Performance of missing transverse momentum reconstruction with the ATLAS detector using proton – proton collisions at √ s = 13 TeV

The performance of the missing transverse momentum (Emiss T ) reconstruction with the ATLAS detector is evaluated using data collected in proton–proton collisions at the LHC at a centre-of-mass energy of 13 TeV in 2015. To reconstruct Emiss T , fully calibrated electrons, muons, photons, hadronically decaying τ -leptons, and jets reconstructed from calorimeter energy deposits and charged-particle tracks are used. These are combined with the soft hadronic activity measured by reconstructed charged-particle tracks not associated with the hard objects. Possible double counting of contributions from reconstructed charged-particle tracks from the inner detector, energy deposits in the calorimeter, and reconstructed muons from the muon spectrometer is avoided by applying a signal ambiguity resolution procedure which rejects already used signals when combining the various Emiss T contributions. The individual terms as well as the overall reconstructed Emiss T are evaluated with various performance metrics for scale (linearity), resolution, and sensitivity to the data-taking conditions. The method developed to determine the systematic uncertainties of the Emiss T scale and resolution is discussed. Results are shown based on the full 2015 data sample corresponding to an integrated luminosity of 3.2 fb−1.


Introduction
The missing transverse momentum (E miss T ) is an important observable serving as an experimental proxy for the transverse momentum carried by undetected particles produced in proton-proton (pp) collisions measured with the ATLAS detector [1] at the Large Hadron Collider (LHC). It is reconstructed from the signals of detected particles in the final state. A value incompatible with zero may indicate not only the production of Standard Model (SM) neutrinos but also the production of new particles suggested in models for physics beyond the SM that escape the ATLAS detector without being detected. The reconstruction of E miss T is challenging because it involves all detector subsystems and requires the most complete and unambiguous representation of the hard interaction of interest by calorimeter and tracking signals. This representation is obscured by limitations introduced by the detector acceptance and by signals and signal remnants from additional pp interactions occurring in the same, previous and subsequent LHC bunch crossings (pile-up) relative to the triggered hard-scattering. ATLAS has developed successful strategies for a high-quality E miss T reconstruction focussing on the minimisation of effects introduced by pile-up for the data recorded between 2010 and 2012 (LHC Run 1) [2,3]. These approaches are the basis for the E miss T reconstruction developed for the data collected in 2015 (LHC Run 2) that is described in this paper, together with results from performance evaluations and the determination of systematic uncertainties. This paper is organised as follows. The subsystems forming the ATLAS detector are described in Section 2. The E miss T reconstruction is discussed in Section 3. The extraction of the data samples and the generation of the Monte Carlo (MC) simulation samples are presented in Section 4. The event selection is outlined in Section 5, followed by results for E miss T performance in Section 6. Section 7 comprises a discussion of methods used to determine systematic uncertainties associated with the E miss T measurement, and the presentation of the corresponding results. Section 8 describes variations of the E miss T reconstruction using calorimeter signals for the soft hadronic event activity, or reconstructed charged-particle tracks only. The paper concludes with a summary and outlook in Section 9. The nomenclature and conventions used by ATLAS for E miss T -related variables and descriptors can be found in Appendix A, while the composition of E miss T reconstruction variants is presented in Appendix B. An evaluation of the effect of alternative jet selections on the E miss T reconstruction performance is given in Appendix C.

ATLAS detector
The ATLAS experiment at the LHC features a multi-purpose particle detector with a forward-backward symmetric cylindrical geometry and a nearly full (4π) coverage in solid angle.1 It consists of an inner detector (ID) tracking system in a 2 T axial magnetic field provided by a superconducting solenoid. The solenoid is surrounded by electromagnetic and hadronic calorimeters, and a muon spectrometer (MS). The ID covers the pseudorapidity range |η| < 2.5, and consists of a silicon pixel detector, a silicon microstrip detector and a transition radiation tracker for |η| < 2.0. During the LHC shutdown between Run 1 and Run 2, a new tracking layer, known as the insertable B-layer [4], was added between the previous innermost pixel layer and a new, narrower beam pipe. 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 upwards. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the z-axis.
The MS surrounds the calorimeters. It consists of three large superconducting air-core toroidal magnets, precision tracking chambers providing precise muon tracking out to |η| = 2.7, and fast detectors for triggering in the region |η| < 2.4.
A two-level trigger system is used to select events [5]. A low-level hardware trigger reduces the data rate, and a high-level software trigger selects events with interesting final states. More details of the ATLAS detector can be found in Ref. [1].

E miss T reconstruction
The reconstructed E miss T in ATLAS is characterised by two contributions. The first one is from the hard-event signals comprising fully reconstructed and calibrated particles and jets (hard objects). The reconstructed particles are electrons, photons, τ-leptons, and muons. While muons are reconstructed from ID and MS tracks, electrons and τ-leptons are identified combining calorimeter signals with tracking information. Photons and jets are principally reconstructed from calorimeter signals, with possible signal refinements from reconstructed tracks. The second contribution to E miss T is from the soft-event signals consisting of reconstructed charged-particle tracks (soft signals) associated with the hard-scatter vertex defined in Appendix A but not with the hard objects.
ATLAS carries out a dedicated reconstruction procedure for each kind of particle as well as for jets, casting a particle or jet hypothesis on the origin of (a group of) detector signals. These procedures are independent of one another. This means that e.g. the same calorimeter signal used to reconstruct an electron is likely also used to reconstruct a jet, thus potentially introducing double counting of the same signal when reconstructing E miss T . This issue is addressed by the explicit signal ambiguity resolution in the object-based E miss T reconstruction originally introduced in Refs. [2] and [3], and by its 2015 implementation described in Sections 3.1 and 3.2.
Additional options for the set of signals used to reconstruct E miss T are available and discussed in detail in Section 8. One of these alternative options is the calorimeter-based E miss T reconstruction discussed in Section 8.1, which uses a soft event built from clusters of topologically connected calorimeter cells (topo-clusters) [6]. Another option is the track-based missing transverse momentum, which differs from E miss T only in the use of tracks in place of jets. It is described in more detail in Section 8.2.

E miss T basics
The missing transverse momentum reconstruction provides a set of observables constructed from the components p x(y) of the transverse momentum vectors (p T ) of the various contributions. The missing transverse momentum components E miss x(y) serve as the basic input for most of these observables. They are given by The set of observables constructed from E miss x(y) is The vector E miss T provides the amount of the missing transverse momentum via its magnitude E miss T , and its direction in the transverse plane in terms of the azimuthal angle φ miss . Consequently, E miss T is non-negative by definition. However, in an experimental environment where not all relevant p T from the hard-scatter interaction can be reconstructed and used in Eq. (1), and the reconstructed p T from each contribution is affected by the limited resolution of the detector, an observation bias towards non-vanishing values for E miss T is introduced even for final states without genuine missing transverse momentum generated by undetectable particles.
The scalar sum of all transverse momenta (p T = |p T |) from the objects contributing to E miss T reconstruction is given by In the context of E miss T reconstruction, ΣE T is calculated in addition to the sum given in Eq. (1), and the derived quantities defining E miss T given in Eqs. (2) to (4). It provides a useful overall scale for evaluating the hardness of the hard-scatter event in the transverse plane, and thus provides a measure for the event activity in physics analyses and E miss T reconstruction performance studies.
In the calculation of E miss x(y) and ΣE T the contributing objects need to be reconstructed from mutually exclusive detector signals. This rule avoids multiple inclusions of the same signal in all constructed observables. The implementation of this rule in terms of the signal ambiguity resolution requires the definition of a sequence for selected contributions, in addition to a rejection mechanism based on common signal usage between different objects. Similarly to the analysis presented in Ref. [3], the most commonly used order for the E miss T reconstruction sequence for the hard-object contribution starts with electrons (e), followed by photons (γ), then hadronically decaying τ-leptons (τ had ), and finally jets. Muons (µ) are principally reconstructed from ID and MS tracks alone, with corrections based on their energy loss in the calorimeter, leading to little or no signal overlap with the other reconstructed particles in the calorimeter.
In the sequence discussed here, all electrons passing the selection enter the E miss T reconstruction first. The lower-priority reconstructed particles (γ, τ had ) are fully rejected if they share their calorimeter signal with a higher-priority object that has already entered the E miss T reconstruction. Muons experience energy loss in the calorimeters, but only non-isolated muons overlap with other hard objects, most likely jets or τ-leptons. In this case the muon's energy deposit in the calorimeter cannot be separated from the overlapping jet-like objects with the required precision, and the calorimeter-signal-overlap resolution based on the shared use of topo-clusters cannot be applied. A discussion of the treatment of isolated and non-isolated muons is given in Section 3.3.4.
Generally, jets are rejected if they overlap with accepted higher-priority particles. To avoid signal losses for E miss Table 1: Overview of the contributions to E miss T and ΣE T from hard objects such as electrons (e), photons (γ), hadronically decaying τ-leptons (τ had ), muons (µ), and jets, together with the signals for the soft term. The configuration shown is the one used as reference for the performance evaluations presented in this paper. The table is ordered descending in priority P of consideration for E miss T reconstruction, with (1) being the first and (5) being the last calculated hard-object contribution. The soft-event contribution is constructed at the lowest priority (6), after all hard objects are considered. The transverse (longitudinal) impact parameter d 0 (z 0 sin(θ)) used to select the ID tracks contributing to E miss,soft T and ΣE soft T in P = (6) is measured relative to the hard-scatter vertex. All variables are explained in Section 3.2. The angular distance ∆R between objects is defined as ∆R = (∆η) 2 + (∆φ) 2 .

P
The hard term in both E miss T and ΣE T is characterised by little dependence on pile-up, as it includes only fully calibrated objects, where the calibration includes a pile-up correction and objects tagged as originating from pile-up are removed. The particular choice of using only tracks from the hard-scatter vertex for the soft term strongly suppresses pile-up contributions to this term as well. The observed residual pile-up dependencies are discussed with the performance results shown in Section 6.

Object selection
The following selections are applied to reconstructed particles and jets used for the performance evaluations presented in Sections 6 to 8. Generally, these selections require refinements to achieve optimal E miss T reconstruction performance in the context of a given physics analysis, and the selections performed in this study are an example set of criteria.

Electron selection
Reconstructed electrons are selected on the basis of their shower shapes in the calorimeter and how well their calorimeter cell clusters are matched to ID tracks [7]. Both are evaluated in a combined likelihoodbased approach [8]. Electrons with at least medium reconstruction quality are selected. They are calibrated using the default calibration given in Ref. [7]. To be considered for E miss T reconstruction, electrons passing the reconstruction quality requirements are in addition required to have p T > 10 GeV and |η| < 1.37 or 1.52 < |η| < 2.47, to avoid the transition region between the central and endcap electromagnetic calorimeters. Any energy deposit by electrons within 1.37 < |η| < 1.52 is likely reconstructed as a jet and enters the E miss T reconstruction as such, if this jet meets the corresponding selection criteria discussed in Section 3.3.5.

Photon selection
The identification and reconstruction of photons exploits the distinctive evolution of their electromagnetic showers in the calorimeters [9]. Photons are selected and calibrated using the tight selection criteria given in Ref. [7]. In addition to the reconstruction quality requirements, photons must have p T > 25 GeV and |η| < 1.37 or 1.52 < |η| < 2.37 to be included in the E miss T reconstruction. Similarly to electrons, photons emitted within 1.37 < |η| < 1.52 may contribute to E miss T as a jet.

τ-lepton selection
Hadronically decaying τ-leptons are reconstructed from narrow jets with low associated track multiplicities [10]. Candidates must pass the medium quality selection given in Ref. [11], and in addition have p T > 20 GeV and |η| < 1.37 or 1.52 < |η| < 2.47. Any τ-lepton not satisfying these τ-identification criteria may contribute to E miss T when passing the jet selection.

Muon selection
Muons are reconstructed within |η| < 2.5 employing a combined MS and ID track fit. Outside of the ID coverage, muons are reconstructed within 2.5 < |η| < 2.7 from a track fit to MS track segments alone. Muons are further selected for E miss T reconstruction by requiring the medium reconstruction quality defined in Ref.

Jet selection
Jets are reconstructed from clusters of topologically connected calorimeter cells (topo-clusters), described in Ref. [6]. The topo-clusters are calibrated at the electromagnetic (EM) energy scale.3 The anti-k t algorithm [13], as provided by the F J toolkit [14], is employed with a radius parameter R = 0.4 to form jets from these topo-clusters. The jets are fully calibrated using the EM+JES scheme [15] including a correction for pile-up [16]. They are required to have p T > 20 GeV after the full calibration. The jet contribution to E miss T and ΣE T is primarily defined by the signal ambiguity resolution.
Jets not rejected at that stage are further filtered using a tagging algorithm to select hard-scatter jets ("jet vertex tagging") [16]. This algorithm provides the jet vertex tagger variable JVT, ranging from 0 (pile-up-like) to 1 (hard-scatter-like), for each jet with matched tracks.4 The matching of tracks with jets is done by ghost association, where tracks are clustered as ghost particles into the jet, as described in Ref.
[3] and based on the approach outlined in Ref. [17].
The overlap resolution can result in a partial overlap of the jet with an electron or photon, in terms of the fraction of common signals contributing to the respective reconstructed energy. This is measured by the ratio κ E of the electron(photon) energy E EM e(γ) to the jet energy E EM jet , with both energies calibrated at the EM scale. In the case of κ E ≤ 50%, the jet is included in E miss T reconstruction, with its p T scaled by 1 − κ E . For κ E > 50%, only the tracks associated with the jet, excluding the track(s) associated with the overlapping particle if any, contribute to the soft term as discussed in Section 3.4.
Jets not rejected by the signal ambiguity resolution and with p T > 20 GeV and |η| > 2.4, or with p T ≥ 60 GeV and |η| < 4.5, are always accepted for E miss T reconstruction. Jets reconstructed with 3 On this scale the energy deposited in the calorimeter by electrons and photons is represented well. The hadron signal at the EM scale is not corrected for the non-compensating signal features of the ATLAS calorimeters. 4 In the calculation of JVT the total amount of p T carried by tracks from the hard-scatter vertex matched to the given jet is related to the total amount of p T carried by all matched tracks, among other inputs, to tag jets from the hard-scatter interaction.
20 GeV < p T < 60 GeV and |η| < 2.4 are only accepted if they are tagged by JVT > 0.59. In both cases, the jet p T thresholds are applied to the jet p T before applying the κ E correction. Additional configurations for selecting jets used in E miss T reconstruction are discussed in Appendix C, together with the effect of the variation of these selection criteria on the E miss T reconstruction performance.

Muon overlap with jets
Jets overlapping with a reconstructed muon affect the E miss T reconstruction in a manner that depends on their origin. If these jets represent a significant (catastrophic) energy loss along the path of the muon through the calorimeter, or if they are pile-up jets tagged by JVT as originating from the hard-scatter interaction due to the muon ID track, they need to be rejected for E miss T reconstruction. On the other hand, jets reconstructed from final state radiation (FSR) off the muon need to be included into E miss T reconstruction.
In all cases, the muon-jet overlap is determined by ghost-associating the muon with the jet. For this, each muon enters the jet clustering as ghost particle with infinitesimal small momentum, together with the EM-scale topo-clusters from the calorimeter. If a given ghost particle becomes part of a jet, the corresponding muon is considered overlapping with this jet. This procedure is very similar to the track associations with jets mentioned in Section 3.3.5.
Tagging jets using JVT efficiently retains those from the hard-scatter vertex for E miss T reconstruction and rejects jets generated by pile-up. A muon overlapping with a pile-up jet can lead to a mis-tag, because the ID track from the muon represents a significant amount of p T from the hard-scatter vertex and thus increases JVT. As a consequence of this fake tag, the pile-up jet p T contributes to E miss T , and thus degrades both the E miss T response and resolution due to the stochastic nature of its contribution.
A jet that is reconstructed from a catastrophic energy loss of a muon tends to be tagged as a hard-scatter jet as well. This jet is reconstructed from topo-clusters in close proximity to the extrapolated trajectory of the ID track associated with the muon bend in the axial magnetic field. Inclusion of such a jet into E miss T reconstruction leads to double-counting of the transverse momentum associated with the muon energy loss, as the fully reconstructed muon p T is already corrected for this effect.
To reject contributions from pile-up jets and jets reconstructed from muon energy loss, the following selection criteria are applied: • N PV track < 5 -the total number of tracks N PV track associated with the jet and emerging from the hardscatter vertex is small.
All jets with overlapping muons meeting these criteria are understood to be either from pile-up or a catastrophic muon energy loss and are rejected for E miss T reconstruction. The muons are retained for the E miss T reconstruction.
Another consideration for muon contributions to E miss T is FSR. Muons can radiate hard photons at small angles, which are typically not reconstructed as such because of the nearby muon ID track violating photon isolation requirements. They are also not reconstructed as electrons, due to the mismatch between the ID track momentum and the energy measured by the calorimeter. Most likely the calorimeter signal generated by the FSR photon is reconstructed as a jet, with the muon ID track associated. As the transverse momentum carried by the FSR photon is not recovered in muon reconstruction, jets representing this photon need to be included in the E miss T reconstruction. Such jets are characterised by the following selections, which are highly indicative of a photon in the ATLAS calorimeter: • N PV track < 3 -the jet has low charged-particle content, indicated by a very small number of tracks from the hard-scatter vertex; • f EMC > 0.9 -the jet energy E jet is largely deposited in the electromagnetic calorimeter (EMC), as expected for photons and measured by the corresponding energy fraction f EMC = E • w jet < 0.1 -the jet is narrow, with a width w jet comparable to a dense electromagnetic shower; w jet is reconstructed according to Jets are accepted for E miss T reconstruction when consistent with an FSR photon defined by the ensemble of these selection criteria, with their energy scale set to the EM scale, to improve the calibration.

E miss T soft term
The soft term introduced in Section 3.2 is exclusively reconstructed from ID tracks from the hard-scatter vertex, thus only using the p T -flow from soft charged particles. It is an important contribution to E miss T for the improvement of both the E miss T scale and resolution, in particular in final states with a low hardobject multiplicity. In this case it is indicative of (hadronic) recoil, comprising the event components not otherwise represented by reconstructed and calibrated particles or jets.
The more inclusive reconstruction of the E miss T soft term including signals from soft neutral particles uses calorimeter topo-clusters. The reconstruction performance using the calorimeter-based E miss,soft,calo T is inferior to the track-only-based E miss,soft T , mostly due to a larger residual dependence on pile-up. More details of the topo-cluster-based E miss,soft,calo T reconstruction are discussed in Section 8.1.

Track and vertex selection
Hits in the ID are used to reconstruct tracks pointing to a particular collision vertex [18]. Both the tracks and vertices need to pass basic quality requirements to be accepted. Each event typically has a number N PV > 1 of reconstructed primary vertices.
Tracks are required to have p T > 400 MeV and |η| < 2.5, in addition to the reconstruction quality requirements given in Ref. [19]. Vertices are constructed from at least two tracks passing selections on the transverse (longitudinal) impact parameter |d 0 | < 1.5 mm (|z 0 sin(θ)| < 1.5 mm) relative to the vertex candidate. These tracks must also pass requirements on the number of hits in the ID. The hard-scatter vertex is identified as described in Appendix A.

Track soft term
The track sample contributing to E miss,soft T for each reconstructed event is collected from high-quality tracks emerging from the hard-scatter vertex but not associated with any electron, τ-lepton, muon, or jet contributing to E miss T reconstruction. The applied signal-overlap resolution removes • ID tracks with ∆R(track,electron/photon cluster) < 0.05; • ID tracks with ∆R(track,τ-lepton) < 0.2; • ID tracks associated with muons; • ID tracks ghost-associated with fully or partially contributing jets.
ID tracks from the hard-scatter vertex that are associated with jets rejected by the overlap removal or are associated with jets that are likely from pile-up, as tagged by the JVT procedure discussed in Section 3.3.5, contribute to E miss,soft T .
Since only reconstructed tracks associated with the hard-scatter vertex are used, the track-based E miss,soft T is largely insensitive to pile-up effects. It does not include contributions from any soft neutral particles, including those produced by the hard-scatter interaction.

Data and simulation samples
The determination of the E miss T reconstruction performance uses selected final states without (E miss,true T = 0) and with genuine missing transverse momentum from neutrinos (E miss,true T = p ν T ). Samples with E miss,true T = 0 are composed of leptonic Z boson decays (Z → ee and Z → µµ) collected by a trigger and event selection that do not depend on the particular pile-up conditions, since both the electron and muon triggers as well as the corresponding reconstructed kinematic variables are only negligibly affected by pile-up. Also using lepton triggers, samples with neutrinos were collected from W → eν and W → µν decays. In addition, samples with neutrinos and higher hard-object multiplicity were collected from top-quark pair (tt ) production with at least either the t or thet decaying semi-leptonically.

Data samples
The data sample used corresponds to a total integrated luminosity of 3.2 fb −1 , collected with a proton bunch-crossing interval of 25 ns. Only high-quality data with a well-functioning calorimeter, inner detector and muon spectrometer are analysed. The data-quality criteria are applied, which reduce the impact of instrumental noise and out-of-time calorimeter deposits from cosmic-ray and beam backgrounds.

Monte Carlo samples
The Z → and W → ν samples were generated using P -B [20] (version v1r2856) employing a matrix element calculation at next-to-leading order (NLO) in perturbative QCD. To generate the particle final state, the (parton-level) matrix element output was interfaced to P 8 [21],5 which generated the parton shower (PS) and the underlying event (UE) using the AZNLO tuned parameter set [22]. Parton distribution functions (PDFs) were taken from the CTEQ6L1 PDF set [23].
The tt-production sample was generated with a P NLO kernel (version v2r3026) interfaced to P 6 [24] (version 6.428) with the Perugia2012 set of tuned parameters [25] for the PS and UE generation. The CT10 NLO PDF set [26] was employed. The resummation of soft-gluon terms in the next-to-next-to-leading-logarithmic (NNLL) approximation with ++ 2.0 [27] was included.
Additional processes contributing to the Z → and W → ν final state samples are the production of dibosons, single top quarks, and multijets. Dibosons were generated using S [28-31] version v2.1.1 employing the CT10 PDF set. Single top quarks were generated using P version v1r2556 with the CT10 PDF set for the t-channel production and P version v1r2819 for the s-channel and the associated top quark (Wt) production, all interfaced to the PS and UE from the same P 6 configuration used for tt production. Multijet events were generated using P 8 with the NNPDF23LO PDF set [32] and the A14 set of tuned PS and UE parameters described in Ref. [33].
Minimum bias (MB) events were generated using P 8 with the MSTW2008LO PDF set [34] and the A2 tuned parameter set [35] for PS and UE. These MB events were used to model pile-up, as discussed in Section 4.3.
For the determination of the systematic uncertainties in E miss T reconstruction, an alternative inclusive sample of Z → µµ events was generated using the M G _ MC@NLO (version v2.2.2) matrix element generator [36] employing the CTEQ6L1 PDF set. Both PS and UE were generated using P 8 with the NNPDF23LO PDF set and the A14 set of tuned parameters.
The MC-generated events were processed with the G 4 software toolkit [37], which simulates the propagation of the generated stable particles6 through the ATLAS detector and their interactions with the detector material [38].

Pile-up
The calorimeter signals are affected by pile-up and the short bunch-crossing period at the LHC. In 2015, an average of about 13 pile-up collisions per bunch crossing was observed. The dominant contribution of the additional pp collisions to the detector signals of the recorded event arises from a diffuse emission of soft particles superimposed to the hard-scatter interaction final state (in-time pile-up). In addition, the LAr calorimeter signals are sensitive to signal remnants from up to 24 previous bunch crossings and one following bunch crossing (out-of-time pile-up), as discussed in Refs. [6,39]. Both types of pile-up affect signals contributing to E miss T . The in-time pile-up activity is measured by the number of reconstructed primary collision vertices N PV . The out-of-time pile-up is proportional to the number of collisions per bunch crossing µ, measured as an average over time periods of up to two minutes by integrated signals from the luminosity detectors in ATLAS [40].
To model in-time pile-up in MC simulations, a number of generated pile-up collisions was drawn from a Poisson distribution around the value of µ recorded in data. The collisions were randomly collected from the MB sample discussed in Section 4.2. The particles emerging from them were overlaid onto the particle-level final state of the generated hard-scatter interaction and converted into detector signals before event reconstruction. The event reconstruction then proceeds as for data.
Similar to the LHC proton-beam structure, events in MC simulations are organised in bunch trains, where the structure in terms of bunch-crossing interval and gaps between trains is taken into account to model the effects of out-of-time pile-up. The fully reconstructed events in MC simulation samples are finally weighted such that the distribution of the number of overlaid collisions over the whole sample corresponds to the µ distribution observed in data.
The effect of pile-up on the signal in the Tile calorimeter is reduced due to its location behind the electromagnetic calorimeter and its fast time response [41]. Reconstructed ID and MS tracks are largely unaffected by pile-up.

Z → µµ event selection
The Z → µµ final state is ideal for the evaluation of E miss T reconstruction performance, since it can be selected with a high signal-to-background ratio and the Z kinematics can be measured with high precision, even in the presence of pile-up. Neutrinos are produced only through very rare heavy-flavour decays in the hadronic recoil. This channel can therefore be considered to have no genuine missing transverse momentum. Thus, the scale and resolution for the reconstructed E miss T are indicative of the reconstruction quality and reflect limitations introduced by both the detector and the ambiguity resolution procedure. The well-defined expectation value E miss,true T = 0 allows the reconstruction quality to be determined in both data and MC simulations. The reconstructed E miss T in this final state is also sensitive to the effectiveness of the muon-jet overlap resolution, which can be explored in this low-multiplicity environment in both data and MC simulations, with a well-defined E miss T .
Events must pass one of three high-level muon triggers with different p µ T thresholds and isolation requirements. The isolation is determined by the ratio of the scalar sum of p T of reconstructed tracks other than the muon track itself, in a cone of size ∆R = 0.2 around the muon track (p cone T ), to p

W → eν event selection
Events with W → eν or W → µν in the final state provide a well-defined topology with neutrinos produced in the hard-scatter interaction. In combination with Z → µµ, the effectiveness of signal ambiguity resolution and lepton energy reconstruction for both the electrons and muons can be observed. The W → eν events in particular provide a good metric with E miss,true T = p ν T > 0 to evaluate and validate the scale, resolution and direction (azimuth) of the reconstructed E miss T , as the E miss T reconstruction is sensitive to the electron-jet overlap resolution performance. This metric is only available in MC simulations where p ν T is known. Candidate W → eν events are required to pass the high-level electron trigger with p T > 17 GeV. Electron candidates are selected according to criteria described in Section 3.3.1. Only events containing exactly one electron are considered.
Further selections using E miss T and the reconstructed transverse mass m T , given by are applied to reduce the multijet background with one jet emulating an isolated electron from the W boson. Here E miss T is calculated as presented in Section 3. The transverse momentum of the electron is denoted by p e T , and ∆φ is the distance between φ miss and the azimuth of the electron. Selected events are required to have E miss T > 25 GeV and m T > 50 GeV.

tt event selection
Events with tt in the final state allow the evaluation of the E miss T performance in interactions with a large jet multiplicity. Electrons and muons used to define these samples are reconstructed as discussed in Section 3.3.1 and Section 3.3.4, respectively, and are required to have p T > 25 GeV.
The final tt sample is selected by imposing additional requirements. Each event must have exactly one electron and no muons passing the selections described above. In addition, at least four jets reconstructed by the anti-k t algorithm with R = 0.4 and selected following the description in Section 3.3.5 are required. At least one of the jets needs to be b-tagged using the tagger configuration for a 77% efficiency working point described in Ref. [42]. All jets are required to be at an angular distance of ∆R > 0.4 from the electron.

Performance of E miss T reconstruction in data and Monte Carlo simulation
Unlike for fully reconstructed and calibrated particles and jets, and in the case of the precise reconstruction of charged particle kinematics provided by ID tracks, E miss T reconstruction yields a non-linear response, especially in regions of phase space where the observation bias discussed in Section 3.1 dominates the reconstructed E miss T . In addition, the E miss T resolution functions are characterised by a high level of complexity, due to the composite character of the observable. Objects with different p T -resolutions contribute, and the E miss T composition can fluctuate significantly for events from the same final state. Due to the dependence of the E miss T response on the resolution, both performance characteristics change as a function of the total event activity and are affected by pile-up. There is no universal way of mitigating these effects, due to the inability to validate in data a stable and universal calibration reference for E miss T . The E miss T reconstruction performance is therefore assessed by comparing a set of reconstructed E miss Trelated observables in data and MC simulations for the same final-state selection, with the same object and event selections applied. Systematic uncertainties in the E miss T response and resolution are derived from these comparisons and are used to quantify the level of understanding of the data from the physics models. The quality of the detector simulation is independently determined for all reconstructed jets, particles and ID tracks, and can thus be propagated to the overall E miss T uncertainty for any given event.
Both the distributions of observables as well as their average behaviour with respect to relevant scales measuring the overall kinematic activity of the hard-scatter event or the pile-up activity are compared. To focus on distribution shapes rather than statistical differences in these comparisons, the overall distribution of a given observable obtained from MC simulations is normalised to the integral of the corresponding distribution in data.
As the reconstructed final state can be produced by different physics processes, the individual process contributions in MC simulations are scaled according to the cross section of the process. This approach is taken to both show the contribution of a given process to the overall distribution, and to identify possible inadequate modelling arising from any individual process, or a subset of processes, by its effect on the overall shape of the MC distribution.
Inclusive event samples considered for the E miss T performance evaluation are obtained by applying selections according to Section 5.1 for a final state without genuine E miss T (Z → µµ), and according to Section 5.2 for a final state with genuine E miss T (W → eν). From these, specific exclusive samples are extracted by applying conditions on the number of jets reconstructed. In particular, zero jet (N jet = 0) samples without any jet with p T > 20 GeV (fully calibrated) and |η| < 4.9 are useful for exclusively studying the performance of the soft term. Samples with events selected on the basis of a non-zero number of reconstructed jets with p T > 20 GeV are useful for evaluating the contribution of jets to E miss T . While the p T response of jets is fully calibrated and provides a better measurement of the overall event p T -flow, the p T resolution for jets is affected by pile-up and can introduce a detrimental effect on E miss T reconstruction performance.
Missing transverse momentum and its related observables presented in Section 3.1 are reconstructed for the performance evaluations shown in the following sections using a standard reconstruction configuration. This configuration implements the signal ambiguity resolution in the E miss T reconstruction sequence discussed in Section 3.1. It employs the hard-object selections defined in Sections 3.3.1 to 3.3.4, with jets selected according to the prescriptions given in Section 3.3.5. The overlap resolution strategy for jets and muons described in Section 3.3.6 is applied. The soft term is formed from ID tracks according to Section 3.4.  observables to data. The results are presented in Fig. 1. The data and MC simulations agree within 20% for the bulk of the E miss T distribution shown in Fig. 1(a), with larger differences not accommodated by the total (systematic and statistical) uncertainties of the distributions for high E miss T . These differences suggest a mismodelling in tt events, the dominant background in the tail regime [43]. The ΣE T distributions compared between data and MC simulations in Fig. 1(b) show discrepancies significantly larger than the overall uncertainties for 200 GeV < ΣE T < 1.2 TeV. These reflect the level of mismodelling of the final state mostly in terms of hard-object composition in MC simulations. The E miss x and E miss y spectra shown in Figs. 1(c) and 1(d), respectively, show good agreement between data and MC simulations for the bulk of the distributions within |E miss x(y) | < 100 GeV, with larger differences observed outside of this range still mostly within the uncertainties. arise from events with one or more high-p T jets balancing the p T of the Z boson.
For the W → eν sample with genuine missing transverse momentum given by p ν T , both the total reconstructed E miss T and the soft term are compared between data and MC simulations in Fig. 3. The level of agreement between the E miss T distributions for data and MC simulations shown in Fig. 3(a) for the inclusive event sample is at ±20%, similar to that observed for the Z → µµ sample in Fig. 1(a), except that for this final state it is found to be within the total uncertainties of the measurement. The differences between the E miss T distributions observed with the exclusive N jet = 0 sample shown in Fig. 3(b) are well below 20%, but show a trend to larger discrepancies for decreasing E miss T 40 GeV. This trend is due to the missing background contribution in MC simulations from multijet final states. The extraction of this contribution is very inefficient and only possible with large statistical uncertainties. Even very large MC samples of multijet final states provide very few events with only one jet that is accidentally reconstructed as an electron, and with the amount of E miss T required in the W → eν selection described in Section 5.2. The comparison of the E miss,soft T distributions from data and MC simulations shown in Fig. 3(c) yields agreement well within the uncertainties, for E miss,soft T 10 GeV. The rising deficiencies observed in the MC distribution for decreasing E miss,soft T 10 GeV are expected to be related to the missing multijet contribution.

E miss T response and resolution
The response in the context of E miss T reconstruction is determined by the deviation of the observed E miss T from the expectation value for a given final state. This deviation sets the scale for the observed E miss T . If this deviation is independent of the genuine missing transverse momentum, or any other hard p T indicative of the overall hard-scatter activity, the E miss Final states balanced in transverse momentum are expected to show a non-linear E miss T response at low event activity, as the response in this case suffers from the observation bias in E miss T reconstruction discussed in Section 3.1. With increasing momentum transfers in the hard-scatter interaction, the E miss T response becomes increasingly dominated by a well-measured hadronic recoil and thus more linear. In the case of final states with genuine missing transverse momentum, the E miss T response is only linear once E miss,true T exceeds the observation bias. These features are discussed in Section 6.2.1 and explored in Section 6.2.2.
Contributions to the fluctuations in the E miss T measurement arise from (1) the limitations in the detector acceptance not allowing the reconstruction of the complete transverse momentum flow from the hard interaction, (2) the irreducible intrinsic signal fluctuations in the detector response, and from (3) the additional response fluctuations due to pile-up. In particular (1) introduces fluctuations driven by the large variations of the particle composition of the final state with respect to their types, momenta and directions. The limited detector coverage of |η| < 4.9 for all particles, together with the need to suppress the pile-up-induced signal fluctuations as much as possible, restricts the contribution of particles to E miss T to the reconstructed and accepted e, γ, τ had and µ, and those being part of a reconstructed and accepted jet. In addition, the p T -flow of not explicitly reconstructed charged particles emerging from the hard-scatter vertex is represented by ID tracks contributing to E miss,soft T given in Eqs. (6) and (7), but only in the phase space defined by the selections given in Section 3.4.1. All other charged and neutral particles do not contribute to E miss T reconstruction.
Like for the E miss T response, resolution-related aspects of E miss T reconstruction are understood from datato-MC-simulations comparisons. The scales used for the corresponding evaluations are the overall event activity represented by ΣE T , and the pile-up activity measured by N PV . The measurement of the E miss T resolution is discussed in Section 6.2.3 and results are presented in Section 6.2.4.

E miss T scale determination
In events with Z → µµ decays, the transverse momentum of the Z boson (p Z T ) is an indicator of the hardness of the interaction. It provides a useful scale for the evaluation of the E miss T response for this final state without genuine missing transverse momentum. The direction of the corresponding Z boson transverse momentum vector p Z T defines an axis A Z in the transverse plane of the collision, which is reconstructed from the p T of the decay products by The magnitude of the component of E miss This projection is sensitive to any limitation in E miss T reconstruction, in particular with respect to the contribution from the hadronic recoil against p Z T , both in terms of response and resolution. Because it can be determined both for data and MC simulations, it provides an important tool for the validation of the E miss T response and the associated systematic uncertainties.
The expectation value for a balanced interaction producing a Z boson against a hadronic recoil is E[P Z ] = 0. Any observed deviation from this value represents a bias in the E miss T reconstruction. For P Z < 0, the reconstructed hadronic activity recoiling against p Z T is too small, while for P Z > 0 too much hadronic  Figure 4 shows P Z as a function of p Z T for the N jet = 0 and the inclusive Z → µµ sample, respectively. MC simulations compare well with the data for N jet = 0, but show larger deviations up to 30% for the inclusive selection. Nevertheless, these differences are still found to be within the total uncertainty of the measurement.
The steep decrease of P Z with increasing p Z T in the N jet = 0 sample seen in Fig. 4(a) reflects the inherent underestimation of the soft term, as in this case the hadronic recoil is exclusively represented by ID tracks with p T > 400 MeV within |η| < 2.5. It thus does not contain any signal from (1) neutral particles, (2) charged particles produced with |η| > 2.5, and (3) charged particles produced within |η| < 2.5 but with p T below threshold, rejected by the track quality requirements, or not represented by a track at all due to insuffcient signals in the ID (e.g., lack of hits for track fitting).
In the case of the inclusive sample shown in Fig. 4(b), the E miss T response is recovered better as p Z T increases, since an increasing number of events enter the sample with a reconstructed recoil containing fully calibrated jets. These provide a more complete representation of the hadronic transverse momentum flow. The residual offsets in P Z of about 8 GeV in data and 6 GeV in MC simulations observed for p Z T 40 GeV in Fig. 4(b) agree within the uncertainties of this measurement.
The persistent bias in P Z is further explored in Fig. 5, which compares variations of P Z respectively using the full E miss T , the soft-term contribution E miss,soft = p ν x(y) is used.

E miss T resolution measurements
The E miss T resolution measured by RMS miss x(y) is evaluated as a function of the event activity measured by ΣE T given in Eq. (7). For the inclusive Z → µµ sample, Fig. 7(a) shows RMS miss x(y) quickly rising from less than 5 GeV to about 10 GeV with increasing ΣE T within 50 GeV ≤ ΣE T < 70 GeV.7 This is due to the fact that in this range the two muons are the dominant hard objects contributing, with a p T resolution proportional to (p  [44] therefore dominates RMS miss x(y) at these higher ΣE T . The MC predictions for RMS miss x(y) (ΣE T ) agree with the data within a few percent and well within the total uncertainties of this measurement. A tendency for slightly poorer resolution in MC simulations is observed, in particular for ΣE T > 200 GeV.

Any contribution from pile-up to RMS miss
x(y) is expected to be associated with the jets. While dedicated corrections applied to the jets largely suppress pile-up contributions in the jet response, residual irreducible fluctuations introduced into the calorimeter signals by pile-up lead to a degradation of the jet energy resolution and thus poorer resolution in the jet-p T measurement. The dependence of RMS miss x(y) on the pile-up activity measured by N PV is shown in Fig. 7(b). Data show a less steep slope of RMS miss x(y) (N PV ) than MC simulations, but with about 10% worse resolution in the low pile-up region of N PV 5. The resolution in data is better than in MC simulations by about 10% for the region of higher pile-up activity at N PV ≈ 20.

The differences between data and MC simulations seen in RMS miss
x(y) (ΣE T ) for the inclusive Z → µµ sample can be further analysed by splitting the sample according to the value of N jet . Figure 8(a) shows the dependence of RMS miss x(y) on ΣE T for Z → µµ events with N jet = 0. The dominant source of fluctuations other than the muon-p T resolution is in this case introduced by the incomplete reconstruction of the hadronic recoil. These fluctuations increase with increasing p Z T , which in turn means higher overall event activity measured by ΣE T . For this sample RMS miss x(y) in data compares well to MC simulations, at a level of a few percent, without any observed dependence on ΣE T .
The exclusive N jet ≥ 1 samples extracted from Z → µµ data and MC simulations show the expected RMS miss x(y) ∝ √ ΣE T scaling in Fig. 8(b). The resolution in data is well represented by MC simulations, at the level of a few percent. The slightly better resolution observed in data with increasing ΣE T follows the trend observed in Fig. 7(a). The similar trends are expected as this kinematic region is largely affected by the jet contribution.

The dependence of RMS miss
x(y) on N PV shown in Fig. 8(c) indicates that the E miss T resolution is basically independent of pile-up, for the N jet = 0 sample. This is expected from the exclusive E miss T composition comprising the (track-based) E miss,µ T and E miss,soft T terms only. Data and MC simulations compare well within a few percent, and without any observable dependence on N PV . Figure 8(d) shows the N PV dependence of RMS miss x(y) for the N jet ≥ 1 sample. Comparing this result to Fig. 7(b) confirms that all pile-up dependence of the E miss T resolution is arising from the jet term. Both trend and magnitude of the data-to-MC comparison follow the observation from the inclusive analysis.

E miss T resolution in final states with neutrinos
The E miss T resolution for final states with E miss,true T > 0 is measured by RMS miss x(y) according to Eq. (12) and evaluated using dedicated inclusive W → eν and W → µν samples from MC simulations, and the inclusive tt MC sample defined in Section 5.3. For these samples, RMS miss x(y) can be determined as a function of E miss,true T = p ν T . The dedicated W → eν and W → µν samples are obtained with an event selection based on the description in Section 5.2, but omitting both the E miss T -based and the m T -based selections.

E miss T tails
Large reconstructed E miss T is an indicator for the production of (potentially new) undetectable particles, but can also be generated by detector problems and/or poor reconstruction of the objects used for its reconstruction. Enhanced tails in the distribution of the E miss T components for final states with well-known expectation values for E miss T are indicative of such inefficiencies.
Non-Gaussian shapes in the distribution arise from a combination of object selection inefficiencies and potentially non-Gaussian resolutions of the E miss T constituents. Even for a well-defined final state, eventby-event fluctuations in terms of which particles, jets, and soft tracks enter the E miss T reconstruction, and with which p T , lead to deviations from a normally distributed (E miss x ,E miss y ) response. Figure 10 shows the combined (E miss x ,E miss y ) distribution for the inclusive Z → µµ sample from MC simulations. To illustrate its symmetric nature and its deviation from a normal distribution in particular with respect to the tails, Gaussian functions are fitted to two limited ranges around the centre of the distribution, ±1 × RMS and ±2 × RMS. The differences between these functions and the data distribution (lower panel of Fig. 10) indicate a more peaked shape around the most probable value for E miss x(y) with near exponential slopes. The result of this comparison supports the choice of RMS miss x(y) defined in Eq. (12) in Section 6.2.3 for the determination of the E miss T resolution, rather than using any of the widths measured by fitting Gauss functions in selected ranges of the distribution.
Here h(E miss T ) is the E miss T distribution for a given event sample, and E miss,threshold T is a threshold set to estimate tails. Any decrease of f tail at a fixed integral H indicates an improvement of the E miss T resolution, and is more sensitive to particular improvements than e.g. RMS miss x(y) . For example, improving the E miss,soft T reconstruction by rejecting ID tracks from the hard-scatter vertex with poor reconstruction quality yields a significantly smaller f tail for the same event sample.
The tails in the E miss T distributions for the final states considered for this study are quantified by the fraction of events above a certain E miss T threshold using MC simulations. Figure 11(a) shows that the Z → events ( = e or = µ) with E miss,true T = 0 have significantly reduced tails when compared to W → ν and tt with this metric, and that the tails do not depend on the lepton flavour. A modification of this metric, taking into account E miss,true T such that the fraction of events with |E miss T − E miss,true T | above a given threshold is determined, shows the universality of the hadronic recoil in Z → and W → ν, as can be seen in Fig. 11(b).
Another finding of this study is that the tail in the |E miss T − E miss,true T | distribution for the higher ΣE jet T tt sample is considerably larger than for the low-ΣE jet T samples with Z → or W → ν final states. As can be seen in Fig. 11(c), the tails are much more consistent between Z → µµ and tt samples when the distribution for the Z → µµ sample is reweighted such that it follows the same ΣE jet T distribution as the tt sample. The enhanced tails are thus likely introduced by the jet response and multiplicity, which has a residual sensitivity to pile-up.

Systematic uncertainties
The systematic uncertainties associated with the measurement of E miss T are provided for the response (E miss T scale) as well as for the resolution. They depend on the composition of the hard terms and on the magnitude of the corresponding soft term. As the hard-term composition is generally defined by optimisations implemented in the context of a given analysis, the contributions of the E miss T terms need to be extracted from the scale and resolution uncertainties for the individual contributing objects comprising electrons, photons, muons, τ-leptons, and jets. In the corresponding propagations, correlations between systematic uncertainties for the same type of object are typically taken into account. However, it is assumed that systematic uncertainties of the different object types entering E miss T reconstruction are uncorrelated. The determination of the E miss T scale and resolution uncertainties arising from the soft term E miss,soft T is described in this section.

Methodology
The extraction of the systematic uncertainties for the reconstructed E miss T is based on data-to-MC comparisons of spectra of observables measuring the contribution of E miss,soft T to the overall E miss T .

Observables
The vector sum of the transverse momentum vectors of all particles and jets emerging from a hard-scatter interaction (p HS T ) is given by .
Here p ν T generally represents the transverse momenta of non-observable particles, which are summed up to form p inv T . All other transverse momenta are carried by particles that are observable in principle, and sum up to p obs T . Momentum conservation dictates p HS T = |p HS T | = 0. Due to detector acceptance limitations and inefficiencies in hard-object reconstruction and calibration, and all other effects discussed in Section 3, only a proxy (p hard T ) for the observable-particle contribution p obs T can be measured. The reconstructed hard final-state objects entering E miss

Procedures
The extraction of the systematic uncertainties introduced into the E miss T measurement by the E miss,soft T term is based on data-to-MC-simulations comparisons of P (p hard T ) for the response, and of RMS 2 (p hard T ) and RMS 2 ⊥ (p hard T ) for the resolution. Alternative MC samples are considered, with variations of either the event generator or the detector simulation (description and shower models). For the highest impact of E miss,soft T on E miss T , the exclusive Z → µµ selection with N jet = 0 is the basis for the determination of the systematic uncertainty components for both data and all MC simulations. In this case, the only hard contribution is from the reconstructed Z boson, i.e. p hard T = p Z T as shown in Fig. 12(a). The uncertainties are determined by comparing P and P ⊥ spectra from data and MC simulations, in bins of p hard T . For P , the smearing of the response and the width both yield scale and (longitudinal) resolution offsets. In the case of P ⊥ , only smearing of the width is applied to provide transverse resolution offsets. These fitted offsets, determined for the various MC configurations, provide the systematic uncertainties with respect to a specific MC modelling configuration. In practice, to account for the resolution offsets, Gaussian smearing is applied in simulation to the longitudinal and transverse components of E miss,soft T relative to the direction of p hard T . To account for differences in response between data and simulation, the longitudinal component of E miss,soft T is scaled up and down to give an uncertainty band.
In order to generate the required number of simulated events, some analyses in ATLAS may have to use the fast detector simulation ATLFAST2 [38, 45] for the calorimeter response. It employs parameterisations for electromagnetic and hadronic showers, instead of the explicit simulation of the particle tracking through matter and the energy-loss mechanisms in a detailed detector geometry. An additional uncertainty is assigned to effects introduced by ATLFAST2. This uncertainty contribution only needs to be considered in analyses using this fast simulation, and does not apply for the results presented in this paper. In analyses where it is applicable, it is added in quadrature to the standard uncertainties.

T response and resolution
The result for the systematic uncertainty of the E miss T scale, determined as discussed in the previous section, is summarised in Fig. 13. The average longitudinal projection of p soft T onto p hard T , P , as a function of p hard T is shown in Fig. 13(a) which compares data to both the standard P +P 8-based simulations and the alternative MC simulation employing M G , as described in Section 4.2. All MC simulation results are expected to have P MC within the uncertainties of the data. The lower panel of Fig. 13(a) confirms that the ratio P MC / P data lies within the systematic uncertainty band over the full p hard T range.
The systematic uncertainty for the E miss T resolution is extracted from the variances of the parallel (RMS 2 ) and perpendicular (RMS 2 ⊥ ) projections of E miss T onto p hard T defined in Section 7.1.2. Figure 13(b) shows the p hard T dependence of RMS 2 measured for the exclusive Z → µµ sample (N jet = 0) in data and two MC simulations. The variances (RMS 2 ) MC calculated for both sets of simulations agree within the systematic uncertainties of (RMS 2 ) data with the data, as illustrated in the lower panel of the figure, where the ratio (RMS 2 ) MC /(RMS 2 ) data is shown as a function of p hard T . The results of the evaluation of the variances RMS 2 ⊥ of the perpendicular projections as a function of p hard T are shown in Fig. 13(c), together with the resulting p hard T dependence of the ratio (RMS 2 ⊥ ) MC /(RMS 2 ⊥ ) data . The systematic uncertainties of the data cover all differences to MC simulations. have an enhanced dependence on pileup, mostly introduced by the soft term. To partly compensate for the irreducible contribution of p Tflow reconstructed from topo-clusters generated by pile-up to E miss,calo T , a modified jet selection and ambiguity resolution is applied in their reconstruction. The considered jets are reconstructed following the prescription in Section 3.3.5, and required to have a fully calibrated p T > 20 GeV. The contribution of these jets to E miss,calo T and ΣE calo T , defined in terms of momentum components (p x , p y ), depends on the overlap with already accepted reconstructed particles, The overlap fraction κ E is given in Eq. (8). Jets with κ E ≥ 50% are not used at all. The JVT-based tagging of non-pile-up jets is omitted. It is found that this strategy reduces the fluctuations in the E miss,calo T reconstruction. The transverse momentum contribution of groups of clusters representing a jet-like p Tflow e.g. from pile-up in a given direction that are not reconstructed and calibrated as a jet, or do not pass the jet-p T threshold applied in E miss T reconstruction, is reduced if all jets and jet fragments, including those from pile-up, are included.

E miss T from tracks
The reference track-based soft term E miss,soft T is largely insensitive to pile-up, as indicated by the dependence of the E miss T resolution RMS miss x(y) on N PV in the exclusive Z → µµ sample (N jet = 0) shown in Fig. 7(c). As discussed in Section 6.2.4 and from the comparison of Figs. 7(c) and 7(d), the pile-up dependence of RMS miss x(y) in the inclusive Z → µµ sample is largely introduced by the jet contribution. This contribution suffers from (1) the lack of pile-up suppression for forward jets with |η| > 2.4, (2) any inefficiency connected with the JVT-based tagging, and (3) irreducible pile-up-induced fluctuations in the calorimeter jet signals. Using a representation of E miss T employing only reconstructed ID tracks from the primary vertex increases stability against pile-up as long as the tracking and vertex resolution is not affected by it. In this representation (p miss T ) all jets and reconstructed particles are ignored, i.e. the p miss T reconstruction does not include any calorimeter or MS signals. The p miss T resolution is then inherently immune to pile-up, while the p miss T response is low as all neutral p T -flow in |η| < 2.5 as well as all p T -flow outside of this region is excluded.

T variants
The main motivation to study E miss T -reconstruction variants is to improve some combination of the E miss T resolution, scale, and stability against pile-up. As with the composition of objects entering E miss T reconstruction in general, the particular choice of variant used for a given analysis strongly depends on the performance requirements for this analysis. The comparison of both the resolution and response of E miss,calo T and p miss T to the corresponding measurements using the reference E miss T illustrates their principal features for the Z → µµ and tt production final state.  In events with jet activity, the degraded p miss T resolution is observable, especially outside the region of highest pile-up activity, as seen in Fig. 15(b) for the E miss T resolution obtained with the inclusive Z → µµ sample in data for N PV 15. This is even more obvious in final states with relatively high jet multiplicity and genuine missing transverse momentum, like for the tt-production sample from MC simulations. As shown in Fig. 15(c) for this final state, both the reference E miss T and the calorimeter-based E miss,calo T have a significantly better resolution than p miss T , at the price of some sensitivity to pile-up, which is absent for p miss T . The N PV dependence of the resolution is enhanced in E miss,calo T , due to the increased contribution from soft calorimeter signals without pile-up suppression at higher N PV . to Eqs. (9) and (10). Figure 16(a) shows the average projection as a function of p Z T for the exclusive Z → µµ sample with N jet = 0 in data. Both E miss T and p miss T show the same increasingly incomplete reconstruction of the hadronic recoil in this sample for rising p Z T . This reconstruction is slightly improved for E miss,calo T , but still insufficient at higher p Z T .
In the inclusive Z → µµ sample, shown in Fig. 16(b), the indication at lower p Z T is that E miss,calo T has a higher response and thus a better representation of the hadronic recoil, due to the more complete E miss,soft T reconstruction and the lack of a JVT-tagging requirement. This effect is partly due to the observation bias in the response introduced by the relatively poor E miss,calo T resolution, as discussed in Section 3.

Summary of performance
Both E miss,calo T and p miss T offer alternative measures for E miss T . The calorimeter-based E miss,calo T uses topo-clusters calibrated at the LCW scale for the soft term, which are neither part of the signal nor otherwise overlapping with the signals of other hard objects contributing to E miss T . This introduces a pile-up dependence into E miss,calo T , due to the lack of pile-up suppression of calorimeter signals outside of reconstructed hard objects. It features a slightly modified jet contribution without the JVT-based selection used in case of the reference E miss T reconstruction, to allow the cancellation of jet-like p T -flow from pile-up in E miss,soft,calo T by pile-up jets in its hard term. The E miss,calo T response in the inclusive Z → µµ sample is better than the reference E miss T response, in particular in the region of small hadronic recoil (p Z T 20 GeV). It is comparable to the reference in tt final states. The observed RMS miss x(y) , in particular in Z → µµ without jets, is significantly more affected by pile-up than is the reference E miss T or the track-only-based p miss T . In final states with a considerable number of jets, like tt, E miss,calo T performs nearly as well as the reference E miss T , with a slight degradation of the E miss T resolution at highest pile-up activities. This variant is useful for physics analyses least sensitive to the soft-term contribution to E miss T resolution but requiring a linear E miss T response.
The track-only-based p miss T displays a degraded response for the inclusive Z → µµ sample, which is expected from the exclusive use of hard-scatter-vertex tracks. As expected, resolution is not affected by pile-up in the considered final states, but is poorer than, or at most comparable to, the reference E miss T algorithm. Nevertheless, p miss T provides a stable observable for event and phase-space selections in analyses sensitive to E miss T resolution.

Conclusion
The performance and features of the missing transverse momentum reconstruction in pp collision data at the LHC, acquired in 2015 with the ATLAS detector at √ s = 13 TeV and corresponding to about 3.2 fb −1 , are evaluated for selected event samples with (W → eν, W → µν, tt) and without (Z → µµ) genuine E miss T . The comparison of the data from the detector with the corresponding MC simulations generally yields good agreement in the covered phase space. The systematic uncertainty contribution from the soft event to the reconstructed E miss T is determined with Z → µµ final states without jets. It is calculated from the data-to-MC-simulations comparison of the parallel and perpendicular projections of the missing transverse momentum vector E miss T onto the vector sum of the transverse momenta of the hard objects p hard T . The parallel projections yield the uncertainty of the E miss T scale, evaluated as a function of the total transverse momentum of the hard objects (p hard T ). The widths of the distributions of the parallel and perpendicular projections yield the respective systematic uncertainties of the E miss T resolution. Simulation tends to underestimate the perpendicular resolution and overestimate the scale and parallel resolution, in each case differing from data by at most 10%.
The performance evaluation of E miss T response and resolution for the inclusive Z → µµ sample shows that data and MC simulations agree within the systematic uncertainties. The E miss T response shows an underestimation of the soft contributions to E miss T . A degradation of the E miss T resolution is observed for increasing ΣE T and N PV , due to pile-up and detector resolution effects. Additional performance measures considered in these studies include the estimate of tails in the E miss T distribution. As expected from the universality of the hadronic recoil, the integral tail fraction of the E miss T distribution is identical for inclusive Z and W boson production, independent of the leptonic decay mode. The tt final states feature a higher jet multiplicity and show larger tails reflecting a higher sensitivity to residual pile-up surviving in the jet contribution to E miss T , in terms of the inclusion of pile-up jets as well as the increased fluctuations of the jet response introduced by pile-up.
From the performance studies presented in this paper, the object-based E miss T reconstruction in ATLAS, which was developed for LHC Run 1 and used in a large number of physics analyses, can be used with the discussed refinements and adjustments for Run 2 as well.

Appendix A Glossary of terms
In this paper several acronyms and qualifiers are used to describe the reconstruction of E miss T and related observables. This brief glossary of terms is intended to help with the nomenclature. All terms should be interpreted in the context of E miss T reconstruction and may have other interpretations in other contexts. E miss T reconstruction: Using this nomenclature usually encompasses the reconstruction of a set of observables comprising the missing transverse momentum vector E miss T , its components E miss x(y) , and its absolute value E miss T . In addition, the scalar sum ΣE T of the p T of all kinematic objects contributing to E miss T is calculated. The calculation of these variables is described in detail in Eqs. (1) to (4) in Section 3.1.

Hard scatter and primary vertices:
The hardest pp interaction in a given event is referred to as the hard scatter. It is normally associated with a reconstructed hard-scatter vertex, which is considered the hardest vertex among all reconstructed primary vertices in this event. The hard-scatter vertex is defined as the one with the largest sum of p 2 T of tracks associated with it. The other primary vertices are assumed to be produced by in-time pile-up interactions. The variable N PV denotes the number of reconstructed primary collision vertices in the event.
Hard event and hard term: The reconstruction of hard objects includes individual particles such as electrons, photons, muons and τ-leptons, and jets. In all cases the final objects are characterised by a kinematic threshold and reconstruction quality requirements. Both the reconstructed chargedparticle tracks from the ID and topo-clusters from the calorimeter are used as the input signals for these objects. In the context of E miss T reconstruction, the use of the same detector signals by different hard objects is excluded, see details in Section 3. The finally accepted hard event objects give rise to the hard term in E miss T reconstruction.
Soft event and soft term: All detector signals recorded for one triggered event and not used by the hard objects discussed above can be considered as soft signals contributing to E miss T . They include signals or signal traces from scattered soft particles arising from the underlying event accompanying the hard-scatter interaction, or from statistically completely independent pile-up interactions producing diffuse particle emissions in the same bunch crossing. In addition, signals from particles and jets which do not satisfy the hard-object quality criteria, or are below the kinematic threshold, can be included in the soft event. The reference E miss T reconstruction configuration for the results presented in Sections 6 and 7 uses reconstructed ID tracks from the soft event to form the soft term in E miss T reconstruction, with the track selection details outlined under priority (6) in Table 1 in Section 3. Alternative configurations employ topo-clusters from the calorimeter, see   ) reconstructed from topoclusters not used by, or not overlapping with, the hard objects used for the hard term composed of items (1)- (5) in Table 1, with the jet selection described in Section 8.1 applied

C Jet selection
As discussed in Section 3.3.5, jets that are not rejected by the signal ambiguity resolution and have p T > 60 GeV contribute to E miss T reconstruction. Jets with less transverse momentum that fall within |η| < 2.4 are subjected to further selection based on JVT calculated by a track-based jet vertex tagger The effects of these selections on the E miss T resolution RMS miss x(y) and response are shown in Fig. C-1, for Z → µµ events in MC simulation. Figure C-1(a) shows that the pile-up dependence of RMS miss x(y) is not significantly affected by the choice for JVT. However, the E miss T response measured by the projection given in Eq. (10) in Section 6.2.1 and evaluated as a function of p Z T in the same sample, shows significant sensitivity to the choice of JVT, as seen in Fig. C-1(b).
In addition to the signal ambiguity resolution and the choice for JVT, the contribution from jets in E miss T reconstruction is controlled by a kinematic threshold requiring the transverse momentum of the jet to be p T > 20 GeV. The effects of variations of this threshold on RMS miss x(y) and the E miss T response are shown in Fig. C-2. Increasing the threshold to 30 GeV for all jets satisfying the JVT medium condition reduces the pile-up dependence of the resolution shown in Fig. C-1(a), but leads to significant loss of E miss T response, as seen in Fig. C-1(b). Depending on the sensitivities observed in a given physics analysis, the p T -threshold choice for the jet contribution to E miss T reconstruction needs to be adjusted to meet the required performance. Extending the p T threshold studies with the option of regional thresholds yields the performance results presented in Fig x(y) shown in Fig. C-3(a), which are very similar to the ones observed in Fig. C-2(a) for a global jet-p T threshold variation. The comparison indicates that the main pile-up contribution to RMS miss x(y) is introduced by forward jets, for which no JVT-based pile-up-mitigation is available.
Increasing the p T threshold only for forward jets reduces the average loss of response observed in case of the global p T threshold increase. This can be seen by comparing the results shown in Fig. C-3(b) for regional p T thresholds with the ones shown in Fig. C-2(b) for global thresholds. Like for the JVT threshold selection, the choice of the appropriate global or regional p T -threshold depends on the E miss T reconstruction performance required in the context of a given analysis.