CERN-PH-EP-2011-191

Cern-Ph-Ep-2011-191

Abstract

The jet energy scale (JES) and its systematic uncertainty are determined for jets measured with the ATLAS detector at the LHC in proton-proton collision data at a centre-of-mass energy of  \TeV corresponding to an integrated luminosity of  \ipb. Jets are reconstructed with the anti- algorithm with distance parameters or . Jet energy and angle corrections are determined from Monte Carlo simulations to calibrate jets with transverse momenta  \GeV and pseudorapidities . The JES systematic uncertainty is estimated using the single isolated hadron response measured in situ and in test-beams, exploiting the transverse momentum balance between central and forward jets in events with dijet topologies and studying systematic variations in Monte Carlo simulations. The JES uncertainty is less than in the central calorimeter region () for jets with  \GeV, and is maximally for  \GeV in the most forward region . The uncertainty for additional energy from multiple proton-proton collisions in the same bunch crossing is less than per additional collision for jets with  \GeV after a dedicated correction for this effect. The JES is validated for jet transverse momenta up to  \TeV to the level of a few percent using several in situ techniques by comparing a well-known reference such as the recoiling photon \pt, the sum of the transverse momenta of tracks associated to the jet, or a system of low-\pt jets recoiling against a high-\pt jet. More sophisticated jet calibration schemes are presented based on calorimeter cell energy density weighting or hadronic properties of jets, providing an improved jet energy resolution and a reduced flavour dependence of the jet response. The JES systematic uncertainty determined from a combination of in situ techniques are consistent with the one derived from single hadron response measurements over a wide kinematic range. The nominal corrections and uncertainties are derived for isolated jets in an inclusive sample of high-\pt jets. Special cases such as event topologies with close-by jets, or selections of samples with an enhanced content of jets originating from light quarks, heavy quarks or gluons are also discussed and the corresponding uncertainties are determined.

Contents:

1 Introduction

Figure 1: Display of the central part of the ATLAS detector in the - view showing the highest mass central dijet event collected during the data taking period. The two leading jets have  \TeV with and  \TeV with , respectively. The two leading jets have an invariant mass of approximately  \TeV. The missing transverse energy in the event is  \GeV. The lines in the inner detector indicate the reconstructed particle trajectories. The energy deposition in the calorimeter cells are displayed as light rectangles. The size of the rectangles is proportional to the energy deposits. The histograms attached to the LAr and the Tile calorimeter illustrate the amount of deposited energy.

Collimated sprays of energetic hadrons, called jets, are the dominant feature of high energy proton-proton interactions at the Large Hadron Collider (LHC) at CERN. In Quantum Chromodynamics (QCD) jets are produced via the fragmentation of quarks and gluons. They are key ingredients for many physics measurements and for searches for new phenomena.

During the year the ATLAS detector collected proton-proton collision data at a centre-of-mass energy of  \TeV corresponding to an integrated luminosity of  \ipb. The uncertainty in the jet energy measurement is the dominant experimental uncertainty for numerous physics results, for example the cross-section measurement of inclusive jets, dijets or multijets (1); (2); (3); (4); (5), as well as of vector bosons accompanied by jets (6); (7), and new physics searches with jets in the final state (8); (9); (10); (11); (12); (13).

Jets are observed as groups of topologically related energy deposits in the ATLAS calorimeters. They are reconstructed with the anti- algorithm (14).

Using a Monte Carlo (MC) simulation the observed jets are calibrated such that, on average, the jet energy corresponds to that of the associated stable particles in the ATLAS detector. The calibration of the jet energy scale (JES) should ensure the correct measurement of the average energy across the whole detector and needs to be independent of additional events produced in proton-proton collisions at high luminosity compounding on the event of interest.

In this document, the jet calibration strategies adopted by the ATLAS experiment are outlined and studies to evaluate the uncertainties in the jet energy measurement are presented. A first estimate of the JES uncertainty, described in Ref. (1), was based on information available before the first LHC collisions. It also exploited transverse momentum balance in events with only two jets at high transverse momenta (\pt). A reduced uncertainty with respect to Ref. (1) is presented that is based on the increased knowledge of the detector performance obtained during the analysis of the first year of ATLAS data taking.

ATLAS has developed several jet calibration schemes (15) with different levels of complexity and different sensitivity to systematic effects, which are complementary in their contribution to the jet energy measurement. Each calibration scheme starts from the measured calorimeter energy at the electromagnetic (EM) energy scale, which correctly measures the energy deposited by electromagnetic showers. In the simplest scheme (EM+JES) the jet calibration is derived as a simple correction relating the calorimeter’s response to the true jet energy. More sophisticated schemes exploit the topology of the calorimeter energy depositions to correct for calorimeter non-compensation (nuclear energy losses, etc.) and other jet reconstruction effects.

For the simple EM+JES calibration scheme based only on the JES correction, the JES uncertainty can be determined from the single hadron response measurements in small data sets collected in situ or in test-beams. With a large data set available the JES uncertainty can also be determined using the ratio of the jet transverse momentum to the momentum of a reference object and by a comparison of the data to the Monte Carlo simulation.

Several techniques have been developed to directly determine the uncertainty on the jet energy measurement in situ. The JES uncertainty can be obtained by comparing the jet energy to a well calibrated reference object. A standard technique to probe the absolute jet energy scale, used also in earlier hadron collider experiments, is to measure the \pt balance between the jet and a well-measured object: a photon or a boson. However, the currently limited data statistics imposes a limit on the \pt range that can be tested with this technique. The JES uncertainty on higher jet transverse momenta up to the \TeV-scale can be assessed using the multijet balance technique where a recoil system of well-calibrated jets at lower \pt is balanced against a single jet at higher \pt. A complementary technique uses the total momentum of the tracks associated to the jets as reference objects. While the resolution of the jet energy measurement using tracks in jets is rather poor, the mean jet energy can be determined to the precision of a few percent.

The standard jet calibration and the corresponding uncertainty on the energy measurement are determined for isolated jets in an inclusive jet data sample. Additional uncertainties are evaluated for differences in the response of jets induced by quarks or gluons and for special topologies with close-by jets.

The outline of the paper is as follows.

First the ATLAS detector (Section 2) is described. An overview of the jet calibration procedures and the various calibration schemes is given in Section 3. The Monte Carlo simulation framework is introduced in Section 4. The data samples, data quality assessment and event selection are described in Section 5. Then, the reconstruction (Section 6), and the selection (Section 7) of jets are discussed. The jet calibration method is outlined in Section 8 which includes a prescription to correct for the extra energy due to multiple proton-proton interactions (pile-up).

Section 9 describes the sources of systematic uncertainties for the jet energy measurement and their estimation using Monte Carlo simulations and collision data. Section 10 describes several in situ techniques used to validate these systematic uncertainties. Section 11 presents a technique to improve the resolution of the energy measurements and to reduce the flavour response differences by exploiting the topology of the jets. The systematic uncertainties associated with this technique are described in Section 12. The jet calibration schemes based on calorimeter cell energy weighting in jets are introduced in Section 13, and the associated JES uncertainties are estimated from the in situ techniques as described in Section 14. Section 15 summarises the systematic uncertainties for all studied jet calibration schemes.

The jet reconstruction efficiency and its uncertainty is discussed in Section 16. The response uncertainty of non-isolated jets is investigated in Section 17, while Section 18 and Section 19 discuss response difference for jets originating from light quarks or gluons and presents a method to determine, on average, the jet flavour content in a given data sample. In Section 20 JES uncertainties for jets where a heavy quark is identified are investigated. Finally, possible effects from lack of full calorimeter containment of jets with high transverse momentum are studied in Section 21. The overall conclusion is given in Section 22.

Figure 2: Zoom of the - view of the ATLAS detector showing one of the high-\pt jets of the event shown in Figure 1. The energy depositions in the calorimeter cells are displayed as light rectangles. The size of the rectangles is proportional to the energy deposits. The dark histograms attached to the LAr (Tile) calorimeter illustrates the amount of deposited energy. The lines in the ID display the reconstructed tracks originating from the interaction vertex.

2 The ATLAS detector

The ATLAS detector is a multi-purpose detector designed to observe particles produced in proton-proton and heavy ion collisions. A detailed description can be found in Ref. (16). The detector consists of an inner detector, sampling electromagnetic and hadronic calorimeters and muon chambers. Figure 1 shows a sketch of the detector outline together with an event with two jets at high transverse momenta.

The inner detector (ID) is a tracking system immersed in a magnetic field of  T provided by a solenoid and covers a pseudorapidity1 . The ID barrel region consists of three layers of pixel detectors (Pixel) close to the beam-pipe, four layers of double-sided silicon micro-strip detectors (SCT) providing eight hits per track at intermediate radii, and a transition radiation tracker (TRT) composed of straw tubes in the outer part providing hits per track. At the ID endcap regions each provide three Pixel discs and nine SCT discs perpendicular to the beam direction.

The liquid argon (LAr) calorimeter is composed of sampling detectors with full azimuthal symmetry, housed in one barrel and two endcap cryostats. A highly granular electromagnetic (EM) calorimeter with accordion-shaped electrodes and lead absorbers in liquid argon covers the pseudorapidity range . It contains a barrel part (EMB, ) and an endcap part (EMEC, ) each with three layers in depth (from innermost to outermost EMB1, EMB2, EMB3 and EMEC1, EMEC2, EMEC3). The middle layer has a granularity in space. The innermost layer (strips) consists of cells with eight times finer granularity in the -direction and with -times coarser granularity in the direction.

For , a presampler (Presampler), consisting of an active LAr layer is installed directly in front of the EM calorimeters, and provides a measurement of the energy lost before the calorimeter.

A copper-liquid argon hadronic endcap calorimeter (HEC, ) is located behind the EMEC. A copper/tungsten-liquid argon forward calorimeter (FCal) covers the region closest to the beam at . The HEC has four layers and the FCAL has three layers. From innermost to outermost these are: HEC0, HEC1, HEC2, HEC3 and FCal0, FCal1, FCal2. Altogether, the LAr calorimeters correspond to a total of readout cells, i.e. of the full ATLAS calorimeter readout.

The hadronic Tile calorimeter () surrounding the LAr cryostats completes the ATLAS calorimetry. It consists of plastic scintillator tiles and steel absorbers covering for the barrel and for the extended barrel. Radially, the hadronic Tile calorimeter is segmented into three layers, approximately , and interaction lengths thick at ; the segmentation is ( in the last radial layer). The last layer is used to catch the tails of the longitudinal shower development. The three radial layers of the Tile calorimeter will be referred to (from innermost to outermost) as Tile0, Tile1, Tile2 2.

Between the barrel and the extended barrels there is a gap of about , which is needed for the ID and the LAr services. Gap scintillators (Gap) covering the region are installed on the inner radial surface of the extended barrel modules in the region between the Tile barrel and the extended barrel. Crack scintillators (Scint) are located on the front of the LAr endcap and cover the region .

The muon spectrometer surrounds the ATLAS calorimeter. A system of three large air-core toroids, a barrel and two endcaps, generates a magnetic field in the pseudorapidity range of . The muon spectrometer measures muon tracks with three layers of precision tracking chambers and is instrumented with separate trigger chambers.

The trigger system for the ATLAS detector consists of a hardware-based Level 1 (L1) and a software-based higher level trigger (HLT) (17). Jets are first identified at L1 using a sliding window algorithm from coarse granularity calorimeter towers. This is refined using jets reconstructed from calorimeter cells in the HLT. The lowest threshold inclusive jet trigger is fully efficient for jets with  \GeV. Events with lower \pt jets are triggered by the minimum bias trigger scintillators (MBTS) mounted at each end of the detector in front of the LAr endcap calorimeter cryostats at  m.

3 Introduction to jet energy calibration methods

Hadronic jets used for ATLAS physics analyses are reconstructed by a jet algorithm starting from the energy depositions of electromagnetic and hadronic showers in the calorimeters. An example of a jet recorded by the ATLAS detector and displayed in the plane transverse to the beam line is shown in Figure 2.

The jet Lorentz four-momentum is reconstructed from the corrected energy and angles with respect to the primary event vertex. For systematic studies and calibration purposes track jets are built from charged particles using their momenta measured in the inner detector. Reference jets in Monte Carlo simulations (truth jets) are formed from simulated stable particles using the same jet algorithm.

The jet energy calibration relates the jet energy measured with the ATLAS calorimeter to the true energy of the corresponding jet of stable particles entering the ATLAS detector.

The jet calibration corrects for the following detector effects that affect the jet energy measurement:

  1. Calorimeter non-compensation: partial measurement of the energy deposited by hadrons.

  2. Dead material: energy losses in inactive regions of the detector.

  3. Leakage: energy of particles reaching outside the calorimeters.

  4. Out of calorimeter jet cone: energy deposits of particles inside the truth jet entering the detector that are not included in the reconstructed jet.

  5. Noise thresholds and particle reconstruction efficiency: signal losses in the calorimeter clustering and jet reconstruction.

Jets reconstructed in the calorimeter system are formed from calorimeter energy depositions reconstructed at the electromagnetic energy scale (EM) or from energy depositions that are corrected for the lower detector response to hadrons. The EM scale correctly reconstructs the energy deposited by particles in an electromagnetic shower in the calorimeter. This energy scale is established using test-beam measurements for electrons in the barrel (18); (19); (20); (21); (22) and the endcap calorimeters (23); (24). The absolute calorimeter response to energy deposited via electromagnetic processes was validated in the hadronic calorimeters using muons, both from test-beams (22); (25) and produced in situ by cosmic rays (26). The energy scale of the electromagnetic calorimeters is corrected using the invariant mass of bosons produced in proton-proton collisions ( events) (27). The correction for the lower response to hadrons is solely based on the topology of the energy depositions observed in the calorimeter.

In the simplest case the measured jet energy is corrected, on average, using Monte Carlo simulations, as follows:

(1)

The variable is the calorimeter energy measured at the electromagnetic scale, is the calibrated jet energy and is the calibration function that depends on the measured jet energy and is evaluated in small jet pseudorapidity regions. The variable denotes the correction for additional energy from multiple proton-proton interactions depending on the number of primary vertices ().

The simplest calibration scheme (called EM+JES) applies the JES corrections to jets reconstructed at the electromagnetic scale. This calibration scheme allows a simple evaluation of the systematic uncertainty from single hadron response measurements and systematic Monte Carlo variations. This can be achieved with small data sets and is therefore suitable for early physics analyses.

Other calibration schemes use additional cluster-by-cluster and/or jet-by-jet information to reduce some of the sources of fluctuations in the jet energy response, thereby improving the jet energy resolution. For these calibration schemes the same jet calibration procedure is applied as for the EM+JES calibration scheme, but the energy corrections are numerically smaller.

The global calorimeter cell weighting (GCW) calibration exploits the observation that electromagnetic showers in the calorimeter leave more compact energy depositions than hadronic showers with the same energy. Energy corrections are derived for each calorimeter cell within a jet, with the constraint that the jet energy resolution is minimised. The cell corrections account for all energy losses of a jet in the ATLAS detector. Since these corrections are only applicable to jets and not to energy depositions in general, they are called “global” corrections.

The local cluster weighting (LCW) calibration method first clusters together topologically connected calorimeter cells and classifies these clusters as either electromagnetic or hadronic. Based on this classification energy corrections are derived from single pion Monte Carlo simulations. Dedicated corrections are derived for the effects of non-compensation, signal losses due to noise threshold effects, and energy lost in non-instrumented regions. They are applied to calorimeter clusters and are defined without reference to a jet definition. They are therefore called “local” corrections. Jets are then built from these calibrated clusters using a jet algorithm.

The final jet energy calibration (see Equation 1) can be applied to EM scale jets, with the resulting calibrated jets referred to as EM+JES, or to GCW and LCW calibrated jets, with the resulting jets referred to as GCW+JES and LCW+JES jets.

A further jet calibration scheme, called global sequential (GS) calibration, starts from jets calibrated with the EM+JES calibration and exploits the topology of the energy deposits in the calorimeter to characterise fluctuations in the jet particle content of the hadronic shower development. Correcting for such fluctuations can improve the jet energy resolution. The corrections are applied such that the mean jet energy is left unchanged. The correction uses several jet properties and each correction is applied sequentially. In particular, the longitudinal and transverse structure of the hadronic shower in the calorimeter is exploited.

The simple EM+JES jet calibration scheme does not provide the best performance, but allows in the central detector region the most direct evaluation of the systematic uncertainties from the calorimeter response to single isolated hadron measured in situ and in test-beams and from systematic variations of the Monte Carlo simulation. For the GS the systematic uncertainty is obtained by studying the response after applying the GS calibration with respect to the EM+JES calibration. For the GCW+JES and LCW+JES calibration schemes the JES uncertainty is determined from in situ techniques.

For all calibration schemes the JES uncertainty in the forward detector regions is derived from the uncertainty in the central region using the transverse momentum balance in events where only two jets are produced.

In the following, the calibrated calorimeter jet transverse momentum will be denoted as , and the jet pseudorapidity as .

4 Monte Carlo simulation

4.1 Event generators

The energy and direction of particles produced in proton-proton collisions are simulated using various event generators. An overview of Monte Carlo event generators for LHC physics can be found in Ref. (28). The samples using different event generators and theoretical models used are described below:

  1. Pythia with the MC10 or AMBT1 tune: The event generator Pythia (29) simulates non-diffractive proton-proton collisions using a matrix element at leading order in the strong coupling to model the hard subprocess, and uses \pt-ordered parton showers to model additional radiation in the leading-logarithmic approximation (30). Multiple parton interactions (31), as well as fragmentation and hadronisation based on the Lund string model (32) are also simulated. The proton parton distribution function (PDF) set used is the modified leading-order PDF set MRST LO* (33). The parameters used for tuning multiple parton interactions include charged particle spectra measured by ATLAS in minimum bias collisions (34), and are denoted as the ATLAS MC10 tune(35).

  2. The Perugia2010 tune is an independent tune of Pythia with increased final state radiation to better reproduce the jet shapes and hadronic event shapes using LEP and Tevatron data (36). In addition, parameters sensitive to the production of particles with strangeness and related to jet fragmentation have been adjusted.

  3. Herwig+Jimmy uses a leading order matrix element supplemented with angular-ordered parton showers in the leading-logarithm approximation (37); (38); (39). The cluster model is used for the hadronisation (40). Multiple parton interactions are modelled using Jimmy (41). The model parameters of Herwig/Jimmy have been tuned to ATLAS data (AUET1 tune) (42). The MRST LO* PDF set (33) is used.

  4. Herwig++ (43) is based on the event generator Herwig, but redesigned in the C++ programming language. The generator contains a few modelling improvements. It also uses angular-ordered parton showers, but with an updated evolution variable and a better phase space treatment. Hadronisation is performed using the cluster model. The underlying event and soft inclusive interactions are described using a hard and soft multiple partonic interactions model (44). The MRST LO* PDF set (33) is used.

  5. Alpgen is a tree level matrix-element generator for hard multi-parton processes () in hadronic collisions  (45). It is interfaced to Herwig to produce parton showers in the leading-logarithmic approximation. Parton showers are matched to the matrix element with the MLM matching scheme (46). For the hadronisation, Herwig is used and soft multiple parton interactions are modelled using Jimmy(41) (with the ATLAS MC09 tune (47)). The PDF set used is CTEQ6L1 (48).

4.2 Simulation of the ATLAS detector

The Geant4 software toolkit (49) within the ATLAS simulation framework (50) propagates the generated particles through the ATLAS detector and simulates their interactions with the detector material. The energy deposited by particles in the active detector material is converted into detector signals with the same format as the ATLAS detector read-out. The simulated detector signals are in turn reconstructed with the same reconstruction software as used for the data.

In Geant4 the model for the interaction of hadrons with the detector material can be specified for various particle types and for various energy ranges. For the simulation of hadronic interactions in the detector, the Geant4 set of processes called QGSP_BERT is chosen (51). In this set of processes, the Quark Gluon String model (52); (53); (54); (55); (56) is used for the fragmentation of the nucleus, and the Bertini cascade model (57); (58); (59); (60) for the description of the interactions of hadrons in the nuclear medium.

The Geant4 simulation and in particular the hadronic interaction model for pions and protons, has been validated with test-beam measurements for the barrel (22); (61); (62); (63); (64) and endcap (24); (23); (65) calorimeters. Agreement within a few percent is found between simulation and data for pion momenta between  \GeV and  \GeV.

Further tests have been carried out in situ comparing the single hadron response, measured using isolated tracks and identified single particles. Agreement within a few percent is found for the inclusive measurement (66); (67) and for identified pions and protons from the decay products of kaon and lambda particles produced in proton-proton collisions at  \TeV (68). With this method particle momenta of pions and protons in the range from a few hundred \MeV to  \GeV can be reached. Good agreement between Monte Carlo simulation and data is found.

4.3 Nominal Monte Carlo simulation samples

The baseline (nominal) Monte Carlo sample used to derive the jet energy scale and to estimate the sources of its systematic uncertainty is a sample containing high-\pt jets produced via strong interactions. It is generated with the Pythia event generator with the MC10 tune (see Section 4.1), passed through the full ATLAS detector simulation and is reconstructed as the data.

The ATLAS detector geometry used in the simulation of the nominal sample reflects the geometry of the detector as best known at the time of these studies. Studies of the material of the inner detector in front of the calorimeters have been performed using secondary hadronic interactions (69). Additional information is obtained from studying photon conversions (70) and the energy flow in minimum bias events (71).

4.4 Simulated pile-up samples

For the study of multiple proton-proton interactions, two samples have been used, one for in-time and one for out-of-time pile-up. The first simulates additional proton-proton interactions per bunch crossing, while the second one also contains pile-up arising from bunches before or after the bunch where the event of interest was triggered (for more details see Section 5 and Section 8.1). The bunch configuration of LHC (organised in bunch trains) is also simulated. The additional number of primary vertices in the in-time (bunch-train) pile-up sample is () on average.

5 Data sample and event selection

5.1 Data taking period and LHC conditions

Proton-proton collisions at a centre-of-mass energy of  \TeV, recorded from March to October are analysed. Only data with a fully functioning calorimeter and inner detector are used. The data set corresponds to an integrated luminosity of  \ipb. Due to different data quality requirements the integrated luminosity can differ for the various selections used in the in situ technique analyses.

Several distinct periods of machine configuration and detector operation were present during the data taking. As the LHC commissioning progressed, changes in the beam optics and proton bunch parameters resulted in changes in the number of pile-up interactions per bunch crossing. The spacing between the bunches was no less than  ns.

Figure 3 shows the evolution of the maximum of the distribution of the number of interactions (peak) derived from the online luminosity measurement and assuming an inelastic proton-proton scattering cross section of  mb (72).

The very first data were essentially devoid of multiple proton-proton interactions until the optics of the accelerator beam (specifically ) were changed in order to decrease the transverse size of the beam and increase the luminosity3. This change alone raised the fraction of events with at least two observed interactions from less than to between and (May-June 2010).

A further increase in the number of interactions occurred when the number of protons per bunch (ppb) was increased from approximately to  ppb. Since the number of proton-proton collisions per bunch crossing is proportional to the square of the bunch intensity, the fraction of events with pile-up increased to more than for runs between June and September 2010.

Finally, further increasing the beam intensity slowly raised the average number of interactions per bunch crossing to more than three by the end of the proton-proton run in November .

Figure 3: The peak number of interactions per bunch crossing (“BX”) as measured online by the ATLAS luminosity detectors (72).

5.2 Event selection

Different triggers are used to select the data samples, in order to be maximally efficient over the entire jet \pt-range of interest. The dijet sample is selected using the hardware-based calorimeter jet triggers (73); (17), which are fully efficient for jets with  \GeV. For lower a trigger based on the minimum bias trigger scintillators is used.

The multijet sample uses either the inclusive jet trigger or a trigger that requires at least two, three or more jets with  \GeV at the EM scale. These triggers are fully efficient for jets with  \GeV.

Each event is required to have a primary hard scattering vertex. A primary vertex is required to have at least five tracks with a transverse momentum of  \MeV. The primary vertex associated to the event of interest (hard scattering vertex) is the one with the highest associated transverse track momentum squared used in the vertex fit , where the sum runs over all tracks used in the vertex fit. This renders the contribution from fake vertices due to beam backgrounds to be negligible.

The -jet sample is selected using a photon trigger (17) that is fully efficient for photons passing offline selections. The higher threshold for the photon \pt is  \GeV and this trigger was not pre-scaled; the lower threshold is  \GeV and this trigger was pre-scaled at high luminosity.

5.3 Data quality assessment

The ATLAS data quality (DQ) selection is based upon inspection of a standard set of distributions that leads to a data quality assessment for each subdetector, usually segmented into barrel, forward and endcap regions, as well as for the trigger and for each type of reconstructed physics object (jets, electrons, muons, etc.). Each subsystem sets its own DQ flags, which are recorded in a conditions database. Each analysis applies DQ selection criteria, and defines a set of luminosity blocks (each corresponds to approximately two minutes of data taking). The good luminosity blocks used are those not flagged for having issues affecting a relevant subdetector.

Events with minimum bias and calorimeter triggers were required to belong to specific runs and run periods in which the detector, trigger and reconstructed physics objects have passed a data quality assessment and are deemed suitable for physics analysis.

The primary systems of interest for this study are the electromagnetic and hadronic calorimeters, and the inner tracking detector for studies of the properties of tracks associated with jets.

Loose Medium
HEC spikes ( and ) Loose or
or  \GeV
Coherent and Loose or
EM noise and and and
Non-collision  ns or Loose or
background ( and and ) ns
or ( and ) or ( and and )
or ( and ) or ( and and )
Table 1: Selection criteria used to reject fake jets and non-collision background.

6 Jet reconstruction

In data and Monte Carlo simulation jets are reconstructed using the anti- algorithm (14) with distance parameters or using the FastJet software (74); (75). The four-momentum recombination scheme is used. Jet finding is done in - coordinates, while jet corrections and performance studies are often done in - coordinates. The jet \pt reconstruction threshold is  \GeV.

In the following, only anti- jets with distance parameter are discussed in detail. The results for jets with are similar, if not stated otherwise.

6.1 Reconstructed calorimeter jets

The input to calorimeter jets can be topological calorimeter clusters (topo-clusters(24); (76) or calorimeter towers. Only topo-clusters or towers with a positive energy are considered as input to jet finding.

Topological calorimeter clusters

Topological clusters are groups of calorimeter cells that are designed to follow the shower development taking advantage of the fine segmentation of the ATLAS calorimeters. The topo-cluster formation algorithm starts from a seed cell, whose signal-to-noise () ratio is above a threshold of . The noise is estimated as the absolute value of the energy deposited in the calorimeter cell divided by the RMS of the energy distribution measured in events triggered at random bunch crossings. Cells neighbouring the seed (or the cluster being formed) that have a signal-to-noise ratio of at least are included iteratively. Finally, all calorimeter cells neighbouring the formed topo-cluster are added. The topo-cluster algorithm efficiently suppresses the calorimeter noise.

The topo-cluster algorithm also includes a splitting step in order to optimise the separation of showers from different close-by particles: All cells in a topo-cluster are searched for local maxima in terms of energy content with a threshold of  \MeV. This means that the selected calorimeter cell has to be more energetic than any of its neighbours. The local maxima are then used as seeds for a new iteration of topological clustering, which splits the original cluster into more topo-clusters.

A topo-cluster is defined to have an energy equal to the energy sum of all the included calorimeter cells, zero mass and a reconstructed direction calculated from the weighted averages of the pseudorapidities and azimuthal angles of the constituent cells. The weight used is the absolute cell energy and the positions of the cells are relative to the nominal ATLAS coordinate system.

Calorimeter towers

Calorimeter towers are static, , grid elements built directly from calorimeter cells4.

ATLAS uses two types of calorimeter towers: with and without noise suppression. Calorimeter towers based on all calorimeter cells are called non-noise-suppressed calorimeter towers in the following. Noise-suppressed towers make use of the topo-clusters algorithm, i.e. only calorimeter cells that are included in topo-clusters are used. Therefore, for a fixed geometrical area, noise-suppressed towers have the same energy content as the topo-clusters.

Both types of calorimeter towers have an energy equal to the energy sum of all included calorimeter cells. The formed Lorentz four-momentum has zero mass.

6.2 Reconstructed track jets

Jets built from charged particle tracks originating from the primary hard scattering vertex (track jets) are used to define jets that are insensitive to the effects of pile-up and provide a stable reference to study close-by jet effects.

Tracks with  \GeV and are selected. They are required to have at least one (six) hit(s) in the Pixel (SCT) detector. The transverse () and longitudinal () impact parameters of the tracks measured with respect to the primary vertex are also required to be  mm and  mm, respectively.

The track jets must have at least two constituent tracks and a total transverse momentum of  \GeV. Since the tracking system has a coverage up to , the performance studies of calorimeter jets is carried out in the range for and for .

6.3 Monte Carlo truth jets and flavour association

Monte Carlo simulation truth jets are built from stable particles defined to have proper lifetimes longer than  ps excluding muons and neutrinos.

For certain studies, jets in the Monte Carlo simulation are additionally identified as jets initiated by light or heavy quarks or by gluons based on the generator event record. The highest energy parton that points to the truth jet5 determines the flavour of the jet. Using this method, only a small fraction of the jets ( at low \pt and less at high \pt) could not be assigned a partonic flavour. This definition is sufficient to study the flavour dependence of the jet response. Any theoretical ambiguities of jet flavour assignment do not need to be addressed in the context of a performance study.

(a)
(b)
(c)
(d)
(e)
(f)
(g)
Figure 4: Jet quality selection efficiency for anti- jets with measured with a tag-and-probe technique as a function of in bins of , for loose and medium selection criteria (see Table 1). Only statistical uncertainties are shown. In (e), (f), (g) the loose and medium results overlap.

7 Jet quality selection

Jets at high transverse momenta produced in proton-proton collisions must be distinguished from background jets not originating from hard scattering events. The main backgrounds are the following:

  1. Beam-gas events, where one proton of the beam collided with the residual gas within the beam pipe.

  2. Beam-halo events, for example caused by interactions in the tertiary collimators in the beam-line far away from the ATLAS detector.

  3. Cosmic ray muons overlapping in-time with collision events.

  4. Large calorimeter noise.

The criteria to efficiently reject jets arising from background are only applied to data. They are discussed in the following sections.

7.1 Criteria to remove non-collision background

Noise in the calorimeters

Two types of calorimeter noise are addressed:

  1. Sporadic noise bursts in the hadronic endcap calorimeter (HEC), where a single noisy calorimeter cell contributes almost all of the jet energy. Jets reconstructed from these problematic cells are characterised by a large energy fraction in the HEC calorimeter () as well as a large fraction of the energy in calorimeter cells with poor signal shape quality6 (). Due to the capacitive coupling between channels, the neighbouring calorimeter cells will have an apparent negative energy ().

  2. Rare coherent noise in the electromagnetic calorimeter. Similarly, fake jets arising from this source are characterised by a large electromagnetic energy fraction ()7, and a large fraction of calorimeter cells with poor signal shape quality ().

Cosmic rays or non-collision background

Cosmic rays or non-collision backgrounds can induce events where the jet candidates are not in-time with the beam collision. A cut on the jet time () is applied to reject these backgrounds. The jet time is reconstructed from the energy deposition in the calorimeter by weighting the reconstructed time of calorimeter cells forming the jet with the square of the cell energy. The calorimeter time is defined with respect to the event time recorded by the trigger.

A cut on the is applied to make sure that the jet has some energy deposited in the calorimeter layer closest to the interaction region as expected for a jet originating from the nominal interaction point.

Since a real jet is expected to have tracks, the cut is applied together with a cut on the minimal jet charged fraction (), defined as the ratio of the scalar sum of the \pt of the tracks associated to the jet divided by the jet \pt, for jets within the tracking acceptance.

A cut on the maximum energy fraction in any single calorimeter layer () is applied to further reject non-collision background.

Jet quality selections

Two quality selections are provided:

  1. A loose selection is designed with an efficiency above , that can be used in most of the ATLAS physics analyses.

  2. A medium selection is designed for analyses that select jets at high transverse momentum, such as for jet cross-section measurements (1).

A tight quality selection has been developed for the measurement of the jet quality selection efficiency described in Section 7.2, but is not used in physics analyses, since the medium jet quality selection is sufficient for removing fake jets. The quality selection criteria used to identify and reject fake jets are listed in Table 1.

7.2 Evaluation of the jet quality selection efficiency

The criteria for the jet quality selection are optimised by studying samples with good and fake jets classified by their amount of missing transverse momentum significance8:

  1. Good jets belong to events where the two leading jets have  \GeV, and are back-to-back ( radian) in the plane transverse to the beam, and with a small missing transverse momentum significance .

  2. Fake jets belong to events with a high transverse momentum significance and with a reconstructed jet back-to-back to the missing transverse momentum direction ( radian).

As the jet quality selection criteria are only applied to data an efficiency correction for data is determined. This efficiency is measured using a tag-and-probe method in events with two jets at high transverse momentum. The reference jet () is required to pass the tightened version of the jet quality selections, and to be back-to-back and well-balanced with the probe jet ():

(2)

The jet quality selection criteria were then applied to the probe jets, measuring the fraction of jets passing as a function of and .

The resulting efficiencies for jets with for loose and medium selections applied to the probe jets are shown in Figure 4. The tight selection of the reference jet was varied to study the systematic uncertainty. The loose selection criteria are close to efficient. In the forward region the medium selection criteria are also close to fully efficient. In the central region they have an efficiency of for  \GeV. For lower \pt jets of about  \GeV an inefficiency of up to is observed.

7.3 Summary of the jet quality selection

Quality selections used to reject fake jets with the ATLAS detector have been developed. Simple variables allow the removal of fake jets due to sporadic noise in the calorimeter or non-collision background at the analysis level, with an efficiency greater than over a wide kinematic range.

8 Jet energy calibration in the EM+JES scheme

The simple EM+JES calibration scheme applies corrections as a function of the jet energy and pseudorapidity to jets reconstructed at the electromagnetic scale.

The additional energy due to multiple proton-proton collisions within the same bunch crossing (pile-up) is corrected before the hadronic energy scale is restored, such that the derivation of the jet energy scale calibration is factorised and does not depend on the number of additional interactions measured.

The EM+JES calibration scheme consists of three subsequent steps as outlined below and detailed in the following subsections:

  1. Pile-up correction: The average additional energy due to additional proton-proton interactions is subtracted from the energy measured in the calorimeters using correction constants obtained from in situ measurements.

  2. Vertex correction: The direction of the jet is corrected such that the jet originates from the primary vertex of the interaction instead of the geometrical centre of the detector.

  3. Jet energy and direction correction: The jet energy and direction as reconstructed in the calorimeters are corrected using constants derived from the comparison of the kinematic observables of reconstructed jets and those from truth jets in Monte Carlo simulation.

Figure 5: Distribution of the number constituent calorimeter towers as a function of the jet pseudorapidity for anti- jets with and  \GeV. The black dots indicate the average number of tower constituents.
(a) Tower offset
(b) Jet offset
Figure 6: Tower offset (a) and jet offset (b) at the EM scale as a function of the tower or jet pseudorapidity in bins of the number of reconstructed primary vertices. The jet offset is shown for anti- jets with . Only statistical uncertainties are shown. They are typically smaller than the marker size.
(a) Tower jets
(b) Topo-cluster jets
Figure 7: Transverse jet energy for calorimeter jets associated to track jets measured at the EM scale using a Landau-Gauss fit as a function of the reconstructed vertex multiplicity, , in bins of . Calorimeter jets are reconstructed at the EM scale with calorimeter towers (a) and topo-clusters (b) as inputs. Systematic uncertainties are not shown. The statistical uncertainties from the fit results are smaller than the marker size.
(a) Tower jet offset (EM scale)
(b) Topo-cluster jet offset (EM scale)
(c) Tower jet offset (EM+JES scale)
(d) Topo-cluster jet offset (EM+JES scale)
Figure 8: Jet offset as a function of the number of primary vertices for several ranges of values. The track jet offset is derived for calorimeter tower jets at the EM scale (a), topo-cluster jets at the EM scale (b), calorimeter tower jets at the EM+JES scale (c), and topo-cluster jets at the EM+JES scale (d). Only statistical uncertainties from the fit results are shown.

8.1 Pile-up correction

Correction strategy

The measured energy of reconstructed jets can be affected by contributions that do not originate from the hard scattering event of interest, but are instead produced by additional proton-proton collisions within the same bunch crossing. An offset correction for pile-up is derived from minimum bias data as a function of the number of reconstructed primary vertices, , the jet pseudorapidity, , and the bunch spacing.

This offset correction applied to the jet transverse energy (\et) at the EM scale as the first step of jet calibration can be written generically as:

(3)

where corrects for the jet offset due to pile-up.

Due to the varying underlying particle spectrum and the variation in the calorimeter geometry the jet offset is derived as a function of the jet pseudorapidity. The amount of in-time pile-up is parameterised by . The spacing between consecutive bunches, , is considered, because it can impact the amount by which collisions in previous bunch crossings affect the jet energy measurement9.

The jet offset correction is proportional to the number of constituent towers in a jet as a measure of the jet area. For jets built directly from dynamically-sized topological clusters, for which no clear geometric definition is available, a model is used that describes the average area of a jet in terms of the equivalent number of constituent towers.

Constituent tower multiplicity of jets

The multiplicity of calorimeter towers in jets depends on the internal jet composition and on the presence of pile-up. The average tower multiplicity can be measured in situ.

Figure 5 depicts the distribution of the constituent tower multiplicity for jets based on towers with  \GeV as a function of the jet pseudorapidity. The average number of constituent towers is also indicated. This distribution is governed by the change in physical size of calorimeter towers for a constant interval in pseudorapidity, as well as by differences in the noise spectrum for the various calorimeters and sampling regions.

Pile-up offset for towers and jets

The calorimeter tower offset at the EM scale is derived by measuring the average tower transverse energy for all towers in events with and comparing directly to events with :

(4)

where the angled brackets denote a statistical average over all events. The average is computed for events at each primary vertex multiplicity. For this measurement non-noise-suppressed calorimeter towers are used (see Section 6.1.2) in order to remain sensitive to low energy depositions that may not rise above noise threshold except inside of a jet. The calorimeter tower offset is shown in Figure a for .

The tower offset can be extrapolated to an EM scale jet offset using:

(5)

where is the jet area that, for jets built from calorimeter towers, can be estimated from the constituent tower multiplicity, . For jets built from topo-clusters, the mean equivalent constituent tower multiplicity () is used10. The small dependencies of the constituent multiplicity on and are neglected in the correction, but incorporated as systematic uncertainties (see Section 9.7).

The jet offset for jets with is shown in Figure b.

Track jet based validation and offset correction

Track jets constructed from charged particles originating from the primary hard-scattering vertex matched to the calorimeter jets provide a stable reference that can be used to measure the variation of the calorimeter as a function of . It is therefore possible to validate the tower-based offset correction and also to directly estimate the pile-up energy contribution to jets.

As this method is only applicable to jets within the inner detector acceptance, it serves primarily as a cross-check for the tower-based method discussed above. It can also be used, however, to derive a dedicated offset correction that can be applied to jets at energy scales other than the electromagnetic energy scale. Studying the variation of the offset correction as a function of can establish the systematic uncertainty of the pile-up correction.

The criterion to match a track jet to a calorimeter jet with is

(6)

where . The offset is calculated by measuring the average calorimeter jet as a function of and the transverse momentum of the matched track jet, :

(7)

The reference is used.

Figure 7 shows the jet as a function of for several bins in . Both tower and topo-cluster jets at the electromagnetic scale are used. The most probable value (MPV) of the calorimeter jet is determined from a fit using a Landau distribution convolved with a Gaussian for each range of . A consistent offset of nearly  \GeV per vertex is found for . No systematic trend of the offset as a function of is observed.

Figure 8 presents the jet-based offset correction as a function of derived with respect to for tower and topo-cluster based jet using the EM and the EM+JES scale. As expected, the magnitude of the offset is higher after EM+JES calibration (see Figure c and Figure d), and the increase corresponds to the average jet energy correction (see Section 8.3).

Figure 9: Average jet energy scale correction as a function of the calibrated jet transverse momentum for three representative -intervals obtained from the nominal Monte Carlo simulation sample. The correction is only shown over the accessible kinematic range.
Figure 10: Average simulated jet response () at the electromagnetic scale in bins of EM+JES calibrated jet energy and as a function of the detector pseudorapidity . Also shown are the -intervals used to evaluate the JES uncertainty (see Table 2). The inverse of the response shown in each bin is equal to the average jet energy scale correction.
Figure 11: Difference between the jet pseudorapidity calculated using an origin correction and the true jet pseudorapidity in bins of the calorimeter jet energy calibrated with the EM+JES scheme as a function of the detector pseudorapidity .

8.2 Jet origin correction

Calorimeter jets are reconstructed using the geometrical centre of the ATLAS detector as reference to calculate the direction of jets and their constituents (see Section 6). The jet four-momentum is corrected for each event such that the direction of each topo-cluster points back to the primary hard-scattering vertex. The kinematic observables of each topo-cluster are recalculated using the vector from the primary hard-scattering vertex to the topo-cluster centroid as its direction. The raw jet four-momentum is thereafter redefined as the vector sum of the topo-cluster four-momenta. The origin-corrected pseudorapidity is called . This correction improves the angular resolution and results in a small improvement () in the jet \pt response. The jet energy is unaffected.

8.3 Jet energy correction

The final step of the EM+JES jet calibration restores the reconstructed jet energy to the energy of the Monte Carlo truth jet. Since pile-up effects have already been corrected for, the Monte Carlo samples used to derive the calibration do not include multiple proton-proton interactions.

The calibration is derived using all isolated calorimeter jets that have a matching isolated truth jet within . Here, an isolated jet is defined as a jet having no other jet with  \GeV within , where is the distance parameter of the jet algorithm. A jet is defined to be isolated, if it is isolated with respect to the same jet type, i.e. either a calorimeter or a truth jet.

The final jet energy scale calibration is first parametrised as a function of uncalibrated jet energy and . Here the detector pseudorapidity is used rather than the origin-corrected (used by default in physics analyses), since it more directly correspond to a region of the calorimeter. Energy is used rather than \pt, since the calorimeter responds to energy, and the response curves can be directly compared to expectation and between bins. The method to derive this calibration is detailed below.

The EM-scale jet energy response

(8)

for each pair of calorimeter and truth jets is measured in bins of the truth jet energy and the calorimeter jet detector pseudorapidity 11. For each -bin, the averaged jet response is defined as the peak position of a Gaussian fit to the distribution. In the same -bin, in addition, the average jet energy response () is derived from the mean of the distribution. For a given -bin , the jet response calibration function is obtained using a fit of the values for each -bin .

The fitting function is parameterised as:

(9)

where are free parameters, and is chosen between and depending on the goodness of the fit.

The final jet energy scale correction that relates the measured calorimeter jet energy to the true energy is then defined as in the following:

(10)

where is the jet response calibration function for the relevant -bin .

The average jet energy scale correction is shown as a function of calibrated jet transverse momentum for three jet -intervals in Figure 9. In this and the following figures the correction is only shown over the accessible kinematic range, i.e. values for jets above the kinematic limit are not shown.

The calorimeter jet response is shown for various energy- and -bins in Figure 10. The values of the jet energy correction factors range from about at low jet energies in the central region to less than for high energy jets in the most forward region.

8.4 Jet pseudorapdity correction

After the jet origin and energy corrections the origin-corrected jet is further corrected for a bias due to poorly instrumented regions of the calorimeter. In these regions topo-clusters are reconstructed with a lower energy with respect to better instrumented regions (see Figure 10). This causes the jet direction to be biased towards the better instrumented calorimeter regions.

The -correction is derived as the average difference in -bins, and is parameterised as a function of the calibrated jet energy and the uncorrected . The correction is very small () for most regions of the calorimeter but larger in the transition regions. The size of the bias is illustrated as a function of the detector pseudorapidity and EM+JES calibrated jet energy in Figure 11.

9 Jet energy scale uncertainties for the EM+JES scheme

The JES systematic uncertainty is derived combining information from the single hadron response measured in situ and single pion test-beam measurements, uncertainties on the amount of material of the ATLAS detector, the description of the electronic noise, and the Monte Carlo modelling used in the event generation. Dedicated Monte Carlo simulation test samples are generated with different conditions with respect to the nominal Monte Carlo sample described in Section 4.3. These variations are expected to provide an estimate of the systematic effects contributing to the JES uncertainty.

The pseudorapidity bins used for the estimate of the JES uncertainty divide the ATLAS detector in the eight -regions specified in Table 2 and Figure 10.

region ATLAS detector regions
Central Barrel
Barrel-Endcap Transition
Endcap
Endcap-Forward Transition
Forward
Table 2: Detector regions used for the JES uncertainty estimate.

The JES systematic uncertainty for all jets with pseudorapidity is determined using the JES uncertainty for the central barrel region () as a baseline, with a contribution from the relative calibration of the jets with respect to the central barrel region. This choice is motivated by the good knowledge of the detector geometry in the central region, and by the use of pion response measurements in the ATLAS combined test-beam, which used a full slice of the ATLAS barrel detector, for the estimate of the calorimeter response uncertainties. The region is the largest fully instrumented region considered where combined test-beam results, used to estimate the calorimeter uncertainty, are available for the entire pseudorapidity range.

This section describes the sources of systematic uncertainties and their effect on the response of EM+JES calibrated jets. In Section 9.1, the selection of jets used to derive Monte Carlo based components of the JES systematic uncertainty is discussed. The contributions to the JES systematics due to the following effects are then described:

  1. JES calibration method (Section 9.2).

  2. Calorimeter response (Section 9.3).

  3. Detector simulation (Section 9.4).

  4. Physics model and parameters employed in the Monte Carlo event generator (Section 9.5).

  5. Relative calibration for jets with (Section 9.6).

  6. Additional proton-proton collisions (pile-up) (Section 9.7).

Section 9.8 discusses how the final uncertainties are calculated. Additional uncertainties such as those for close-by jets are mentioned in Section 9.9 and discussed in more detail in Section 17.

9.1 Jet response definition for the JES uncertainty evaluation

The components of the JES uncertainty derived from Monte Carlo samples are obtained by studying the average calorimeter energy response of calibrated jets. The average energy or \pt response, defined as

(11)

is obtained as the peak position from a Gaussian fit to the distribution of the ratio of the kinematic quantities for reconstructed and truth jets by matching isolated calorimeter jets to Monte Carlo truth jets as described in Section 8.3, but without the isolation cut for truth jets12. This is done separately for the nominal and each of the alternative Monte Carlo samples. Only MC truth jets with  \GeV, and calorimeter jets with  \GeV after calibration, are considered. The calibrated response is studied in bins of the truth jet transverse momentum . For each -bin, an associated calibrated \pt value is calculated by multiplying the bin centre with the average response.

The shifts between the Monte Carlo truth level bin centres and the reconstructed bin centres are negligible with respect to the chosen \pt bin widths. Hence the average jet response can be obtained to a good approximation as a function of .

9.2 Uncertainty in the JES calibration

After the jets in the nominal jet Monte Carlo simulation sample are calibrated (see Section 8), the jet energy and \pt response still show slight deviations from unity at low \pt (non-closure). This can be seen in Figure 12, showing the jet response for \pt and energy as a function of for the nominal Monte Carlo sample in the barrel (a) and endcap (b) and the most forward (c) regions for anti- jets with .

Any deviation from unity in the jet energy or \pt response after the application of the JES to the nominal Monte Carlo sample implies that the kinematic observables of the calibrated calorimeter jet are not restored to that of the corresponding truth jet (non-closure). Besides approximations made when deriving the calibration (fit quality, parametrisation of calibration curve), the non-closure is due to the application of the same correction factor for energy and transverse momentum. Closure can therefore only be achieved if the reconstructed jet mass is close to the true jet mass. If this is not the case, such as for low \pt jets, restoring only the jet energy and pseudorapidity will lead to a bias in the \pt calibration. The non-closure is also affected by jet resolution and by details how the Monte Carlo samples are produced in order to cover the large kinematic range in jet transverse momentum.

(a)
(b)
(c)
Figure 12: Average simulated jet \pt response (open squares) after the EM+JES calibration and jet energy response (full circles) as a function of for the nominal Monte Carlo sample for jets in the central (a), endcap (b) and most forward (c) calorimeter regions. Systematic uncertainties are not shown. Statistical uncertainties are smaller than the marker size.

The systematic uncertainty due to the non-closure of the nominal JES calibration is taken as the larger deviation of the response in either energy or \pt from unity. In the barrel region () this contribution amounts to about at low and less than for  \GeV. In the endcap and forward regions, the closure is less than for  \GeV, and the energy response is within for jets with transverse momentum above  \GeV. The deviation of the jet response from unity after calibration is taken as a source of systematic uncertainty.

For physics analysis the non-closure uncertainty only needs to be considered when an absolute jet energy or transverse momentum is needed. For analyses where only the description of the data by the Monte Carlo simulation is important, this uncertainty does not need to be considered.

(a) Energy response
(b) Transverse momentum response
Figure 13: Average simulated jet response in energy (a) and in \pt (b) as a function of in the central region ( ) in the case of additional dead material in the inner detector (full triangles) and in both the inner detector and the calorimeters (open squares). The response within the nominal Monte Carlo sample is shown for comparison (full circles). Only statistical uncertainties are shown.
(a) Energy response
(b) Transverse momentum response
Figure 14: Average simulated response in energy (a) and in \pt (b) as a function of in the central region ( ) for Alpgen+Herwig+Jimmy (open squares) and Pythia with the Perugia2010 tune (full triangles). The response of the nominal Monte Carlo simulation sample is shown for comparison (full circles). Only statistical uncertainties are shown.

9.3 Uncertainty on the calorimeter response

The response and corresponding uncertainties for single particles interacting in the ATLAS calorimeters can be used to derive the jet energy scale uncertainty in the central calorimeter region as detailed in Ref. (77); (67).

In the ATLAS simulation infrastructure the true calorimeter energy deposits in each calorimeter cell can be traced to the particles generated in the collision. The uncertainty in the calorimeter response to jets can then be obtained from the response uncertainty in the individual particles constituting the jet. The in situ measurement of the single particle response detailed in Ref. (67) significantly reduces the uncertainty due to the limited knowledge of the exact detector geometry, in particular that due to the presence of additional dead material, and the modelling of the exact way particles interact in the detector.

The following single particle response measurements are used:

  1. The single hadron energy measured in a cone around an isolated track with respect to the track momentum () in the momentum range from  \GeV.

  2. The pion response measurements performed in the combined test-beam, where a full slice of the ATLAS detector was exposed to pion beams with momenta between  \GeV and  \GeV (63).

Uncertainties for charged hadrons are estimated from these measurements as detailed in Ref. (67). Additional uncertainties are related to:

  1. The calorimeter acceptance for low \pt particles that do not reach the calorimeter or are not reconstructed in a topo-cluster due to the noise thresholds.

  2. Calorimeter response to particles with  \GeV for which the uncertainty is conservatively estimated as , to account for possible calorimeter non-linearities and longitudinal leakage.

  3. The baseline absolute electromagnetic scale for the hadronic and electromagnetic calorimeters for particles in the kinematic range not measured in situ.

  4. The calorimeter response to neutral hadrons is estimated by comparing various models in Geant4. An uncertainty of for particles with an energy  \GeV and for higher energies is obtained.

At high transverse momentum, the dominant contribution to the calorimeter response uncertainties is due to particles with momenta covered by the test-beam. In the pseudorapidity range the shift of the relative jet energy scale expected from the single hadron response measurements in the test-beam is up to , and the uncertainty on the shift is from to . The total envelope (the shift added linearly to the uncertainty) of about , depending on the jet transverse momentum, is taken as the relative JES calorimeter uncertainty. The calorimeter uncertainty is shown in Figure c.

9.4 Uncertainties due to the detector simulation

Calorimeter cell noise thresholds

As described in Section 6.1.1, topo-clusters are constructed based on the signal-to-noise ratio of calorimeter cells, where the noise is defined as the RMS of the measured cell energy distribution in events with no energy depositions from collision events. Discrepancies between the simulated noise and the real noise in data can lead to differences in the cluster shapes and to the presence of fake topo-clusters. For data, the noise can change over time13, while the noise RMS used in the simulation is fixed at the time of the production of the simulated data sets. These effects can lead to biases in the jet reconstruction and calibration, if the electronic noise injected in the Monte Carlo simulation does not reflect that data.

The effect of the calorimeter cell noise mis-modelling on the jet response is estimated by reconstructing topo-clusters, and thereafter jets, in Monte Carlo using the noise RMS measured from data. The actual energy and noise simulated in the Monte Carlo are left unchanged, but the values of the thresholds used to include a given calorimeter cell in a topo-cluster are shifted according to the cell noise RMS measured in data. The response for jets reconstructed with the modified noise thresholds are compared with the response for jets reconstructed in exactly the same sample using the default Monte Carlo noise thresholds.

To further understand the effect of the noise thresholds on the jet response, the noise thresholds were shifted. An increase of each calorimeter cell threshold by in the Monte Carlo simulation is found to give a similar shift in the jet response as using the noise RMS from data. Raising and lowering the cell thresholds by shows that the effect on the jet response from varying the cell noise thresholds is symmetric. This allows the use of the calorimeter cell noise thresholds derived from data as a representative sample to determine the jet energy scale uncertainty and covers the cases when the data have either more or less noise than the simulation.

The maximal observed change in jet response is used to estimate the uncertainty on the jet energy measurement due to the calorimeter cell noise modelling. It is found to be below 3% for the whole pseudorapidity range, and negligible for jets with transverse momenta above  \GeV. The uncertainties assigned to jets with transverse momenta below  \GeV are:

  • and for for anti- jets with and jets, respectively,

  • for for both values.

Additional detector material

The jet energy scale is affected by possible deviations in the material description as the jet energy scale calibration has been derived to restore the energy lost assuming a geometry as simulated in the nominal Monte Carlo sample. Simulated detector geometries that include systematic variations of the amount of material have been designed using test-beam measurements (19), in addition to  \GeV and  \TeV data (70); (71); (78); (79). The possible additional material amount is estimated from these in situ measurements and the a priori knowledge of the detector construction. Specific Monte Carlo simulation samples have been produced using these distorted geometries.

In the case of uncertainties derived with in situ techniques, such as those coming from the single hadron response measurements detailed in Section 9.3, most of the effects on the jet response due to additional dead material do not apply, because in situ measurements do not rely on any simulation where the material could be misrepresented. However, the quality criteria of the track selection for the single hadron response measurement effectively only allow particles that have not interacted in the Pixel and SCT layers of the inner detector to be included in the measurement.

Therefore the effect of dead material in these inner detector layers on the jet response needs to be taken into account for particles in the momentum range of the single hadron response measurement. This is achieved using a specific Monte Carlo sample where the amount of material is systematically varied by adding of material to the existing inner detector services (27). The jet response in the two cases is shown in Figure 13.

Electrons, photons, and hadrons with momenta  \GeV are not included in the single hadron response measurements and therefore there is no estimate based on in situ techniques for the effect of any additional material in front of the calorimeters. This uncertainty is estimated using a dedicated Monte Carlo simulation sample where the overall detector material is systematically varied within the current uncertainties(27) on the detector geometry. The overall changes in the detector geometry include:

  1. The increase in the inner detector material mentioned above.

  2. An extra radiation length () in the cryostat in front of the barrel of the electromagnetic calorimeter ().

  3. An extra between the presampler and the first layer of the electromagnetic calorimeter.

  4. An extra in the cryostat after the barrel of the electromagnetic calorimeter.

  5. Extra material in the barrel-endcap transition region in the electromagnetic calorimeter ().

The uncertainty contribution due to the overall additional detector material is estimated by comparing the EM+JES jet response in the nominal Monte Carlo simulation sample with the jet response in a Monte Carlo simulation sample with a distorted geometry (see Figure 13), and scaled by the average energy fraction of electrons, photons and high transverse momentum hadrons within a jet as a function of \pt.

9.5 Uncertainties due to the event modelling in Monte Carlo generators

The contributions to the JES uncertainty from the modelling of the fragmentation, the underlying event and other choices in the event modelling of the Monte Carlo event generator are obtained from samples based on Alpgen+Herwig+Jimmy and the Pythia Perugia2010 tune discussed in Section 4.

By comparing the baseline Pythia Monte Carlo sample to the Pythia Perugia2010 tune, the effects of soft physics modelling are tested. The Perugia2010 tune provides, in particular, a better description of the internal jet structure recently measured with ATLAS (3). The Alpgen Monte Carlo uses different theoretical models for all steps of the event generation and therefore gives a reasonable estimate of the systematic variations. However, the possible compensation of modelling effects that shift the jet response in opposite directions cannot be excluded.

Figure 14 shows the calibrated jet kinematic response for the two Monte Carlo generators and tunes used to estimate the effect of the Monte Carlo theoretical model on the jet energy scale uncertainty. The kinematic response for the nominal sample is shown for comparison. The ratio of the nominal response to that for each of the two samples is used to estimate the systematic uncertainty to the jet energy scale, and the procedure is further detailed in Section 9.8.

9.6 In situ intercalibration using events with dijet topologies

The response of the ATLAS calorimeters to jets depends on the jet direction, due to the different calorimeter technology and to the varying amounts of dead material in front of the calorimeters. A calibration is therefore needed to ensure a uniform calorimeter response to jets. This can be achieved by applying correction factors derived from Monte Carlo simulations. Such corrections need to be validated in situ given the non-compensating nature of the calorimeters in conjunction with the complex calorimeter geometry and material distribution.

The relative jet calorimeter response and its uncertainty is studied by comparing the transverse momenta of a well-calibrated central jet and a jet in the forward region in events with only two jets at high transverse momenta (dijets). Such techniques have been applied in previous hadron collider experiments(80); (81).

Intercalibration method using a fixed central reference region

The traditional approach for -intercalibration with dijet events is to use a fixed central region of the calorimeters as the reference region. The relative calorimeter response to jets in other calorimeter regions is then quantified by the \pt balance between the reference jet and the probe jet, exploiting the fact that these jets are expected to have equal \pt due to transverse momentum conservation. The \pt balance can be characterised by the asymmetry , defined as

(12)

with . The reference region is chosen as the central region of the barrel: . If both jets fall into the reference region, each jet is used, in turn, as the reference jet. As a consequence, the average asymmetry in the reference region will be zero by construction.

The asymmetry is then used to measure an -intercalibration factor for the probe jet, or its response relative to the reference jet , using the relation

(13)

The asymmetry distribution is calculated in bins of jet and : The bins are labeled for each probe jet and for each -bin. Intercalibration factors are calculated for each bin according to Equation (13):

(14)

where the is the mean value of the asymmetry distribution in each bin. The uncertainty on is taken to be the RMS/ of each distribution, where is the number of events per bin.

Intercalibration using the matrix method

A disadvantage with the method outlined above is that all events are required to have a jet in the central reference region. This results in a significant loss of event statistics, especially in the forward region, where the dijet cross section drops steeply as the rapidity interval between the jets increases. In order to use the full event statistics, the default method can be extended by replacing the “probe” and “reference” jets by “left” and “right” jets defined as . Equations (12) and (13) then become:

(15)

where the term denotes the ratio of the responses, and and are the -intercalibration factors for the left and right jets, respectively.

In this approach there is a response ratio distribution, , whose average value is evaluated for each -bin , -bin  and -bin . The relative correction factor for a given jet -bin and for a fixed -bin , is obtained by minimising a matrix of linear equations:

(16)

where denotes the number of -bins, is the statistical uncertainty of and the function is used to quadratically suppress deviations from unity of the average corrections14. Note that if the jet response does not vary with , then the relative response will be unity for each -bin combination (see Equation 15). A perfect minimization is achieved when all correction factors equal unity.

The minimisation of Equation 16 is done separately for each -bin , and the resulting calibration factors (for each jet -bin ) are scaled such that the average calibration factor in the reference region equals unity.

(a)  \GeV
(b)  \GeV
Figure 15: Relative response of anti- jets with calibrated with the EM+JES scheme, , as a function of the pseudorapidity measured using the matrix and fixed central reference region -intercalibration methods. Results are presented for two bins of :  \GeV measured in minimum bias data (a), and  \GeV measured in data collected using jet triggers (b). The lower part of the figures shows the ratio of the two methods. The central reference region is . Only statistical uncertainties are shown.

Selection of dijet events

Events are retained if there were at least two jets above the jet reconstruction threshold of  \GeV. The event is rejected if either of the two leading jets did not satisfy the standard jet selection criteria (see Section 7).

Events are required to satisfy a specific logic using one central and one forward jet trigger, which select events based on jet activity in the central () and forward () trigger regions, respectively (17). The requirements are chosen such that the trigger efficiency, for a specific region of , was greater than and approximately flat as a function of the pseudorapidity of the probe jet.

To cover the region  \GeV, events triggered by the minimum bias trigger scintillators were used. To enhance events which have only two jets at high \pt, the following selection criteria are applied;

(17)
(18)

where denotes the highest \pt jet in the event and is the azimuthal angle between the two leading jets.

The lowest -bins are likely to suffer from biases. At very low , it is expected that this technique may not measure accurately the relative response to jets, because the assumption of dijet balance at hadron level may start to fail. First, there are residual low- jet effects since the selection criterion on the third jet, which is used to suppress the unbalancing effects of soft QCD radiation, is not as efficient due to the jet reconstruction threshold of  \GeV. Second, the jet reconstruction efficiency is worse for low-\pt jets.

(a)  \GeV
(b)  \GeV
(c)  \GeV
(d)  \GeV
Figure 16: Relative jet response, , of anti- jets with as a function of the jet pseudorapidity measured using the matrix -intercalibration method in bins of the average \pt of the two leading jets (a)  \GeV, (b)  \GeV, (c)  \GeV and  \GeV. The lower part of each figure shows the ratio of Monte Carlo simulation to data. Only statistical uncertainties are shown.
(a)
(b)
Figure 17: Relative jet response, , of anti- jets with as a function of found using the matrix -intercalibration method for (a) and (b) . For  \GeV, the data are collected using the minimum bias trigger stream. For  \GeV, the data are collected using the calorimeter trigger stream. The lower part of each figure shows the ratio of Monte Carlo simulation to data. Only statistical uncertainties are shown.

Comparison of intercalibration methods

The relative jet response obtained with the matrix method is compared to the relative jet response obtained using the method with a fixed reference region. Figure b shows the jet response relative to central jets () for two -bins,  \GeV and  \GeV. These results are obtained for a reference region and therefore not directly comparable to the results discussed below where is used.

The response observed using the fixed reference region method is compatible with those obtained using the matrix method15. These results are representative of all the phase space regions studied in this analysis and the matrix method is therefore used to give the final uncertainty on the in situ -intercalibration due to its higher statistical precision.

Comparison of data with Monte Carlo simulation

Figure d shows the relative response obtained with the matrix method as a function of the jet pseudorapidity for data and Monte Carlo simulations in four regions.

The response in data is reasonably well reproduced by the Monte Carlo simulations for  \GeV, with the Monte Carlo simulation and data agreeing typically better than in the central region () and (depending on ) in the forward region (). At lower values of \pt, the data do not agree as well with the Monte Carlo simulations and the Monte Carlo simulations themselves show a large spread around the data. For  \GeV, the Monte Carlo simulation deviates from the data by about for , with the different Monte Carlo simulations predicting both higher and lower relative responses than that observed in the data.

The main differences, due to residual low- jet effects (see Section 9.6.3), occur between Pythia with the MC10 or the Perugia tune on one side and Alpgen/Herwig++ on the other. The differences therefore apparently reflect a difference in physics modelling between the event generators.

Figure b shows the relative response as a function of . The distributions are shown for jets in the region and also for those in the region . Again, the response is reasonably well described by the Monte Carlo simulation for all calorimeter regions at high \pt and the more central region at low \pt.

Total uncertainties in the forward region

The Monte Carlo simulation predictions for the relative jet response diverge at low values of . The data themselves lie between the different predictions. The uncertainty on the relative jet response must reflect this disagreement because there is no a priori reason to believe one theoretical prediction over another.

The uncertainty on the relative response is taken to be the RMS deviation of the Monte Carlo predictions from the data. At high , where the spread of Monte Carlo simulation predictions is small, the uncertainty mainly reflects the true difference between the response in data and simulation. At low and large , the uncertainty mainly reflects the physics modelling uncertainty, although the detector-based differences between data and simulation are also accounted for. Other uncertainty sources, such as trigger selection or the QCD radiation suppression using the third jet, are either negligible, or included in the total uncertainty assigned from the spread of Monte Carlo predictions around the data.

Figure b shows the uncertainty in the jet response, relative to jets in the central region , as a function of the jet and . The JES uncertainty, determined in the central detector region using the single particle response and systematic variations of the Monte Carlo simulations, is transferred to the forward regions using the results from the dijet balance. These uncertainties are included in the final uncertainty as follows:

  1. The total JES uncertainty in the central region is kept as a baseline.

  2. The uncertainty from the relative intercalibration is taken as the RMS deviation of the MC predictions from the data and is added in quadrature to the baseline uncertainty.

The measurements are performed for transverse momenta in the range  \GeV. The uncertainty for jets with  \GeV is taken as the uncertainty of the last available -bin16. The uncertainties are evaluated separately for jets reconstructed with distance parameters and , and are in general found to be slightly larger for .

Figure 19 shows the relative jet response, and the associated intercalibration uncertainty calculated as detailed above, as a function of jet for two representative -bins.

(a) Transverse momentum
(b) Pseudorapidity
Figure 18: Fractional response uncertainty for anti- jets with calibrated with the EM+JES scheme as obtained from the dijet balance in situ technique as a function of for various -regions of the calorimeter (a) and as a function of in various bins (b).
(a)  \GeV
(b)  \GeV
Figure 19: Average jet response for anti- jets with calibrated with the EM+JES scheme measured relative to a central reference jet within in data and various Monte Carlo generator samples as a function of for in the ranges  \GeV (a) and  \GeV (b). The resulting systematic uncertainty component is shown as a shaded band around the data points. The errors bars on the data points only show the statistical uncertainties.
(a) Tower jets (tower-based correction)
(b) Tower jets (jet-based correction)
(c) Topo-cluster jets (jet-based correction)
Tower jets (tower-based correction)
Figure 20: Jet residual offset measured at the EM scale after pile-up correction using the most probable value obtained from a fit to a Landau+Gauss distribution for various bins in track jet transverse momentum () as a function of the primary vertex multiplicity: tower jets corrected with tower-based offset correction (using the actual number constituent towers) (a), tower jets corrected with the jet-based offset correction (using the average number of constituent towers) (b) and topo-cluster jets corrected with the jet-based offset correction (using the average number of equivalent constituent towers) (c). The axis ranges are identical to Figure 8 for ease of comparison. The jet offset is given for anti- jets at the EM scale with . Only the statistical uncertainties of the fit results are shown.

Figure 21: Relative JES uncertainty from pile-up for anti- jets with in the case of two measured primary vertices, , for central ( , full circles), endcap ( , open squares) and forward ( , full triangles) jets as a function of jet .

9.7 Uncertainties due to multiple proton-proton collisions

Systematic Tower-based offset Jet-based offset Comments
Trigger selection MBTS vs Jet triggers
Tower multiplicity variation vs and
variation Variation of \MeV/vertex
Total (quadrature sum) Assumes uncorrelated errors
Result from closure test Determined from average
Table 3: Summary of systematic uncertainties associated with the offset correction for both the tower-based offset applied jet-by-jet to tower jets and the jet-level offset applied to topo-cluster jets. The uncertainty is expressed as a percentage of the average offset correction, shown in Table 4.
Track jet \pT Tower jets [\GeV/vertex] Topo-cluster jets [\GeV/vertex]
Before After Before After
- \GeV
- \GeV
- \GeV
- \GeV
- \GeV
- \GeV
Average
Table 4: Variation of the calorimeter with pile-up for several bins in track jet \pT. Slopes are given in \GeV/vertex at the electromagnetic scale for each primary vertex from additional proton-proton collisions in the event, and represent the slope of the jet offset before and after the tower-based offset correction. Tower-based corrections are applied to tower jets and jet-based corrections are applied to topo-cluster jets. The reported uncertainties are purely statistical.

The offset to the jet transverse energy due to pile-up interactions can be measured at the EM scale from the average energy in calorimeter towers in minimum bias events. The uncertainty in the pile-up corrections can be obtained by varying certain analysis choices and by studying the jet response with respect to the transverse momentum of track jets as a function of the number of primary vertices.

Tower-based offset closure test using track jets

The systematic uncertainty in the jet offset correction can be evaluated using track jets. Figure 8 shows the variation of the offset among the various ranges of . The result indicates a systematic uncertainty on the correction of approximately  \MeV per additional vertex at the EM scale and  \MeV per additional vertex at the EM+JES scale. Since the jet pile-up offset was about  \MeV before correction, even with this conservative estimate the application of the offset correction represents an improvement of a factor of five obtained over the systematic bias associated with pile-up effects on the calorimeter jet transverse momentum.

The full offset correction shows reasonable closure when using the actual constituent tower multiplicity directly (tower-based) and a slight under-correction using the average constituent multiplicity in the jet (jet-based). Figure a shows the tower-based correction applied to tower jets at the EM scale as a function of the reconstructed vertex multiplicity. The tower-based correction exhibits a closure consistent with zero slope in as a function of . Figure b and Figure c show the jet-based correction applied to both tower jets and topo-cluster jets, respectively. The use of the jet-based offset correction slightly under-corrects for the effect of pile-up for jets constructed from both towers and topo-clusters.

The implication of this observation is two-fold:

  1. There is no significant difference in the sensitivity of topo-cluster jets to pile-up as compared to tower jets.

  2. There is a systematic underestimation of the average tower multiplicity in jets due to the effect of pile-up or due to differences in the jet transverse energy distribution in the derivation and the validation of the pile-up correction.

Jet offset correction uncertainties

The contributions to the jet offset correction uncertainty are estimated from studies that account for:

  1. The effect of variations of the trigger selection on the measured non-noise-suppressed tower energy distribution that is input to the offset correction.

  2. The variation with and of the tower multiplicity in jets based on topo-clusters17.

  3. The variation of the offset correction derived from track jets as a function of the number of primary vertices for various values of track jet \pt.

  4. The non-closure of the tower-based offset correction as evaluated by the dependence of the corrected calorimeter jet energy for calorimeter jets matched to track jets as a function of the number of primary vertices.

The JES uncertainty is estimated by adding all uncertainties in quadrature, including the one from the non-closure of the correction. The track jet method can be used only up to , if a full coverage of the jet area by the tracking acceptance is needed. Beyond