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 ( E T miss ) 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 E T miss , 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 E T miss contributions. The individual terms as well as the overall reconstructed E T miss 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 E T miss 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 () is an important observable serving as an experimental proxy for the transverse momentum carried by undetected particles produced in proton–proton () 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 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 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 reconstruction focussing on the minimisation of effects introduced by pile-up for the data recorded between 2010 and 2012 (LHC ) [2, 3]. These approaches are the basis for the reconstruction developed for the data collected in 2015 (LHC ) 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 Sect. 2. The reconstruction is discussed in Sect. 3. The extraction of the data samples and the generation of the Monte Carlo (MC) simulation samples are presented in Sect. 4. The event selection is outlined in Sect. 5, followed by results for performance in Sect. 6. Section 7 comprises a discussion of methods used to determine systematic uncertainties associated with the measurement, and the presentation of the corresponding results. Section 8 describes variations of the 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 Sect. 9. The nomenclature and conventions used by ATLAS for -related variables and descriptors can be found in Appendix A, while the composition of reconstruction variants is presented in Appendix B. An evaluation of the effect of alternative jet selections on the 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 () coverage in solid angle.1 It consists of an inner detector (ID) tracking system in a 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 , and consists of a silicon pixel detector, a silicon microstrip detector and a transition radiation tracker for . During the LHC shutdown between and , 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.

The high-granularity lead/liquid-argon (LAr) sampling electromagnetic calorimeter covers the region . The regions and are instrumented with presamplers in front of the LAr calorimeter in the same cryostat. A steel/scintillator-tile calorimeter (Tile) provides hadronic coverage in the central pseudorapidity range . LAr technology is also used for the hadronic calorimeters in the endcap region and for electromagnetic and hadronic energy measurements in the forward calorimeters covering .

The MS surrounds the calorimeters. It consists of three large superconducting air-core toroidal magnets, precision tracking chambers providing precise muon tracking out to , and fast detectors for triggering in the region .

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].

reconstruction

The reconstructed 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, , and muons. While muons are reconstructed from ID and MS tracks, electrons and 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 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 . This issue is addressed by the explicit signal ambiguity resolution in the object-based reconstruction originally introduced in Refs. [2, 3], and by its 2015 implementation described in Sects. 3.1 and 3.2.

Additional options for the set of signals used to reconstruct are available and discussed in detail in Sect. 8. One of these alternative options is the calorimeter-based reconstruction discussed in Sect. 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 only in the use of tracks in place of jets. It is described in more detail in Sect. 8.2.

basics

The missing transverse momentum reconstruction provides a set of observables constructed from the components of the transverse momentum vectors () of the various contributions. The missing transverse momentum components serve as the basic input for most of these observables. They are given byThe set of observables constructed from is The vector provides the amount of the missing transverse momentum via its magnitude , and its direction in the transverse plane in terms of the azimuthal angle . Consequently, is non-negative by definition. However, in an experimental environment where not all relevant from the hard-scatter interaction can be reconstructed and used in Eq. (1), and the reconstructed from each contribution is affected by the limited resolution of the detector, an observation bias towards non-vanishing values for is introduced even for final states without genuine missing transverse momentum generated by undetectable particles.

The scalar sum of all transverse momenta () from the objects contributing to reconstruction is given byIn the context of reconstruction, is calculated in addition to the sum given in Eq. (1), and the derived quantities defining given in Eqs. (2)–(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 reconstruction performance studies.

In the calculation of and 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 reconstruction sequence for the hard-object contribution starts with electrons (), followed by photons (), then hadronically decaying (), and finally jets. Muons () 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 reconstruction first. The lower-priority reconstructed particles (, ) are fully rejected if they share their calorimeter signal with a higher-priority object that has already entered the reconstruction. Muons experience energy loss in the calorimeters, but only non-isolated muons overlap with other hard objects, most likely jets or . 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 Sect. 3.3.4.

Generally, jets are rejected if they overlap with accepted higher-priority particles. To avoid signal losses for reconstruction in the case of partial or marginal overlap, and to suppress the accidental inclusion of jets reconstructed from calorimeter signals from large muon energy losses or pile-up, the more refined overlap resolution strategies described in Sects. 3.3.5 and 3.3.6 are applied.

Excluding ID tracks associated with any of the accepted hard objects contributing to , ID tracks from the hard-scatter collision vertex are used to construct the soft-event signal for the results presented in this paper.

terms

Particle and jet selections in a given analysis should be reflected in and for a consistent interpretation of a given event. Each reconstructed particle and jet has its own dedicated calibration translating the detector signals into a fully corrected four-momentum. This means that e.g. rejecting certain electrons in a given analysis can change both and , if the corresponding calorimeter signal is included and calibrated as a jet or a significant part of a jet. This also means that systematic uncertainties for the different particles can be consistently propagated to . The applied selections are presented in Sect. 3.3, and summarised in Table 1.

Table 1

Overview of the contributions to and from hard objects such as electrons (), photons (), hadronically decaying (), muons (), 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 of consideration for 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 () used to select the ID tracks contributing to and in is measured relative to the hard-scatter vertex. All variables are explained in Sect. 3.2. The angular distance between objects is defined as

P	Objects contributing to ETmiss and ΣE_T
	Type	Selections	Variables	Comments
(1)	e	|η|<1.37or1.52<|η|<2.47	ETmiss,e	All e^± passing medium reconstruction quality and kinematic selections
		p_T>10Ge	ΣETe
(2)	γ	|η|<1.37or1.52<|η|<2.47	ETmiss,γ	All γ passing tight quality and kinematic selections in reconstruction, and without signal overlap with (1)
		p_T>25Ge	ΣETγ
(3)	τ_had	|η|<1.37or1.52<|η|<2.47	ETmiss,τ_had	All τ_had passing medium reconstruction quality and kinematic selections, and without signal overlap with (1) and (2)
		p_T>20Ge	ΣETτ_had
(4)	μ	|η|<2.7	ETmiss,μ	All μ passing medium quality and kinematic selections in reconstruction; for the discussion of the μ–jet overlap removal see Sect. 3.3.6
		p_T>10Ge	ΣETμ
(5)	Jet	|η|<4.5	ETmiss,jet	All jets passing reconstruction quality (jet cleaning) and kinematic selections, and without signal overlap^a with (1)–(3); for the dedicated overlap removal strategy with μ from (4) see Sect. 3.3.6
		p_T>60Ge	ΣETjet
		2.4<|η|<4.5
		20Ge<p_T<60Ge
		|η|<2.4
		20Ge<p_T<60Ge
		JVT>0.59
(6)	ID track	p_T>400Me	ETmiss,soft	All ID tracks from the hard-scatter vertex passing reconstruction quality and kinematic selections, and not associated with any particle from (1), (3) or (4), or ghost-associated with a jet from (5)
		|d_0|<1.5mm	ΣETsoft
		|z_0sin(θ)|<1.5mm
		ΔR(track,e-/γcluster)>0.05
		ΔR(track,τ_had)>0.2

While for single reconstructed particles no overlap is accepted at all, jets with a signal overlap fraction % can still contribute their associated tracks to if those pass the selections for , as discussed in Sect. 3.3.5. The definition of is given in Eq. (8)

In ATLAS the flexibility needed to recalculate and under changing analysis requirements for the same event is implemented using dedicated variables corresponding to specific object contributions. In this approach the full is the vectorial sum of missing transverse momentum terms , with reconstructed from the of accepted particles and jets, and the corresponding soft term from the soft-event signals introduced in Sect. 3.1 and further specified in Sect. 3.4. This yields2 The and observables can be constructed according to Eqs. (3) and (4), respectively, for the overall missing transverse momentum (from ) as well as for each individual term indicated in Eq. (6). In the priority-ordered reconstruction sequence for , contributions are defined by a combination of analysis-dependent selections and a possible rejection due to the applied signal ambiguity resolution. The muon and electron contributions are typically not subjected to the signal overlap resolution and are thus exclusively defined by the selection requirements. Unused tracks in Eq. (6) refers to those tracks associated with the hard-scatter vertex but not with any hard object. Neutral particle signals from the calorimeter suffer from significant contributions from pile-up and are not included in the soft term.

Correspondingly, is calculated from the scalar sums of the transverse momenta of hard objects entering the reconstruction and the soft term,The hard term in both and 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 Sect. 6.

Object selection

The following selections are applied to reconstructed particles and jets used for the performance evaluations presented in Sects. 6–8. Generally, these selections require refinements to achieve optimal 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 likelihood-based 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 reconstruction, electrons passing the reconstruction quality requirements are in addition required to have and or , to avoid the transition region between the central and endcap electromagnetic calorimeters. Any energy deposit by electrons within is likely reconstructed as a jet and enters the reconstruction as such, if this jet meets the corresponding selection criteria discussed in Sect. 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 and or to be included in the reconstruction. Similarly to electrons, photons emitted within may contribute to as a jet.

-Lepton selection

Hadronically decaying 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 and or . Any not satisfying these -identification criteria may contribute to when passing the jet selection.

Muon selection

Muons are reconstructed within employing a combined MS and ID track fit. Outside of the ID coverage, muons are reconstructed within from a track fit to MS track segments alone. Muons are further selected for reconstruction by requiring the medium reconstruction quality defined in Ref. [12], , and an association with the hard-scatter vertex for those within .

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- algorithm [13], as provided by the FastJet toolkit [14], is employed with a radius parameter 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 after the full calibration. The jet contribution to and 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 of the electron(photon) energy to the jet energy ,with both energies calibrated at the EM scale. In the case of %, the jet is included in reconstruction, with its scaled by . For %, 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 Sect. 3.4.

Jets not rejected by the signal ambiguity resolution and with and , or with and , are always accepted for reconstruction. Jets reconstructed with and are only accepted if they are tagged by . In both cases, the jet thresholds are applied to the jet before applying the correction. Additional configurations for selecting jets used in reconstruction are discussed in Appendix A, together with the effect of the variation of these selection criteria on the reconstruction performance.

Muon overlap with jets

Jets overlapping with a reconstructed muon affect the 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 reconstruction. On the other hand, jets reconstructed from final state radiation (FSR) off the muon need to be included into 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 Sect. 3.3.5.

Tagging jets using JVT efficiently retains those from the hard-scatter vertex for 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 from the hard-scatter vertex and thus increases JVT. As a consequence of this fake tag, the pile-up jet contributes to , and thus degrades both the 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 reconstruction leads to double-counting of the transverse momentum associated with the muon energy loss, as the fully reconstructed muon 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: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 reconstruction. The muons are retained for the reconstruction.

– the transverse momentum of the ID track associated with the muon () represents a significant fraction of the transverse momentum , the sum of the transverse momenta of all ID tracks associated with the jet;

– the overall transverse momentum of the jet is not too large compared to ;

– the total number of tracks associated with the jet and emerging from the hard-scatter vertex is small.

Another consideration for muon contributions to 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 reconstruction. Such jets are characterised by the following selections, which are highly indicative of a photon in the ATLAS calorimeter:Jets are accepted for 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.

– the jet has low charged-particle content, indicated by a very small number of tracks from the hard-scatter vertex;

– the jet energy is largely deposited in the electromagnetic calorimeter (EMC), as expected for photons and measured by the corresponding energy fraction ;

– the transverse momentum contribution from presampler signals to indicates an early starting point for the shower;

– the jet is narrow, with a width comparable to a dense electromagnetic shower; is reconstructed according to where is the angular distance of topo-cluster i from the jet axis, and is the transverse momentum of this cluster;

– the transverse momentum carried by all tracks associated with the jet is close to .

soft term

The soft term introduced in Sect. 3.2 is exclusively reconstructed from ID tracks from the hard-scatter vertex, thus only using the -flow from soft charged particles. It is an important contribution to for the improvement of both the scale and resolution, in particular in final states with a low hard-object 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 soft term including signals from soft neutral particles uses calorimeter topo-clusters. The reconstruction performance using the calorimeter-based is inferior to the track-only-based , mostly due to a larger residual dependence on pile-up. More details of the topo-cluster-based reconstruction are discussed in Sect. 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 of reconstructed primary vertices.

Tracks are required to have and , 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 () 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 for each reconstructed event is collected from high-quality tracks emerging from the hard-scatter vertex but not associated with any electron, , muon, or jet contributing to reconstruction. The applied signal-overlap resolution removesID 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 Sect. 3.3.5, contribute to .

ID tracks with ;

ID tracks with ;

ID tracks associated with muons;

ID tracks ghost-associated with fully or partially contributing jets.

Since only reconstructed tracks associated with the hard-scatter vertex are used, the track-based 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 reconstruction performance uses selected final states without () and with genuine missing transverse momentum from neutrinos (). Samples with are composed of leptonic boson decays ( and ) 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 and decays. In addition, samples with neutrinos and higher hard-object multiplicity were collected from top-quark pair () production with at least either the t or the decaying semi-leptonically.

Data samples

The data sample used corresponds to a total integrated luminosity of , collected with a proton bunch-crossing interval of . 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 and samples were generated using Powheg-Box  [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 Pythia8  [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 -production sample was generated with a Powheg NLO kernel (version v2r3026) interfaced to Pythia6  [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 top++  2.0  [27] was included.

Additional processes contributing to the and final state samples are the production of dibosons, single top quarks, and multijets. Dibosons were generated using Sherpa [28-31] version v2.1.1 employing the CT10 PDF set. Single top quarks were generated using Powheg version v1r2556 with the CT10 PDF set for the t-channel production and Powheg version v1r2819 for the s-channel and the associated top quark () production, all interfaced to the PS and UE from the same Pythia6 configuration used for production. Multijet events were generated using Pythia8 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 Pythia8 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 Sect. 4.3.

For the determination of the systematic uncertainties in reconstruction, an alternative inclusive sample of events was generated using the MadGraph_aMC@NLO (version v2.2.2) matrix element generator [36] employing the CTEQ6L1 PDF set. Both PS and UE were generated using Pythia8 with the NNPDF23LO PDF set and the A14 set of tuned parameters.

The MC-generated events were processed with the Geant4 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 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 .

The in-time pile-up activity is measured by the number of reconstructed primary collision vertices . The out-of-time pile-up is proportional to the number of collisions per bunch crossing , 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 recorded in data. The collisions were randomly collected from the MB sample discussed in Sect. 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 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.

Event selection

event selection

The final state is ideal for the evaluation of reconstruction performance, since it can be selected with a high signal-to-background ratio and the 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 are indicative of the reconstruction quality and reflect limitations introduced by both the detector and the ambiguity resolution procedure. The well-defined expectation value allows the reconstruction quality to be determined in both data and MC simulations. The reconstructed 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 .

Events must pass one of three high-level muon triggers with different thresholds and isolation requirements. The isolation is determined by the ratio of the scalar sum of of reconstructed tracks other than the muon track itself, in a cone of size around the muon track (), to . The individual triggers require (1) and , or (2) and , or (3) without isolation requirement.

The offline selection of events requires exactly two muons, each selected as defined in Sect. 3.3.4, with the additional criteria that (1) the muons must have opposite charge, (2) , and (3) the reconstructed invariant mass of the dimuon system is consistent with the mass of the boson, .

Events with or in the final state provide a well-defined topology with neutrinos produced in the hard-scatter interaction. In combination with , the effectiveness of signal ambiguity resolution and lepton energy reconstruction for both the electrons and muons can be observed. The events in particular provide a good metric with to evaluate and validate the scale, resolution and direction (azimuth) of the reconstructed , as the reconstruction is sensitive to the electron–jet overlap resolution performance. This metric is only available in MC simulations where is known. Candidate events are required to pass the high-level electron trigger with . Electron candidates are selected according to criteria described in Sect. 3.3.1. Only events containing exactly one electron are considered.

Further selections using and the reconstructed transverse mass , given byare applied to reduce the multijet background with one jet emulating an isolated electron from the boson. Here is calculated as presented in Sect. 3. The transverse momentum of the electron is denoted by , and is the distance between and the azimuth of the electron. Selected events are required to have and .

Events with in the final state allow the evaluation of the performance in interactions with a large jet multiplicity. Electrons and muons used to define these samples are reconstructed as discussed in Sects. 3.3.1 and 3.3.4, respectively, and are required to have .

The final 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- algorithm with and selected following the description in Sect. 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 from the electron.

Performance of 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, reconstruction yields a non-linear response, especially in regions of phase space where the observation bias discussed in Sect. 3.1 dominates the reconstructed . In addition, the resolution functions are characterised by a high level of complexity, due to the composite character of the observable. Objects with different -resolutions contribute, and the composition can fluctuate significantly for events from the same final state. Due to the dependence of the 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 .

The reconstruction performance is therefore assessed by comparing a set of reconstructed -related observables in data and MC simulations for the same final-state selection, with the same object and event selections applied. Systematic uncertainties in the 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 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 performance evaluation are obtained by applying selections according to Sect. 5.1 for a final state without genuine (), and according to Sect. 5.2 for a final state with genuine (). From these, specific exclusive samples are extracted by applying conditions on the number of jets reconstructed. In particular, zero jet () samples without any jet with (fully calibrated) and 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 are useful for evaluating the contribution of jets to . While the response of jets is fully calibrated and provides a better measurement of the overall event -flow, the resolution for jets is affected by pile-up and can introduce a detrimental effect on reconstruction performance.

Missing transverse momentum and its related observables presented in Sect. 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 reconstruction sequence discussed in Sect. 3.1. It employs the hard-object selections defined in Sects. 3.3.1–3.3.4, with jets selected according to the prescriptions given in Sect. 3.3.5. The overlap resolution strategy for jets and muons described in Sect. 3.3.6 is applied. The soft term is formed from ID tracks according to Sect. 3.4.

modelling in Monte Carlo simulations

The quality of the MC modelling of , , and , reconstructed as given in Eqs. (1), (3) and (5), is evaluated for an inclusive sample of events by comparing the distributions of these observables to data. The results are presented in Fig. 1. The data and MC simulations agree within 20% for the bulk of the distribution shown in Fig. 1a, with larger differences not accommodated by the total (systematic and statistical) uncertainties of the distributions for high . These differences suggest a mismodelling in events, the dominant background in the tail regime [43]. The distributions compared between data and MC simulations in Fig. 1b show discrepancies significantly larger than the overall uncertainties for . These reflect the level of mismodelling of the final state mostly in terms of hard-object composition in MC simulations. The and spectra shown in Fig. 1c, d, respectively, show good agreement between data and MC simulations for the bulk of the distributions within , with larger differences observed outside of this range still mostly within the uncertainties.

Fig. 1

Distributions of a , b , c and d for an inclusive sample of events extracted from data and compared to MC simulations including all relevant backgrounds. The shaded areas indicate the total uncertainty for MC simulations, including the overall statistical uncertainty combined with systematic uncertainties from the scale and resolution which are contributed by muons, jets, and the soft term. The last bin of each distribution includes the overflow, and the first bin contains the underflow in c and d. The respective ratios between data and MC simulations are shown below the distributions, with the shaded areas showing the total uncertainties for MC simulations

The distributions of individual contributions to from jets (), muons (), and the soft term (), as defined in Eq. (6), are compared between data and MC simulations for the same inclusive sample in Fig. 2. Agreement between data and MC simulations for in Fig. 2a is of the order of % and within the total uncertainties for , but beyond those for higher . A similar observation holds for in Fig. 2b, where data and MC simulations agree within the uncertainties for low but significantly beyond them for larger . Agreement between data and MC simulations is better for the soft term , with differences up to 10% for , as seen in Fig. 2c. Larger differences for larger are still found to be within the uncertainties.

Fig. 2

Distributions of a the jet term , b the muon term , and c the soft term for the inclusive samples of events in data, compared to MC simulations including all relevant backgrounds. The shaded areas indicate the total uncertainty from MC simulations, including the overall statistical uncertainty combined with the respective systematic uncertainties from a the jet, b the muon, and c the soft term. The last bin of each distribution includes the overflow entries. The respective ratios between data and MC simulations are shown below the distributions, with the shaded areas showing the corresponding total uncertainties from MC simulations

The peak around indicates the onset of single-jet events at the threshold for jets contributing to . Larger values of arise from events with one or more high- jets balancing the of the boson.

For the sample with genuine missing transverse momentum given by , both the total reconstructed and the soft term are compared between data and MC simulations in Fig. 3. The level of agreement between the distributions for data and MC simulations shown in Fig. 3a for the inclusive event sample is at , similar to that observed for the sample in Fig. 1a, except that for this final state it is found to be within the total uncertainties of the measurement. The differences between the distributions observed with the exclusive sample shown in Fig. 3b are well below 20%, but show a trend to larger discrepancies for decreasing . 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 required in the selection described in Sect. 5.2. The comparison of the distributions from data and MC simulations shown in Fig. 3c yields agreement well within the uncertainties, for . The rising deficiencies observed in the MC distribution for decreasing are expected to be related to the missing multijet contribution.

Fig. 3

Distributions of the total in a the inclusive case and b the case, as well as c the soft term reconstructed in events with in data. The expectation from MC simulation is superimposed and includes all relevant background final states passing the event selection. The inclusive distribution from MC simulations contains a small contribution from multijet final states at low , which is absent for the selection. The shaded areas indicate the total uncertainty for MC simulations, including the overall statistical uncertainty combined with systematic uncertainties comprising contributions from the electron, jet, and the soft term. The last bins contain the respective overflows. The respective ratios between data and MC simulations are shown below the distributions, with the shaded areas indicating the total uncertainties for MC simulations

response and resolution

The response in the context of reconstruction is determined by the deviation of the observed from the expectation value for a given final state. This deviation sets the scale for the observed . If this deviation is independent of the genuine missing transverse momentum, or any other hard indicative of the overall hard-scatter activity, the response is linear. In this case, a constant bias in the reconstructed is still possible due to detector inefficiencies and coverage (acceptance) limitations.

Final states balanced in transverse momentum are expected to show a non-linear response at low event activity, as the response in this case suffers from the observation bias in reconstruction discussed in Sect. 3.1. With increasing momentum transfers in the hard-scatter interaction, the 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 response is only linear once exceeds the observation bias. These features are discussed in Sect. 6.2.1 and explored in Sect. 6.2.2.

Contributions to the fluctuations in the 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 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 to the reconstructed and accepted , , and , and those being part of a reconstructed and accepted jet. In addition, the -flow of not explicitly reconstructed charged particles emerging from the hard-scatter vertex is represented by ID tracks contributing to given in Eqs. (6) and (7), but only in the phase space defined by the selections given in Sect. 3.4.1. All other charged and neutral particles do not contribute to reconstruction.

Like for the response, resolution-related aspects of reconstruction are understood from data-to-MC-simulations comparisons. The scales used for the corresponding evaluations are the overall event activity represented by , and the pile-up activity measured by . The measurement of the resolution is discussed in Sect. 6.2.3 and results are presented in Sect. 6.2.4.

scale determination

In events with decays, the transverse momentum of the boson () is an indicator of the hardness of the interaction. It provides a useful scale for the evaluation of the response for this final state without genuine missing transverse momentum. The direction of the corresponding boson transverse momentum vector defines an axis in the transverse plane of the collision, which is reconstructed from the of the decay products byThe magnitude of the component of parallel to isThis projection is sensitive to any limitation in reconstruction, in particular with respect to the contribution from the hadronic recoil against , 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 response and the associated systematic uncertainties.

The expectation value for a balanced interaction producing a boson against a hadronic recoil is . Any observed deviation from this value represents a bias in the reconstruction. For , the reconstructed hadronic activity recoiling against is too small, while for too much hadronic recoil is reconstructed. The evolution of as a function of the hardness of the boson production can be measured by evaluating the mean in bins of the hard-scatter scale .

In addition to measuring the response in data and MC simulation without genuine , its linearity can be determined using samples of final states with genuine in MC simulations. This is done by evaluating the relative deviation of the reconstructed from the expected as a function of ,

Measuring the response

Figure 4 shows as a function of for the and the inclusive sample, respectively. MC simulations compare well with the data for , 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.

Fig. 4

The average projection of onto the direction of the boson’s transverse momentum vector , as given in Eq. (10), is shown as a function of in events from a the sample and from b the inclusive sample. In both cases data are compared to MC simulations. The ratio of the averages from data and MC simulations are shown below the plots. The shaded areas indicate the overall statistical uncertainty combined with systematic uncertainties comprising contributions from the muon and soft-term systematic uncertainties in a, and including the additional jet systematic uncertainties in b, for MC simulations

The steep decrease of with increasing in the sample seen in Fig. 4a reflects the inherent underestimation of the soft term, as in this case the hadronic recoil is exclusively represented by ID tracks with within . It thus does not contain any signal from (1) neutral particles, (2) charged particles produced with , and (3) charged particles produced within but with below threshold, rejected by the track quality requirements, or not represented by a track at all due to insufficient signals in the ID (e.g., lack of hits for track fitting).

In the case of the inclusive sample shown in Fig. 4b, the response is recovered better as 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 of about in data and in MC simulations observed for in Fig. 4b agree within the uncertainties of this measurement.

The persistent bias in is further explored in Fig. 5, which compares variations of respectively using the full , the soft-term contribution only, the hard-term contribution , and the true soft term only, as a function of , for the sample from MC simulations. In particular the difference between the projections using and indicates the lack of reconstructed hadronic response, when is expected for a fully measured recoil. The parallel projection using only the soft terms is larger than zero for all due to the missing -boson contribution to given by .

Fig. 5

The average projection of onto the direction of the boson’s transverse momentum vector , as given in Eq. (10), is shown as a function of in events from the inclusive MC sample. The average projection of the soft term and the true soft term are also shown, to demonstrate the source of the deviation from zero

The deviation from linearity in reconstruction, measured by given in Eq. (11), is shown as a function of for MC simulations of , and production in Fig. 6. The observed at low indicates an overestimation of by the reconstructed due to the observation biases arising from the finite resolution, as discussed in Sect. 3.1. This bias overcompensates the lack of reconstructed -flow from the incompletely measured hadronic recoil in and events for with an increasing non-linearity observed with decreasing . For the response is directly proportional to , with the reconstructed recoil being approximately 2% too small. The and final states show very similar , thus indicating the universality of the recoil reconstruction and the independence on the lepton flavour of the reconstructed in a low-multiplicity final state with .

Fig. 6

The deviation of the response from linearity, measured as a function of the expected by in Eq. (11), in , , and final states in MC simulations. The lower plot shows a zoomed-in view on the dependence on with a highly suppressed ordinate

In final-state reconstruction, resolution effects tend to dominate at . Compared to the and final states, a significantly poorer resolution is observed in this kinematic region, due to the presence of at least four jets with relatively low and high sensitivity to pile-up-induced fluctuations in each event of the sample. For , % indicates a proportional response with a systematic shift similar to the one observed in inclusive -boson production.

Determination of the resolution

The resolution is determined by the width of the combined distribution of the differences between the measured and the components of the true missing transverse momentum vector . The width is measured in terms of the , withThis metric does not capture all of the effects driving the fluctuations in reconstruction, such as biases between individual terms or the behaviour of outliers, but it is an appropriate general measure of how well represents .

Using the sample allows direct comparisons of between data and MC simulations, as in this case. The resolution in final states with genuine is determined with MC simulations alone. For and final states, is used.

resolution measurements

The resolution measured by is evaluated as a function of the event activity measured by given in Eq. (7). For the inclusive sample, Fig. 7a shows quickly rising from less than to about with increasing within .7 This is due to the fact that in this range the two muons are the dominant hard objects contributing, with a resolution proportional to . A convolution of the muon resolution with a small contribution from is possible for . This component is on average about 60% of , and subject to the stochastic fluctuations further discussed below.

Fig. 7

The RMS width of the distributions a in bins of and b in bins of the number of primary vertices in an inclusive sample of events. Predictions from MC simulations are overlaid on the data points, and the ratios are shown below the respective plot. The shaded bands indicate the combined statistical and systematic uncertainties of the resolution measurements

The increase of jet topologies in the sample leads to an additional source of fluctuations affecting for . In general the sample collected for this study covers with relevant statistics. At this limit it is expected that the hadronic recoil contains two reconstructed jets, with the onset of this contribution at of about . The corresponding change of the dominant final state composition for leads to a change of shape of , as the transverse momentum of the individual jets rises and the number of contributing jets slowly increases. The expected scaling driven by the jet- resolution [44] therefore dominates at these higher . The MC predictions for 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 .

Any contribution from pile-up to 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- measurement. The dependence of on the pile-up activity measured by is shown in Fig. 7b. Data show a less steep slope of than MC simulations, but with about 10% worse resolution in the low pile-up region of . The resolution in data is better than in MC simulations by about 10% for the region of higher pile-up activity at .

The differences between data and MC simulations seen in for the inclusive sample can be further analysed by splitting the sample according to the value of . Figure 8a shows the dependence of on for events with . The dominant source of fluctuations other than the muon- resolution is in this case introduced by the incomplete reconstruction of the hadronic recoil. These fluctuations increase with increasing , which in turn means higher overall event activity measured by . For this sample in data compares well to MC simulations, at a level of a few percent, without any observed dependence on .

Fig. 8

The resolution determined for a an exclusive sample without jets with () and for b an exclusive sample with at least one jet above this threshold (), as a function of in data and MC simulations. The dependence of on the pile-up activity, as measured by , for these two samples is shown in c and d, respectively. The shaded bands indicate the combined statistical and systematic uncertainties associated with the measurement

The exclusive samples extracted from data and MC simulations show the expected scaling in Fig. 8b. 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 follows the trend observed in Fig. 7a. The similar trends are expected as this kinematic region is largely affected by the jet contribution.

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

resolution in final states with neutrinos

The resolution for final states with is measured by according to Eq. (12) and evaluated using dedicated inclusive and samples from MC simulations, and the inclusive MC sample defined in Sect. 5.3. For these samples, can be determined as a function of . The dedicated and samples are obtained with an event selection based on the description in Sect. 5.2, but omitting both the -based and the -based selections.

Figure 9 shows evaluated as a function of for these samples. The universality of the response to the hadronic recoil observed in Fig. 6, together with the different but subdominant contributions from the resolutions of the electrons and muons, yield a very similar resolution for and final states. Generally, poorer resolution is observed in final states. The deviation from the expected scaling behaviour for at lower reflects the kinematic features of the boson and its decay. Events with low , and therefore small hadronic recoil, lie predominantly in the region . Since the hadronic recoil is generally the poorly measured component of an event and the reconstructed is dominated by the lepton in this region, the resolution tends to be better here than for events with larger hadronic recoil populating and .

Fig. 9

The resolution measured by as a function of the true missing transverse momentum for the , , and samples from MC simulations

tails

Large reconstructed 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 components for final states with well-known expectation values for 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 constituents. Even for a well-defined final state, event-by-event fluctuations in terms of which particles, jets, and soft tracks enter the reconstruction, and with which , lead to deviations from a normally distributed (,) response.

Figure 10 shows the combined (,) distribution for the inclusive 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, and . 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 with near exponential slopes. The result of this comparison supports the choice of defined in Eq. (12) in Sect. 6.2.3 for the determination of the resolution, rather than using any of the widths measured by fitting Gauss functions in selected ranges of the distribution.

Fig. 10

The combined distribution of and for an inclusive from simulation. Gaussian fits limited to the and ranges around the centre of the distribution are shown, together with the respective differences between the fitted functions and the actual distribution

The tails in this shape are reflected in the distribution of itself and can be estimated by measuring the fraction of events with ,Here is the distribution for a given event sample, and is a threshold set to estimate tails. Any decrease of at a fixed integral indicates an improvement of the resolution, and is more sensitive to particular improvements than e.g. . For example, improving the reconstruction by rejecting ID tracks from the hard-scatter vertex with poor reconstruction quality yields a significantly smaller for the same event sample.

The tails in the distributions for the final states considered for this study are quantified by the fraction of events above a certain threshold using MC simulations. Figure 11a shows that the events ( or ) with have significantly reduced tails when compared to and with this metric, and that the tails do not depend on the lepton flavour. A modification of this metric, taking into account such that the fraction of events with above a given threshold is determined, shows the universality of the hadronic recoil in and , as can be seen in Fig. 11b.

Fig. 11

In a the integral tail fraction given in Eq. (13) is shown as a function of the integration threshold , for MC simulations of , , and final states. The tail fraction in terms of a threshold applied to , the distance between the reconstructed () and the expected ( ) vectors, is shown in b for all considered final states. The same fraction is shown in c for the distributions for before and after a reweighting following the distribution for is applied, together with from the final state

Another finding of this study is that the tail in the distribution for the higher sample is considerably larger than for the low- samples with or final states. As can be seen in Fig. 11c, the tails are much more consistent between and samples when the distribution for the sample is reweighted such that it follows the same distribution as the 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 are provided for the response ( 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 terms need to be extracted from the scale and resolution uncertainties for the individual contributing objects comprising electrons, photons, muons, , 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 reconstruction are uncorrelated. The determination of the scale and resolution uncertainties arising from the soft term is described in this section.

Methodology

The extraction of the systematic uncertainties for the reconstructed is based on data-to-MC comparisons of spectra of observables measuring the contribution of to the overall .

Observables

The vector sum of the transverse momentum vectors of all particles and jets emerging from a hard-scatter interaction () is given byHere generally represents the transverse momenta of non-observable particles, which are summed up to form . All other transverse momenta are carried by particles that are observable in principle, and sum up to . Momentum conservation dictates .

Due to detector acceptance limitations and inefficiencies in hard-object reconstruction and calibration, and all other effects discussed in Sect. 3, only a proxy () for the observable-particle contribution can be measured. The reconstructed hard final-state objects entering as described in Sect. 3.2 are used to measure asThe expectation is that and . Adding , with defined in Eq. (6), to yields an improved estimate of the net transverse momentum carried by undetectable particles, as some of the experimental inefficiencies are mitigated.8

In the final state without genuine missing transverse momentum the expectation is that . While this expectation does not hold due to the experimental inefficiencies, it nevertheless raises the expectation that for events without jets points into the direction of the hadronic recoil, i.e. opposite to in the transverse-momentum plane. The deviation from this expectation is measured in terms of the parallel () and perpendicular () projections of onto . Figure 12 schematically shows these projections for -jet and -jet topologies.

Fig. 12

Schematic view of the parallel () and perpendicular () projections of on for events without genuine , for a a final state without any jets and b a final state with one jet. The expectation values for a perfect reconstruction are for and for , with in all cases. a topology. b topology

The average in a given bin k of phase space defined by measures the response, with indicating a perfect response in this bin. The resolution contribution from reconstruction is measured by two components, the fluctuations in response () and the fluctuations of the (transverse) angular deflection around the axis, measured by . These fluctuations are expressed in terms of variances, with

Procedures

The extraction of the systematic uncertainties introduced into the measurement by the term is based on data-to-MC-simulations comparisons of for the response, and of and 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 on , the exclusive selection with 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 boson, i.e.  as shown in Fig. 12a.

The uncertainties are determined by comparing and spectra from data and MC simulations, in bins of . For , the smearing of the response and the width both yield scale and (longitudinal) resolution offsets. In the case of , 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 relative to the direction of . To account for differences in response between data and simulation, the longitudinal component of 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.

Systematic uncertainties in response and resolution

The result for the systematic uncertainty of the scale, determined as discussed in the previous section, is summarised in Fig. 13. The average longitudinal projection of onto , , as a function of is shown in Fig. 13a which compares data to both the standard Powheg +Pythia8-based simulations and the alternative MC simulation employing MadGraph, as described in Sect. 4.2. All MC simulation results are expected to have within the uncertainties of the data. The lower panel of Fig. 13a confirms that the ratio lies within the systematic uncertainty band over the full range.

Fig. 13

The a average value of the longitudinal projection and the b variance of the longitudinal projection of onto for event with , for data and two different MC simulations, shown as a function of . The variance of the perpendicular projection is shown in c for the same event samples. The shaded band indicates the systematic uncertainties derived as described in the text

The systematic uncertainty for the resolution is extracted from the variances of the parallel () and perpendicular () projections of onto defined in Sect. 7.1.2. Figure 13b shows the dependence of measured for the exclusive sample () in data and two MC simulations. The variances calculated for both sets of simulations agree within the systematic uncertainties of with the data, as illustrated in the lower panel of the figure, where the ratio is shown as a function of . The results of the evaluation of the variances of the perpendicular projections as a function of are shown in Fig. 13c, together with the resulting dependence of the ratio . The systematic uncertainties of the data cover all differences to MC simulations.

Missing transverse momentum reconstruction variants

Calorimeter-based

The soft term from the calorimeter is reconstructed from topo-clusters. As discussed in Ref. [6], each topo-cluster provides a basic EM scale signal as well as a calibrated signal reconstructed using local cell weighting (LCW), and is calculated from topo-clusters calibrated at the LCW scale. Only topo-clusters with a calibrated energy , not contributing to the reconstruction of the hard objects used to calculate the hard term given in Eq. (6), are considered for . In addition, topo-clusters that are formed at the same location as the hard object signals are not considered for even if their signals are not directly contributing to the reconstruction of the hard objects. The fully reconstructed using is .

Compared to the reference and , and have an enhanced dependence on pile-up, mostly introduced by the soft term. To partly compensate for the irreducible contribution of -flow reconstructed from topo-clusters generated by pile-up to , a modified jet selection and ambiguity resolution is applied in their reconstruction. The considered jets are reconstructed following the prescription in Sect. 3.3.5, and required to have a fully calibrated . The contribution of these jets to and , defined in terms of momentum components , depends on the overlap with already accepted reconstructed particles,The overlap fraction is given in Eq. (8). Jets with 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 reconstruction. The transverse momentum contribution of groups of clusters representing a jet-like -flow e.g. from pile-up in a given direction that are not reconstructed and calibrated as a jet, or do not pass the jet- threshold applied in reconstruction, is reduced if all jets and jet fragments, including those from pile-up, are included.

from tracks

The reference track-based soft term is largely insensitive to pile-up, as indicated by the dependence of the resolution on in the exclusive sample () shown in Fig. 7c. As discussed in Sect. 6.2.4 and from the comparison of Fig. 7c, d, the pile-up dependence of in the inclusive sample is largely introduced by the jet contribution. This contribution suffers from (1) the lack of pile-up suppression for forward jets with , (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 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 () all jets and reconstructed particles are ignored, i.e. the reconstruction does not include any calorimeter or MS signals. The resolution is then inherently immune to pile-up, while the response is low as all neutral -flow in as well as all -flow outside of this region is excluded.

Performance evaluations for variants

The main motivation to study -reconstruction variants is to improve some combination of the resolution, scale, and stability against pile-up. As with the composition of objects entering 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 and to the corresponding measurements using the reference illustrates their principal features for the and production final state.

Comparisons of resolution

Figure 14 compares the and resolutions with the one obtained from the reference , for the inclusive sample in data. Each is shown as a function of corresponding to the reference , giving an estimate of the total hard-scatter activity. The low- region is dominated by events with , where the contribution of in yields a poorer resolution than for , and where and have identical performance. The high- region is dominated by events with higher jet multiplicity, where resolution is degraded relative to the reference by the incomplete measurement of jets.

Fig. 14

Comparison of the reference resolution with the resolutions of the track-only-based variant described in Sect. 8.2, and the reconstruction variant employing a calorimeter-based soft term, as discussed in Sect. 8.1. The resolutions are determined as described in Sect. 6.2.3 and shown as a function of the . For consistency, for all three variants, the value is taken from

Figure 15a compares the and resolution as functions of the pile-up activity measured by , with the one obtained from the reference for the exclusive samples with in data. The resolution is dominated by pile-up and shows significantly degraded performance relative to and the reference . The exclusive use of only tracks from the hard-scatter vertex for both and yields the same stability against pile-up.

Fig. 15

Comparison of the reference resolution with the resolutions of the track-only-based variant described in Sect. 8.2, and the reconstruction variant employing a calorimeter-based soft term, as discussed in Sect. 8.1. The resolutions are determined as described in Sect. 6.2.3 and shown as a function of the pile-up activity measured in terms of the number of reconstructed vertices for a an exclusive sample without jets with and b an inclusive sample, both selected from data. In c, the resolution of the reconstruction-variants in a final state with significant jet activity and is compared using MC simulations of production

In events with jet activity, the degraded resolution is observable, especially outside the region of highest pile-up activity, as seen in Fig. 15b for the resolution obtained with the inclusive sample in data for . This is even more obvious in final states with relatively high jet multiplicity and genuine missing transverse momentum, like for the -production sample from MC simulations. As shown in Fig. 15c for this final state, both the reference and the calorimeter-based have a significantly better resolution than , at the price of some sensitivity to pile-up, which is absent for . The dependence of the resolution is enhanced in , due to the increased contribution from soft calorimeter signals without pile-up suppression at higher .

Comparisons of scale

Following the description in Sect. 6.2.1, the response is evaluated for the reference , , and using the respective projections of , , and onto the direction of , according to Eqs. (9) and (10). Figure 16a shows the average projection as a function of for the exclusive sample with in data. Both and show the same increasingly incomplete reconstruction of the hadronic recoil in this sample for rising . This reconstruction is slightly improved for , but still insufficient at higher .

Fig. 16

Comparison of the reference , the calorimeter-based and track-only-based response in an a exclusive and an b inclusive sample from data. The projections of the respective , , and onto the direction of , calculated according to Eqs. (9) and (10), are shown as a function of . In c, the linearity of the reference , , and scales, calculated according to Eq. (11), is shown as a function of the true for the -production MC simulation sample

In the inclusive sample, shown in Fig. 16b, the indication at lower is that has a higher response and thus a better representation of the hadronic recoil, due to the more complete 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 resolution, as discussed in Sect. 3.1. Both and show comparable response for , owing to the JVT cut-off at . The slightly larger response of about reflects the contribution from neutral signals to the soft term. The degraded response associated with related to the exclusion of hard objects is clearly visible in this figure.

Figure 16c shows the linearity of the various reconstruction approaches as a function of for the -production sample from MC simulations. Beyond both the reference and show the same good linearity, while the lack of a jet contribution to shows a loss of response up to about 50% at higher . The overestimation of by all three reconstruction variants at lower reflects the observation bias in the response introduced by the resolution. The poorer resolution associated with observed in Fig. 15c for this sample leads to a faster rise of the response with decreasing than for the reference and , which show a very similar dependence on .

Summary of performance

Both and offer alternative measures for . The calorimeter-based 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 . This introduces a pile-up dependence into , 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 reconstruction, to allow the cancellation of jet-like -flow from pile-up in by pile-up jets in its hard term. The response in the inclusive sample is better than the reference response, in particular in the region of small hadronic recoil (). It is comparable to the reference in final states. The observed , in particular in without jets, is significantly more affected by pile-up than is the reference or the track-only-based . In final states with a considerable number of jets, like , performs nearly as well as the reference , with a slight degradation of the resolution at highest pile-up activities. This variant is useful for physics analyses least sensitive to the soft-term contribution to resolution but requiring a linear response.

The track-only-based displays a degraded response for the inclusive 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 algorithm. Nevertheless, provides a stable observable for event and phase-space selections in analyses sensitive to resolution.

Conclusion

The performance and features of the missing transverse momentum reconstruction in collision data at the LHC, acquired in 2015 with the ATLAS detector at and corresponding to about , are evaluated for selected event samples with (, , ) and without () genuine . 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 is determined with 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 onto the vector sum of the transverse momenta of the hard objects . The parallel projections yield the uncertainty of the scale, evaluated as a function of the total transverse momentum of the hard objects (). The widths of the distributions of the parallel and perpendicular projections yield the respective systematic uncertainties of the 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 response and resolution for the inclusive sample shows that data and MC simulations agree within the systematic uncertainties. The response shows an underestimation of the soft contributions to . A degradation of the resolution is observed for increasing and , due to pile-up and detector resolution effects. Additional performance measures considered in these studies include the estimate of tails in the distribution. As expected from the universality of the hadronic recoil, the integral tail fraction of the distribution is identical for inclusive and boson production, independent of the leptonic decay mode. The 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 , 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 reconstruction in ATLAS, which was developed for LHC and used in a large number of physics analyses, can be used with the discussed refinements and adjustments for as well.

Table 2

Representations of and calculated from (1) reconstructed charged-particle tracks from the ID or (2) using a soft term from topo-clusters in the calorimeter only

#	Objects contributing to ETmiss and ΣE_T
	Type	Selections	Variables	Comments
(1)	ID track	|η|<2.5	pTmiss	Charged-particle-based estimators for ETmiss, ΣE_T using all reconstructed tracks from the hard-scatter vertex passing requirements for high-quality reconstruction in addition to kinematic selections
		p_T>400Me	Σp_T
		|d_0|<1.5mm
		|z_0sin(θ)|<1.5mm
(2)	Topo-cluster	EclusLCW > 0 (soft term)	ETmiss,soft,calo	Variant reconstructing ETmiss,calo (ΣETcalo) using a soft term ETmiss,soft,calo (ΣETsoft,calo) reconstructed from topo-clusters 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 Sect. 8.1 applied
		ΣETsoft,calo