Performance of algorithms that reconstruct missing transverse momentum in \(\sqrt{s}\) = 8 TeV proton–proton collisions in the ATLAS detector

The European Physical Journal C, Apr 2017

The reconstruction and calibration algorithms used to calculate missing transverse momentum (\(E_{\text {T}}^{\text {miss}}\) ) with the ATLAS detector exploit energy deposits in the calorimeter and tracks reconstructed in the inner detector as well as the muon spectrometer. Various strategies are used to suppress effects arising from additional proton–proton interactions, called pileup, concurrent with the hard-scatter processes. Tracking information is used to distinguish contributions from the pileup interactions using their vertex separation along the beam axis. The performance of the \(E_{\text {T}}^{\text {miss}}\) reconstruction algorithms, especially with respect to the amount of pileup, is evaluated using data collected in proton–proton collisions at a centre-of-mass energy of 8 \(\text {TeV}\) during 2012, and results are shown for a data sample corresponding to an integrated luminosity of \(20.3\, \mathrm{fb}^{-1}\). The simulation and modelling of \(E_{\text {T}}^{\text {miss}}\) in events containing a Z boson decaying to two charged leptons (electrons or muons) or a W boson decaying to a charged lepton and a neutrino are compared to data. The acceptance for different event topologies, with and without high transverse momentum neutrinos, is shown for a range of threshold criteria for \(E_{\text {T}}^{\text {miss}}\) , and estimates of the systematic uncertainties in the \(E_{\text {T}}^{\text {miss}}\) measurements are presented.

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Performance of algorithms that reconstruct missing transverse momentum in \(\sqrt{s}\) = 8 TeV proton–proton collisions in the ATLAS detector

Eur. Phys. J. C Performance of algorithms that reconstruct missing transverse √ momentum in s = 8 TeV proton-proton collisions in the ATLAS detector ATLAS Collaboration 0 0 CERN , 1211 Geneva 23 , Switzerland 1 Also at Department of Physics, California State University , Fresno, CA , USA 2 Also at TRIUMF , Vancouver, BC , Canada 3 Also at Department of Physics and Astronomy, University of Louisville , Louisville, KY , USA 4 Also at Institute of Physics, Azerbaijan Academy of Sciences , Baku , Azerbaijan 5 Also at Novosibirsk State University , Novosibirsk , Russia 6 Also at Department of Physics, King's College London , London , UK The reconstruction and calibration algorithms used to calculate missing transverse momentum (ETmiss) with the ATLAS detector exploit energy deposits in the calorimeter and tracks reconstructed in the inner detector as well as the muon spectrometer. Various strategies are used to suppress effects arising from additional proton-proton interactions, called pileup, concurrent with the hard-scatter processes. Tracking information is used to distinguish contributions from the pileup interactions using their vertex separation along the beam axis. The performance of the E miss reconT struction algorithms, especially with respect to the amount of pileup, is evaluated using data collected in proton-proton collisions at a centre-of-mass energy of 8 TeV during 2012, and results are shown for a data sample corresponding to an integrated luminosity of 20.3 fb−1. The simulation and modelling of E miss in events containing a Z boson decaying T to two charged leptons (electrons or muons) or a W boson decaying to a charged lepton and a neutrino are compared to data. The acceptance for different event topologies, with and without high transverse momentum neutrinos, is shown for a range of threshold criteria for E miss, and estimates of T the systematic uncertainties in the E miss measurements are T presented. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . 2 ATLAS detector . . . . . . . . . . . . . . . . . . . . 3 Data samples and event selection . . . . . . . . . . . 3.1 Track and vertex selection . . . . . . . . . . . . . 3.2 Event selection for Z → . . . . . . . . . . . . 3.3 Event selection for W → ν . . . . . . . . . . . 3.4 Monte Carlo simulation samples . . . . . . . . . 4 Reconstruction and calibration of the E miss . . . . . . T 4.1 Reconstruction of the E miss . . . . . . . . . . . . T 4.1.1 Reconstruction and calibration of the E miss T hard terms . . . . . . . . . . . . . . . . . . 4.1.2 Reconstruction and calibration of the E miss soft T term . . . . . . . . . . . . . . . . . . . . . 4.1.3 Jet pT threshold and JVF selection . . . . 4.2 Track E miss . . . . . . . . . . . . . . . . . . . . T 5 Comparison of E miss distributions in data and MC T simulation . . . . . . . . . . . . . . . . . . . . . . . 5.1 Modelling of Z → events . . . . . . . . . . . 5.2 Modelling of W → ν events . . . . . . . . . . 6 Performance of the E miss in data and MC simulation . T 6.1 Resolution of E miss . . . . . . . . . . . . . . . . T 6.1.1 Resolution of the E miss as a function of T the number of reconstructed vertices . . . . 6.1.2 Resolution of the ETmiss as a function of ET 6.2 The E miss response . . . . . . . . . . . . . . . . T 6.2.1 Measuring E miss recoil versus pTZ . . . . . T 6.2.2 Measuring E miss response in simulated T W → ν events . . . . . . . . . . . . . . 6.3 The E miss angular resolution . . . . . . . . . . . T 6.4 Transverse mass in W → ν events . . . . . . . 6.5 Proxy for ETmiss significance . . . . . . . . . . . 6.6 Tails of E miss distributions . . . . . . . . . . . . T 6.7 Correlation of fake E miss between algorithms . . T 7 Jet- pT threshold and vertex association selection . . . 8 Systematic uncertainties of the soft term . . . . . . . 8.1 Methodology for CST . . . . . . . . . . . . . . . 8.1.1 Evaluation of balance between the soft term and the hard term . . . . . . . . . . . 8.1.2 Cross-check method for the CST system atic uncertainties . . . . . . . . . . . . . . 8.2 Methodology for TST and Track E miss . . . . . . T 8.2.1 Propagation of systematic uncertainties . . 8.2.2 Closure of systematic uncertainties . . . . . 8.2.3 Systematic uncertainties from tracks inside jets . . . . . . . . . . . . . . . . . . . . . 9 Conclusions . . . . . . . . . . . . . . . . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . A. Calculation of EJAF . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). Sources of fake E miss may include pT mismeasurement, T miscalibration, and particles going through un-instrumented regions of the detector. In MC simulations, the E miss from T each algorithm is compared to the true E miss (ETmiss,True), T which is defined as the magnitude of the vector sum of pT of stable2 weakly interacting particles from the hard-scatter collision. Then the selection efficiency after a E miss-threshold T requirement is studied in simulated events with high- pT neutrinos (such as top-quark pair production and vector-boson fusion H → τ τ ) or possible new weakly interacting particles that escape detection (such as the lightest supersymmetric particles). This paper is organized as follows. Section 2 gives a brief introduction to the ATLAS detector. Section 3 describes the data and MC simulation used as well as the event selections applied. Section 4 outlines how the E miss is reconstructed T and calibrated while Sect. 5 presents the level of agreement between data and MC simulation in W and Z boson production events. Performance studies of the E miss algorithms on T data and MC simulation are shown for samples with different event topologies in Sect. 6. The choice of jet selection criteria used in the E miss reconstruction is discussed in Sect. 7. T Finally, the systematic uncertainty in the absolute scale and resolution of the E miss is discussed in Sect. 8. To provide T a reference, Table 1 summarizes the different E miss terms T discussed in this paper. 2 ATLAS detector The ATLAS detector [2] is a multi-purpose particle physics apparatus with a forward-backward symmetric cylindrical geometry and nearly 4π coverage in solid angle. For tracking, the inner detector (ID) covers the pseudorapidity range of |η| < 2.5, and consists of a silicon-based pixel detector, a semiconductor tracker (SCT) based on microstrip technology, and, for |η| < 2.0, a transition radiation tracker (TRT). The ID is surrounded by a thin superconducting solenoid providing a 2 T magnetic field, which allows the measurement of the momenta of charged particles. A high-granularity electromagnetic sampling calorimeter based on lead and liquid argon (LAr) technology covers the region of |η| < 3.2. A hadronic calorimeter based on steel absorbers and plasticscintillator tiles provides coverage for hadrons, jets, and τ leptons in the range of |η| < 1.7. LAr technology using a copper absorber is also used for the hadronic calorimeters in the end-cap region of 1.5 < |η| < 3.2 and for electromagnetic and hadronic measurements with copper and tungsten absorbing materials in the forward region of 3.1 < |η| < 4.9. The muon spectrometer (MS) surrounds the calorimeters. It 2 ATLAS defines stable particles as those having a mean lifetime > Table 1 Summary of definitions for ETmiss terms used in this paper Missing transverse momentum arising from the presence of neutrinos or other non-interacting particles in an event. In case of simulated events the true E miss (ETmiss,True) corresponds to the E miss in such events T T defined as the magnitude of the vector sum of pT of non-interacting particles computed from the generator information Missing transverse momentum arising from the miscalibration or misidentification of physics objects in the event. It is typically studied in Z → μμ events where the intrinsic E miss is normally expected to be T zero The component of the E miss computed from high- pT physics objects, which includes reconstructed T electrons, photons, muons, τ -leptons, and jets Typically low- pT calorimeter energy deposits or tracks, depending on the soft-term definition, that are not associated to physics objects included in the hard terms All E miss reconstruction algorithms in Sect. 4.1.2 except the Calorimeter Soft Term, which does not apply T pileup suppression This refers to all reconstruction algorithms in Sect. 4.1.2 except the Track E miss, namely the Calorimeter T Soft Term, Track Soft Term, Extrapolated Jet Area with Filter, and Soft-Term Vertex-Fraction algorithms. These consider the physics objects such as electrons, photons, muons, τ -leptons, and jets during the E miss reconstruction T consists of three air-core superconducting toroid magnet systems, precision tracking chambers to provide accurate muon tracking out to |η| = 2.7, and additional detectors for triggering in the region of |η| < 2.4. A precision measurement of the track coordinates is provided by layers of drift tubes at three radial positions within |η| < 2.0. For 2.0 < |η| < 2.7, cathode-strip chambers with high granularity are instead used in the innermost plane. The muon trigger system consists of resistive-plate chambers in the barrel (|η| < 1.05) and thingap chambers in the end-cap regions (1.05 < |η| < 2.4). 3 Data samples and event selection ATLAS recorded pp collisions at a centre-of-mass energy of 8 TeV with a bunch crossing interval (bunch spacing) of 50 ns in 2012. The resulting integrated luminosity is 20.3 fb−1 [3]. Multiple inelastic pp interactions occurred in each bunch crossing, and the mean number of inelastic collisions per bunch crossing ( μ ) over the full dataset is 21 [4], exceptionally reaching as high as about 70. Data are analysed only if they satisfy the standard ATLAS data-quality assessment criteria [5]. Jet-cleaning cuts [5] are applied to minimize the impact of instrumental noise and outof-time energy deposits in the calorimeter from cosmic rays or beam-induced backgrounds. This ensures that the residual sources of E miss mismeasurement due to those instrumental T effects are suppressed. 3.1 Track and vertex selection The ATLAS detector measures the momenta of charged particles using the ID [6]. Hits from charged particles are recorded and are used to reconstruct tracks; these are used to reconstruct vertices [7, 8]. Each vertex must have at least two tracks with pT > 0.4 GeV; for the primary hard-scatter vertex (PV), the requirement on the number of tracks is raised to three. The PV in each event is selected as the vertex with the largest value of ( pT)2, where the scalar sum is taken over all the tracks matched to the vertex. The following track selection criteria3 [7] are used throughout this paper, including the vertex reconstruction: These tracks are then matched to the PV by applying the following selections: The transverse (longitudinal) impact parameter d0 (z0) is the transverse (longitudinal) distance of the track from the PV and is computed at the point of closest approach to the PV in the plane transverse to the beam axis. The requirements on the number of hits ensures that the track has an 3 The track reconstruction for electrons and for muons does not strictly follow these definitions. For example, a Gaussian Sum Filter [9] algorithm is used for electrons to improve the measurements of its track parameters, which can be degraded due to Bremsstrahlung losses. accurate pT measurement. The |η| requirement keeps only the tracks within the ID acceptance, and the requirement of pT > 0.4 GeV ensures that the track reaches the outer layers of the ID. Tracks with low pT have large curvature and are more susceptible to multiple scattering. The average spread along the beamline direction for pp collisions in ATLAS during 2012 data taking is around 50 mm, and the typical track z0 resolution for those with |η| < 0.2 and 0.5 < pT < 0.6 GeV is 0.34 mm. The typical track d0 resolution is around 0.19 mm for the same η and pT ranges, and both the z0 and d0 resolutions improve with higher track pT. Pileup effects come from two sources: in-time and out-oftime. In-time pileup is the result of multiple pp interactions in the same LHC bunch crossing. It is possible to distinguish the in-time pileup interactions by using their vertex positions, which are spread along the beam axis. At μ = 21, the efficiency to reconstruct and select the correct vertex for Z → μμ simulated events is around 93.5% and rises to more than 98% when requiring two generated muons with pT > 10 GeV inside the ID acceptance [10]. When vertices are separated along the beam axis by a distance smaller than the position resolution, they can be reconstructed as a single vertex. Each track in the reconstructed vertex is assigned a weight based upon its compatibility with the fitted vertex, which depends on the χ 2 of the fit. The fraction of Z → μμ reconstructed vertices with more than 50% of the sum of track weights coming from pileup interactions is around 3% at μ = 21 [7,10]. Out-of-time pileup comes from pp collisions in earlier and later bunch crossings, which leave signals in the calorimeters that can take up to 450 ns for the charge collection time. This is longer than the 50 ns between subsequent collisions and occurs because the integration time of the calorimeters is significantly larger than the time between the bunch crossings. By contrast the charge collection time of the silicon tracker is less than 25 ns. 3.2 Event selection for Z → Candidate Z → events are required to pass an electron or muon trigger [11,12]. The lowest pT threshold for the unprescaled single-electron (single-muon) trigger is pT > 25 (24) GeV, and both triggers apply a track-based isolation as well as quality selection criteria for the particle identification. Triggers with higher pT thresholds, without the isolation requirements, are used to improve acceptance at high pT. These triggers require pT > 60 (36) GeV for electrons (muons). Events are accepted if they pass any of the above trigger criteria. Each event must contain at least one primary vertex with a z displacement from the nominal pp interaction point of less than 200 mm and with at least three associated tracks. The offline selection of Z → μμ events requires the presence of exactly two identified muons [13]. An identified muon is reconstructed in the MS and is matched to a track in the ID. The combined ID+MS track must have pT > 25 GeV and |η| < 2.5. The z displacement of the muon track from the primary vertex is required to be less than 10 mm. An isolation criterion is applied to the muon track, where the scalar sum of the pT of additional tracks within a cone of size R = ( η)2 + ( φ)2 = 0.2 around the muon is required to be less than 10% of the muon pT. In addition, the two leptons are required to have opposite charge, and the reconstructed dilepton invariant mass, m , is required to be consistent with the Z boson mass: 66 < m < 116 GeV. The E miss modelling and performance results obtained in T Z → μμ and Z → ee events are very similar. For the sake of brevity, only the Z → μμ distributions are shown in all sections except for Sect. 6.6. 3.3 Event selection for W → Leptonically decaying W bosons (W → ν) provide an important event topology with intrinsic E miss; the E miss T T distribution for such events is presented in Sect. 5.2. Similar to Z → events, a sample dominated by leptonically decaying W bosons is used to study the E miss scale in T Sect. 6.2.2, the resolution of the E miss direction in Sect. 6.3, T and the impact on a reconstructed kinematic observable in Sect. 6.4. The E miss distributions for W boson events in Sect. 5.2 T use the electron final state. These electrons are selected with |η| < 2.47, are required to meet the “medium” identification criteria [14] and satisfy pT > 25 GeV. Electron candidates in the region 1.37 < |η| < 1.52 suffer from degraded momentum resolution and particle identification due to the transition from the barrel to the end-cap detector and are therefore discarded in these studies. The electrons are required to be isolated, such that the sum of the energy in the calorimeter within a cone of size R = 0.3 around the electron is less than 14% of the electron pT. The summed pT of other tracks within the same cone is required to be less than 7% of the electron pT. The calorimeter isolation variable [14] is corrected by subtracting estimated contributions from the electron itself, the underlying event [15], and pileup. The Table 2 Generators, cross-section normalizations, PDF sets, and MC tunes used in this analysis electron tracks are then matched to the PV by applying the following selections: and reconstruction performance between muons and electrons differ. mT = 3.4 Monte Carlo simulation samples Table 2 summarizes the MC simulation samples used in this paper. The Z → and W → ν samples are generated with Alpgen [16] interfaced with Pythia [17] (denoted by Alpgen+Pythia) to model the parton shower and hadronization, and underlying event using the PERUGIA2011C set [18] of tunable parameters. One exception is the Z → τ τ sample with leptonically decaying τ -leptons, which is generated with Alpgen interfaced with Herwig [19] with the underlying event modelled using Jimmy [20] and the AUET2 tunes [21]. Alpgen is a multi-leg generator that provides tree-level calculations for diagrams with up to five additional partons. The matrix-element MC calculations are matched to a model of the parton shower, underlying event and hadronization. The main processes that are backgrounds to Z → and W → ν are events with one or more top quarks (t t¯ and single-top-quark processes) and diboson production (W W , W Z , Z Z ). The t t¯ and t W processes are generated with Powheg [22] interfaced with Pythia [17] for hadronization and parton showering, and PERUGIA2011C for the underlying event modelling. All the diboson processes are generated with Sherpa [23]. Powheg is a leading-order generator with corrections at next-to-leading order in αS, whereas Sherpa is a multi-leg generator at tree level. To study event topologies with high jet multiplicities and to investigate the tails of the E miss distributions, t t¯ events T with at least one leptonically decaying W boson are considered in Sect. 6.6. The single top quark (t W ) production is considered with at least one leptonically decaying W boson. Both the t t¯ and t W processes contribute to the W and Z boson distributions shown in Sect. 5 as well as Z boson distributions in Sects. 4, 6, and 8 that compare data and simulation. A supersymmetric (SUSY) model comprising pair-produced 500 GeV gluinos each decaying to a t t¯ pair and a neutralino is simulated with Herwig++ [24]. Finally, to study events with forward jets, the vector-boson fusion (VBF) production of H → τ τ , generated with Powheg+Pythia8 [25], is considered. Both τ -leptons are forced to decay leptonically in this sample. To estimate the systematic uncertainties in the data/MC ratio arising from the modelling of the soft hadronic recoil, E miss distributions simulated with different MC T generators, parton shower and underlying event models are compared. The estimation of systematic uncertainties is performed using a comparison of data and MC simulation, as shown in Sect. 8.2. The following combinations of generators and parton shower models are considered: Sherpa, Alpgen+Herwig, Alpgen+Pythia, and Powheg+Pythia8. The corresponding underlying event tunes are mentioned in Table 2. Parton distribution functions are taken from CT10 [30] for Powheg and Sherpa samples and CTEQ6L1 [38] for Alpgen samples. Generated events are propagated through a Geant4 simulation [39, 40] of the ATLAS detector. Pileup collisions are generated with Pythia8 for all samples, and are overlaid on top of simulated hard-scatter events before event reconstruction. Each simulation sample is weighted by its corresponding cross-section and normalized to the integrated luminosity of the data. 4 Reconstruction and calibration of the Emiss Several algorithms have been developed to reconstruct the E miss in ATLAS. They differ in the information used to recon T struct the pT of the particles, using either energy deposits in the calorimeters, tracks reconstructed in the ID, or both. This section describes these various reconstruction algorithms, and the remaining sections discuss the agreement between data and MC simulation as well as performance studies. 4.1 Reconstruction of the E miss The E miss reconstruction uses calibrated physics objects to T estimate the amount of missing transverse momentum in the detector. The E miss is calculated using the components along T the x and y axes: where each term is calculated as the negative vectorial sum of transverse momenta of energy deposits and/or tracks. To avoid double counting, energy deposits in the calorimeters and tracks are matched to reconstructed physics objects in the following order: electrons (e), photons (γ ), the visible parts of hadronically decaying τ -leptons (τhad-vis; labelled as τ ), jets and muons (μ). Each type of physics object is represented by a separate term in Eq. (2). The signals not associated with physics objects form the “soft term”, whereas those associated with the physics objects are collectively referred to as the “hard term”. The magnitude and azimuthal angle4 (φmiss) of E miss are T calculated as: The total transverse energy in the detector, labelled as ET, quantifies the total event activity and is an important observable for understanding the resolution of the E miss, especially T with increasing pileup contributions. It is defined as: ET = which is the scalar sum of the transverse momenta of reconstructed physics objects and soft-term signals that contribute to the E miss reconstruction. The physics objects included in T psoft depend on the E miss definition, so both calorimeter T T objects and track-based objects may be included in the sum, despite differences in pT resolution. 4.1.1 Reconstruction and calibration of the E miss hard The hard term of the E miss, which is computed from the T reconstructed electrons, photons, muons, τ -leptons, and jets, is described in more detail in this section. Electrons are reconstructed from clusters in the electromagnetic (EM) calorimeter which are associated with an ID track [14]. Electron identification is restricted to the range of |η| < 2.47, excluding the transition region between the barrel and end-cap EM calorimeters, 1.37 < |η| < 1.52. They are calibrated at the EM scale5 with the default electron calibra 4 The arctan function returns values from [−π, +π ] and uses the sign of both coordinates to determine the quadrant. 5 The EM scale is the basic signal scale for the ATLAS calorime ters. It accounts correctly for the energy deposited by EM showers in the calorimeter, but it does not consider energy losses in the uninstrumented material. tion, and those satisfying the “medium” selection criteria [14] with pT > 10 GeV are included in the E miss reconstruction. T The photon reconstruction is also seeded from clusters of energy deposited in the EM calorimeter and is designed to separate electrons from photons. Photons are calibrated at the EM scale and are required to satisfy the “tight” photon selection criteria with pT > 10 GeV [14]. Muon candidates are identified by matching an ID track with an MS track or segment [13]. MS tracks are used for 2.5 < |η| < 2.7 to extend the η coverage. Muons are required to satisfy pT > 5 GeV to be included in the E miss reconT struction. The contribution of muon energy deposited in the calorimeter is taken into account using either parameterized estimates or direct measurements, to avoid double counting a small fraction of their momenta. Jets are reconstructed from three-dimensional topological clusters (topoclusters) [41] of energy deposits in the calorimeter using the anti-kt algorithm [42] with a distance parameter R = 0.4. The topological clustering algorithm suppresses noise by forming contiguous clusters of calorimeter cells with significant energy deposits. The local cluster weighting (LCW) [43,44] calibration is used to account for different calorimeter responses to electrons, photons and hadrons. Each cluster is classified as coming from an EM or hadronic shower, using information from its shape and energy density, and calibrated accordingly. The jets are reconstructed from calibrated topoclusters and then corrected for in-time and out-of-time pileup as well as the position of the PV [4]. Finally, the jet energy scale (JES) corrects for jet-level effects by restoring, on average, the energy of reconstructed jets to that of the MC generator-level jets. The complete procedure is referred to as the LCW+JES scheme [43,44]. Without changing the average calibration, additional corrections are made based upon the internal properties of the jet (global sequential calibration) to reduce the flavour dependence and energy leakage effects [44]. Only jets with calibrated pT greater than 20 GeV are used to calculate the jet term Exm(iys)s,jets in Eq. (2), and the optimization of the 20 GeV threshold is discussed in Sect. 7. To suppress contributions from jets originating from pileup interactions, a requirement on the jet vertex-fraction (JVF) [4] may be applied to selected jet candidates. Tracks matched to jets are extrapolated back to the beamline to ascertain whether they originate from the hard scatter or from a pileup collision. The JVF is then computed as the ratio shown below: JVF = This is the ratio of the scalar sum of transverse momentum of all tracks matched to the jet and the primary vertex to the pT sum of all tracks matched to the jet, where the sum is performed over all tracks with pT > 0.5 GeV and |η| < 2.5 and the matching is performed using the “ghost-association” procedure [45,46]. The JVF distribution is peaked toward 1 for hard-scatter jets and toward 0 for pileup jets. No JVF selection requirement is applied to jets that have no associated tracks. Requirements on the JVF are made in the STVF, EJAF, and TST E miss algorithms as described in Table 3 and Sect. 4.1.3. T Hadronically decaying τ -leptons are seeded by calorimeter jets with |η| < 2.5 and pT > 10 GeV. As described for jets, the LCW calibration is applied, corrections are made to subtract the energy due to pileup interactions, and the energy of the hadronically decaying τ candidates is calibrated at the τ -lepton energy scale (TES) [47]. The TES is independent of the JES and is determined using an MC-based procedure. Hadronically decaying τ -leptons passing the “medium” requirements [47] and having pT > 20 GeV after TES corrections are considered for the E miss reconstruction. T 4.1.2 Reconstruction and calibration of the E miss soft term T The soft term is a necessary but challenging ingredient of the E miss reconstruction. It comprises all the detector sig T nals not matched to the physics objects defined above and can contain contributions from the hard scatter as well as the underlying event and pileup interactions. Several algorithms designed to reconstruct and calibrate the soft term have been developed, as well as methods to suppress the pileup contributions. A summary of the E miss and soft-term reconstruction T algorithms is given in Table 3. Four soft-term reconstruction algorithms are considered in this paper. Below the first two are defined, and then some motivation is given for the remaining two prior to their definition. • Calorimeter Soft Term (CST) This reconstruction algorithm [1] uses information mainly from the calorimeter and is widely used by ATLAS. The algorithm also includes corrections based on tracks but does not attempt to resolve the various pp interactions based on the track z0 measurement. The soft term is referred to as the CST, whereas the entire E miss is writT ten as CST E miss. Corresponding naming schemes are T used for the other reconstruction algorithms. The CST is reconstructed using energy deposits in the calorimeter which are not matched to the high- pT physics objects used in the E miss. To avoid fake signals in the calorimeter, T noise suppression is important. This is achieved by calculating the soft term using only cells belonging to topoclusters, which are calibrated at the LCW scale [43,44]. The tracker and calorimeter provide redundant pT measurements for charged particles, so an energy-flow algorithm is used to determine which measurement to use. Tracks Table 3 Summary of ETmiss and soft-term reconstruction algorithms used in this paper The Calorimeter Soft Term (CST) E miss takes its soft term from energy deposits in T the calorimeter which are not matched to high- pT physics objects. Although noise suppression is applied to reduce fake signals, no additional pileup suppression techniques are used The Track Soft Term (TST) E miss algorithm uses a soft term that is calculated using T tracks within the inner detector that are not associated with high- pT physics objects. The JVF selection requirement is applied to jets The Extrapolated Jet Area with Filter E miss algorithm applies pileup subtraction to T the CST based on the idea of jet-area corrections. The JVF selection requirement is applied to jets The Soft-Term Vertex-Fraction (STVF) E miss algorithm suppresses pileup effects in T the CST by scaling the soft term by a multiplicative factor calculated based on the fraction of scalar-summed track pT not associated with high- pT physics objects that can be matched to the primary vertex. The JVF selection requirement is applied to jets The Track E miss is reconstructed entirely from tracks to avoid pileup contamination T that affects the other algorithms with pT > 0.4 GeV that are not matched to a highpT physics objects are used instead of the calorimeter pT measurement, if their pT resolution is better than the expected calorimeter pT resolution. The calorimeter resolution is estimated as 0.4 · √ pT GeV, in which the pT is the transverse momentum of the reconstructed track. Geometrical matching between tracks and topoclusters (or high- pT physics objects) is performed using the R significance defined as R/σ R , where σ R is the R resolution, parameterized as a function of the track pT. A track is considered to be associated to a topocluster in the soft term when its minimum R/σ R is less than 4. To veto tracks matched to high- pT physics objects, tracks are required to have R/σ R > 8. The ETmiss calculated using the CST algorithm is documented in previous publications such as Ref. [1] and is the standard algorithm in most ATLAS 8 TeV analyses. • Track Soft Term (TST) The TST is reconstructed purely from tracks that pass the selections outlined in Sect. 3.1 and are not associated with the high- pT physics objects defined in Sect. 4.1.1. The detector coverage of the TST is the ID tracking volume (|η| < 2.5), and no calorimeter topoclusters inside or beyond this region are included. This algorithm allows excellent vertex matching for the soft term, which almost completely removes the in-time pileup dependence, but misses contributions from soft neutral particles. The track-based reconstruction also entirely removes the outof-time pileup contributions that affect the CST. To avoid double counting the pT of particles, the tracks matched to the high- pT physics objects need to be removed from the soft term. All of the following classes of tracks are excluded from the soft term: – tracks within a cone of size R = 0.05 around electrons and photons – tracks within a cone of size R = 0.2 around τhad-vis – ID tracks associated with identified muons – tracks matched to jets using the ghost-association technique described in Sect. 4.1.1 – isolated tracks with pT ≥ 120 GeV (≥200 GeV for |η| < 1.5) having transverse momentum uncertainties larger than 40% or having no associated calorimeter energy deposit with pT larger than 65% of the track pT. The pT thresholds are chosen to ensure that muons not in the coverage of the MS are still included in the soft term. This is a cleaning cut to remove mismeasured tracks. A deterioration of the CST E miss resolution is observed T as the average number of pileup interactions increases [1]. All E miss terms in Eq. (2) are affected by pileup, but the T terms which are most affected are the jet term and CST, because their constituents are spread over larger regions in the calorimeters than those of the E miss hard terms. Methods T to suppress pileup are therefore needed, which can restore the E miss resolution to values similar to those observed in T the absence of pileup. The TST algorithm is very stable with respect to pileup but does not include neutral particles. Two other pileupsuppressing algorithms were developed, which consider contributions from neutral particles. One uses an η-dependent event-by-event estimator for the transverse momentum density from pileup, using calorimeter information, while the other applies an event-by-event global correction based on the amount of charged-particle pT from the hard-scatter vertex, relative to all other pp collisions. The definitions of these two soft-term algorithms are described in the following: • Extrapolated Jet Area with Filter (EJAF) The jet-area method for the pileup subtraction uses a soft term based on the idea of jet-area corrections [45]. This technique uses direct event-by-event measurements of the energy flow throughout the entire ATLAS detector to estimate the pT density of pileup energy deposits and was geometry of the ATLAS calorimeters and their cluster reconstruction algorithms.6 In order to extrapolate ρemvetd into the forward regions of the detector, the average topocluster pT in slices of η, NPV, and μ is converted to an average pT density ρ (η, NPV, μ) for the soft term. As described for the ρemvetd, ρ (η, NPV, μ) is found to be uniform in the central region of the detector with |η| < ηplateau = 1.8. The transverse momentum density profile is then computed as where ρ central(NPV, μ) is the average ρ (η, NPV, μ) for |η| < ηplateau. The Pρ (η, NPV, μ ) is therefore 1, by definition, for |η| < ηplateau and decreases for larger |η|. A functional form of Pρ (η, NPV, μ ) is used to parameterize its dependence on η, NPV, and μ and is defined as developed from the strategy applied to jets as described in Ref. [4]. The topoclusters belonging to the soft term are used for jet finding with the kt algorithm [48,49] with distance parameter R = 0.6 and jet pT > 0. The catchment areas [45,46] for these reconstructed jets are labelled Ajet; this provides a measure of the jet’s susceptibility to contamination from pileup. Jets with pT < 20 GeV are referred to as soft-term jets, and the pT-density of each soft-term jet i is then measured by computing: In a given event, the median pT-density ρemvetd for all softterm kt jets in the event (Njets) found within a given range −ηmax < ηjet < ηmax can be calculated as ρemvetd = median{ρjet,i } for i = 1 . . . Njets in |ηjet| < ηmax. (7) This median pT-density ρemvetd gives a good estimate of the in-time pileup activity in each detector region. If determined with ηmax = 2, it is found to also be an appropriate indicator of out-of-time pileup contributions [45]. A lower value for ρemvetd is computed by using jets with |ηjet| larger than 2, which is mostly due to the particular where the central region |η| < ηplateau = 1.8 is plateaued at 1, and then a pair of Gaussian functions Gcore(|η| − ηplateau) and Gbase(η) are added for the fit in the forward regions of the calorimeter. The value of Gcore(0) = 1 so that Eq. (9) is continuous at η = ηplateau. Two example fits are shown in Fig. 1 for NPV = 3 and 8 with μ = 7.5–9.5 interactions per bunch crossing. For both distributions the value is defined to be unity in the central region (|η| < ηplateau), and the sum of two Gaussian functions provides a good description of the change in the amount of in-time pileup beyond ηplateau. The baseline Gaussian function Gbase(η) has a larger width and is used to describe the larger amount of in-time pileup in the forward region as seen in Fig. 1. Fitting with Eq. (9) provides a parameterized function for in-time and outof-time pileup which is valid for the whole 2012 dataset. The soft term for the EJAF E miss algorithm is calcuT lated as Exm(iys)s,soft = − i=0 jet,corr, of which sums the transverse momenta, labelled px(y),i the corrected soft-term jets matched to the primary vertex. The number of these filtered jets, which are selected 6 The forward ATLAS calorimeters are less granular than those in the central region, which leads to fewer clusters being reconstructed. ATLAS 10−1 10−2 regions coming from more in-time pileup with NPV = 8 in b can be seen by the flatter shape of the Gaussian fit of the forward activity Gbase(NPV, μ ) (blue dashed line) Fig. 1 The average transverse momentum density shape Pρ (η, NPV, μ ) for jets in data is compared to the model in Eq. (9) with μ = 7.5–9.5 and with a three reconstructed vertices and b eight reconstructed vertices. The increase of jet activity in the forward after the pileup correction based on their JVF and pT, is labelled Nfilter-jet. More details of the jet selection and the application of the pileup correction to the jets are given in Appendix A. • Soft-Term Vertex-Fraction (STVF) The algorithm, called the soft-term vertex-fraction, utilizes an event-level parameter computed from the ID track information, which can be reliably matched to the hard-scatter collision, to suppress pileup effects in the CST. This correction is applied as a multiplicative factor (αSTVF) to the CST, event by event, and the resulting STVF-corrected CST is simply referred to as STVF. The αSTVF is calculated as which is the scalar sum of pT of tracks matched to the PV divided by the total scalar sum of track pT in the event, including pileup. The sums are taken over the tracks that do not match high- pT physics objects belonging to the hard term. The mean αSTVF value is shown versus the number of reconstructed vertices (NPV) in Fig. 2. Data and simulation (including Z , diboson, t t¯, and t W samples) are shown with only statistical uncertainties and agree within 4–7% across the full range of NPV in the 8 TeV dataset. The differences mostly arise from the mod elling of the amount of the underlying event and p Z . T The 0-jet and inclusive samples have similar values of αSTVF, with that for the inclusive sample being around 2% larger. 10−1 10−2 10−1 10 15 20 25 30 Number of Reconstructed Vertices (NPV) Fig. 2 The mean αSTVF weight is shown versus the number of reconstructed vertices (NPV) for 0-jet and inclusive events in Z → μμ data. The inset at the bottom of the figure shows the ratio of the data to the MC predictions with only the statistical uncertainties on the data and MC simulation. The bin boundary always includes the lower edge and not the upper edge 4.1.3 Jet pT threshold and JVF selection The TST, STVF, and EJAF E miss algorithms complement T the pileup reduction in the soft term with additional requirements on the jets entering the E miss hard term, which are also T aimed at reducing pileup dependence. These E miss reconT struction algorithms apply a requirement of JVF > 0.25 to jets with pT < 50 GeV and |η| < 2.4 in order to suppress those originating from pileup interactions. The maximum |η| value is lowered to 2.4 to ensure that the core of each jet is within the tracking volume (|η| < 2.5) [4]. Charged particles from jets below the pT threshold are considered in the soft terms for the STVF, TST, and EJAF (see Sect. 4.1.2 for details). The same JVF requirements are not applied to the CST E miss because its soft term includes the soft recoil from all T interactions, so removing jets not associated with the hardscatter interaction could create an imbalance. The procedure for choosing the jet pT and JVF criteria is summarized in Sect. 7. Throughout most of this paper the number of jets is computed without a JVF requirement so that the E miss algorithms T are compared on the same subset of events. However, the JVF > 0.25 requirement is applied in jet counting when 1-jet and ≥ 2-jet samples are studied using the TST E miss reconT struction, which includes Figs. 8 and 22. The JVF removes pileup jets that obscure trends in samples with different jet multiplicities. 4.2 Track E miss 5 Comparison of Emiss distributions in data and MC T simulation In this section, basic E miss distributions before and after T pileup suppression in Z → and W → ν data events are compared to the distributions from the MC signal plus relevant background samples. All distributions in this section include the dominant systematic uncertainties on the highpT objects, the ETmiss,soft (described in Sect. 8) and pileup modelling [7]. The systematics listed above are the largest systematic uncertainties in the E miss for Z and W samples. T 5.1 Modelling of Z → The CST, EJAF, TST, STVF, and Track E miss distributions T for Z → μμ data and simulation are shown in Fig. 3. The Z boson signal region, which is defined in Sect. 3.2, has better than 99% signal purity. The MC simulation agrees with data for all E miss reconstruction algorithms within the T assigned systematic uncertainties. The mean and the standard deviation of the E miss distribution is shown for all of T the ETmiss algorithms in Z → μμ inclusive simulation in Table 4. The CST E miss has the highest mean E miss and T T thus the broadest E miss distribution. All of the E miss algo T T rithms with pileup suppression have narrower E miss distribuT tions as shown by their smaller mean E miss values. However, T those algorithms also have non-Gaussian tails in the E miss x and E miss distributions, which contribute to the region with y ETmiss 50 GeV. The Track ETmiss has the largest tail because it does not include contributions from the neutral particles, and this results in it having the largest standard deviation. The tails of the ETmiss distributions in Fig. 3 for Z → μμ data are observed to be compatible with the sum of expected signal and background contributions, namely t t¯ and the summed diboson (V V ) processes including W W , W Z , and Z Z , which all have high- pT neutrinos in their final states. Instrumental effects can show up in the tails of the E miss, but T such effects are small. The E miss φ distribution is not shown in this paper but is T very uniform, having less than 4 parts in a thousand difference from positive and negative φ. Thus the φ-asymmetry is greatly reduced from that observed in Ref. [1]. The increase in systematic uncertainties in the range 50– 120 GeV in Fig. 3 comes from the tail of the E miss distribution T for the simulated Z → μμ events. The increased width in the uncertainty band is asymmetric because many systematic uncertainties increase the E miss tail in Z → μμ events T by creating an imbalance in the transverse momentum. The largest of these systematic uncertainties are those associated with the jet energy resolution, the jet energy scale, and pileup. The pileup systematic uncertainties affect mostly the CST and EJAF E miss, while the jet energy scale uncertainty T eV 108 G 10 107 / tsn 106 e vE 105 eV 108 G 10 107 / tsn 106 e vE 105 eV 108 G 10 107 / tsn 106 e vE 105 eV 108 G 10 107 / tsn 106 e vE 105 eV 108 G 10 107 / tsn 106 e vE 105 the ratio of data to MC simulation, and the bands correspond to the combined systematic and MC statistical uncertainties. The far right bin includes the integral of all events with E miss above 300 GeV T V eG108 /4 107 s t en 106 v E 105 81050 100200120 215400 16300 CSCTSETTmiEssTm,siosfst [GeV] causes the larger systematic uncertainty for the TST and STVF E miss. The Track E miss does not have the same increase T T in systematic uncertainties because it does not make use of reconstructed jets. Above 120 GeV, most events have a large intrinsic E miss, and the systematic uncertainties on the E miss, T T especially the soft term, are smaller. Figure 4 shows the soft-term distributions. The pileupsuppressed E miss algorithms generally have a smaller mean T soft term as well as a sharper peak near zero compared to the CST. Among the E miss algorithms, the soft term from T the EJAF algorithm shows the smallest change relative to the CST. The TST has a sharp peak near zero similar to the STVF but with a longer tail, which mostly comes from individual tracks. These tracks are possibly mismeasured and further studies are planned. The simulation under-predicts the TST relative to the observed data between 60–85 GeV, and the differences exceed the assigned systematic uncertainties. This Fig. 4 Distributions of the soft term for the a CST, b EJAF, c TST, and d STVF are shown in data and MC simulation events satisfying the Z → μμ selection. The lower panel of the figures show the ratio of data to MC simulation, and the bands correspond to the combined systematic and MC statistical uncertainties. The far right bin includes the integral of all events with E miss,soft above 160 GeV T V 108 e 0G107 1 t/s 106 n ve 105 E V 108 e 0G107 1 t/s 106 n ve 105 E 20205040400 6100060080081105000011020200014200 12165400 181063000 (a) CSΣCTESETT(TmCiEsSsTm,sTiosf)st [GeV] 20205040400 6100060080081105000011020200014200 12165400 181063000 (b) TSΣTESETT(TmTiEsSsTm,sTiosf)st [GeV] Fig. 5 Distributions of a ET (CST) and b ET (TST) are shown in data and MC simulation events satisfying the Z → μμ selection. The lower panel of the figures show the ratio of data to MC simulation, and the bands correspond to the combined systematic and MC statistical uncertainties. The far right bin includes the integral of all events with ET above 2000 GeV region corresponds to the transition from the narrow core to the tail coming from high- pT tracks. The differences between data and simulation could be due to mismodelling of the rate of mismeasured tracks, for which no systematic uncertainty is applied. The mismeasured-track cleaning, as discussed in Sect. 4.1.2, reduces the TST tail starting at 120 GeV, and this region is modelled within the assigned uncertainties. The mismeasured-track cleaning for tracks below 120 GeV and entering the TST is not optimal, and future studies aim to improve this. The E miss resolution is expected to be proportional to √ ET whTen both quantities are measured with the calorimeter alone [1]. While this proportionality does not hold for tracks, it is nevertheless interesting to understand the modelling of ET and the dependence of ETmiss resolution on it. Figure 5 shows the ET distribution for Z → μμ data and MC simulation both for the TST and the CST algorithms. The ET is typically larger for the CST algorithm than for the TST because the former includes energy deposits from pileup as well as neutral particles and forward contributions beyond the ID volume. The reduction of pileup contributions in the soft and jet terms leads to the ET (TST) having a sharper peak at around 100 GeV followed by a large tail, due to highpT muons and large pTjets. The data and simulation agree within the uncertainties for the ET (CST) and ET (TST) distributions. 5.2 Modelling of W → ν events In this section, the selection requirements for the mT and E miss distributions are defined using the same E miss algo T T rithm as that labelling the distribution (e.g. selection criteria are applied to the CST E miss for distributions showing the T CST ETmiss). The intrinsic ETmiss in W → ν events allows a comparison of the E miss scale between data and simula T tion. The level of agreement between data and MC simulation for the E miss reconstruction algorithms is studied using T W → eν events with the selection defined in Sect. 3.3. The CST and TST ETmiss distributions in W → eν events are shown in Fig. 6. The W → τ ν contributions are combined with W → eν events in the figure. The data and MC simulation agree within the assigned systematic uncertainties for both the CST and TST E miss algorithms. The other T E miss algorithms show similar levels of agreement between T data and MC simulation. 6 Performance of the Emiss in data and MC simulation T 6.1 Resolution of E miss The E miss and E miss are expected to be approximately Gausx y sian distributed for Z → events as discussed in Ref. [1]. However, because of the non-Gaussian tails in these distributions, especially for the pileup-suppressing E miss algorithms, T the root-mean-square (RMS) is used to estimate the resolution. This includes important information about the tails, which would be lost if the result of a Gaussian fit over only the core of the distribution were used instead. The resolution of the E miss distribution is extracted using the RMS T from the combined distribution of E miss and E miss, which x y are determined to be independent from correlation studies. eV 109 G 01 108 / ts 107 n veE 106 Fig. 6 Distributions of the a CST and b TST E miss as measured in a data sample of W → eν events. The lower paneTl of the figures show the ratio of data to MC simulation, and the bands correspond to the The previous ATLAS E miss performance paper [1] studied T the resolution defined by the width of Gaussian fits in a narrow range of ±2RMS around the mean and used a separate study to investigate the tails. Therefore, the results of this paper are not directly comparable to those of the previous study. The resolutions presented in this paper are expected to be larger than the width of the Gaussian fitted in this manner because the RMS takes into account the tails. In this section, the resolution for the E miss is presented T for Z → μμ events using both data and MC simulation. Unless it is a simulation-only figure (labelled with “Simulation” under the ATLAS label), the MC distribution includes the signal sample (e.g. Z → μμ) as well as diboson, t t¯, and t W samples. 6.1.1 Resolution of the E miss as a function of the number of T reconstructed vertices combined systematic and MC statistical uncertainties. The far right bin includes the integral of all events with E miss above 300 GeV T to around 5–10% for NPV > 25, which might be attributed to the decreasing sample size. All of the E miss distributions T show a similar level of agreement between data and simulation across the full range of NPV. For the 0-jet sample in Fig. 7a, the STVF, TST, and Track E miss resolutions all have a small slope with respect to NPV, T which implies stability of the resolution against pileup. In addition, their resolutions agree within 1 GeV throughout the NPV range. In the 0-jet sample, the TST and Track E miss are T both primarily reconstructed from tracks; however, small differences arise mostly from accounting for photons in the TST E miss reconstruction algorithm. The CST E miss is directly T T affected by the pileup as its reconstruction does not apply any pileup suppression techniques. Therefore, the CST E miss has T the largest dependence on NPV, with a resolution ranging from 7 GeV at NPV = 2 to around 23 GeV at NPV = 25. The E miss resolution of the EJAF distribution, while better T than that of the CST E miss, is not as good as that of the other T pileup-suppressing algorithms. For the inclusive sample in Fig. 7b, the Track E miss is T the most stable with respect to pileup with almost no dependence on NPV. For NPV > 20, the Track E miss has the best T resolution showing that pileup creates a larger degradation in the resolution of the other E miss distributions than excludT ing neutral particles, as the Track E miss algorithm does. The T EJAF E miss algorithm does not reduce the pileup dependence T as much as the TST and STVF E miss algorithms, and the CST T E miss again has the largest dependence on NPV. T Figure 7 also shows that the pileup dependence of the TST, CST, EJAF and STVF E miss is smaller in the 0-jet T sample than in the inclusive sample. Hence, the evolution 10 15 20 25 30 35 40 Number of Reconstructed Vertices (NPV) (a) Fig. 7 The resolution obtained from the combined distribution of Exmiss and Eymiss for the CST, STVF, EJAF, TST, and Track ETmiss algorithms as a function of NPV in a 0-jet and b inclusive Z → μμ events ATLAS Data Closed, MC Open Markers 5 10 15 20 25 30 35 40 Number of Reconstructed Vertices (NPV) of the E miss resolution is shown for different numbers of jets T in Fig. 8 with the TST E miss algorithm as a representative T example. The jet counting for this figure includes only the jets used by the TST E miss algorithm, so the JVF criterion T discussed in Sect. 4.1.3 is applied. Comparing the 0-jet, 1-jet and ≥2-jet distributions, the resolution is degraded by 4–5 GeV with each additional jet, which is much larger than any dependence on NPV. The inclusive distribution has a larger slope with respect to NPV than the individual jet categories, which indicates that the behaviour seen in the inclusive sample is driven by an increased number of pileup jets included in the E miss calculation at larger NPV. T 6.1.2 Resolution of the E miss as a function of ET Number of Reconstructed Vertices (NPV) in data. The insets at the bottom of the figures show the ratios of the data to the MC predictions sum of transverse momentum in the event, as calculated using Eq. (4). The CST E miss resolution is observed to depend lin T early on the square root of the ET computed with the CST ETmiss components in Ref. [1]. However, the ET used in this subsection is calculated with the TST E miss algorithm. T This allows studies of the resolution as a function of the momenta of particles from the selected PV without including the amount of pileup activity in the event. Figure 9 shows the resolution as a function of ET (TST) for Z → μμ data and MC simulation in the 0-jet and inclusive samples. In the 0-jet sample shown in Fig. 9a, the use of tracking information in the soft term, especially for the STVF, TST, and Track E miss, greatly improves the resolution relative to T the CST E miss. The EJAF E miss has a better resolution than T T that of the CST E miss but does not perform as well as the T other reconstruction algorithms. All of the resolution curves have an approximately linear increase with ET (TST); however, the Track E miss resolution increases sharply starting at T ET (TST) = 200 GeV due to missed neutral contributions like photons. The resolution predicted by the simulation is about 5% larger than in data for all ETmiss algorithms at ET (TST) = 50 GeV, but agreement improves as ET (TST) increases until around ET (TST) = 200 GeV. Events with jets can end up in the 0-jet event selection, for example, if a jet is misidentified as a hadronically decaying τ -lepton. The pTτ increases with ET (TST), and the rate of jets misreconstructed as hadronically decaying τ -leptons is not well modelled by the simulation, which leads to larger E miss resoT lution at high ET (TST) than that observed in the data. The Track E miss can be more strongly affected by misidentified T jets because neutral particles from the high- pT jets are not included. For the inclusive sample in Fig. 9b, the pileup-suppressed E miss distributions have better resolution than the CST T ETmiss for ET (TST) < 200 GeV, but these events are mostly those with no associated jets. For higher ET (TST), the Fig. 9 The resolution of the combined distribution of Exmiss and Eymiss for the CST, STVF, EJAF, TST, and Track ETmiss as a function of ET (TST) in Z → μμ events in data for the a 0-jet and b inclusive impact from the E Tjets term starts to dominate the resolution as well as the ET (TST). Since the vector sum of jet momenta is mostly common7 to all E miss algorithms except T for the Track E miss, those algorithms show similar perfor T mance in terms of the resolution. At larger ET (TST), the Track E miss resolution begins to degrade relative to the other T algorithms because it does not include the high- pT neutral particles coming from jets. The ratio of data to MC simulation for the Track E miss distribution is close to one, while T for other algorithms the MC simulation is below the data by about 5% at large ET (TST). While the Track ETmiss appears well modelled for the Alpgen+Pythia simulation used in this figure, the modelling depends strongly on the parton shower model. 6.2 The E miss response 6.2.1 Measuring E miss recoil versus p Z In events with Z → μμ decays, the pT of the Z boson defines an axis in the transverse plane of the ATLAS detector, and 7 As defined in Sect. 4.1.3, the CST E miss does not apply a JVF require ] 120 V e [G 100 S RM 80 CST TST STVF EJAF Track 0 100 200 300 400 500 600 700 800 900 1000 (b) Σ ET(TST) [GeV] samples. The insets at the bottom of the figures show the ratios of the data to the MC predictions for events with 0-jets, the E miss should balance the pT of the T Z boson ( pTZ ) along this axis. Comparing the response in events with and without jets allows distinction between the jet and soft-term responses. The component of the E miss along T the pTZ axis is sensitive to biases in detector responses [50]. The unit vector of pTZ is labelled as Aˆ Z and is defined as: Aˆ Z = where pT + and pT − are the transverse momentum vectors of the leptons from the Z boson decay. The recoil of the Z boson is measured by removing the Z boson decay products from the E miss and is computed as T R = ETmiss + pTZ . Since the E miss includes a negative vector sum over the lep T ton momenta, the addition of p Z removes its contribution. T With an ideal detector and E miss reconstruction algorithm, T Z → events have no ETmiss, and the R balances with pTZ exactly. For the real detector and E miss reconstruction algoT rithm, the degree of balance is measured by projecting the recoil onto Aˆ Z , and the relative recoil is defined as the projection R · Aˆ Z divided by p Z , which gives a dimensionless T estimate that is unity if the E miss is ideally reconstructed and T calibrated. Figure 10 shows the mean relative recoil versus pTZ for Z → μμ events where the average value is indicated by angle brackets. The data and MC simulation agree within around 10% for all E miss algorithms for all pTZ ; however, the T agreement is a few percent worse for pTZ > 50 GeV in the 0-jet sample. The Z → μμ events in the 0-jet sample in Fig. 10a have a relative recoil significantly lower than unity ( R · Aˆ Z / pTZ < 1) throughout the pTZ range. In the 0-jet sample, STVF EJAF Track 20 40 60 80 100 120 140 160 180 200 (b) pZT [GeV] Fig. 10 R · AˆZ / pTZ as a function pTZ for the a 0-jet and b inclusive events in Z → μμ data. The insets at the bottom of the figures show the ratios of the data to the MC predictions among the object-based E miss algorithms as discussed above T for Fig. 10a, even lower than the Track E miss for pTZ < 16 T GeV. 6.2.2 Measuring E miss response in simulated T W → ν events For simulated events with intrinsic E miss, the response is T studied by looking at the relative mismeasurement of the reconstructed E miss. This is referred to here as the “linearity”, T and is a measure of how consistent the reconstructed E miss is T with the E miss,True. The linearity is defined as the mean value T of the ratio, (ETmiss − ETmiss,True)/ETmiss,True and is expected to be zero if the E miss is reconstructed at the correct scale. T For the linearity studies, no selection on the E miss or T mT is applied, in order to avoid biases as these are purely simulation-based studies. In Fig. 11, the linearity for W → μν simulated events is presented as a function of the E miss,True. Despite the relaxed selection, a positive linearity T is evident for E miss,True< 40 GeV, due to the finite resolution T of the E miss reconstruction and the fact that the reconstructed T E miss is positive by definition. The CST E miss has the largest T T deviation from zero at low E miss,True because it has the largest T E miss resolution. T For the events in the 0-jet sample in Fig. 11a, all E miss algorithms have a negative linearity for E miss,True > T T 40 GeV, which diminishes for ETmiss,True 60 GeV. The region of E miss,True between 40 and 60 GeV mostly includes T events lying in the Jacobian peak of the W transverse mass, and these events include mostly on-shell W bosons. For ETmiss 40 GeV, the on-shell W boson must have nonzero pT, which typically comes from its recoil against jets. However, no reconstructed or generator-level jets are found in this 0-jet sample. Therefore, most of the events with 40 < E miss,True < 60 GeV have jets below the 20 GeV thresh T old contributing to the soft term, and the soft term is not cality 1 rae 0.8 iLn 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −10 40 60 80 100 120 140 160 180 200 (b) ETmiss,True [GeV] Fig. 11 E miss linearity in W → μν MC simulation is shown versus ETmiss,True in the a 0-jet and b inclusive events T 6.3 The E miss angular resolution T The angular resolution is important for the reconstruction of kinematic observables such as the transverse mass of the W boson and the invariant mass in H → τ τ events [51]. For simulated W → ν events, the direction of the reconstructed E miss is compared to the E miss,True for each E miss reconstruc T T T tion algorithm using the difference in the azimuthal angles, φ (ETmiss, E miss,True), which has a mean value of zero. The T RMS of the distribution is taken as the resolution, which is labelled RMS ( φ). No selection on the E miss or mT is applied in order to T avoid biases. The RMS ( φ) is shown as a function of ETmiss,True in Fig. 12a for the 0-jet sample in W → μν simulation; the angular resolution generally improves as the ETmiss,True increases, for all algorithms. For ETmiss,True 120 GeV, the pileup-suppressing algorithms improve the resolution over the CST E miss algorithm, but all of the algorithms T produce distributions with similar resolutions in the higher E miss,True region. The increase in RMS ( φ) at around 40– T 60 GeV in the 0-jet sample is due to the larger contribution of jets below 20 GeV entering the soft term as mentioned in Sect. 6.2.2. The distribution from the inclusive sample shown in Fig. 12b has the same pattern as the one from the 0-jet sample, except that the performance of the Track E miss algorithm T is again significantly worse. In addition, the transition region near 40 < E miss,True < 60 GeV is smoother as the under T estimation of the soft term becomes less significant due to the presence of events with high- pT calibrated jets. The TST E miss algorithm has the best angular resolution for both the T 0-jet and inclusive topologies throughout the entire range of E miss,True. T 6.4 Transverse mass in W → ν events The W boson events are selected using kinematic observables that are computed from the E miss and lepton transverse T momentum. This section evaluates the scale of the mT, as defined in Eq. (1), reconstructed with each E miss definition. T The mT computed using the reconstructed E miss is compared T to the mTTrue, which is calculated using the ETmiss,True in W → μν MC simulation. The mean of the difference between the reconstructed and generator-level mT, ( mT − mTrue ), is T shown as a function of mTrue in Fig. 13 for the 0-jet and T inclusive samples. No E miss or mT selection is made in these T figures, to avoid biases. All distributions for the E miss algoT rithms have a positive bias at low values of mTrue coming T from the positive-definite nature of the mT and the finite E miss resolution. For the 0-jet sample, the CST algorithm T has the smallest bias for mT 60 GeV because it includes the neutral particles with no corrections for pileup. However, for the inclusive sample the TST E miss has the smallest bias T as the E miss resolution plays a larger role. The STVF and T Track E miss have the largest bias for mTrue < 50 GeV in T T the 0-jet and inclusive samples, respectively. This is due to ]d 1.8 [ra 1.6 φ) Δ( 1.4 S RM 1.2 1 0.8 0.6 ]d 1.8 [ra 1.6 φ) Δ( 1.4 S RM 1.2 1 0.8 0.6 20 40 60 80 100 120 140 160 180 200 (b) ETmiss,True [GeV] the over-correction in the soft term by αSTVF for the former and from the missing neutral particles in the latter case. For events with mT 60 GeV, all of the ETmiss algorithms have mT − mTrue close to zero, with a spread of less than 3 GeV. T 6.5 Proxy for E miss significance choice is motivated by the linear relationship for the CST ETmiss between its √ ET and its ETmiss resolution. The same procedure does not work for the TST E miss resolution, so a T value of 2.27 GeV1/2 is used to tune the x -axis so that integral of Z → μμ simulation fits the multiples of the standard deviation of a normal distribution at the value of 2. Ideally, only events with large intrinsic E miss have large values of T a1 ·ETmiss/√ ET, while events with no intrinsic ETmiss such as Z → μμ have low values. It is important to point out that in tgieenseorarllZarg→e √μμ is not a process with large E miss uncertainT ET. However, when there are many additional jets (large ET), there is a significant probability that one of them is mismeasured, which generates fake E miss. T The distribution of a1 ·ETmiss/√ ET is shown for the CST and TST ETmiss algorithms in Fig. 14 in Z → μμ data and MC simulation. The data and MC simulation agree within the assigned uncertainties for both algorithms. The CST E miss distribution in Fig. 14a has a very narrow core T for the Z → μμ process, having 97% of data events with 1.03·ETmiss/√ ET < 2. The proxy of the ETmiss significance, therefore, provides discrimination power between events −250 10 15 20 25 30 35 40 Number of Reconstructed Vertices (NPV) (a) the Z → μμ simulation. JVF > 0.25 is required for all jets with pT > 20 GeV and |η| < 2.4 E miss becomes strongly biased in the direction opposite to T the pTZ . Therefore, the pT threshold of 20 GeV is preferred. however, here the soft term is compared to the hard term rather than comparing the E miss to the recoil of the Z . T 8 Systematic uncertainties of the soft term pThard= 8.1 Methodology for CST Two sets of systematic uncertainties are considered for the CST. The same approach is used for the STVF and EJAF algorithms to evaluate their soft-term systematic uncertainties. The first approach decomposes the systematic uncertainties into the longitudinal and transverse components along the direction of pThard, whereas the second approach estimates the global scale and resolution uncertainties. While both methods were recommended for analyses of the 8 TeV dataset, the first method, described in Sect. 8.1.1, gives smaller uncertainties. Therefore, the second method, which is discussed in Sect. 8.1.2, is now treated as a cross-check. Both methods consider a subset of Z → μμ events that do not have any jets with pT > 20 GeV and |η| < 4.5. Such an event topology is optimal for estimation of the soft-term systematic uncertainties because only the muons and the soft term contribute to the E miss. In principle the methods are T valid in event topologies with any jet multiplicity, but the Z → μμ + ≥1-jet events are more susceptible to jet-related systematic uncertainties. 8.1.1 Evaluation of balance between the soft term and the hard term The primary or “balance” method exploits the momentum balance in the transverse plane between the soft and hard terms in Z → events, and the level of disagreement between data and simulation is assigned as a systematic uncertainty. The ETmiss,soft is decomposed along the pˆThard direction. The direction orthogonal to pˆThard is referred to as the perCM 1.10 1 t/a 0.9 a D pendicular direction while the component parallel to pˆThard is labelled as the longitudinal direction. The projections of ETmiss,soft along those directions are defined as: E miss,soft = E miss,soft cos φ (ETmiss,soft, p hard), T T E miss,soft = E miss,soft sin φ (ETmiss,soft, pThard), ⊥ T The E miss,soft is sensitive to scale and resolution differences between the data and simulation because the soft term should balance the p hard in Z → μμ events. For a narrow range of T phard values, the mean and width of the E miss,soft are comT pared between data and MC simulation. On the other hand, the perpendicular component, E miss,soft, is only sensitive to ⊥ differences in resolution. A Gaussian function is fit to the E miss projected onto pˆThard in bins of phard, and the resulting T T Gaussian mean and width are shown in Fig. 20. The mean increases linearly with phard, because the soft term is not T calibrated to the correct energy scale. On the other hand, the width is relatively independent of phard, because the width is T mostly coming from pileup contributions. The small discrepancies in mean and width between data and simulation are taken as the systematic uncertainties for the scale and resolution, respectively. A small dependence on the average number of collisions per bunch crossing is observed for the scale and resolution uncertainties for high phard, so the uncertainties are computed in three ranges T of pileup and three ranges of phard. The scale uncertainty T varies from −0.4 to 0.3 GeV depending on the bin, which reduces the uncertainties from the 5% shown in Fig. 20 for phard > 10 GeV. A small difference in the uncertainties for T the resolution along the longitudinal and perpendicular directions is observed, so they are considered separately. The average uncertainty is about 2.1% (1.8%) for the longitudinal (perpendicular) direction. 8.1.2 Cross-check method for the CST systematic uncertainties As a cross-check of the method used to estimate the CST uncertainties, the sample of Z → μμ +0-jet events is also used to evaluate the level of agreement between data and simulation. The projection of the E miss onto pˆThard provides T a test for potential biases in the E miss scale. The systematic T uncertainty in the soft-term scale is estimated by comparing the ratio of data to MC simulation for ETmiss · pˆThard versus ET (CST) as shown in Fig. 21a. The average deviation from unity in the ratio of data to MC simulation is about 8%, which is taken as a flat uncertainty in the absolute scale. The systematic uncertainty in the soft-term resolution is estimated by evaluating the level of agreement between data and MC simulation in the E miss and E miss resolution as a function x y of the ET (CST) (Fig. 21b). The uncertainty on the softterm resolution is about 2.5% and is shown as the band in the data/MC ratio. Even though the distributions appear similar, the results in this section are derived by projecting the full E miss onto the T p hard in the 0-jet events, and are not directly comparable to ˆT the ones in Sect. 8.1.1, in which only the soft term is projected onto pˆThard. 8.2 Methodology for TST and Track E miss T A slightly different data-driven methodology is used to evaluate the systematic uncertainties in the TST and Track E miss. T Tracks matched to jets that are included in the hard term are removed from the Track E miss and are treated separately, as T described in Sect. 8.2.3. The method exploits the balance between the soft track term and p hard and is similar to the balance method for the T CST. The systematic uncertainties are split into two compo ATLAS in the lower portion of the plot with the solid band representing the assigned systematic uncertainty MC nents: the longitudinal (E miss,soft) and transverse (E miss,soft) ⊥ MC Fit Smeared MC 0−10 Fig. 22 Fit to the TST E miss,soft for μ < 19 and 25 < phard < 30 GeV ⊥ T in the 1-jet sample. The nominal MC simulation, the jet-related systematic uncertainties (hashed band), and the data are shown. The nominal MC simulation is convolved with a Gaussian function until it matches the data, and the resulting fit is shown with the solid curve. The jet counting for the 1-jet selection uses the same JVF criterion as the TST E miss reconstruction algorithm T smearing parameters and offsets applied to the simulation are used as the systematic uncertainties in the soft term. The phard > 50 GeV bin has the smallest number of data entries; T therefore, it has the largest uncertainties in the fitted mean and width. In this bin of the distribution shown in Fig. 23(a), the statistical uncertainty from the Alpgen+Herwig simulation, which is not the most discrepant from data, is added to the uncertainty band, and this results in a systematic uncertainty band that spans the differences in MC generators for σ 2(E miss,soft) for events with phard > 50 GeV. T The impact of uncertainties coming from the parton shower model, the number of jets, μ dependence, JER/JES uncertainties, and forward versus central jet differences was evaluated. Among the uncertainties, the differences between the generator and parton shower models have the most dominant effects. The total TST systematic uncertainty is summarized in Table 6. 8.2.1 Propagation of systematic uncertainties The CST systematic uncertainties from the balance method defined in Sect. 8.1.1 are propagated to the nominal ETmiss,soft as follows: E m(i⊥ss),,sroefsto = (1 ± R (⊥))(E m(i⊥ss),soft − E m(i⊥ss),soft ) where E m(i⊥ss),,sroefsto and E m,siscsa,lseo±ft are the values after propagating the resolution and scale uncertainties, respectively, in the errors from the Gaussian fits. The solid band, which is centred on the data, shows the parameter’s systematic uncertainties from Table 6. The insets at the bottom of the figures show the ratios of the MC predictions to the data Table 6 The TST scale ( TST) and resolution uncertainties (σ and σ⊥) are shown in bins of phard T longitudinal (perpendicular) directions. The mean values of parameters are denoted using angled brackets. The CST is the scale uncertainty, and the R (⊥) is the fractional resolution uncertainty taken from the lower portion of Fig. 20b. Both depend on the phard and the average number of pileup T interactions per bunch crossing. Each propagation of the systematic uncertainties in Eq. (17b) is called a variation, and all of the variations are used in ATLAS analyses. The systematic uncertainties in the resolution and scale for the CST using the cross-check method defined in Sect. 8.1.2 are propagated to the nominal ETmiss,soft as follows: Exm(iys)s,,sscoaftle± = Exm(iys)s,soft · (1 ± δ), where Exm(iys)s,,rseosfot and Exm(iys)s,,sscoaftle± are the values after propagating the resolution and scale uncertainties, respectively, in the x (y) directions. Here, δ is the fractional scale uncertainty, and σˆCST corrects for the differences in resolution between the data and simulation. The systematic uncertainties in the resolution and scale for the TST ETmiss,soft are propagated to the nominal ETmiss,soft as follows: E m(i⊥ss),,sroefsto = E m(i⊥ss),soft + Gaus( TST, σ (⊥)), E m,siscsa,lseo±ft = E miss,soft ± where the square of the yield of the nominal distribution, Y ( X ), is divided by the yield of events after applying the variation with Gaussian smearing to the kinematic variable, Ysmeared( X ). In practice, the yields are typically the content of histogram bins before (Y ( X )) and after (Ysmeared( X )) the systematic uncertainty variations. This procedure can be applied to any kinematic observable by propagating only the smeared soft-term variation to the calculation of the kinematic observable X and then computing the yield Ydown( X ) as defined in Eq. (20). There are six total systematic uncertainties associated with the TST: • Decrease scale (E m,siscsa,lseo−ft) • Gaussian smearing of E miss,soft (E m,risess,osoft) • The downward variation of the above E m,risess,osoft computed using Eq. (20) • Gaussian smearing of E miss,soft (E⊥m,irsess,sooft) ⊥ • The downward variation of the above E⊥m,irsess,sooft computed using Eq. (20) 8.2.2 Closure of systematic uncertainties The systematic uncertainties derived in this section for the CST and TST E miss are validated by applying them to the T Z → μμ sample to confirm that the differences between data and MC simulation are covered. resulting changes from the variations are added in quadrature, and the insets at the bottom of the figures show the ratios of the data to the MC predictions. The uncertainties are estimated using the balance method described in Sect. 8.1.1 V 107 e G 106 4 / ts 105 n veE 104 ATLAS V 107 e G 106 4 / ts 105 n veE 104 resulting changes from the variations are added in quadrature, and the insets at the bottom of the figures show the ratios of the data to the MC predictions. The uncertainties are estimated from the data/simulation ratio in Sect. 8.1.2 The effects of these systematic uncertainty variations on the CST E miss are shown for the Z → μμ events in Figs. 24 T and 25 for the primary (Sect. 8.1.1) and the cross-check (Sect. 8.1.2) methods, respectively. The uncertainties are larger for the cross-check method, reaching around 50% for E miss,soft > 60 GeV in Fig. 25a. T The corresponding plots for the TST E miss are shown in T Fig. 26 using the Z → μμ +0-jet control sample, where the uncertainty band is the quadratic sum of the variations with the MC statistical uncertainty. The systematic uncertainty band for the TST is larger in Fig. 26a than the one for the primary CST algorithm. In all the distributions, the systematic uncertainties in the soft term alone cover the disagreement between data and MC simulation. and the insets at the bottom of the figures show the ratios of the data to the MC predictions. The uncertainties are estimated from the method in Sect. 8.2 8.2.3 Systematic uncertainties from tracks inside jets A separate systematic uncertainty is applied to the scalar summed pT of tracks associated with high- pT jets in the Track E miss because these tracks are not included in the TST. T The fraction of the momentum carried by charged particles within jets was studied in ATLAS [57], and its uncertainty varies from 3 to 5% depending on the jet η and pT. These uncertainties affect the azimuthal angle between the Track E miss and the TST E miss, so the modelling is checked with T T Z → μμ events produced with one jet. The azimuthal angle between the Track E miss and the TST E miss directions is T T well modelled, and the differences between data and MC simulation are within the systematic uncertainties. 9 Conclusions dominate the E miss performance, making the differences in T soft-term reconstruction less important. The Extrapolated Jet Area with Filter (EJAF) and Soft Term Vertex-Fraction (STVF) E miss reconstruction algo T rithms correct for pileup effects in the CST E miss by uti T lizing a combination of the ATLAS tracker and calorimeter measurements. Both apply a vertex association to the jets used in the E miss calculation. The EJAF soft-term recon T struction subtracts the pileup contributions to the soft term using a procedure similar to jet area-based pileup corrections, and the EJAF E miss resolution has a reduced dependence on T the amount of pileup, relative to the CST algorithm. The STVF reconstruction algorithm uses an event-level correction of the CST, which is the scalar sum of charged-particle pT from the hard-scatter vertex divided by the scalar sum of all charged-particle pT. The STVF correction to the soft term greatly decreases the dependence of the E miss resolution on T the amount of pileup but causes the largest under-estimation of all the soft-term algorithms. Finally, the Track E miss reconstruction uses only the inner T detector tracks with the exception of the reconstructed electron objects, which use the calorimeter ET measurement. The resolutions on the Track E miss magnitude and direction are T very stable against pileup, but the limited |η| coverage of the tracker degrades the E miss response, as does not accounting T for high- pT neutral particles, especially in events with many jets. The different E miss algorithms have their own advantages T and disadvantages, which need to be considered in the context of each analysis. For example, removing large backgrounds with low E miss, such as Drell–Yan events, may require the T use of more than one E miss definition. The tails of the track T and calorimeter E miss distributions remain uncorrelated, and T exploiting both definitions in parallel allows one to suppress such backgrounds even under increasing pileup conditions. The systematic uncertainties in the E miss are estimated T with Z → μμ events for each reconstruction algorithm, and are found to be small. Acknowledgements We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DSM/IRFU, France; GNSF, Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece; RGC, Hong Kong SAR, China; ISF, I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; FOM and NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russian Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzer Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecomm ons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Funded by SCOAP3. A. Calculation of EJAF ρηmed(η) = ρemvetd · Pfρct(η, NPV, μ ), and it is computed as selection. The pileup-corrected jet pT is labelled pTfil,tier-jet,corr, selection, the label of “filter-jet” is added to the catchment area ( Aifilter-jet), to the transverse momentum ( pTfil,tier-jet), and While all other jets used in this paper use an R = 0.4 reconstruction, the larger value of R = 0.6 is used to reduce the number of kt soft-term jets with pT = 0 (see Eq. (22)) in the central detector region. While negative energy deposits are possible in the ATLAS calorimeters, their contributions cannot be matched to the soft-term jets by ghost-association. Studies that modify the cluster-to-jet matching to include negative- pT clusters indicate no change in the E miss perfor T mance, so negative- pT clusters are excluded from the softterm jets. Finally, only filter-jets with pTfil,tier-jet larger than the pileup correction contribute to the EJAF soft term. The x and y components of pTfil,tier-jet,corr are used to compute the EJAF soft term using Eq. (10), and only soft-term jets matched to the PV with JVF > 0.25 for |ηifilter-jet| < 2.4 filter-jet or jets with |ηi | ≥ 2.4 are used. Because of this JVF ATLAS Collaboration G. Aad87, B. Abbott114, J. Abdallah65, O. Abdinov12, B. Abeloos118, R. Aben108, M. Abolins92, O. S. AbouZeid159, H. Abramowicz154, H. Abreu153, R. Abreu117, Y. Abulaiti147a,147b, B. S. Acharya164a,164b,a, L. Adamczyk40a, D. L. Adams27, J. Adelman109, S. Adomeit101, T. Adye132, A. A. Affolder76, T. Agatonovic-Jovin14, J. Agricola56, J. A. Aguilar-Saavedra127a,127f, S. P. Ahlen24, F. Ahmadov67,b, G. Aielli134a,134b, H. Akerstedt147a,147b, T. P. A. Åkesson83, A. V. Akimov97, G. L. Alberghi22a,22b, J. Albert169, S. Albrand57, M. J. Alconada Verzini73, M. Aleksa32, I. N. Aleksandrov67, C. Alexa28b, G. Alexander154, T. Alexopoulos10, M. Alhroob114, G. Alimonti93a, L. Alio87, J. Alison33, S. P. Alkire37, B. M. M. 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Britton55, 1 Department of Physics, University of Adelaide, Adelaide, Australia 2 Physics Department, SUNY Albany, Albany, NY, USA 3 Department of Physics, University of Alberta, Edmonton, AB, Canada 5 LAPP, CNRS/IN2P3 and Université Savoie Mont Blanc, Annecy-le-Vieux, France 6 High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA 7 Department of Physics, University of Arizona, Tucson, AZ, USA 8 Department of Physics, The University of Texas at Arlington, Arlington, TX, USA 9 Physics Department, University of Athens, Athens, Greece 26 (a)Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil; (b)Electrical Circuits Department, Federal University of Juiz de Fora (UFJF), Juiz de Fora, Brazil; (c)Federal University of Sao Joao del Rei (UFSJ), Sao Joao del Rei, Brazil; (d)Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, Brazil 27 Physics Department, Brookhaven National Laboratory, Upton, NY, USA 28 (a)Transilvania University of Brasov, Brasov, Romania; (b)National Institute of Physics and Nuclear Engineering, Bucharest, Romania; (c)Physics Department, National Institute for Research and Development of Isotopic and Molecular Technologies, Cluj Napoca, Romania; (d)University Politehnica Bucharest, Bucharest, Romania; (e)West University in Timisoara, Timisoara, Romania 29 Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina 30 Cavendish Laboratory, University of Cambridge, Cambridge, UK 31 Department of Physics, Carleton University, Ottawa, ON, Canada 32 CERN, Geneva, Switzerland 33 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA 34 (a)Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile; (b)Departamento de Física, Universidad Técnica Federico Santa María, Valparaiso, Chile 35 (a)Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China; (b)Department of Modern Physics, University of Science and Technology of China, Anhui, China; (c)Department of Physics, Nanjing University, Jiangsu, China; (d)School of Physics, Shandong University, Shandong, China; (e)Department of Physics and Astronomy, Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai (also affiliated with PKU-CHEP), China; (f)Physics Department, Tsinghua University, Beijing 100084, China 36 Laboratoire de Physique Corpusculaire, Clermont Université and Université Blaise Pascal and CNRS/IN2P3, Clermont-Ferrand, France 37 Nevis Laboratory, Columbia University, Irvington, NY, USA 38 Niels Bohr Institute, University of Copenhagen, Kobenhavn, Denmark 39 (a)INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Frascati, Italy; (b)Dipartimento di Fisica, Università della Calabria, Rende, Italy 40 (a)Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, Kraków, Poland; (b)Marian Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland 41 Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland 42 Physics Department, Southern Methodist University, Dallas, TX, USA 43 Physics Department, University of Texas at Dallas, Richardson, TX, USA 44 DESY, Hamburg and Zeuthen, Germany 45 Institut für Experimentelle Physik IV, Technische Universität Dortmund, Dortmund, Germany 46 Institut für Kern-und Teilchenphysik, Technische Universität Dresden, Dresden, Germany 47 Department of Physics, Duke University, Durham, NC, USA 48 SUPA-School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK 49 INFN Laboratori Nazionali di Frascati, Frascati, Italy 50 Fakultät für Mathematik und Physik, Albert-Ludwigs-Universität, Freiburg, Germany 51 Section de Physique, Université de Genève, Geneva, Switzerland 52 (a)INFN Sezione di Genova, Genoa, Italy; (b)Dipartimento di Fisica, Università di Genova, Genoa, Italy 53 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia; (b)High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 54 II Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 55 SUPA-School of Physics and Astronomy, University of Glasgow, Glasgow, UK 56 II Physikalisches Institut, Georg-August-Universität, Göttingen, Germany 57 Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS/IN2P3, Grenoble, France 58 Department of Physics, Hampton University, Hampton, VA, USA 59 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA 60 (a)Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany; (b)Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany; (c)ZITI Institut für technische Informatik, Ruprecht-Karls-Universität Heidelberg, Mannheim, Germany 61 Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan 62 (a)Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong; (b)Department of Physics, The University of Hong Kong, Hong Kong, China; (c)Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 63 Department of Physics, Indiana University, Bloomington, IN, USA 64 Institut für Astro- und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria 65 University of Iowa, Iowa City, IA, USA 66 Department of Physics and Astronomy, Iowa State University, Ames, IA, USA 67 Joint Institute for Nuclear Research, JINR Dubna, Dubna, Russia 68 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 69 Graduate School of Science, Kobe University, Kobe, Japan 70 Faculty of Science, Kyoto University, Kyoto, Japan 71 Kyoto University of Education, Kyoto, Japan 72 Department of Physics, Kyushu University, Fukuoka, Japan 73 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 74 Physics Department, Lancaster University, Lancaster, UK 75 (a)INFN Sezione di Lecce, Lecce, Italy; (b)Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy 76 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK 77 Department of Physics, Jožef Stefan Institute, University of Ljubljana, Ljubljana, Slovenia 78 School of Physics and Astronomy, Queen Mary University of London, London, UK 79 Department of Physics, Royal Holloway University of London, Surrey, UK 80 Department of Physics and Astronomy, University College London, London, UK 81 Louisiana Tech University, Ruston, LA, USA 82 Laboratoire de Physique Nucléaire et de Hautes Energies, UPMC and Université Paris-Diderot and CNRS/IN2P3, Paris, France 83 Fysiska institutionen, Lunds universitet, Lund, Sweden 84 Departamento de Fisica Teorica C-15, Universidad Autonoma de Madrid, Madrid, Spain 85 Institut für Physik, Universität Mainz, Mainz, Germany 86 School of Physics and Astronomy, University of Manchester, Manchester, UK 87 CPPM, Aix-Marseille Université and CNRS/IN2P3, Marseille, France 88 Department of Physics, University of Massachusetts, Amherst, MA, USA 89 Department of Physics, McGill University, Montreal, QC, Canada 90 School of Physics, University of Melbourne, Victoria, Australia 91 Department of Physics, The University of Michigan, Ann Arbor, MI, USA 92 Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA 93 (a)INFN Sezione di Milano, Milan, Italy; (b)Dipartimento di Fisica, Università di Milano, Milan, Italy 94 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Republic of Belarus 95 National Scientific and Educational Centre for Particle and High Energy Physics, Minsk, Republic of Belarus 96 Group of Particle Physics, University of Montreal, Montreal, QC, Canada 97 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia 98 Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia 99 National Research Nuclear University MEPhI, Moscow, Russia 100 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia 101 Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany 102 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany 103 Nagasaki Institute of Applied Science, Nagasaki, Japan 104 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 105 (a)INFN Sezione di Napoli, Naples, Italy; (b)Dipartimento di Fisica, Università di Napoli, Naples, Italy 106 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA 107 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, The Netherlands 108 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands 109 Department of Physics, Northern Illinois University, DeKalb, IL, USA 110 Budker Institute of Nuclear Physics, SB RAS, Novosibirsk, Russia EPLANET , ERC, FP7, Horizon 2020 and Marie Skłodowska-Curie acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands) , PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG in Ref. 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G. Aad, B. Abbott, J. Abdallah, O. Abdinov, B. Abeloos, R. Aben, M. Abolins, O. S. AbouZeid, H. Abramowicz, H. Abreu, R. Abreu, Y. Abulaiti, B. S. Acharya, L. Adamczyk, D. L. Adams, J. Adelman, S. Adomeit, T. Adye, A. A. Affolder, T. Agatonovic-Jovin, J. Agricola, J. A. Aguilar-Saavedra, S. P. Ahlen, F. Ahmadov, G. Aielli, H. Akerstedt, T. P. A. Åkesson, A. V. Akimov, G. L. Alberghi, J. Albert, S. Albrand, M. J. Alconada Verzini, M. Aleksa, I. N. Aleksandrov, C. Alexa, G. Alexander, T. Alexopoulos, M. Alhroob, G. Alimonti, L. Alio, J. Alison, S. P. Alkire, B. M. M. Allbrooke, B. W. Allen, P. P. Allport, A. Aloisio, A. Alonso, F. Alonso, C. Alpigiani, B. Alvarez Gonzalez, D. Álvarez Piqueras, M. G. Alviggi, B. T. Amadio, K. Amako, Y. Amaral Coutinho, C. Amelung, D. Amidei, S. P. Amor Dos Santos, A. Amorim, S. Amoroso, N. Amram, G. Amundsen, C. Anastopoulos, L. S. Ancu, N. Andari, T. Andeen, C. F. Anders, G. Anders, J. K. Anders, K. J. Anderson, A. Andreazza, V. Andrei, S. Angelidakis, I. Angelozzi, P. Anger, A. Angerami, F. Anghinolfi, A. V. Anisenkov, N. Anjos, A. Annovi, M. Antonelli, A. Antonov, J. Antos, F. Anulli, M. Aoki, L. Aperio Bella, G. Arabidze, Y. Arai, J. P. Araque, A. T. H. Arce, F. A. Arduh, J-F. Arguin, S. Argyropoulos, M. Arik, A. J. Armbruster, O. Arnaez, H. Arnold, M. Arratia, O. Arslan, A. Artamonov, G. Artoni, S. Artz, S. Asai, N. Asbah, A. Ashkenazi, B. Åsman, L. Asquith, K. Assamagan, R. Astalos, M. Atkinson, N. B. Atlay, K. Augsten, G. Avolio, B. Axen, M. K. Ayoub, G. Azuelos, M. A. Baak, A. E. Baas, M. J. Baca, H. Bachacou, K. Bachas, M. Backes, M. Backhaus, P. Bagiacchi, P. Bagnaia, Y. Bai, J. T. Baines, O. K. Baker, E. M. Baldin, P. Balek, T. Balestri, F. Balli, W. K. Balunas, E. Banas, Sw. Banerjee, A. A. E. Bannoura, L. Barak, E. L. Barberio, D. Barberis, M. Barbero, T. Barillari, T. Barklow, N. Barlow, S. L. Barnes, B. M. Barnett, R. M. Barnett, Z. Barnovska, A. Baroncelli, G. Barone, A. J. Barr, L. Barranco Navarro, F. 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Bessidskaia Bylund, M. Bessner, N. Besson, C. Betancourt, S. Bethke, A. J. Bevan, W. Bhimji, R. M. Bianchi, L. Bianchini, M. Bianco, O. Biebel, D. Biedermann, N. V. Biesuz, M. Biglietti, J. Bilbao De Mendizabal, H. Bilokon, M. Bindi, S. Binet, A. Bingul, C. Bini, S. Biondi, D. M. Bjergaard, C. W. Black, J. E. Black, K. M. Black, D. Blackburn, R. E. Blair, J. -B. Blanchard, J. E. Blanco, T. Blazek, I. Bloch, C. Blocker, W. Blum, U. Blumenschein, S. Blunier, G. J. Bobbink, V. S. Bobrovnikov, S. S. Bocchetta, A. Bocci, C. Bock, M. Boehler, D. Boerner, J. A. Bogaerts, D. Bogavac, A. G. Bogdanchikov, C. Bohm, V. Boisvert, T. Bold, V. Boldea, A. S. Boldyrev, M. Bomben, M. Bona, M. Boonekamp, A. Borisov, G. Borissov, J. Bortfeldt, V. Bortolotto, K. Bos, D. Boscherini, M. Bosman, J. Boudreau, J. Bouffard, E. V. Bouhova-Thacker, D. Boumediene, C. Bourdarios, N. Bousson, S. K. Boutle, A. Boveia, J. Boyd, I. R. Boyko, J. Bracinik, A. Brandt, G. Brandt, O. Brandt, U. Bratzler, B. Brau, J. E. 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Campana, M. Campanelli. Performance of algorithms that reconstruct missing transverse momentum in \(\sqrt{s}\) = 8 TeV proton–proton collisions in the ATLAS detector, The European Physical Journal C, 2017, 241, DOI: 10.1140/epjc/s10052-017-4780-2