than unity because the jets are corrected with JEC from QCD dijet events with lower jet resonse than Z+jet events due to higher gluon fraction and larger underlying event. he remaining effects of UE and OOC affect MPF and balance slightly differently. It can be shown that, having corrected for ISR+FSR, the balancing and MPF resonses can be written as R jet, = R jet OOC, tcl + UE, tcl, (6.), tcl, tcl ( R jet,mpf = R jet R ) OOC OOC (, tcl + R ) UE UE, tcl, (6.2) R jet, tcl R jet, tcl α where, OOC tcl, UE, tcl are OOC and UE transverse momenta rojected to the reference object axis, and R OOC, R UE are their effective resonses. Comared to the balance, the residual biases for MPF are multilied by a factor that is tyically about 0% or less, and can be safely ignored. he corrections for OOC and UE comensate each other, but for jet radii R 0.5 the OOC effect is smaller than the one coming from the UE at low. We can therefore estimate an uer limit on these biases by assuming an UE energy density of about GeV er unit of jet area, which gives 33

37 µ I 8 ev MPF Simulation η < ,Z (GeV) RMS((Rtcl Rjet,MPF)/Rtcl) µ I 8 ev balance Simulation η < ,Z (GeV) Figure 20. Relative resolution (blue scale) in the lane of mean number of ileu events (µ) and Z boson transverse momentum (,Z ) for the MPF balance (left) and -balance methods (right). a correction of at most 2.6% for, tcl = 30 GeV and jet distance arameter R = 0.5. his is comatible with the magnitude and sign of the observed difference of less than 2% between MPF and balance at the α 0 limit in figure 9. Although the MPF and -balance methods are biased in different ways, both can be corrected for ISR+FSR and are comlementary to each other. he remaining biases from OOC and UE (both magnitude and resonse, see eqs. (6.) and (6.2)) affect the balance and MPF methods differently, and therefore fitting both simultaneously reduces the overall systematic uncertainty in the global fit. he relative statistical ower (quantified by the relative resolution of the measured resonse, comared to the article-level resonse) of balance and MPF deends on the jet and the level of PU, as seen in figure 20. he MPF method is sensitive to smearing in miss caused by PU, while the balance is sensitive to the smearing in the momentum balance caused by ISR+FSR. he former effect dominates at low, while the latter dominates at high, such that both methods have similar sensitivity at 00 GeV for µ = 20. Z+jet and γ+jet balance. he event selection is described in section 3.2. he JES is determined relative to recisely measured muons, electrons, and hotons, with a tracker scale uncertainty of 0.2% for muons at η < 2.4 [29], an ECAL scale uncertainty of 0.5% for electrons at η < 2.4 [48], and 0.2% for hotons at η <.3 [32]. he eak of the invariant-mass distribution of Z µµ(ee) events is used to validate the muon (electron) energy scale between data and simulation. hese are found to agree within 0.2% (0.5%). Additional checks ensure that the miss used in the MPF method is not biased by minimum-ionizing article deosits of muons in the calorimeters, or by residual leakage of electron and hoton energy into ECAL or HCAL not clustered in the reconstructed electron or hoton. As the hoton energy scale includes corrections for these unclustered contributions, secial care is taken in order to avoid double counting of the leakage energy from fully calibrated PF hoton suerclusters to miss (such double counting will be referred to as electromagnetic footrint effect) RMS((Rtcl Rjet, )/R tcl) 34