Determination of jet energy calibration and transverse momentum resolution in CMS This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2011 JINST 6 P11002 (http://iopscience.iop.org/1748-0221/6/11/P11002) Download details: IP Address: 200.145.174.189 The article was downloaded on 09/09/2013 at 15:13 Please note that terms and conditions apply. View the table of contents for this issue, or go to the journal homepage for more Home Search Collections Journals About Contact us My IOPscience http://iopscience.iop.org/page/terms http://iopscience.iop.org/1748-0221/6/11 http://iopscience.iop.org/1748-0221 http://iopscience.iop.org/ http://iopscience.iop.org/search http://iopscience.iop.org/collections http://iopscience.iop.org/journals http://iopscience.iop.org/page/aboutioppublishing http://iopscience.iop.org/contact http://iopscience.iop.org/myiopscience 2 0 1 1 J I N S T 6 P 1 1 0 0 2 PUBLISHED BY IOP PUBLISHING FOR SISSA RECEIVED: July 22, 2011 ACCEPTED: October 22, 2011 PUBLISHED: November 8, 2011 LHC REFERENCE VOLUME Determination of jet energy calibration and transverse momentum resolution in CMS The CMS collaboration E-mail: cms-publication-committee-chair@cern.ch ABSTRACT: Measurements of the jet energy calibration and transverse momentum resolution in CMS are presented, performed with a data sample collected in proton-proton collisions at a centre- of-mass energy of 7TeV, corresponding to an integrated luminosity of 36pb−1. The transverse momentum balance in dijet and γ/Z+jets events is used to measure the jet energy response in the CMS detector, as well as the transverse momentum resolution. The results are presented for three different methods to reconstruct jets: a calorimeter-based approach, the “Jet-Plus-Track” approach, which improves the measurement of calorimeter jets by exploiting the associated tracks, and the “Particle Flow” approach, which attempts to reconstruct individually each particle in the event, prior to the jet clustering, based on information from all relevant subdetectors. KEYWORDS: Si microstrip and pad detectors; Calorimeter methods; Detector modelling and sim- ulations I (interaction of radiation with matter, interaction of photons with matter, interaction of hadrons with matter, etc) ARXIV EPRINT: 1107.4277 c© 2011 CERN for the benefit of the CMS collaboration, published under license by IOP Publishing Ltd and SISSA. Content may be used under the terms of the Creative Commons Attribution-Non-Commercial-ShareAlike 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation and DOI. doi:10.1088/1748-0221/6/11/P11002 mailto:cms-publication-committee-chair@cern.ch http://arxiv.org/abs/1107.4277 http://dx.doi.org/10.1088/1748-0221/6/11/P11002 2 0 1 1 J I N S T 6 P 1 1 0 0 2 Contents 1 Introduction 1 2 The CMS detector 1 3 Jet reconstruction 2 4 Event samples and selection criteria 3 4.1 Zero bias and minimum bias samples 3 4.2 Dijet sample 4 4.3 γ+jets sample 4 4.4 Z(µ+µ−)+jets sample 4 4.5 Z(e+e−)+jets sample 5 5 Experimental techniques 5 5.1 Dijet pT -balancing 5 5.2 γ/Z+jet pT -balancing 6 5.3 Missing transverse energy projection fraction 7 5.4 Biases 7 5.4.1 Resolution bias 7 5.4.2 Radiation imbalance 8 6 Jet energy calibration 8 6.1 Overview of the calibration strategy 8 6.2 Offset correction 9 6.2.1 Jet area method 9 6.2.2 Average offset method 10 6.2.3 Hybrid jet area method 12 6.2.4 Offset uncertainty 13 6.3 Monte Carlo calibration 14 6.4 Relative jet energy scale 16 6.4.1 Measurement 16 6.4.2 Uncertainty 19 6.5 Absolute jet energy scale 19 6.5.1 Measurement 19 6.5.2 Uncertainty sources 23 6.5.3 Uncertainty 27 6.6 Combined jet energy correction 29 – i – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 7 Jet transverse momentum resolutions 30 7.1 Monte Carlo resolutions 31 7.2 Dijet measurements 32 7.3 γ + jet measurements 38 7.4 Measurement of jet resolution tails 43 7.4.1 Dijet asymmetry measurement 44 7.4.2 γ + jet measurement 45 8 Summary 46 The CMS collaboration 49 1 Introduction Jets are the experimental signatures of quarks and gluons produced in high-energy processes such as hard scattering of partons in proton-proton collisions. The detailed understanding of both the jet energy scale and of the transverse momentum resolution is of crucial importance for many physics analyses, and it is an important component of the systematic uncertainty. This paper presents studies for the determination of the energy scale and resolution of jets, performed with the Compact Muon Solenoid (CMS) at the CERN Large Hadron Collider (LHC), on proton-proton collisions at√ s = 7TeV, using a data sample corresponding to an integrated luminosity of 36pb−1. The paper is organized as follows: section 2 describes briefly the CMS detector, while sec- tion 3 describes the jet reconstruction methods considered here. Sections 4 and 5 present the data samples and the experimental techniques used for the various measurements. The jet energy cali- bration scheme is discussed in section 6 and the jet transverse momentum resolution is presented in section 7. 2 The CMS detector A detailed description of the CMS detector can be found elsewhere [1]. A right-handed coordinate system is used with the origin at the nominal interaction point (IP). The x-axis points to the center of the LHC ring, the y-axis is vertical and points upward, and the z-axis is parallel to the counterclock- wise beam direction. The azimuthal angle φ is measured with respect to the x-axis in the xy-plane and the polar angle θ is defined with respect to the z-axis, while the pseudorapidity is defined as η = − ln [tan(θ/2)]. The central feature of the CMS apparatus is a superconducting solenoid, of 6 m internal diameter, that produces a magnetic field of 3.8 T. Within the field volume are the silicon pixel and strip tracker and the barrel and endcap calorimeters (|η |< 3), composed of a crystal elec- tromagnetic calorimeter (ECAL) and a brass/scintillator hadronic calorimeter (HCAL). Outside the field volume, in the forward region (3 < |η |< 5), there is an iron/quartz-fibre hadronic calorimeter. The steel return yoke outside the solenoid is instrumented with gaseous detectors used to identify muons. The CMS experiment collects data using a two-level trigger system, the first-level hardware trigger (L1) [2] and the high-level software trigger (HLT) [3]. – 1 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 3 Jet reconstruction Jets considered in this paper are reconstructed using the anti-kT clustering algorithm [4] with a size parameter R = 0.5 in the y−φ space, implemented in the FastJet package [5, 6]. In some cases, jets with a size parameter R = 0.7 are also considered. The clustering is performed by four-momentum summation. The rapidity y and the transverse momentum pT of a jet with energy E and momentum ~p = (px, py, pz) are defined as y = 1 2 ln ( E+pz E−pz ) and pT = √ p2 x + p2 y respectively. The inputs to the clustering algorithm are the four-momentum vectors of detector energy deposits or of particles in the Monte Carlo (MC) simulations. Detector jets belong to three types, depending on the way the individual contributions from subdetectors are combined: Calorimeter jets, Jet-Plus-Track jets and Particle-Flow jets. Calorimeter (CALO) jets are reconstructed from energy deposits in the calorimeter towers. A calorimeter tower consists of one or more HCAL cells and the geometrically corresponding ECAL crystals. In the barrel region of the calorimeters, the unweighted sum of one single HCAL cell and 5x5 ECAL crystals form a projective calorimeter tower. The association between HCAL cells and ECAL crystals is more complex in the endcap regions. In the forward region, a different calori- meter technology is employed, using the Cerenkov light signals collected by short and long quartz readout fibers to aid the separation of electromagnetic and hadronic signals. A four-momentum is associated to each tower deposit above a certain threshold, assuming zero mass, and taking as a direction the tower position as seen from the interaction point. Jet-Plus-Track (JPT) jets are reconstructed calorimeter jets whose energy response and reso- lution are improved by incorporating tracking information, according to the Jet-Plus-Track algo- rithm [7]. Calorimeter jets are first reconstructed as described above, and then charged particle tracks are associated with each jet, based on the spatial separation between the jet axis and the track momentum vector, measured at the interaction vertex, in the η − φ space. The associated tracks are projected onto the front surface of the calorimeter and are classified as in-cone tracks if they point to within the jet cone around the jet axis on the calorimeter surface. The tracks that are bent out of the jet cone because of the CMS magnetic field are classified as out-of-cone tracks. The momenta of charged tracks are then used to improve the measurement of the energy of the associ- ated calorimeter jet: for in-cone tracks, the expected average energy deposition in the calorimeters is subtracted and the momentum of the tracks is added to the jet energy. For out-of-cone tracks the momentum is added directly to the jet energy. The Jet-Plus-Track algorithm corrects both the energy and the direction of the axis of the original calorimeter jet. The Particle-Flow (PF) jets are reconstructed by clustering the four-momentum vectors of particle-flow candidates. The particle-flow algorithm [8, 9] combines the information from all rele- vant CMS sub-detectors to identify and reconstruct all visible particles in the event, namely muons, electrons, photons, charged hadrons, and neutral hadrons. Charged hadrons, electrons and muons are reconstructed from tracks in the tracker. Photons and neutral hadrons are reconstructed from energy clusters separated from the extrapolated positions of tracks in ECAL and HCAL, respec- tively. A neutral particle overlapping with charged particles in the calorimeters is identified as a calorimeter energy excess with respect to the sum of the associated track momenta. The energy of photons is directly obtained from the ECAL measurement, corrected for zero-suppression effects. The energy of electrons is determined from a combination of the track momentum at the main in- – 2 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 teraction vertex, the corresponding ECAL cluster energy, and the energy sum of all bremsstrahlung photons associated with the track. The energy of muons is obtained from the corresponding track momentum. The energy of charged hadrons is determined from a combination of the track momen- tum and the corresponding ECAL and HCAL energy, corrected for zero-suppression effects, and calibrated for the non-linear response of the calorimeters. Finally, the energy of neutral hadrons is obtained from the corresponding calibrated ECAL and HCAL energy. The PF jet momentum and spatial resolutions are greatly improved with respect to calorimeter jets, as the use of the track- ing detectors and of the high granularity of ECAL allows resolution and measurement of charged hadrons and photons inside a jet, which together constitute ∼85% of the jet energy. The Monte Carlo particle jets are reconstructed by clustering the four-momentum vectors of all stable (cτ > 1 cm) particles generated in the simulation. In particular, there are two types of MC particle jets: those where the neutrinos are excluded from the clustering, and those where both the neutrinos and the muons are excluded. The former are used for the study of the PF and JPT jet response in the simulation, while the latter are used for the study of the CALO jet response (because muons are minimum ionizing particles and therefore do not contribute appreciably to the CALO jet reconstruction). The Particle-Flow missing transverse energy (~/ET ), which is needed for the absolute jet energy response measurement, is reconstructed from the particle-flow candidates and is defined as ~/ET = −∑ i (Ei sinθi cosφix̂+Ei sinθi sinφiŷ) = /Exx̂+ /Eyŷ, where the sum refers to all candidates and x̂, ŷ are the unit vectors in the direction of the x and y axes. 4 Event samples and selection criteria In this section, the data samples used for the various measurements are defined. In all samples described below, basic common event preselection criteria are applied in order to ensure that the triggered events do come from real proton-proton interactions. First, the presence of at least one well-reconstructed primary vertex (PV) is required, with at least four tracks considered in the vertex fit, and with |z(PV)| < 24cm, where z(PV) represents the position of the proton-proton collision along the beams. In addition, the radial position of the primary vertex, ρ(PV), has to satisfy the condition ρ(PV) < 2cm. Jet quality criteria (“Jet ID”) have been developed for CALO jets [10] and PF jets [11], which are found to retain the vast majority (> 99%) of genuine jets in the simulation, while rejecting most of the misidentified jets arising from calorimeter and/or readout electronics noise in pure noise non- collision data samples: such as cosmic-ray trigger data or data from triggers on empty bunches during LHC operation. Jets used in the analysis are required to satisfy proper identification criteria. 4.1 Zero bias and minimum bias samples The zero bias and minimum bias samples are used for the measurement of the energy clustered inside a jet due to noise and additional proton-proton collisions in the same bunch crossing (pile- up, or PU), as described in section 6.2. The zero bias sample is collected using a random trigger in the presence of a beam crossing. The minimum bias sample is collected by requiring coincidental hits in the beam scintillating counter [3] on either side of the CMS detector. – 3 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 4.2 Dijet sample The dijet sample is composed of events with at least two reconstructed jets in the final state and is used for the measurement of the relative jet energy scale and of the jet pT resolution. This sample is collected using dedicated high-level triggers which accept the events based on the value of the average uncorrected pT (pT not corrected for the non-uniform response of the calorimeter) of the two CALO jets with the highest pT (leading jets) in the event. The selected dijet sample covers the average jet pT range from 15GeV up to around 1TeV. 4.3 γ+jets sample The γ+jets sample is used for the measurement of the absolute jet energy response and of the jet pT resolution. This sample is collected with single-photon triggers that accept an event if at least one reconstructed photon has pT > 15GeV. Offline, photons are required to have transverse mo- mentum pγ T > 15GeV and |η | < 1.3. The jets used in the γ+jets sample are required to lie in the |η | < 1.3 region. The γ+jets sample is dominated by dijet background, where a jet mimics the photon. To suppress this background, the following additional photon isolation and shower-shape requirements [12] are applied: • HCAL isolation: the energy deposited in the HCAL within a cone of radius R = 0.4 in the η −φ space, around the photon direction, must be smaller than 2.4GeV or less than 5% of the photon energy (Eγ ); • ECAL isolation: the energy deposited in the ECAL within a cone of radius R = 0.4 in the η −φ space, around the photon direction, excluding the energy associated with the photon, must be smaller than 3GeV or less than 5% of the photon energy; • Tracker isolation: the number of tracks in a cone of radius R = 0.35 in the η − φ space, around the photon direction, must be less than three, and the total transverse momentum of the tracks must be less than 10% of the photon transverse momentum; • Shower shape: the photon cluster major and minor must be in the range of 0.15-0.35, and 0.15-0.3, respectively. Cluster major and minor are defined as second moments of the energy distribution along the direction of the maximum and minimum spread of the ECAL cluster in the η−φ space; The selected γ+jets sample covers the pγ T range from 15GeV up to around 400GeV. 4.4 Z(µ+µ−)+jets sample The Z(µ+µ−)+jets sample is used for the measurement of the absolute jet energy response. It is collected using single-muon triggers with various pT thresholds. Offline, the events are required to have at least two opposite-sign reconstructed global muons with pT > 15GeV and |ηµ |< 2.3 and at least one jet with |η |< 1.3. A global muon is reconstructed by a combined fit to the muon system hits and tracker hits, seeded by a track found in the muon systems only. The reconstructed muons must satisfy identification and isolation requirements, as described in ref. [13]. Furthermore, the invariant mass Mµµ of the two muons must satisfy the condition 70 < Mµµ < 110GeV. Finally, the – 4 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 reconstructed Z is required to be back-to-back in the transverse plane with respect to the jet with the highest pT : |∆φ(Z, jet)|> 2.8rad. 4.5 Z(e+e−)+jets sample The Z(e+e−)+jets sample is used for the measurement of the absolute jet energy response. It is collected using single-electron triggers with various pT thresholds. Offline, the events are required to have at least two opposite-sign reconstructed electrons with pT > 20GeV in the fiducial region |η | < 1.44 and 1.57 < |η | < 2.5 and at least one jet with |η | < 1.3. The reconstructed electrons must satisfy identification and isolation requirements, as described in ref. [13]. Furthermore, the invariant mass Mee of the electron-positron pair must satisfy the condition 85 < Mee < 100GeV. Finally, the reconstructed Z is required to be back-to-back in the transverse plane with respect to the jet with the highest pT : |∆φ(Z, jet)|> 2.7rad. 5 Experimental techniques 5.1 Dijet pT -balancing The dijet pT -balancing method is used for the measurement of the relative jet energy response as a function of η . It is also used for the measurement of the jet pT resolution. The technique was intro- duced at the CERN pp̄ collider (SPP̄S) [14] and later refined by the Tevatron experiments [15, 16]. The method is based on transverse momentum conservation and utilizes the pT -balance in dijet events, back-to-back in azimuth. For the measurement of the relative jet energy response, one jet (barrel jet) is required to lie in the central region of the detector (|η |< 1.3) and the other jet (probe jet) at arbitrary η . The central region is chosen as a reference because of the uniformity of the detector, the small variation of the jet energy response, and because it provides the highest jet pT -reach. It is also the easiest region to calibrate in absolute terms, using γ+jet and Z+jet events. The dijet calibration sample is collected as described in section 4.2. Offline, events are required to contain at least two jets. The two leading jets in the event must be azimuthally separated by ∆φ > 2.7rad, and one of them must lie in the |η |< 1.3 region. The balance quantity B is defined as: B = pprobe T − pbarrel T pave T , (5.1) where pave T is the average pT of the two leading jets: pave T = pbarrel T + pprobe T 2 . (5.2) The balance is recorded in bins of ηprobe and pave T . In order to avoid a trigger bias, each pave T bin is populated by events satisfying the conditions of the fully efficient trigger with the highest threshold. The average value of the B distribution, 〈B〉, in a given ηprobe and pave T bin, is used to deter- mine the relative response Rrel: Rrel(ηprobe, pave T ) = 2+ 〈B〉 2−〈B〉 . (5.3) – 5 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 The variable Rrel defined above is mathematically equivalent to 〈pprobe T 〉/〈pbarrel T 〉 for narrow bins of pave T . The choice of pave T minimizes the resolution-bias effect (as opposed to binning in pbarrel T , which leads to maximum bias) as discussed in section 5.4.1 below. A slightly modified version of the dijet pT -balance method is applied for the measurement of the jet pT resolution. The use of dijet events for the measurement of the jet pT resolution was in- troduced by the D0 experiment at the Tevatron [17] while a feasibility study at CMS was presented using simulated events [18]. In events with at least two jets, the asymmetry variable A is defined as: A = pJet1 T − pJet2 T pJet1 T + pJet2 T , (5.4) where pJet1 T and pJet2 T refer to the randomly ordered transverse momenta of the two leading jets. The variance of the asymmetry variable σA can be formally expressed as: σ 2 A = ∣∣∣∣ ∂A ∂ pJet1 T ∣∣∣∣2 ·σ2(pJet1 T )+ ∣∣∣∣ ∂A ∂ pJet2 T ∣∣∣∣2 ·σ2(pJet2 T ). (5.5) If the two jets lie in the same η region, pT ≡ 〈pJet1 T 〉= 〈pJet2 T 〉 and σ(pT )≡σ(pJet1 T ) = σ(pJet2 T ). The fractional jet pT resolution is calculated to be: σ(pT ) pT = √ 2σA . (5.6) The fractional jet pT resolution in the above expression is an estimator of the true resolution, in the limiting case of no extra jet activity in the event that spoil the pT balance of the two leading jets. The distribution of the variable A is recorded in bins of the average pT of the two leading jets, pave T = ( pJet1 T + pJet2 T ) /2, and its variance is proportional to the relative jet pT resolution, as described above. 5.2 γ/Z+jet pT -balancing The γ/Z+jet pT -balancing method is used for the measurement of the jet energy response and the jet pT resolution with respect to a reference object, which can be a γ or a Z boson. The pT resolution of the reference object is typically much better than the jet resolution and the absolute response Rabs is expressed as: Rabs = pjet T pγ,Z T . (5.7) The absolute response variable is recorded in bins of pγ,Z T . It should be noted that, because of the much worse jet pT resolution, compared to the γ or Z pT resolution, the method is not affected by the resolution bias effect (see section 5.4.1), as it happens in the dijet pT -balancing method. Also, for the same reason, the absolute response can be defined as above, without the need of more complicated observables, such as the balance B or the asymmetry A . – 6 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 5.3 Missing transverse energy projection fraction The missing transverse energy projection fraction (MPF) method (extensively used at the Teva- tron [15]) is based on the fact that the γ,Z+jets events have no intrinsic~/ET and that, at parton level, the γ or Z is perfectly balanced by the hadronic recoil in the transverse plane: ~pT γ,Z + ~pT recoil = 0. (5.8) For reconstructed objects, this equation can be re-written as: Rγ,Z ~pT γ,Z +Rrecoil ~pT recoil =−~/ET , (5.9) where Rγ,Z and Rrecoil are the detector responses to the γ or Z and the hadronic recoil, respectively. Solving the two above equations for Rrecoil gives: Rrecoil = Rγ,Z + ~/ET · ~pT γ,Z (pγ,Z T )2 ≡ RMPF . (5.10) This equation forms the definition of the MPF response RMPF . The additional step needed is to extract the jet energy response from the measured MPF response. In general, the recoil consists of additional jets, beyond the leading one, soft particles and unclustered energy. The relation Rlead jet = Rrecoil holds to a good approximation if the particles, that are not clustered into the leading jet, have a response similar to the ones inside the jet, or if these particles are in a direction perpendicular to the photon axis. Small response differences are irrelevant if most of the recoil is clustered into the leading jet. This is ensured by vetoing secondary jets in the selected back-to-back γ,Z+jets events. The MPF method is less sensitive to various systematic biases compared to the γ,Z pT - balancing method and is used in CMS as the main method to measure the jet energy response, while the γ,Z pT -balancing is used to facilitate a better understanding of various systematic uncer- tainties and to perform cross-checks. 5.4 Biases All the methods based on data are affected by inherent biases related to detector effects (e.g. pT resolution) and to the physics properties (e.g. steeply falling jet pT spectrum). In this section, the two most important biases related to the jet energy scale and to the pT resolution measurements are discussed: the resolution bias and the radiation imbalance. 5.4.1 Resolution bias The measurement of the jet energy response is always performed by comparison to a reference ob- ject. Typically, the object with the best resolution is chosen as a reference object, as in the γ/Z+jet balancing where the γ and the Z objects have much better pT resolution than the jets. However, in other cases, such as the dijet pT -balancing, the two objects have comparable resolutions. When such a situation occurs, the measured relative response is biased in favor of the object with the worse resolution. This happens because a reconstructed jet pT bin is populated not only by jets whose true (particle-level) pT lies in the same bin, but also from jets outside the bin, whose re- sponse has fluctuated high or low. If the jet spectrum is flat, for a given bin the numbers of true – 7 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 jets migrating in and out are equal and no bias is observed. In the presence of a steeply falling spectrum, the number of incoming jets with lower true pT that fluctuated high is larger and the measured response is systematically higher. In the dijet pT -balancing, the effect described above affects both jets. In order to reduce the resolution bias, the measurement of the relative response is performed in bins of pave T , so that if the two jets have the same resolution, the bias is cancelled on average. This is true for the resolution measurement with the asymmetry method where both jets lie in the same η region. For the relative response measurement, the two jets lie in general in different η regions, and the bias cancellation is only partial. 5.4.2 Radiation imbalance The other source of bias is the pT -imbalance caused by gluon radiation. In general, the mea- sured pT -imbalance is caused by the response difference of the balancing objects, but also from any additional objects with significant pT . The effect can by demonstrated as follows: an esti- mator Rmeas of the response of an object with respect to a reference object, is Rmeas = pT /pref T where pT and pref T are the measured transverse momenta of the objects. These are related to the true pT (ptrue T,re f ) through the true response: pT = Rtrue · ptrue T and pref T = Rtrue ref · ptrue T,re f . In the presence of additional hard objects in the event, ptrue T = ptrue T,re f −∆pT , where ∆pT quantifies the imbalance due to radiation. By combining all the above, the estimator Rmeas is expressed as: Rmeas = Rtrue/Rtrue ref ( 1−∆pT /ptrue T,re f ) . This relation indicates that the pT -ratio between two recon- structed objects is a good estimator of the relative response, only in the case where the additional objects are soft, such that ∆pT /ptrue T,re f → 0. The above considerations are important for all pT -balancing measurements presented in this paper (the dijet pT -balancing and the γ/Z+jet pT -balancing), both for the scale and the resolution determination. Practically, the measurements are performed with a varying veto on an estimator of atrue = ∆pT /ptrue T,re f and then extrapolated linearly to atrue = 0. For the dijet pT -balancing, the estimator of atrue is the ratio pJet3 T /pave T , while for the γ,Z+jet pT -balancing it is the ratio pJet2 T /pγ,Z T . 6 Jet energy calibration 6.1 Overview of the calibration strategy The purpose of the jet energy calibration is to relate, on average, the energy measured for the detector jet to the energy of the corresponding true particle jet. A true particle jet results from the clustering (with the same clustering algorithm applied to detector jets) of all stable particles originating from the fragmenting parton, as well as of the particles from the underlying event (UE) activity. The correction is applied as a multiplicative factor C to each component of the raw jet four-momentum vector praw µ (components are indexed by µ in the following): pcor µ = C · praw µ . (6.1) The correction factor C is composed of the offset correction Coffset, the MC calibration factor CMC, and the residual calibrations Crel and Cabs for the relative and absolute energy scales, re- spectively. The offset correction removes the extra energy due to noise and pile-up, and the MC correction removes the bulk of the non-uniformity in η and the non-linearity in pT . Finally, the – 8 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 residual corrections account for the small differences between data and simulation. The various components are applied in sequence as described by the equation below: C = Coffset(praw T ) ·CMC(p′T ,η) ·Crel(η) ·Cabs(p′′T ), (6.2) where p′T is the transverse momentum of the jet after applying the offset correction and p′′T is the pT of the jet after all previous corrections. In the following sections, each component of the jet energy calibration will be discussed separately. 6.2 Offset correction The offset correction is the first step in the chain of the factorized corrections. Its purpose is to estimate and subtract the energy not associated with the high-pT scattering. The excess energy includes contributions from electronics noise and pile-up. In CMS, three approaches are followed for the offset correction: the jet area, the average offset and the hybrid jet area methods. 6.2.1 Jet area method Recent developments in the jet reconstruction algorithms have allowed a novel approach for the treatment of pile-up [19, 20]: for each event, an average pT -density ρ per unit area is estimated, which characterizes the soft jet activity and is a combination of the underlying event, the electron- ics noise, and the pile-up. The two latter components contaminate the hard jet energy measurement and need to be corrected for with the offset correction. The key element for this approach is the jet area A j. A very large number of infinitely soft four-momentum vectors (soft enough not to change the properties of the true jets) are artificially added in the event and clustered by the jet algorithm together with the true jet components. The extent of the region in the y−φ space occupied by the soft particles clustered in each jet defines the active jet area. The other important quantity for the pile-up subtraction is the pT density ρ , which is calculated with the kT jet clustering algorithm [21–23] with a distance parameter R = 0.6. The kT algorithm naturally clusters a large number of soft jets in each event, which effectively cover the entire y−φ space, and can be used to estimate an average pT -density. The quantity ρ is defined on an event-by-event basis as the median of the distribution of the variable pT j/A j, where j runs over all jets in the event across full detector acceptance (|η |< 5), and is not sensitive to the presence of hard jets. At the detector level, the measured density ρ is the convolution of the true particle-level activity (underlying event, pile-up) with the detector response to the various particle types. Based on the knowledge of the jet area and the event density ρ , an event-by-event and jet-by-jet pile-up correction factor can be defined: Carea(praw T ,A j,ρ) = 1− (ρ−〈ρUE〉) ·A j praw T . (6.3) In the formula above, 〈ρUE〉 is the pT -density component due to the UE and electronics noise, and is measured in events with exactly one reconstructed primary vertex (no pile-up). Figure 1 shows the PF pT -density ρ , as a function of the leading jet pT in QCD events and for various pile- up conditions. The fact that ρ does not depend on the hard scale of the event confirms that it is really a measure of the soft jet activity. Finally, the density ρ shows linear scaling properties with respect to the amount of pile-up. – 9 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 [GeV] T jet p 100 200 300 [G eV /A ] ρ 0 1 2 3 4 5 1.081 1.618 2.157 2.673 0.00058 GeV±UE: 1.08 0.00052 GeV/PU±PU: 0.534 =1PVN =2PVN =3PVN =4PVN =7 TeVs-1, L=36 pbCMS QCD (PFJets) Figure 1. Pile-up and underlying event PF pT -density ρ , as a function of the leading jet pT in the QCD multijet sample for various pile-up conditions (here NPV denotes the number of reconstructed vertices, and A denotes the unit area in the y−φ space). 6.2.2 Average offset method The average offset method attempts to measure the average energy due to noise and pile-up, clus- tered inside the jet area, in addition to the energy associated with the jet shower itself. The measure- ment of the noise contribution is made in zero bias events by vetoing those that pass the minimum bias trigger. In the remaining events, the energy inside a cone of radius R = 0.5 in the η−φ space is summed. The measurement is performed in cones centered at a specific η bin and averaged across φ . The noise contribution is found to be less than 250MeV in pT , over the entire η range. The total average offset (over the entire dataset) is determined from inclusive zero bias events (with no veto on minimum bias triggers) and is classified according to the number of reconstructed vertices. Figure 2 shows the average offset pT as a function of η and for different pile-up conditions. The calorimetric offset pT shows strong variations as a function of η , which follow the non-uniform particle response in the calorimeter, while for PF candidates, the offset pT is more uniform ver- sus η . The higher measured offset pT for the PF-candidates is due to the much higher response with respect to the pure calorimetric objects. The observed η-asymmetry is related to calorimeter instrumental effects. For the highest number of vertices, in particular, the asymmetry is also of statistical nature (the adjacent points are highly correlated because at a given η a large fraction of the energy in a cone of R = 0.5 also ends up in overlapping cones). Figure 3 shows the breakdown, in terms of PF candidates, of the average offset pT in events with one PU interaction, as measured in the data and compared to the MC prediction. The slight asymmetry observed in the MC is due to the asymmetric noise description in the specific version of the simulation. The average offset in pT scales linearly with the number of reconstructed primary vertices, as shown in figure 4. The linear scaling allows the expression of the jet offset correction as follows: Coffset(η , praw T ,NPV) = 1− (NPV−1) ·O(η) praw T , (6.4) – 10 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 η -5 -4 -3 -2 -1 0 1 2 3 4 5 > , G eV T ,o ffs et < p 0 1 2 3 4 5 6 7 8 = 1PV N = 2PV N = 3PV N = 4PV N = 5PV N = 6PV N = 7PV N = 8PV N -1CMS, L = 36 pb Calojets η -5 -4 -3 -2 -1 0 1 2 3 4 5 > , G eV T ,o ffs et < p 0 1 2 3 4 5 6 7 8 = 1PV N = 2PV N = 3PV N = 4PV N = 5PV N = 6PV N = 7PV N = 8PV N -1CMS, L = 36 pb PFlow Jets Figure 2. Average offset in pT , as a function of η , measured in minimum bias events for different pile-up conditions (categorized according to the number NPV of reconstructed primary vertices). Left: CALO jets. Right: PF jets. η -5 -4 -3 -2 -1 0 1 2 3 4 5 , G eV 〉 T ,o ffs et p〈 0 0.2 0.4 0.6 0.8 1 1.2 photons em deposits e+mu neutral hadrons hadronic deposits charged hadrons Minimum Bias - Noise =1〉PU〈 Markers: Data, Histograms: MC -1CMS, L = 36 pb = 7 TeVs η -5 -4 -3 -2 -1 0 1 2 3 4 5 , G eV 〉 T ,o ffs et p〈 0 0.2 0.4 0.6 0.8 1 1.2 Figure 3. Breakdown of the average offset pT , in terms of the PF candidates, as a function of η , for events with one PU interaction. Data are shown by markers and MC is shown as filled histograms. where O(η) is the slope of the average offset pT per number of vertices as a function of η , praw T is the pT of the uncorrected jet, and NPV is the number of reconstructed primary vertices. The average offset method can be applied to jet algorithms that produce circular jets, while the quantity O(η) scales to larger cone sizes in proportion to the jet area. It should be noted that, in both the average offset subtraction and in the jet area method, the noise contribution and the UE are not subtracted. Because of the good description of the noise contribution in the simulation, the noise is taken into account with the MC-based correction. – 11 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 1 2 3 4 5 6 7 8 9 P F A K 5 pT p ile -u p (G eV ) 0 1 2 3 4 5 6 7 Average Offset Jet Area Hybrid Jet Area PV0.53 GeV/N PV0.54 GeV/N PV0.52 GeV/N |<0.5η| 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 PV0.45 GeV/N PV0.53 GeV/N PV0.43 GeV/N |<2.0η|≤1.5 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 PV0.51 GeV/N PV0.54 GeV/N PV0.50 GeV/N |<1.0η|≤0.5 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 PV0.41 GeV/N PV0.54 GeV/N PV0.41 GeV/N |<2.5η|≤2.0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 PV0.49 GeV/N PV0.53 GeV/N PV0.47 GeV/N |<1.5η|≤1.0 Number of Primary Vertices 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 PV0.50 GeV/N PV0.54 GeV/N PV0.49 GeV/N |<3.0η|≤2.5 = 7 TeVs-1CMS, L = 36 pb Figure 4. Average PF jet pile-up pT , as a function of the number of reconstructed vertices (NPV) for the jet area, the average offset, and the hybrid jet area methods in 6 different η regions. In the y-axis title, PFAK5 denotes the PF jets reconstructed with the anti-kT algorithm with distance parameter R = 0.5. 6.2.3 Hybrid jet area method The measurement of the average offset presented in the previous paragraph confirms the η- dependence of the offset energy. This is explained by the fact that the measured offset is the convolution of the pile-up activity with the detector response. In order to take into account the η-dependence, a hybrid jet area method is employed: Chybrid(praw T ,η ,A j,ρ) = 1− (ρ−〈ρUE〉) ·β (η) ·A j praw T . (6.5) In eq. (6.5), the pT density ρ and the corresponding density due to the UE, 〈ρUE〉 are constants over the entire η range. The multiplicative factor β (η) corrects for the non-uniformity of the energy response and is calculated from the modulation of the average offset in pT (figure 2): β (η) = O(η) 〈O〉η , (6.6) where O(η) is the slope of the average offset pT per number of vertices, as a function of η (as in equation 6.4), and 〈O〉η is the average, across η , of this slope. In the case of PF jets, the response variation versus η is relatively small and the hybrid jet area method is found to be in excellent agreement with the average offset method. Figure 4 shows the average offset in pT as a function of the number of reconstructed primary vertices, for the three dif- ferent methods (jet area, average offset, hybrid jet area). It can be seen that the differences between – 12 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 (GeV) T p 20 100 200 1000 U nc er ta in ty fr om O ffs et [% ] Tp 0 1 2 3 4 5 6 7 8 9 10 =1 (UE)PVN =2 (UE + 1 PU)PVN =3 (UE + 2 PU)PVN =4 (UE + 3 PU)PVN 0.5 CALOTAnti-k = 7 TeVs-1CMS, L = 36 pb (GeV) T p 20 100 200 1000 U nc er ta in ty fr om O ffs et [% ] Tp 0 1 2 3 4 5 6 7 8 9 10 (GeV) T p 20 100 200 1000 U nc er ta in ty fr om O ffs et [% ] Tp 0 1 2 3 4 5 6 7 8 9 10 =1 (UE)PVN =2 (UE + 1 PU)PVN =3 (UE + 2 PU)PVN =4 (UE + 3 PU)PVN 0.5 PFTAnti-k = 7 TeVs-1CMS, L = 36 pb (GeV) T p 20 100 200 1000 U nc er ta in ty fr om O ffs et [% ] Tp 0 1 2 3 4 5 6 7 8 9 10 Figure 5. Offset jet-energy-correction uncertainty as a function of jet pT . Left: CALO jets. Right: PF jets. the jet area method and the average offset method are entirely due to the response dependence on η . The hybrid jet area method is chosen for the pile-up correction of PF jets. In the case of CALO jets, and also JPT jets (initially reconstructed as CALO jets), the average offset method is the one chosen for the pile-up correction. The ρ energy density calculation used in the jet area methods relies on the assumption that the median energy density is a good approxi- mation of the mean energy density, excluding hard contributions from jets. This is a reasonable as- sumption when the PU energy density is approximately Gaussian (e.g. at the high-PU limit, or when including tracks, as it happens in the PF reconstruction) and when the energy density is relatively flat versus η . For CALO jets, neither of these assumptions is valid: the offset energy density is non- Gaussian for the low-PU conditions studied in this paper due to the magnetic field and zero suppres- sion, effectively removing PU-particles of pT < 1GeV, while the CALO jet response has a strong η dependence. Therefore, the traditional average offset method is more suitable for CALO jets. 6.2.4 Offset uncertainty The uncertainty of the offset correction is quantified using the jet area method. Specifically, the quantities ρ and 〈ρUE〉 in eq. (6.3) are varied independently and the resulting shifts are added in quadrature. The event pT -density ρ uncertainty is estimated as 0.2GeV per unit jet area and per pile-up event. This uncertainty is based on the maximum slope difference between the jet area and the average offset methods, and the residual non-closure in the average offset method. The UE pT -density 〈ρUE〉 uncertainty is estimated as 0.15GeV per unit jet area, based on the differences observed between the QCD multijet and Z+jets samples, and on the effective difference when applied in the inclusive jet cross-section measurement. Figure 5 shows the uncertainty of the offset correction, as a function of jet pT and the number of primary vertices. – 13 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 6.3 Monte Carlo calibration The MC calibration is based on the simulation and corrects the energy of the reconstructed jets such that it is equal on average to the energy of the generated MC particle jets. Simulated QCD events are generated with PYTHIA6.4.22 [24], tune Z2 (the Z2 tune is identical to the Z1 tune described in [25] except that Z2 uses the CTEQ6L PDF, while Z1 uses CTEQ5L) and processed through the CMS detector simulation, based on GEANT4 [26]. The jet reconstruction is identical to the one applied to the data. Each reconstructed jet is spatially matched in the η−φ space with a MC particle jet by requiring ∆R < 0.25. In each bin of the MC particle transverse momentum pgen T , the response variable R = preco T /pgen T and the detector jet preco T are recorded. The average correction in each bin is defined as the inverse of the average response CMC(preco T ) = 1 , and is expressed as a function of the average detector jet pT < preco T >. Figure 6 shows the MC jet energy correction factor for the three jet types, vs. η , for different corrected jet pT values. Figure 7 shows the average correction in |η |< 1.3, as a function of the corrected jet pT . Calorimeter jets require a large correction factor due to the non-linear response of the CMS calorimeters. The structures observed at |η | ∼ 1.3 are due to the barrel-endcap boundary and to the tracker material budget, which is maximum in this region. The fast drop observed in the endcap region 1.3 < |η |< 3.0 is due to the fact that the jet energy response depends on energy rather than on jet pT . For higher values of |η | more energy corresponds to a fixed pT value E ≈ pT · cosh(η), which means that the jet response is higher and the required correction factor is smaller. The structure observed at |η | ∼ 3.0 coincides with the boundary between the endcap and the forward calorimeters. Finally, in the region |η |> 4.0, the jet energy response is lower because parts of the jets pointing toward this region extend beyond the forward calorimeter acceptance. The track-based jet types (JPT and PF) require much smaller correction factors because the charged component of the jet shower is measured accurately in the CMS tracker which extends up to |η | = 2.4. The fast rise of the correction factor for JPT jets in the region 2.0 < |η | < 2.5 is explained by the fact that part of the jets lying in this region extends beyond the tracker coverage. For PF jets, the transition beyond the tracker acceptance is smoother because the PF candidates, which are input to the clustering of PF jets, are individually calibrated prior to the clustering. While both PF jets and JPT jets exploit the tracker measurements, the JPT jets require lower correction in the region |η |< 2.0 because the tracker inefficiency is explicitly corrected for by the JPT algorithm. In the forward region (|η |> 3.0) all three jet types converge to simple calorimetric objects and therefore require almost identical corrections. The default MC calibration is derived from the QCD sample and corresponds to a jet flavour composition enriched in low-pT gluon jets. The jet energy response and resolution depend on the fragmentation properties of the initial parton: gluons and heavy-flavour quarks tend to produce more particles with a softer energy spectrum than light quarks. The investigation of the jet energy response of the various flavour types, for the different jet reconstruction techniques, is done with MC matching between the generated particle jet and the reconstructed jet. For each MC particle jet, the corresponding parton is found by spatial matching in the η −φ space. Figure 8 shows the response of each flavour type (gluon, b-quark, c-quark, uds-quark), as predicted by PYTHIA6 (Z2 tune), in the region |η | < 1.3, normalized to the average response in the QCD flavour mixture. The QCD flavour composition varies significantly with jet pT , being dominated by gluon jets at – 14 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 ηJet -4 -2 0 2 4 Je t E ne rg y C or re ct io n F ac to r 1 1.5 2 2.5 CALO jets JPT jets PF jets R = 0.5Tanti-k = 50 GeV T p = 7 TeVsCMS Simulation ηJet -2 0 2 Je t E ne rg y C or re ct io n F ac to r 0.8 1 1.2 1.4 1.6 1.8 CALO jets JPT jets PF jets R = 0.5Tanti-k = 200 GeV T p = 7 TeVsCMS Simulation Figure 6. Monte Carlo jet-energy-correction factors for the different jet types, as a function of jet η . Left: correction factor required to get a corrected jet pT = 50GeV. Right: correction factor required to get a corrected jet pT = 200GeV. (GeV) T Jet p 10 20 30 100 200 1000 Je t E ne rg y C or re ct io n F ac to r 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 CALO jets JPT jets PF jets R = 0.5Tanti-k | < 1.3η| = 7 TeVsCMS Simulation Figure 7. Monte Carlo jet-energy-correction factors for the different jet types, as a function of jet pT . low pT and by quark jets at high pT . Calorimeter jets show strong dependence on the flavour type with differences up to 10%. This is attributed to the non-linear single-particle response in the calorimeters. For the track-based reconstructed jets, the flavour dependence is significantly reduced and not larger than 5% and 3% for JPT and PF jets respectively. The ability to measure precisely the charged particle momenta in the tracker reduces the contribution of calorimetry at low jet pT . In all jet types, the jets originated from a light quark (u/d/s) have a systematically higher response than those from the other flavours, which is attributed to the harder spectrum of the particles that are produced in the fragmentation process. For comparison, figure 9 shows the flavour dependent response ratio of a different fragmentation model (HERWIG++) with respect to PYTHIA6. – 15 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 (GeV) T Monte Carlo Particle Jet p 30 100 200 1000 F la vo r R es po ns e/ A ll R es po ns e 0.9 0.95 1 1.05 1.1 1.15 uds gluon b c , R=0.5, CaloJetsTAnti k | < 1.3η| = 7 TeVsCMS simulation (GeV) T Monte Carlo Particle Jet p 20 30 100 200 1000 F la vo r R es po ns e/ A ll R es po ns e 0.9 0.95 1 1.05 1.1 1.15 uds gluon b c , R=0.5, JPTJetsTAnti k | < 1.3η| = 7 TeVsCMS simulation (GeV) T Monte Carlo Particle Jet p 20 30 100 200 1000 F la vo r R es po ns e/ A ll R es po ns e 0.9 0.95 1 1.05 1.1 1.15 uds gluon b c , R=0.5, PFlowJetsTAnti k | < 1.3η| = 7 TeVsCMS simulation Figure 8. Simulated jet energy response, in PYTHIA6 Z2 tune, of different jet flavours normalized to the response of the QCD flavour mixture, as a function of the true particle jet pT , in the region |η |< 1.3 for the three jet types. (GeV) T p 30 40 100 200 300H er w ig + + / P yt hi a Z 2 (R es po ns e) 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 0.5 T |y| < 1.3, anti-k Gluon (CALO) Gluon (JPT) Gluon (PF) Quark (PF) Quark (JPT) Quark (CALO) Figure 9. Response ratio predicted by HERWIG++ and PYTHIA6 for jets originated by light quarks (uds) and gluons for the various jet types. 6.4 Relative jet energy scale 6.4.1 Measurement The dijet pT -balance technique, described in section 5, is used to measure the response of a jet at any η relative to the jet energy response in the region |η | < 1.3. Figure 10 shows example distributions of the balance quantity B for PF jets in two pseudorapidity bins. Figure 11 shows the relative response as a function of η in the range 100GeV < pave T < 130GeV. Ideally, the relative response of the corrected jets in the simulation should be equal to unity. However, because of the resolution bias effect (section 5.4.1), the relative response in the simulation is found to deviate from unity by an amount equal to the resolution bias. The comparison of the data with the MC simulations implicitly assumes that the resolution bias in the data is the same as in the simulation. This assumption is the dominant systematic uncertainty related to the measurement of the relative response with the dijet balance method. – 16 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 Balance -1 -0.5 0 0.5 1 E ve nt s 0 500 1000 1500 PF Jets Data Simulation < 170 GeV ave T 130 < p | < 0.522η0.261 < | = 7 TeVs-1CMS, 36 pb Balance -1 -0.5 0 0.5 1 E ve nt s 0 200 400 PF Jets Data Simulation < 170 GeV ave T 130 < p | < 2.411η2.322 < | = 7 TeVs-1CMS, 36 pb Figure 10. Example distributions of the dijet balance quantity for PF jets in two η regions. In order to reduce the radiation bias (section 5.4.2), a selection is applied on the ratio α = pJet3 T /pave T and the nominal analysis value is α < 0.2. The residual relative correction calculation is done in three steps: first, the η-symmetric part, Csym, is measured in bins of |η |, in order to maxi- mize the available statistics, with the nominal requirement α < 0.2. Then, a correction factor krad is applied to take care of the extrapolation to α = 0, and finally the asymmetry in η , AR(|η |), is taken into account. The residual correction for the relative jet energy scale is formally expressed below: Crel(±η) = krad(|η |) ·Csym(|η |) 1∓AR(|η |) . (6.7) The Csym component is defined by comparing the relative response in data and MC simulations: Csym(|η |) = 〈 Rα<0.2 MC Rα<0.2 data 〉 pT , (6.8) averaged over the entire pT range. This is justified by the fact that no statistically significant pT - dependence is observed in the comparison between data and simulation. Since the additional radiation and the UE are not perfectly modeled in the simulation, a cor- rection needs to be applied by extrapolating to zero third-jet activity, as discussed in section 5.4.2. The radiation correction krad is defined as: krad = lim α→0  〈 Rα MC Rα data 〉 pT〈 Rα<0.2 MC Rα<0.2 data 〉 pT  . (6.9) Figure 12 (left) shows the radiation correction that needs to be applied to the measurement at the working point α < 0.2. The correction is negligible in the central region while it reaches the value of 3% at larger rapidities. – 17 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 η -4 -2 0 2 4 R el at iv e R es po ns e 0.9 1 1.1 1.2 CALO Jets Data Simulation < 130 GeV dijet T 100 < p = 7 TeVs-1CMS, 36 pb η -4 -2 0 2 4 R el at iv e R es po ns e 0.9 1 1.1 1.2 JPT Jets Data Simulation < 130 GeV dijet T 100 < p = 7 TeVs-1CMS, 36 pb η -4 -2 0 2 4 R el at iv e R es po ns e 0.9 1 1.1 1.2 PF Jets Data Simulation < 130 GeV dijet T 100 < p = 7 TeVs-1CMS, 36 pb Figure 11. Relative jet energy response as a function of η , measured with the dijet balance method for CALO, JPT and PF jets respectively. The asymmetry of the response in η is quantified through the variable AR: AR(|η |) = R(+|η |)−R(−|η |) R(+|η |)+R(−|η |) , (6.10) where R(+|η |) (R(−|η |)) is the relative response measured in the data at the detector part lying in the direction of the positive (negative) z-axis. Figure 12 (right) shows the measured asymmetry. It is found to be similar for the different jet types. Figure 13 shows the final residual correction, as a function of η , for all jet types. This correction is typically of the order of 2-3%, with the exception of the region 2.5 < |η | < 3.0 where it reaches the value of 10%. The region where the larger discrepancy between data and MC simulations is observed (figure 11), coincides with the border between the endcap and the forward calorimeters. It has also been observed [27] that the single-particle response shows similar behavior in this region. – 18 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 |η| 0 1 2 3 4 5 F S R C or re ct io n 0.99 1 1.01 1.02 1.03 1.04 1.05 |)ηcosh(| 2 1+p |)ηcosh(| 1 p + 0 p fit uncertainty = 7 TeVs-1CMS, 36 pb |η| 0 1 2 3 4 5 A sy m m et ry [% ] -3 -2 -1 0 1 2 3 PF Jets R(+) + R(-) R(+) - R(-) A = = 7 TeVs-1CMS, 36 pb Figure 12. Left: correction krad of the relative jet energy residual due to initial and final state radiation. Right: relative jet energy response asymmetry as a function of jet |η |, for α < 0.2. Finally, figure 14 demonstrates that the derived residual correction establishes an almost per- fect agreement between data and simulation. 6.4.2 Uncertainty The dominant uncertainty of the relative residual correction is due to the simulation of the jet energy resolution, which defines the magnitude of the resolution bias. The estimate of the systematic uncertainty is achieved by varying the jet pT resolution according to the comparisons between data and MC simulations shown in section 7. Other sources of uncertainty, such as lack of available events, radiation correction and asymmetry in η are found to be smaller than 1%. The total uncertainty of the relative jet energy scale is shown in figure 15 as a function of the jet |η | for two characteristic values of jet pT (50GeV, 200GeV). The CALO jets have systematically larger uncertainty, as opposed to PF jets which have the smallest while the JPT jets uncertainty lies between the values for the other two jet types. This pattern is consistent with the behavior of the jet energy resolution. Also, it is observed that the relative scale uncertainty grows toward larger rapidities because of the larger resolution uncertainty. 6.5 Absolute jet energy scale 6.5.1 Measurement The absolute jet energy response is measured in the reference region |η | < 1.3 with the MPF method using γ/Z+jets events, and the result is verified with the pT -balancing method. The γ or the Z are used as reference objects because their energy is accurately measured in ECAL (photon, Z→ e+e−) or in the tracker and muon detectors (Z→ µ+µ−). Figure 16 shows example distributions of the MPF and pT -balancing methods for PF jets in the γ+jet sample. The actual measurement is performed only for PF jets because of the full consistency between the jet and the ~/ET reconstruction (both use the same PF candidates as inputs). The absolute energy – 19 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 CALO Jets Correction Uncertainty = 7 TeVs-1CMS, 36 pb η -4 -2 0 2 4 R es id ua l C or re ct io n 0.9 0.95 1 1.05 1.1 η -4 -2 0 2 4 R es id ua l C or re ct io n 0.9 0.95 1 1.05 1.1 JPT Jets Correction Uncertainty = 7 TeVs-1CMS, 36 pb η -4 -2 0 2 4 R es id ua l C or re ct io n 0.9 0.95 1 1.05 1.1 η -4 -2 0 2 4 R es id ua l C or re ct io n 0.9 0.95 1 1.05 1.1 PF Jets Correction Uncertainty = 7 TeVs-1CMS, 36 pb η -4 -2 0 2 4 R es id ua l C or re ct io n 0.9 0.95 1 1.05 1.1 η -4 -2 0 2 4 R es id ua l C or re ct io n 0.9 0.95 1 1.05 1.1 Figure 13. Relative jet energy residual correction as a function of jet η for CALO, JPT and PF jets respec- tively. The band shows the uncertainty due to statistics, radiation corrections, and asymmetry in η . scale of the remaining jet types (CALO, PF) is determined by comparison to the corresponding PF jet after jet-by-jet matching in the η−φ space. In the selected γ+jets sample, the presence of a barrel jet (|η | < 1.3) recoiling against the photon candidate in azimuth by ∆φ > 2.7 is required. To reduce the effect of initial and final state gluon radiation that degrades the jet-photon pT -balance, events containing additional jets with pJet2 T > α · pγ T and outside the ∆R = 0.25 cone around the photon direction are vetoed. The pT -balance and MPF response measurements are performed in the same way with data and MC samples with different values of the threshold on α and the data/MC ratio is extrapolated to α = 0. This procedure allows the separation of the γ-jet intrinsic pT -imbalance from the imbalance caused by hard radiation (section 5.4.2). Figure 17 (left) shows the data/MC jet-energy-response ratio, relative to the γ ECAL scale, extrapolated as a function of the threshold on the second jet pT . In the pT -balancing method, the secondary jet effect is more pronounced because it affects directly the transverse momentum – 20 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 η -4 -2 0 2 4 D at a / M on te C ar lo 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 Before residual correction After residual correction = 7 TeVs-1CMS, 36 pb PF Jets Figure 14. Relative response ratio between data and MC simulation before and after the residual correction. |η| 0 1 2 3 4 5 R el at iv e JE S U nc er ta in ty [% ] 0 2 4 6 8 10 CALO jets JPT jets PF jets R = 0.5Tanti-k = 50 GeV T p = 7 TeVs-1CMS, 36 pb |η| 1 2 3 R el at iv e JE S U nc er ta in ty [% ] 0 2 4 6 8 10 CALO jets JPT jets PF jets R = 0.5Tanti-k = 200 GeV T p = 7 TeVs-1CMS, 36 pb Figure 15. Relative jet energy residual correction uncertainty, as a function of η for jet pT = 50GeV (left) and pT = 200GeV (right). balance between the photon and the leading jet. In the MPF method, the presence of the secondary jet(s) affects the measurement to a lesser extent, and mainly through the response difference between the leading jet and the secondary softer jet(s). For loose veto values, the ratio data/MC in both methods is lower than unity, while the agreement improves by tightening the veto. Figure 17 (right) shows the data/MC response ratio after the extrapolation to α = 0 for both MPF and pT -balancing methods, as a function of pγ T . The two measurements are statistically uncorrelated to a good approximation and the two sets of points are fitted together with a constant value. The fit gives data/MC = 0.985±0.001, relative to the γ ECAL scale, which leads to an absolute response residual correction Cabs = 1/0.985 = 1.015 (eq. (6.2)), constant in pT . – 21 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 Balanceγ+jet 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 E ve nt s 0 100 200 300 400 500 | < 1.3γη| Data +jet MCγ 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 E ve nt s 0 100 200 300 400 500 -1CMS, 36 pb = 7 TeVs R = 0.5 PFJetsTAnti-k < 70 GeV γ T 47 < p 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 E ve nt s 0 100 200 300 400 500 γ+jet MPF 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 E ve nt s 0 50 100 150 200 250 300 | < 1.3γη| Data +jet MCγ 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 E ve nt s 0 50 100 150 200 250 300 -1CMS, 36 pb = 7 TeVs R = 0.5 PFJetsTAnti-k < 70 GeV γ T 47 < p 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 E ve nt s 0 50 100 150 200 250 300 Figure 16. Example response distributions for PF jets from pT -balancing (left) and MPF (right) in the γ+jets sample. γ T / pJet2 T p 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 D at a / M C 0.95 0.96 0.97 0.98 0.99 1 > 30 GeVγ T p MPF balance T p R=0.5 PFTanti-k = 7 TeVs-1CMS, L = 36 pb (GeV)γ T p 20 30 40 100 200 D at a / M C 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 balance T p MPF 0.001± = 0.985 data / MCR / NDF = 13.6 / 132χ Stat. uncertainty Syst. uncertainty Extrapolation⊕ Syst. ⊕Stat. Data/MC corrected for FSR+ISR R=0.5 PFTanti-k = 7 TeVs-1CMS, L = 36 pb (GeV)γ T p 20 30 40 100 200 D at a / M C 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 Figure 17. Left: dependence of the data/MC ratio of the jet energy response on the second jet pT threshold. Right: data/MC ratio of the jet energy response, after extrapolation to zero second jet pT , as a function of pγ T . Solid squares and solid circles correspond to the pT -balancing and the MPF methods, respectively. In addition to the γ+jets sample, the absolute jet energy response is also measured from the Z+jets sample. Figure 18 shows two characteristic response distributions in the 30GeV < pZ T < 60GeV bin, as an example, measured from the Z(µ+µ−)+jets sample with the pT -balancing and the MPF methods. The Z+jets samples cover the pZ T range from 20GeV to 200GeV. In order to combine the results from the photon+jet and Z+jet samples, the more precise MPF method is employed identically in all relevant samples. Figure 19 shows the data/MC ratio as a function of pγ,Z T after correcting for the final and initial state radiation differences between data and simulation (extrapolation to α = 0). Although the size of the Z+jets data sample is smaller than – 22 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 Figure 18. Left: jet energy response from Z(µ+µ−)+jets pT -balancing in the bin 30 < pZ T < 60GeV. Right: jet energy response from Z(µ+µ−)+jets MPF in the bin 30 < pZ T < 60GeV. (GeV)γ/Z T p 20 30 40 100 200 D at a / M C ( M P F ) 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 +jetγ Zee+jet +jetµµZ Data/MC corrected for FSR+ISR R=0.5 PFTanti-k 0.001± = 0.985data / MCR /NDF = 13.9 / 152χ = 7 TeVs-1CMS, L = 36 pb (GeV)γ T p 20 30 40 100 200 D at a / M C ( M P F ) 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 Figure 19. Ratio of data over MC for the MPF response, as a function of pγ,Z T in the photon+jet sample (circles), Z(e+e−)+jet sample (triangles) and Z(µ+µ−)+jet sample (squares). the γ+jets sample, the results from all samples are in good agreement, within the corresponding statistical uncertainties. 6.5.2 Uncertainty sources The uncertainty of the absolute jet energy scale measurement has six components: uncertainty in the MPF method for PF jets, photon energy scale, MC extrapolation beyond the reach of the available dataset, offset due to noise and pile-up at low-pT (as discussed in section 6.2.4), MC residuals (the level of closure of the MC correction in the MC), and the jet-by-jet matching residuals for CALO and JPT jets. – 23 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 (GeV) T p 20 100 200 1000 M P F u nc er ta in ty [% ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 MPF method Quark/gluon mix ISR+FSR Out-of-cone + UE QCD background Proton fragments Pile-up R=0.5 PFTAnti-k = 7 TeVs-1CMS, L = 36 pb (GeV) T p 20 100 200 1000 M P F u nc er ta in ty [% ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Figure 20. Jet energy scale uncertainty in the MPF method for PF jets. MPF uncertainty for PF jets. The MPF method is affected by several small uncertainties that mainly contribute at low pT : flavour mapping, parton-to-particle level sensitivity, QCD back- ground, secondary jets, and proton fragments. The various contributions are shown in figure 20. The flavour mapping uncertainty accounts for the response difference between jets in the quark-rich γ+jets sample used to measure the absolute jet energy scale, and those in the reference, gluon-rich QCD multijet sample. This is estimated from the average quark-gluon response difference between PYTHIA6 and HERWIG++ (figure 9) in the region 30− 150GeV. The latter is chosen because it is the pT region best constrained by the available data. For PF jets, the flavour mapping uncertainty amounts to ∼ 0.5%. By definition, the MPF response refers to the parton level because the photon is perfectly balanced in the transverse plane, against the outgoing partons. However, the default jet energy response refers to the particle level, which includes the UE and the hadronization effects. The parton-to-particle level response interpretation therefore is sensitive to the UE and the out-of-cone showering (OOC). The corresponding uncertainty is estimated from the simulation by using jets reconstructed with larger size parameter (R = 0.7, more sensitive to UE and OOC) and comparing the extrapolation to the zero secondary jet activity with respect to the nominal size parameter (R = 0.5). The resulting uncertainty has a weak pT -dependence and is smaller than 0.2%. The dominant background for γ+jets events is the QCD dijet production where one leading jet fragments into a hard isolated π0 → γ + γ . Such events can alter the measured pT -balance because the leading neutral π0 carries only a fraction of the initial parton energy. The QCD background uncertainty is estimated by repeating the measurement, using a loose and a tight photon identification, and is found to be negligible compared to the current statistical precision. The MPF response at low pT is sensitive to the undetected energy that leaks outside the forward calorimeter acceptance at |η | > 5 (proton fragments). This results in an underestimation of the MPF response, compared to the true response. The uncertainty due to the undetected energy is taken from the simulation and is estimated to be 50% of the difference between the MPF response and the true response. – 24 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 (GeV) T p 30 100 200 1000 R es po ns e ra tio 0.96 0.98 1 1.02 1.04 3%, calo±SPR 3%, jpt±SPR 3%, pf±SPR | < 1.3η R = 0.5, |Tanti-k = 7 TeVsCMS simulation (GeV) T p 20 100 200 1000 R es po ns e ra tio to P yt hi a Z 2 0.98 0.99 1 1.01 1.02 1.03 1.04 Herwig++ / PZ2 CALO JPT PF AK7PF Pythia D6T / PZ2 CALO JPT PF AK7PF Calo-based envelope Track-based envelope = 7 TeVsCMS simulation (GeV) T p 20 100 200 1000 R es po ns e ra tio to P yt hi a Z 2 0.98 0.99 1 1.01 1.02 1.03 1.04 Figure 21. Left: sensitivity of the jet energy response in |η | < 1.3 to the single-particle response (SPR) uncertainty. Right: dependence of the jet energy response on the fragmentation model. Here AK7PF stands for PF jets reconstructed with the anti-kT algorithm with size parameter R = 0.7. The secondary jet activity is found to be significantly different between data and MC, and it is corrected by extrapolating the data/MC ratio for the MPF and pT -balance methods to zero secondary jet activity. The related uncertainty is estimated as half of the radiation bias correction applied to the MPF method. Photon energy scale uncertainty. The MPF and pT -balancing methods are directly sensitive to the uncertainty in the energy of the γ used as a reference object. The γ energy scale uncertainty is estimated to be ∼ 1% based on studies presented elsewhere [28]. Monte Carlo extrapolation. The in situ measurement of the absolute jet energy scale is feasible only in the pT range where γ+jets data are available. For the current dataset this range extends to around 300GeV. However, the jet pT range probed in the entire dataset is generally more than three times higher than in the γ+jets sample. In QCD dijet events, jets as high as pT = 1TeV are observed. Because of the absence of data for direct response measurement at high pT , the calibration relies on the simulation. Based on the data vs. MC comparison in the region of available γ+jets data, conclusions can be drawn for the extrapolation of the jet energy correction at the highest jet pT . The simulation uncertainty for the high-pT jets arises from two main sources: the single- particle response (SPR) for hadrons and the fragmentation modeling. The former is measured directly in data by using isolated tracks and comparing the energy deposited in the calorimeters with the momentum measured by the tracker. The currently available measurement [27] indicates that the data/MC disagreement is less than 3%. The SPR uncertainty is translated to a jet energy response uncertainty by modifying accordingly the simulation. Figure 21 (left) shows the impact of the SPR uncertainty on the response of the different jet types, in the region |η |< 1.3. For CALO jets, the induced uncertainty is roughly constant vs. pT and approximately equal to 2%. The track- based algorithms are less affected at low-pT by the SPR uncertainty because the energy is primarily – 25 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 measured by the tracker. However, as the jet pT increases and the track momentum measurement becomes less precise compared to the calorimetric measurement, the track-based jet types behave like CALO jets. The transition is smooth and is completed at jet pT ∼ 300GeV. The other source of systematic uncertainty is related to the fragmentation properties, which include the parton shower and the hadronization simulation. Since jets are composite objects, realized as “sprays” of highly collimated particles, and the calorimeter response is non-linear, the jet energy response depends on the number and the spectrum of the particles it consists of. The sensitivity to the fragmentation modelling is studied by generating QCD events from various MC generators which are then processed by the full simulation of the CMS detector. The MC generators employed are: PYTHIA6 (tunes D6T [25] and Z2) and HERWIG++ [29]. Figure 21 (right) shows the response ratio of the various models with respect to PYTHIA6,with Z2 tune, which is the default. The differences between the models are negligible at pT ∼ 80GeV, while they grow up to 1.5% at low and high jet pT . The combined MC uncertainty of the absolute jet energy response due to SPR and fragmen- tation is shown in figure 22. The particle-flow algorithm reconstructs individual particles, prior to jet clustering. This allows the detailed study of the PF jet composition in terms of charged hadrons, photons and neutral hadrons. In particular, the jet energy response is closely related to the energy fraction carried by the three major composition species. The purpose of this study is to demonstrate that the MC simulation is able to describe accurately the PF jet composition observed in data and therefore can be trusted to predict the PF jet response in the kinematic regions where the in situ measurement is not possible. Figure 23 (left) shows the fraction of jet energy carried by the various particle types. Charged hadrons, photons, and neutral hadrons carry ∼ 65%, 20%, and 15% of the jet energy respectively at low jet pT , as expected from the general properties of the fragmentation process. As the jet pT increases, charged hadrons become more energetic and more collimated, while the tracking efficiency and momentum resolution worsen. This increases the probability for a charged hadron to leave detectable energy only in the calorimeters and to be classified either as a neutral electromagnetic object (photon) or as a neutral hadron. Therefore, for higher jet pT , the energy fraction carried by photons and neutral hadrons is increased. The excellent agreement between data and simulation quantified in figure 23 (right) proves that the simulation can be safely trusted to predict the absolute jet energy response. Jet-by-jet matching. Once the jet energy scale is established for PF jets, the estimated uncer- tainties are transfered to the other jet types. This is done by direct jet-by-jet comparison between different jet types in the QCD dijet sample. The PF and CALO (JPT) jets are spatially matched in the η , φ space by requiring ∆R < 0.25. For the matched jet pairs the relative response of CALO (JPT) jets pCALO T /pPF T (pJPT T /pPF T ) is measured as a function of pPF T (the study is described in detail in ref. [11]). A cross-check of the direct jet matching is done with a tag-and-probe method in dijet events, with the PF jet being the tag object and the CALO/JPT jets being the probe objects. The re- sults are summarized in figure 24 where the response ratio data/MC of the CALO and JPT response relative to the PF jets is shown. The observed disagreement is at the level of 0.5%, indicating that the precision of the CALO and JPT calibration is comparable to that of the PF jets. The observed – 26 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 (GeV) T p 20 100 200 1000 E xt ra po la tio n un ce rt ai nt y [% ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Total uncertainty Fragmentation Single pion response R=0.5 CALOTAnti-k = 7 TeVs-1CMS simulation, L = 36 pb (GeV) T p 20 100 200 1000 E xt ra po la tio n un ce rt ai nt y [% ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 (GeV) T p 20 100 200 1000 E xt ra po la tio n un ce rt ai nt y [% ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Total uncertainty Fragmentation Single pion response R=0.5 JPTTAnti-k = 7 TeVs-1CMS simulation, L = 36 pb (GeV) T p 20 100 200 1000 E xt ra po la tio n un ce rt ai nt y [% ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 (GeV) T p 20 100 200 1000 E xt ra po la tio n un ce rt ai nt y [% ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Total uncertainty Fragmentation Single pion response R=0.5 PFTAnti-k = 7 TeVs-1CMS simulation, L = 36 pb (GeV) T p 20 100 200 1000 E xt ra po la tio n un ce rt ai nt y [% ] 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Figure 22. Uncertainty of the absolute jet energy response in the region |η |< 1.3 related to the MC extrap- olation for CALO, JPT and PF jets respectively. 0.5% level of data/MC disagreement is taken into account as an additional systematic uncertainty for CALO and JPT jets. 6.5.3 Uncertainty As described in the previous sections, the absolute jet energy response is measured in situ for PF jets with the MPF method in γ/Z+jets events. The systematic uncertainties related to the measurement itself are summarized in figure 20. The estimation of the systematic uncertainty in the kinematic region beyond the reach of the γ+jets sample is based on the simulation and its sensitivity to the single-particle response and the fragmentation models. In addition, the uncertainty on the γ energy scale needs to be taken into account since the jet energy response is measured relative to the γ scale. The direct jet-by-jet spatial matching, allows the transfer of the PF jet-energy- scale uncertainty to the other jet types (CALO, JPT). Finally, a flavour uncertainty is assigned from the response differences between the quark and gluon originated jets. These are – 27 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 (GeV) T p 20 30 100 200 1000 C om po ne nt fr ac tio n st ac k 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Data NHF Data NEF Data CHF MC NHF MC NEF MC CHF |<0.5ηInclusive jets | = 7 TeVs-1CMS, L = 36 pb (GeV) T p 20 30 100 200 1000 C om po ne nt fr ac tio n st ac k 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (GeV) T p 20 30 100 200 1000 fr ac tio n [% ] T D at a - M C fo r p -6 -4 -2 0 2 4 6 < 300 GeV T 56 < p 0.0%± = -0.0 ∆CHF, 0.0%± = +0.1 ∆NEF, 0.0%± = -0.1 ∆NHF, |<0.5ηInclusive jets | (GeV) T p 20 30 100 200 1000 fr ac tio n [% ] T D at a - M C fo r p -6 -4 -2 0 2 4 6 = 7 TeVs-1CMS, L = 36 pb Figure 23. PF jet composition. Left: energy fraction carried by charged hadrons (CHF), photons (NEF), and neutral hadrons (NHF) as a function of jet pT in the region |η |< 0.5. The filled histograms and the markers represent the data and the simulation respectively. Right: pT fraction difference between data and MC. (GeV) T PFJet p 40 100 200 1000 D at a / M C ( C al oJ et / P F Je t) 0.98 0.99 1 1.01 1.02 = 7 TeVs-1CMS, L = 36 pb | < 1.3η|Direct match Tag-and-probe Extrapolation+offset 0.001± = 0.995CALO/PFR (GeV) T PFJet p 40 100 200 1000 D at a / M C ( C al oJ et / P F Je t) 0.98 0.99 1 1.01 1.02 (GeV) T PFJet p 40 100 200 1000 D at a / M C ( JP T Je t / P F Je t) 0.98 0.99 1 1.01 1.02 = 7 TeVs-1CMS, L = 36 pb | < 1.3η|Direct match Tag-and-probe Extrapolation+offset 0.001± = 0.991JPT/PFR (GeV) T PFJet p 40 100 200 1000 D at a / M C ( JP T Je t / P F Je t) 0.98 0.99 1 1.01 1.02 Figure 24. Left: CALO vs. PF jet pT response ratio between data and MC simulation. Right: JPT vs. PF jet pT response ratio between data and MC simulation. The solid circles correspond to direct matching in the η−φ space and the open circles correspond to a tag (PF jet) and probe (CALO/JPT jet) method. taken from figure 9 and cover the absolute scale uncertainty in physics samples with a different flavour mixture than the reference QCD multijet sample. Figure 25 shows the absolute energy scale uncertainties for the three jet types, combined with the offset correction uncertainty corresponding to the average number of pile-up events in the datasets considered for this paper. The low jet pT threshold indicates the minimum recommended pT for each jet type: 30GeV, 20GeV, and 10GeV for CALO, JPT, and PF jets respectively. At low jet pT the offset uncertainty dominates with significant contribution from the MC truth – 28 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 (GeV) T p 20 100 200 1000 A bs ol ut e sc al e un ce rt ai nt y [% ] 0 1 2 3 4 5 6 7 8 9 10 Total uncertainty MPF method Photon scale Extrapolation Offset (2010) Residuals Jet flavor R=0.5 CaloTAnti-k = 7 TeVs-1CMS, L = 36 pb (GeV) T p 20 100 200 1000 A bs ol ut e sc al e un ce rt ai nt y [% ] 0 1 2 3 4 5 6 7 8 9 10 (GeV) T p 20 100 200 1000 A bs ol ut e sc al e un ce rt ai nt y [% ] 0 1 2 3 4 5 6 7 8 9 10 Total uncertainty MPF method Photon scale Extrapolation Offset (2010) Residuals Jet flavor R=0.5 JPTTAnti-k = 7 TeVs-1CMS, L = 36 pb (GeV) T p 20 100 200 1000 A bs ol ut e sc al e un ce rt ai nt y [% ] 0 1 2 3 4 5 6 7 8 9 10 (GeV) T p 20 100 200 1000 A bs ol ut e sc al e un ce rt ai nt y [% ] 0 1 2 3 4 5 6 7 8 9 10 Total uncertainty MPF method Photon scale Extrapolation Offset (2010) Residuals Jet flavor R=0.5 PFTAnti-k = 7 TeVs-1CMS, L = 36 pb (GeV) T p 20 100 200 1000 A bs ol ut e sc al e un ce rt ai nt y [% ] 0 1 2 3 4 5 6 7 8 9 10 Figure 25. Absolute jet energy scale uncertainty as a function of jet pT for CALO, JPT and PF jets respec- tively. and jet-by-jet matching residuals. At the intermediate jet pT , where enough data for the in situ measurements are available, the γ energy scale uncertainty dominates. At high jet pT , the uncertainty due to the MC extrapolation is dominant. Overall, the absolute jet energy scale uncertainty for all jet types is smaller than 2% for pT > 40GeV. 6.6 Combined jet energy correction In this section, the combined MC and residual calibration is presented along with the total jet energy scale systematic uncertainty. Following eq. (6.2), the residual corrections for the relative and absolute response are multiplied with the generator-level MC correction, while the corresponding uncertainties are added in quadrature. Figure 26 shows the combined calibration factor as a function of jet-η for pT = 50, 200GeV. Because of the smallness of the residual corrections, the combined correction has the shape of the MC component, shown in figure 6. The total correction as a function of jet pT is shown in figure 27 for various η values. Figure 28 shows the total jet energy scale – 29 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 ηJet -4 -2 0 2 4 Je t E ne rg y C or re ct io n F ac to r 1 1.5 2 2.5 CALO jets JPT jets PF jets R = 0.5Tanti-k = 50 GeV T p = 7 TeVs-1CMS, 36 pb ηJet -2 0 2 Je t E ne rg y C or re ct io n F ac to r 0.8 1 1.2 1.4 1.6 1.8 CALO jets JPT jets PF jets R = 0.5Tanti-k = 200 GeV T p = 7 TeVs-1CMS, 36 pb Figure 26. Total jet-energy-correction factor, as a function of jet η for pT = 50GeV (left) and pT = 200GeV (right). The bands indicate the corresponding uncertainty. uncertainty as a function of jet pT . At low jet pT the relative energy scale uncertainty makes a significant contribution to the total uncertainty while it becomes negligible at high pT . In the forward region, the relative scale uncertainty remains significant in the entire pT -range. In general PF jets have the smallest systematic uncertainty while CALO jets have the largest. 7 Jet transverse momentum resolutions In the following sections, results on jet pT resolutions are presented, extracted from generator-level MC information, and measured from the collider data. Unless stated otherwise, CALO, PF and JPT jets are corrected for the jet energy scale, as described in the previous section. The jet pT resolution is measured from two different samples, in both data and MC samples, using methods described in section 5: • The dijet asymmetry method, applied to the dijet sample, • The photon-plus-jet balance method, applied to the γ+jet sample. The dijet asymmetry method exploits momentum conservation in the transverse plane of the dijet system and is based (almost) exclusively on the measured kinematics of the dijet events. This measurement uses two ways of describing the jet resolution distributions in data and simulated events. The first method makes use of a truncated RMS to characterize the core of the distributions. The second method employs functional fitting of the full jet resolution function, and is currently limited to a Gaussian approximation for the jet pT probability density. The γ+jet balance method exploits the balance in the transverse plane between the photon and the recoiling jet, and it uses the photon as a reference object whose pT is accurately measured in ECAL. The width of the pT /pγ T distribution provides information on the jet pT resolution in a given pγ T bin. The resolution is determined independently for both data and simulated events. The – 30 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 (GeV) T Jet p 10 20 30 100 200 1000 Je t E ne rg y C or re ct io n F ac to r 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 CALO jets JPT jets PF jets R = 0.5Tanti-k = 0.0η = 7 TeVs-1CMS, 36 pb (GeV) T Jet p 10 20 30 100 200 1000 Je t E ne rg y C or re ct io n F ac to r 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 CALO jets JPT jets PF jets R = 0.5Tanti-k = 1.0η = 7 TeVs-1CMS, 36 pb (GeV) T Jet p 10 20 30 100 200 Je t E ne rg y C or re ct io n F ac to r 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 CALO jets JPT jets PF jets R = 0.5Tanti-k = 2.0η = 7 TeVs-1CMS, 36 pb (GeV) T Jet p 10 20 30 40 50 100 Je t E ne rg y C or re ct io n F ac to r 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 CALO jets JPT jets PF jets R = 0.5Tanti-k = 4.0η = 7 TeVs-1CMS, 36 pb Figure 27. Total jet-energy-correction factor, as a function of jet pT for various η values. The bands indicate the corresponding uncertainty. results extracted from γ+jet pT balancing provide useful input for validating the CMS detector simulation, and serve as an independent and complementary cross-check of the results obtained with the dijet asymmetry method. In the studies presented in this paper, the resolution broadening from extra radiation activity is removed by extrapolating to the ideal case of a two-body process, both in data and in MC. In addition, the data/MC resolution ratio is derived. 7.1 Monte Carlo resolutions The jet pT resolution derived from generator-level MC information information in the simulation, serves as a benchmark for the measurements of the jet resolution in collision data samples, using the methods introduced above and discussed in the following sections. The measurement of the jet pT resolution in the simulation is performed using PYTHIA QCD dijet events. The MC particle jets are matched geometrically to the reconstructed jets (CALO, JPT, or PF) by requiring their distance in η−φ space to be ∆R < ∆RMax. – 31 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 (GeV) T Jet p 10 20 100 200 1000 T ot al J E S U nc er ta in ty [% ] 0 5 10 15 CALO jets JPT jets PF jets R = 0.5Tanti-k = 0.0η = 7 TeVs-1CMS, 36 pb (GeV) T Jet p 10 20 30 100 200 T ot al J E S U nc er ta in ty [% ] 0 5 10 15 CALO jets JPT jets PF jets R = 0.5Tanti-k = 2.0η = 7 TeVs-1CMS, 36 pb (GeV) T Jet p 10 20 30 40 50 100 T ot al J E S U nc er ta in ty [% ] 0 5 10 15 CALO jets JPT jets PF jets R = 0.5Tanti-k = 4.0η = 7 TeVs-1CMS, 36 pb Figure 28. Total jet-energy-scale uncertainty, as a function of jet pT for various η values. The jet pT response is defined as the ratio preco T /pgen T where preco T and pgen T refer to the transverse momenta of the reconstructed jet and its matched reference MC particle jet respectively. The width of the jet pT response distribution, in a given |η | and pgen T bin, is interpreted as the generator-level MC jet pT resolution. Figure 29 shows an example of preco T /pgen T distribution for CALO jets in |η |< 0.5 and with 250 < pgen T < 320GeV. 7.2 Dijet measurements The principles of the dijet asymmetry method for the measurement of the jet pT resolution were presented in section 5. Here, the results of the measurement are presented. The idealized topology of two jets with exactly compensating transverse momenta is spoiled in realistic collision events by the presence of extra activity, e.g. from additional soft radiation or from the UE. The resulting asymmetry distributions are broadened and the jet pT resolution is system- atically underestimated. Other effects can also cause jet imbalance. For example, fragmentation effects cause some energy to be showered outside the jet cone (“out of cone radiation”). The width – 32 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 ref T /p T p 0 0.5 1 1.5 -110 1 10 210 310 =7 TeVs CMS Simulation CaloJets R=0.5) T (Anti-k | < 0.5η0.0 < | | < 320 GeV T REF250 < |p Figure 29. Distribution of the simulated CALO jet response, preco T /pgen T , in a particular |η | and pgen T range. Fit examples with a Gaussian and a double-sided Crystal-Ball function are shown. of the asymmetry distribution is thus a convolution of these different contributions: σA = σintrinsic⊕σimbalance (7.1) To account for soft radiation in dijet events, the measurement of the asymmetry in each η and pave T bin is carried out multiple times, for decreasing amounts of extra activity, and the jet pT resolution is extracted by extrapolating the extra event activity to zero, as discussed in sec- tion 5.4.2. The ratio of the transverse momentum of the third jet in the event over the dijet average pT , pJet3,rel T = pJet3 T /pave T , is used as a measure of the extra activity. The extrapolation procedure is illustrated in figure 30 (left) for the 120 < pave T < 147GeV bin of PF jets and for the correspond- ing bin of MC particle jets (right). The width of each asymmetry distribution σA , as well as the resolutions obtained using generator-level MC information, are derived based on the RMS of the corresponding distributions. Some characteristic example distributions for the raw asymmetry are shown for PF jets in figure 31. To account for the particle-level imbalance contribution to the measured jet pT resolution, the asymmetry method is applied to the generated MC particle jets. Then the extrapolated particle-level resolution is subtracted in quadrature from the measurement. Figure 32 illustrates the different steps of the asymmetry procedure for CALO, JPT, and PF jets respectively. The total pT resolution derived from the extrapolation of the reconstructed asymmetry is shown in green circle, the estimation of the particle-level imbalance resolution from the application to MC particle jets is shown in magenta diamond, and the quadrature subtraction to the final asymmetry result is shown in blue square. All three can be described by a fit to a variation of the standard formula for calorimeter-based resolutions, σ(pT ) pT = √ sgn(N) · ( N pT )2 +S2 · p(M−1) T +C2, (7.2) – 33 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 3,relp 0.05 0.1 0.15 0.2 Aσ2 0.05 0.1 0.15 0.05 0.1 0.15 0.2 Aσ2 0.05 0.1 0.15 Extrapolation (MC) Extrapolation (data) -1=7 TeV, L=35.9 pbs CMS preliminary PFJets R=0.5) T (Anti-k < 147 GeV T ave| < 0.5 120 < pη0 < | T 3,relp 0.05 0.1 0.15 0.2 [% ] po in t (p oi nt -f it) -5 5 =7 TeV, L=35.9 pb CMS 3,relp 0.05 0.1 0.15 0.2 Aσ2 0.05 0.1 0.05 0.1 0.15 0.2 Aσ2 0.05 0.1 Extrapolation (MC) =7 TeVs CMS Simulation GenJets R=0.5) T (Anti-k < 147 GeV T ave| < 0.5 120 < pη0 < | T 3,relp 0.05 0.1 0.15 0.2 [% ] po in t (p oi nt -f it) -4 -2 2 4 Figure 30. Examples of extrapolations of √ 2σA as a function of pJet3 T /pave T to zero for PF jets (R = 0.5) in |η | < 0.5 and 120 < pave T < 147GeV (left). Example of a corresponding extrapolation for MC particle jets (right). where, N refers to the “noise”, S to the “stochastic”, and C to the “constant” term. The additional parameter M is introduced, and the negative sign of the noise term is allowed, to improve the fits to the jet pT resolution vs. pT , for jets that include tracking information (JPT, PF), while retaining a similar functional form as the one used for CALO jets. The resolution estimated from generator-level MC information is shown in red triangles, and good agreement with the result of the asymmetry method is observed. The ratio MC(generator−level) MC(asymmetry) is obtained as a function of pT , for each jet type and in each η-bin and is later applied to the data measurement as a bias correction. Several sources of systematic uncertainties are identified: The linear extrapolation at half-the-distance between the standard working point (at pJet3 T /pave T = 0.15) and zero is evaluated, and the difference from the full extrapolation to zero is assigned as an uncertainty. The size of the particle-level imbalance is varied by 25% and the impact of the measurement is studied when subtracting 75% and 125% of the original particle jet pT resolution in quadrature. Performing the analysis on simulated events, we observe deviations (biases) from the obtained and expected values, referred to as “MC closure residuals”. A conservative 50% of the MC closure residuals MC(generator−level)−MC(asymmetry) MC(asymmetry) is taken as an additional relative systematic uncertainty, corresponding to the bias correction. By comparing the asymmetry measured in data with the expectation from MC simulations, an additional constant term is fitted, describing the observed discrepancy between data and simulation, as described below. The statistical uncertainty from the fit of the constant term is assigned as a systematic uncertainty. Figure 33 shows the size of the different systematic uncertainties as a function of pave T and for a central η bin, for the three jets types. The particle-level imbalance uncertainty is shown in opaque orange, the solid yellow contribution corresponds to the uncertainty from the soft radiation variation, and the dashed-red line depicts the impact from the remaining differences in the MC closure. The relative uncertainty – 34 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 Asymmetry -0.5 0 0.5 E nt rie s -410 -310 -210 -110 1 -1=7 TeV, L=35.9 pbs CMS preliminary PFJets R=0.5) T (Anti-k < 0.15 cut < 59 GeV p T ave| < 0.5 43 < pη0 < | MC data MC data =7 TeV, L=35.9 pb CMS Asymmetry -0.5 0 0.5 E nt rie s -410 -310 -210 -110 1 -1=7 TeV, L=35.9 pbs CMS preliminary PFJets R=0.5) T (Anti-k < 0.15 cut < 147 GeV p T ave| < 0.5 120 < pη0 < | MC data MC data =7 TeV, L=35.9 pb CMS Asymmetry -0.5 0 0.5 E nt rie s -410 -310 -210 -110 1 -1=7 TeV, L=35.9 pbs CMS preliminary PFJets R=0.5) T (Anti-k < 0.15 cut < 800 GeV p T ave| < 0.5 600 < pη0 < | MC data MC data =7 TeV, L=35.9 pb CMS Figure 31. Examples of PF jet asymmetry distributions for |η |< 0.5 and a low-pave T bin (top left), a medium- pave T bin (top right) and a high-pave T bin (bottom), determined from QCD simulation (blue histograms) and compared with the result from data (black dots). due to particle-level imbalance is larger for JPT and PF jets than for CALO jets because the absolute values of the raw resolutions are significantly smaller for JPT and PF, and thus more sensitive to the imbalance subtraction, than in the CALO jet case. The dashed blue line shows the contribution of the uncertainty on the additional constant term. The total systematic uncertainty for each resolution measurement is obtained by summing all individual components in quadrature, and is represented by the grey filled area in figure 33. The sensitivity of the method to the presence of additional collisions due to pile-up has been assessed by applying the measurement to the subsample of the data where exactly one primary vertex candidate is reconstructed, and no significant deviations from the inclusive measurement are observed. The presented measurements of the jet pT resolution, obtained by applying the asymmetry method to data, yield systematically poorer resolution compared to the simulation. This dis- crepancy is quantified by taking the fits to the MC asymmetry results, fixing all parameters, and – 35 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 [GeV]p 50 100 200 1000 > R E F T /p T ) / < p R E F T /p T (pσ 0.1 0.2 0.3 50 100200 1000 > R E F T /p T ) / < p R E F T /p T (pσ 0.1 0.2 0.3 asymmetry reconstructed resolution MC-truth particle level imbalance =7 TeVs CMS Simulation CaloJets R=0.5) T (Anti-k | < 0.5 η0 < | [GeV] T p 50 100 200 300 400 1000 [% ] A sy m . A sy m .- M C -20 -10 10 20 [GeV]p 50 100 200 1000 > R E F T /p T ) / < p R E F T /p T (pσ 0.1 0.2 0.3 50 100200 1000 > R E F T /p T ) / < p R E F T /p T (pσ 0.1 0.2 0.3 asymmetry reconstructed resolution MC-truth particle level imbalance =7 TeVs CMS Simulation JPTJets R=0.5) T (Anti-k | < 0.5 η0 < | [GeV] T p 50 100 200 300 400 1000 [% ] A sy m . A sy m .- M C -20 -10 10 20 [GeV]p 50 100 200 1000 > R E F T /p T ) / < p R E F T /p T (pσ 0.1 0.2 0.3 50 100200 1000 > R E F T /p T ) / < p R E F T /p T (pσ 0.1 0.2 0.3 asymmetry reconstructed resolution MC-truth particle level imbalance =7 TeVs CMS Simulation PFJets R=0.5) T (Anti-k | < 0.5 η0 < | [GeV] T p 50 100 200 300 400 1000 [% ] A sy m . A sy m .- M C -20 -10 10 20 Figure 32. Application of the asymmetry method to simulated CALO (top left), JPT (top right), and PF jets (bottom) in |η | < 0.5. The reconstruction-level (green circle) and particle-level (magenta diamond) results are shown together with the final measurement (blue square), compared to the generator-level MC (denoted as MC-truth) derived resolution (red triangle). adding in quadrature an additional constant term, as the only free parameter in a subsequent fit to the data asymmetry. The fitted additional constant term provides a good characterization of the discrepancy, which was verified by several closure tests based on MC. A likely source of the discrepancy is an imperfect intercalibration of the CMS calorimeters, which affects analyses based on the corresponding datasets. The final results are presented in figures 34 (for all three types of jets, in the central region) and 35 (for PF jets in all remaining η bins). In each case, the solid red line depicts the resolution from generator-level MC, corrected for the measured discrepancy between data and simulation (constant term), and represents the best estimate of the jet pT resolution in data. Consequently, it is central to the total systematic uncertainty band, drawn in yellow. The uncorrected generator- level MC resolution is shown as a red-dashed line for reference. The black dots are the bias- corrected data measurements, which are found to be in good agreement with the discrepancy- – 36 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 [GeV] T p 50 100 200 re la tiv e un ce rt ai nt y [% ] -20 0 20 40 60 total systematic uncertainty soft radiation (50%) particle level imbalance (25%) MC scaling MC closure (50%) 50 100 200 -20 0 20 40 60 =7 TeVs CMS simulation 2010 CaloJets R=0.5) T (Anti-k 0.5≤| η0 < | CMS simulation [GeV] T p 50 100 200 re la tiv e un ce rt ai nt y [% ] -20 0 20 40 60 total systematic uncertainty soft radiation (50%) particle level imbalance (25%) MC scaling MC closure (50%) 50 100 200 -20 0 20 40 60 =7 TeVs CMS simulation 2010 JPTJets R=0.5) T (Anti-k 0.5≤| η0 < | CMS simulation [GeV] T p 50 100 200 re la tiv e un ce rt ai nt y [% ] -20 0 20 40 60 total systematic uncertainty soft radiation (50%) particle level imbalance (25%) MC scaling MC closure (50%) 50 100 200 -20 0 20 40 60 =7 TeVs CMS simulation 2010 PFJets R=0.5) T (Anti-k 0.5≤| η0 < | CMS simulation Figure 33. Relative systematic uncertainty of the asymmetry method to simulated CALO (top left), JPT (top right), and PF jets (bottom) for |η |< 0.5. corrected generator-level MC, within the statistical and systematic uncertainties. Note in particular that the agreement with the uncorrected generator-level MC resolution is considerably worse. The dijet data are also investigated within the framework of the unbinned likelihood fit to the jet pT resolution parameterization. This approach is developed in order to provide a cross-check of the results. It also serves as a tool for the determination of the full jet pT resolution function, once larger collider data samples become available. This method directly takes into account biases in the event selection caused by the jet pT resolution and the steeply falling jet pT spectrum. At the present stage, the jet pT probability densities are approximated by a truncated Gaussian, providing direct correspondence with the binned fits discussed above. The resulting determination of the widths of the jet pT resolution (as function of pT and η) is also affected by the soft-radiation and hadronization (out-of-cone) effects. The fitted resolution values are thus extrapolated to zero-radiation activity. The MC particle-level imbalance is subtracted in quadrature to correct for effects of hadronization. The method is applied to both data and MC, and the results are – 37 – 2 0 1 1 J I N S T 6 P 1 1 0 0 2 [GeV] T p 50 100 200 r es ol ut io n T je t p 0 0.1 0.2 0.3 total systematic uncertainty MC