ATLAS draft

Page 1

EUROPEAN ORGANISATION FOR NUCLEAR RESEARCH (CERN)

Eur. Phys. J. C 78 (2018) 903

DOI: 10.1140/epjc/s10052-018-6288-9

CERN-EP-2017-274

14th December 2018

Performance of missing transverse momentum

reconstruction with the ATLAS detector using

proton–proton collisions at

√

s = 13 TeV

The ATLAS Collaboration

The performance of the missing transverse momentum (Emiss

) reconstruction with the ATLAS

detector is evaluated using data collected in proton–proton collisions at the LHC at a centre-

of-mass energy of 13TeV in 2015. To reconstruct Emiss

, 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 ob-

jects. 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

contributions. The individual

terms as well as the overall reconstructed Emiss

are evaluated with various performance met-

rics for scale (linearity), resolution, and sensitivity to the data-taking conditions. The method

developed to determine the systematic uncertainties of the Emiss

scale and resolution is dis-

cussed. Results are shown based on the full 2015 data sample corresponding to an integrated

luminosity of 3.2fb

−1

Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.

arXiv:1802.08168v2 [hep-ex] 13 Dec 2018

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Contents

1 Introduction

2 ATLAS detector

3 Emiss

reconstruction

3.1 Emiss

basics

3.2 Emiss

terms

3.3 Object selection

3.3.1 Electron selection

3.3.2 Photon selection

3.3.3 τ-lepton selection

3.3.4 Muon selection

3.3.5 Jet selection

3.3.6 Muon overlap with jets

3.4 Emiss

soft term

3.4.1 Track and vertex selection

3.4.2 Track soft term

4 Data and simulation samples

4.1 Data samples

4.2 Monte Carlo samples

4.3 Pile-up

5 Event selection

5.1 Z → µµ event selection

5.2 W → eν event selection

5.3 t¯t event selection

6 Performance of Emiss

reconstruction in data and Monte Carlo simulation

6.1 Emiss

modelling in Monte Carlo simulations

6.2 Emiss

response and resolution

6.2.1 Emiss

scale determination

6.2.2 Measuring the Emiss

response

6.2.3 Determination of the Emiss

resolution

6.2.4 Emiss

resolution measurements

6.2.5 Emiss

resolution in final states with neutrinos

6.3 Emiss

tails

7 Systematic uncertainties

7.1 Methodology

7.1.1 Observables

7.1.2 Procedures

7.2 Systematic uncertainties in Emiss

response and resolution

8 Missing transverse momentum reconstruction variants

8.1 Calorimeter-based Emiss

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8.2 Emiss

from tracks

8.3 Performance evaluations for Emiss

variants

8.3.1 Comparisons of Emiss

resolution

8.3.2 Comparisons of Emiss

scale

8.3.3 Summary of performance

9 Conclusion

Appendix

A Glossary of terms

B Alternative Emiss

composition

C Jet selection

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1 Introduction

The missing transverse momentum (Emiss

) 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 Emiss

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 Emiss

reconstruction focussing on the minimisation of effects introduced by pile-up for

the data recorded between 2010 and 2012 (LHC Run1) [2, 3]. These approaches are the basis for the

Emiss

reconstruction developed for the data collected in 2015 (LHC Run2) 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 Emiss

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 Emiss

performance in Section 6. Section 7 comprises a discussion

of methods used to determine systematic uncertainties associated with the Emiss

measurement, and the

presentation of the corresponding results. Section 8 describes variations of the Emiss

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 Emiss

-related variables and descriptors can be found in Appendix A, while the composition

of Emiss

reconstruction variants is presented in Appendix B. An evaluation of the effect of alternative jet

selections on the Emiss

reconstruction performance is given in Appendix C.

2 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 2T 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 Run1 and

Run2, 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 pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). Angular distance is measured in units of

∆R ≡√(∆η)2 + (∆φ)2.

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The high-granularity lead/liquid-argon (LAr) sampling electromagnetic calorimeter covers the region

|η| < 3.2. The regions |η| < 1.37 and 1.5 < |η| < 1.8 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 |η| < 1.7. LAr technology is also used for the hadronic calorimeters

in the endcap region 1.5 < |η| < 3.2 and for electromagnetic and hadronic energy measurements in the

forward calorimeters covering 3.2 < |η| < 4.9.

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].

3 Emiss

reconstruction

The reconstructed Emiss

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 Emiss

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 Emiss

. This issue is addressed by the explicit signal ambiguity resolution in the

object-based Emiss

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 Emiss

are available and discussed in detail

in Section 8. One of these alternative options is the calorimeter-based Emiss

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

Emiss

only in the use of tracks in place of jets. It is described in more detail in Section 8.2.

3.1 Emiss

basics

The missing transverse momentum reconstruction provides a set of observables constructed from the

components px(y) of the transverse momentum vectors (p

T) of the various contributions. The missing

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transverse momentum components Emiss

x(y) serve as the basic input for most of these observables. They are

given by

Emiss

x(y) = −

i∈{hard objects}

px(y),i −

j∈{soft signals}

px(y),j .

(1)

The set of observables constructed from Emiss

x(y) is

Emiss

= (Emiss

, Emiss

(2)

Emiss

= |Emiss

| =

√

(Emiss

)2 + (Emiss

)2 ,

(3)

φmiss = tan−1(Emiss

/Emiss

) .

(4)

The vector Emiss

provides the amount of the missing transverse momentum via its magnitude Emiss

, and its

direction in the transverse plane in terms of the azimuthal angle φmiss. Consequently, Emiss

is non-negative

by definition. However, in an experimental environment where not all relevant pT from the hard-scatter

interaction can be reconstructed and used in Eq. (1), and the reconstructed pT from each contribution

is affected by the limited resolution of the detector, an observation bias towards non-vanishing values

for Emiss

is introduced even for final states without genuine missing transverse momentum generated by

undetectable particles.

The scalar sum of all transverse momenta (pT = |p

T|) from the objects contributing to Emiss

reconstruction

is given by

ΣET =

i∈{hard objects}

pT,i +

j∈{soft signals}

pT,j .

(5)

In the context of Emiss

reconstruction, ΣET is calculated in addition to the sum given in Eq. (1), and the

derived quantities defining Emiss

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 Emiss

reconstruction performance studies.

In the calculation of Emiss

x(y) and ΣET 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 Emiss

reconstruction sequence for the hard-object contribution starts with electrons (e),

followed by photons (γ), then hadronically decaying τ-leptons (τhad), 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 Emiss

reconstruction first. The

lower-priority reconstructed particles (γ, τhad) are fully rejected if they share their calorimeter signal with

a higher-priority object that has already entered the Emiss

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.

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Generally, jets are rejected if they overlap with accepted higher-priority particles. To avoid signal losses

for Emiss

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 Sections 3.3.5 and 3.3.6 are applied.

Excluding ID tracks associated with any of the accepted hard objects contributing to Emiss

, ID tracks from

the hard-scatter collision vertex are used to construct the soft-event signal for the results presented in this

paper.

3.2 Emiss

terms

Particle and jet selections in a given analysis should be reflected in Emiss

and ΣET 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 Emiss

and ΣET, 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 Emiss

. The applied selections are

presented in Section 3.3, and summarised in Table 1.

In ATLAS the flexibility needed to recalculate Emiss

and ΣET under changing analysis requirements for

the same event is implemented using dedicated variables corresponding to specific object contributions.

In this approach the full Emiss

is the vectorial sum of missing transverse momentum terms Emiss,p

with p ∈ {e, γ, τhad, µ, jet} reconstructed from the p

T = (px, py) of accepted particles and jets, and the

corresponding soft term Emiss,soft

from the soft-event signals introduced in Section 3.1 and further specified

in Section 3.4. This yields2

Emiss

= −

selected

electrons

Emiss,e

−

accepted

photons

Emiss,γ

−

accepted

τ-leptons

τhad

Emiss,τhad

−

selected

muons

Emiss,µ

−

accepted

jets

pjet

Emiss,jet

hard term

−

unused

tracks

ptrack

Emiss,soft

soft term

(6)

The Emiss

and φmiss observables can be constructed according to Eqs. (3) and (4), respectively, for the

overall missing transverse momentum (from Emiss

) as well as for each individual term indicated in Eq. (6).

In the priority-ordered reconstruction sequence for Emiss

, 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.

2 In this formula the notion of selected, which is only applicable to electrons and muons, means that the choice of reconstructed

particles is purely given by a set of criteria similar to those given in Sections 3.3.1 and 3.3.4, respectively, with possible

modifications imposed by a given analysis. The notion of accepted indicates a modification of the set of initially selected

objects imposed by the signal ambiguity resolution.

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Table 1: Overview of the contributions to Emiss

and ΣET from hard objects such as electrons (e), photons (γ),

hadronically decaying τ-leptons (τhad), 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 Emiss

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 d0 (z0 sin(θ)) used to select the

ID tracks contributing to E

miss,soft

and ΣEsoft

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.

Objects contributing to Emiss

and ΣET

Type

Selections

Variables Comments

(1) e

|η| < 1.37 or 1.52 < |η| < 2.47

pT > 10GeV

Emiss,e

ΣEe

all e

passing medium reconstruc-

tion quality and kinematic selec-

tions

(2) γ

|η| < 1.37 or 1.52 < |η| < 2.47

pT > 25GeV

Emiss,γ

ΣE

all γ passing tight quality and kin-

ematic selections in reconstruction,

and without signal overlap with (1)

(3) τhad

|η| < 1.37 or 1.52 < |η| < 2.47

pT > 20GeV

Emiss,τhad

ΣE

τhad

all τhad passing medium reconstruc-

tion quality and kinematic selec-

tions, and without signal overlap

with (1) and (2)

(4) µ

|η| < 2.7

pT > 10GeV

Emiss,µ

ΣE

all µ passing medium quality and

kinematic selections in reconstruc-

tion; for the discussion of the µ–jet

overlap removal see Section 3.3.6

(5) jet

|η| < 4.5

pT > 60GeV

2.4 < |η| < 4.5

20GeV < pT < 60GeV

|η| < 2.4

20GeV < pT < 60GeV

JVT > 0.59

Emiss,jet

ΣEjet

all jets passing reconstruction qual-

ity (jet cleaning) and kinematic se-

lections, and without signal overlap

†

with (1)–(3); for the dedicated over-

lap removal strategy with µ from

(4) see Section 3.3.6

(6) ID track

pT > 400MeV

|d0| < 1.5mm

|z0 sin(θ)| < 1.5mm

∆R(track, e-/γ cluster) > 0.05

∆R(track, τhad) > 0.2

Emiss,soft

ΣEsoft

all ID tracks from the hard-scatter

vertex passing reconstruction qual-

ity and kinematic selections, and

not associated with any particle

from (1), (3) or (4), or ghost-

associated with a jet from (5)

†

While for single reconstructed particles no overlap is accepted at all, jets with a signal overlap fraction κE < 50% can still

contribute their associated tracks to E

miss,soft

if those pass the selections for P = (6), as discussed in Section 3.3.5. The

definition of κE is given in Eq. (8).

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Correspondingly, ΣET is calculated from the scalar sums of the transverse momenta of hard objects

entering the Emiss

reconstruction and the soft term,

ΣET =

selected

electrons

T +

accepted

photons

accepted

τ-leptons

τhad

selected

muons

accepted

jets

pjet

hard term

unused

tracks

ptrack

soft term

(7)

The hard term in both Emiss

and ΣET 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.

3.3 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 Emiss

reconstruction performance in the context of a given physics analysis, and the selections performed in this

study are an example set of criteria.

3.3.1 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 Emiss

reconstruction, electrons passing

the reconstruction quality requirements are in addition required to have pT > 10GeV 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 Emiss

reconstruction as such, if this jet meets the corresponding selection criteria discussed

in Section 3.3.5.

3.3.2 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 pT > 25GeV and

|η| < 1.37 or 1.52 < |η| < 2.37 to be included in the Emiss

reconstruction. Similarly to electrons, photons

emitted within 1.37 < |η| < 1.52 may contribute to Emiss

as a jet.

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3.3.3 τ-lepton selection

Hadronically decaying τ-leptons are reconstructed from narrow jets with low associated track multipli-

cities [10]. Candidates must pass the medium quality selection given in Ref. [11], and in addition have

pT > 20GeV and |η| < 1.37 or 1.52 < |η| < 2.47. Any τ-lepton not satisfying these τ-identification

criteria may contribute to Emiss

when passing the jet selection.

3.3.4 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 Emiss

reconstruction by requiring the medium reconstruction quality defined

in Ref. [12], pT > 10GeV, and an association with the hard-scatter vertex for those within |η| < 2.5.

3.3.5 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-kt

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 pT > 20GeV after the full calibration. The jet

contribution to Emiss

and ΣET 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 κE of the electron(photon) energy EEM

e(γ) to the jet energy EEM

jet ,

κE =

EEM

e(γ)

EEM

jet

(8)

with both energies calibrated at the EM scale. In the case of κE ≤ 50%, the jet is included in Emiss

reconstruction, with its pT scaled by 1 − κE. For κE > 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 pT > 20GeV and |η| > 2.4, or with

pT≥ 60GeV and |η| < 4.5, are always accepted for Emiss

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 pT carried by tracks from the hard-scatter vertex matched to the given jet is

related to the total amount of pT carried by all matched tracks, among other inputs, to tag jets from the hard-scatter interaction.

Page 11

20GeV < pT < 60GeV and |η| < 2.4 are only accepted if they are tagged by JVT > 0.59. In both cases,

the jet pT thresholds are applied to the jet pT before applying the κE correction. Additional configurations

for selecting jets used in Emiss

reconstruction are discussed in Appendix C, together with the effect of the

variation of these selection criteria on the Emiss

reconstruction performance.

3.3.6 Muon overlap with jets

Jets overlapping with a reconstructed muon affect the Emiss

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 Emiss

reconstruction. On the other

hand, jets reconstructed from final state radiation (FSR) off the muon need to be included into Emiss

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 Emiss

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 pT from the hard-scatter vertex and thus

increases JVT. As a consequence of this fake tag, the pile-up jet pT contributes to Emiss

, and thus degrades

both the Emiss

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 Emiss

reconstruction leads to double-counting of the transverse momentum associated with the muon energy

loss, as the fully reconstructed muon pT 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:

• p

T,track

/pjet

T,track

> 0.8 – the transverse momentum of the ID track associated with the muon (p

T,track

)

represents a significant fraction of the transverse momentum p

jet

T,track

, the sum of the transverse

momenta of all ID tracks associated with the jet;

• p

jet

T,track

< 2 – the overall transverse momentum pjet

of the jet is not too large compared to

T,track

;

• NPV

track

< 5 – the total number of tracks NPV

track

associated with the jet and emerging from the hard-

scatter 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 Emiss

reconstruction. The muons are retained for the

Emiss

reconstruction.

Page 12

Another consideration for muon contributions to Emiss

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 Emiss

reconstruction. Such jets are characterised by the following selections,

which are highly indicative of a photon in the ATLAS calorimeter:

• NPV

track

< 3 – the jet has low charged-particle content, indicated by a very small number of tracks

from the hard-scatter vertex;

• fEMC > 0.9 – the jet energy Ejet is largely deposited in the electromagnetic calorimeter (EMC), as

expected for photons and measured by the corresponding energy fraction fEMC = Ejet

EMC

/Ejet;

• p

jet

T,PS

> 2.5GeV – the transverse momentum contribution pjet

T,PS

from presampler signals to p

jet

indicates an early starting point for the shower;

• wjet < 0.1 – the jet is narrow, with a width wjet comparable to a dense electromagnetic shower; wjet

is reconstructed according to

wjet = i ∆Ri pT,i

i pT,i

where ∆Ri = √(∆ηi)2 + (∆φi)2 is the angular distance of topo-cluster i from the jet axis, and pT,i is

the transverse momentum of this cluster;

• p

jet

T,track

> 0.8 – the transverse momentum pjet

T,track

carried by all tracks associated with the

jet is close to p

T,track

Jets are accepted for Emiss

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.

3.4 Emiss

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 pT-flow from soft charged particles. It is an important contribution to Emiss

for the improvement of both the Emiss

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 Emiss

soft term including signals from soft neutral particles uses

calorimeter topo-clusters. The reconstruction performance using the calorimeter-based E

miss,soft,calo

inferior to the track-only-based E

miss,soft

, mostly due to a larger residual dependence on pile-up. More

details of the topo-cluster-based E

miss,soft,calo

reconstruction are discussed in Section 8.1.

Page 13

3.4.1 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

NPV > 1 of reconstructed primary vertices.

Tracks are required to have pT > 400MeV 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 |d0| < 1.5mm (|z0 sin(θ)| < 1.5mm) 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.

3.4.2 Track soft term

The track sample contributing to E

miss,soft

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 Emiss

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

Since only reconstructed tracks associated with the hard-scatter vertex are used, the track-based E

miss,soft

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.

4 Data and simulation samples

The determination of the Emiss

reconstruction performance uses selected final states without (E

miss,true

0) and with genuine missing transverse momentum from neutrinos (E

miss,true

= pν

). Samples with

Emiss,true

= 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 (t¯t) production with at least either the t or the ¯t decaying semi-leptonically.

Page 14

4.1 Data samples

The data sample used corresponds to a total integrated luminosity of 3.2fb

−1

, collected with a proton

bunch-crossing interval of25ns. 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.

4.2 Monte Carlo samples

The Z → ll and W → lν 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 t¯t-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 → ll and W → lν 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 t¯tproduction. 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 Emiss

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].

5 Version 8.186 was used for all final states generated with P 8.

6 In ATLAS stable particles are those with an expected laboratory lifetime τ corresponding to cτ > 10 mm.

Page 15

4.3 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 Emiss

The in-time pile-up activity is measured by the number of reconstructed primary collision vertices NPV.

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.

5 Event selection

5.1 Z → µµ event selection

The Z → µµ final state is ideal for the evaluation of Emiss

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 Emiss

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

= 0 allows the reconstruction quality to be determined in both

data and MC simulations. The reconstructed Emiss

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 Emiss

Page 16

Events must pass one of three high-level muon triggers with different p

thresholds and isolation require-

ments. The isolation is determined by the ratio of the scalar sum of pT of reconstructed tracks other than

the muon track itself, in a cone of size ∆R = 0.2 around the muon track (pcone

), to p

. The individual

triggers require (1) p

> 20GeV and pcone

< 0.12, or (2) p

> 24GeV and pcone

< 0.06, or (3)

> 50GeV without isolation requirement.

The offline selection of Z → µµ events requires exactly two muons, each selected as defined in Sec-

tion 3.3.4, with the additional criteria that (1) the muons must have opposite charge, (2) p

> 25GeV, and

(3) the reconstructed invariant mass mµµ of the dimuon system is consistent with the mass mZ of the Z

boson, |mµµ − mZ | < 25GeV.

5.2 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.

TheW → eν events in particular provide a good metric with E

miss,true

= pν

> 0 to evaluate and validate the

scale, resolution and direction (azimuth) of the reconstructed Emiss

, as the Emiss

reconstruction is sensitive

to the electron–jet overlap resolution performance. This metric is only available in MC simulations

where p

is known. Candidate W → eν events are required to pass the high-level electron trigger with

pT > 17GeV. Electron candidates are selected according to criteria described in Section 3.3.1. Only

events containing exactly one electron are considered.

Further selections using Emiss

and the reconstructed transverse mass mT, given by

mT =

√

Emiss

(1 − cos∆φ),

are applied to reduce the multijet background with one jet emulating an isolated electron from the W

boson. Here Emiss

is calculated as presented in Section 3. The transverse momentum of the electron is

denoted by p

, and ∆φ is the distance between φmiss and the azimuth of the electron. Selected events are

required to have Emiss

> 25GeV and mT > 50GeV.

5.3 t ¯t event selection

Events with t¯t in the final state allow the evaluation of the Emiss

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 pT > 25GeV.

The final t¯t 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-kt 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.

Page 17

6 Performance of Emiss

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, Emiss

reconstruction yields a non-linear response,

especially in regions of phase space where the observation bias discussed in Section 3.1 dominates

the reconstructed Emiss

. In addition, the Emiss

resolution functions are characterised by a high level

of complexity, due to the composite character of the observable. Objects with different pT-resolutions

contribute, and the Emiss

composition can fluctuate significantly for events from the same final state. Due

to the dependence of the Emiss

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 Emiss

The Emiss

reconstruction performance is therefore assessed by comparing a set of reconstructed Emiss

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 Emiss

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 Emiss

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 Emiss

performance evaluation are obtained by applying se-

lections according to Section 5.1 for a final state without genuine Emiss

(Z → µµ), and according to

Section 5.2 for a final state with genuine Emiss

(W → eν). From these, specific exclusive samples are

extracted by applying conditions on the number of jets reconstructed. In particular, zero jet (Njet = 0)

samples without any jet with pT > 20GeV (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 pT > 20GeV are useful for evaluating the contribution of jets to Emiss

While the pT response of jets is fully calibrated and provides a better measurement of the overall event

pT-flow, the pT resolution for jets is affected by pile-up and can introduce a detrimental effect on Emiss

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 Emiss

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.

Page 18

(a)

(b)

(c)

(d)

Figure 1: Distributions of (a) Emiss

, (b) ΣET, (c) Emiss

and (d) Emiss

for an inclusive sample of Z → µµ 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 pT 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.

6.1 Emiss

modelling in Monte Carlo simulations

The quality of the MC modelling of Emiss

, Emiss

and ΣET, reconstructed as given in Eqs. (1), (3)

and (5), is evaluated for an inclusive sample of Z → µµ events by comparing the distributions of these

Page 19

(a)

(b)

(c)

Figure 2: Distributions of (a) the jet term E

miss,jet

, (b) the muon term E

miss,µ

, and (c) the soft term E

miss,soft

for

the inclusive samples of Z → µµ 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.

observables to data. The results are presented in Fig. 1. The data and MC simulations agree within 20%

for the bulk of the Emiss

distribution shown in Fig. 1(a), with larger differences not accommodated by the

total (systematic and statistical) uncertainties of the distributions for high Emiss

. These differences suggest

Page 20

a mismodelling in t¯t events, the dominant background in the tail regime [43]. The ΣET distributions

compared between data and MC simulations in Fig. 1(b) show discrepancies significantly larger than the

overall uncertainties for 200GeV < ΣET < 1.2TeV. These reflect the level of mismodelling of the final

state mostly in terms of hard-object composition in MC simulations. The Emiss

and Emiss

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 |Emiss

x(y)| < 100GeV, with larger differences observed outside of this range still

mostly within the uncertainties.

The distributions of individual contributions to Emiss

from jets (E

miss,jet

), muons (E

miss,µ

), and the soft

term (E

miss,soft

), as defined in Eq. (6), are compared between data and MC simulations for the same

inclusive Z → µµ sample in Fig. 2. Agreement between data and MC simulations for E

miss,jet

in Fig. 2(a)

is of the order of ±20% and within the total uncertainties for E

miss,jet

≲ 120GeV, but beyond those for

higher E

miss,jet

. A similar observation holds for E

miss,µ

in Fig. 2(b), where data and MC simulations

agree within the uncertainties for low E

miss,µ

but significantly beyond them for larger E

miss,µ

. Agreement

between data and MC simulations is better for the soft term E

miss,soft

, with differences up to 10% for

Emiss,soft

≲ 30GeV, as seen in Fig. 2(c). Larger differences for larger E

miss,soft

are still found to be within

the uncertainties.

The peak around E

miss,jet

= 20GeV indicates the onset of single-jet events at the threshold pT = 20GeV

for jets contributing to E

miss,jet

. Larger values of E

miss,jet

arise from events with one or more high-pT jets

balancing the pT of the Z boson.

For the W → eν sample with genuine missing transverse momentum given by p

, both the total recon-

structed Emiss

and the soft term are compared between data and MC simulations in Fig. 3. The level

of agreement between the Emiss

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 Emiss

distributions observed with the exclusive Njet = 0 sample shown in Fig. 3(b) are well

below 20%, but show a trend to larger discrepancies for decreasing Emiss

≲ 40GeV. 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 Emiss

required in the W → eν selection described in Section 5.2.

The comparison of the E

miss,soft

distributions from data and MC simulations shown in Fig. 3(c) yields

agreement well within the uncertainties, for E

miss,soft

≳ 10GeV. The rising deficiencies observed in

the MC distribution for decreasing E

miss,soft

≲ 10GeV are expected to be related to the missing multijet

contribution.

6.2 Emiss

response and resolution

The response in the context of Emiss

reconstruction is determined by the deviation of the observed Emiss

from the expectation value for a given final state. This deviation sets the scale for the observed Emiss

. If this

deviation is independent of the genuine missing transverse momentum, or any other hard pT indicative of

the overall hard-scatter activity, the Emiss

response is linear. In this case, a constant bias in the reconstructed

Emiss

is still possible due to detector inefficiencies and coverage (acceptance) limitations.

Page 21

(a)

(b)

(c)

Figure 3: Distributions of the total Emiss

in (a) the inclusive case and (b) the Njet = 0 case, as well as (c) the soft

term E

miss,soft

reconstructed in Njet = 0 events with W → eν in data. The expectation from MC simulation is

superimposed and includes all relevant background final states passing the event selection. The inclusive Emiss

distribution from MC simulations contains a small contribution from multijet final states at low Emiss

, which is

absent for the Njet = 0 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.

Final states balanced in transverse momentum are expected to show a non-linear Emiss

response at low

event activity, as the response in this case suffers from the observation bias in Emiss

reconstruction

Page 22

discussed in Section 3.1. With increasing momentum transfers in the hard-scatter interaction, the Emiss

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 Emiss

response is only linear once

Emiss,true

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 Emiss

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 Emiss

to the reconstructed and accepted e, γ, τhad and µ, and those being part of a reconstructed and accepted jet.

In addition, the pT-flow of not explicitly reconstructed charged particles emerging from the hard-scatter

vertex is represented by ID tracks contributing to E

miss,soft

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 Emiss

reconstruction.

Like for the Emiss

response, resolution-related aspects of Emiss

reconstruction are understood from data-

to-MC-simulations comparisons. The scales used for the corresponding evaluations are the overall event

activity represented by ΣET, and the pile-up activity measured by NPV. The measurement of the Emiss

resolution is discussed in Section 6.2.3 and results are presented in Section 6.2.4.

6.2.1 Emiss

scale determination

In events with Z → µµ decays, the transverse momentum of the Z boson (p

) is an indicator of the

hardness of the interaction. It provides a useful scale for the evaluation of the Emiss

response for this

final state without genuine missing transverse momentum. The direction of the corresponding Z boson

transverse momentum vector pZ

defines an axis AZ in the transverse plane of the collision, which is

reconstructed from the p

T of the decay products by

AZ =

µ+

+ p

µ−

µ+

+ p

µ−

(9)

The magnitude of the component of Emiss

parallel to AZ is

PZ = Emiss

· AZ .

(10)

This projection is sensitive to any limitation in Emiss

reconstruction, in particular with respect to the

contribution from the hadronic recoil against pZ

, 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

Emiss

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 Emiss

reconstruction. For P

Z < 0, the

reconstructed hadronic activity recoiling against pZ

is too small, while for P

Z > 0 too much hadronic

Page 23

(a)

(b)

Figure 4: The average projection of Emiss

onto the direction AZ of the Z boson’s transverse momentum vector pZ

T , as

given in Eq. (10), is shown as a function of p

T = |pZ

T| in Z → µµ events from (a) the Njet = 0 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.

recoil is reconstructed. The evolution of P

as a function of the hardness of the Z boson production can

be measured by evaluating the mean 〈P

Z〉 in bins of the hard-scatter scale phard

= pZ

In addition to measuring the Emiss

response in data and MC simulation without genuine Emiss

, its linearity

can be determined using samples of final states with genuine Emiss

in MC simulations. This is done

by evaluating the relative deviation ∆lin

of the reconstructed Emiss

from the expected E

miss,true

> 0 as a

function of E

miss,true

∆lin

(Emiss,true

) =

Emiss

− Emiss,true

Emiss,true

(11)

6.2.2 Measuring the Emiss

response

Figure 4 shows 〈P

Z〉 as a function of pZ

for the Njet = 0 and the inclusive Z → µµ sample, respectively.

MC simulations compare well with the data for Njet = 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 pZ

in the Njet = 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 pT > 400MeV 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

Page 24

Figure 5: The average projection of Emiss

onto the direction AZ of the Z boson’s transverse momentum vector pZ

T ,

as given in Eq. (10), is shown as a function of p

T = |pZ

T| in Z → µµ 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.

pT 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 Emiss

response is recovered better as p

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 8GeV in data and 6GeV in MC simulations observed for

≳ 40GeV 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 Emiss

, the soft-term contribution Emiss,soft

only, the hard-term contribution Emiss

−Emiss,soft

and the true soft term Emiss,true soft

only, as a function of p

, for the Z → µµ sample from MC simulations.

In particular the difference between the projections using Emiss,true soft

and Emiss,soft

indicates the lack of

reconstructed hadronic response, when Emiss,soft

= Emiss,true soft

is expected for a fully measured recoil.

The parallel projection using only the soft terms is larger than zero for all p

due to the missing Z-boson

contribution to Emiss

given by −pZ

The deviation from linearity in Emiss

reconstruction, measured by ∆lin

given in Eq. (11), is shown as

a function of E

miss,true

for MC simulations of W → eν, W → µν and t¯t production in Fig. 6. The

observed ∆lin

> 0 at low Emiss,true

indicates an overestimation of E

miss,true

by the reconstructed Emiss

due

to the observation biases arising from the finite Emiss

resolution, as discussed in Section 3.1. This bias

overcompensates the lack of reconstructed pT-flow from the incompletely measured hadronic recoil in

W → eν and W → µν events for Emiss,true

≲ 40GeV with an increasing non-linearity observed with

decreasing E

miss,true

. For E

miss,true

≳ 70GeV the Emiss

response is directly proportional to E

miss,true

with the reconstructed recoil being approximately 2% too small. The W → eν and W → µν final

states show very similar ∆lin

(Emiss,true

), thus indicating the universality of the recoil reconstruction and

Page 25

Figure 6: The deviation of the Emiss

response from linearity, measured as a function of the expected E

miss,true

by ∆lin

in Eq. (11), in W → eν, W → µν, and t¯t final states in MC simulations. The lower plot shows a zoomed-in view

on the ∆lin

T dependence on E

miss,true

with a highly suppressed ordinate.

the independence on the lepton flavour of the reconstructed Emiss

in a low-multiplicity final state with

Emiss,true

> 0.

In t¯tfinal-state reconstruction, resolution effects tend to dominate ∆lin

at E

miss,true

≲ 120GeV. Compared

to the W → eν and W → µν final states, a significantly poorer Emiss

resolution is observed in this

kinematic region, due to the presence of at least four jets with relatively low pT and high sensitivity to

pile-up-induced fluctuations in each event of the t¯tsample. For E

miss,true

> 120GeV, ∆lin

(Emiss,true

) ≈ 2%

indicates a proportional Emiss

response with a systematic shift similar to the one observed in inclusive

W-boson production.

6.2.3 Determination of the Emiss

resolution

The Emiss

resolution is determined by the width of the combined distribution of the differences between

the measured Emiss

x(y) and the components of the true missing transverse momentum vector Emiss,true

(Emiss,true

, Emiss,true

). The width is measured in terms of the RMS, with

RMS

miss

x(y) =

{

RMS(Emiss

x(y)

− Emiss,true

x(y)

) W → eν or t¯t sample (Emiss,true

> 0)

RMS(Emiss

x(y)

)

Z → µµ sample (Emiss,true

= 0)

(12)

This metric does not capture all of the effects driving the fluctuations in Emiss

reconstruction, such as

biases between individual Emiss

terms or the behaviour of outliers, but it is an appropriate general measure

of how well Emiss

represents E

miss,true

Page 26

(a)

(b)

Figure 7: The RMS width of the Emiss

x(y) distributions (a) in bins of ΣET and (b) in bins of the number of primary

vertices in an inclusive sample of Z → µµ 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.

Using the Z → µµ sample allows direct comparisons of RMS

miss

x(y) between data and MC simulations,

as E

miss,true

= 0 in this case. The resolution in final states with genuine Emiss

is determined with MC

simulations alone. For W → eν and t¯t final states, E

miss,true

x(y)

= pν

x(y) is used.

6.2.4 Emiss

resolution measurements

The Emiss

resolution measured by RMS

miss

x(y) is evaluated as a function of the event activity measured by

ΣET given in Eq. (7). For the inclusive Z → µµ sample, Fig. 7(a) shows RMS

miss

x(y) quickly rising from

less than 5GeV to about 10GeV with increasing ΣET within 50GeV ≤ ΣET < 70GeV.7 This is due to

the fact that in this range the two muons are the dominant hard objects contributing, with a pT resolution

proportional to (p

)2. A convolution of the muon resolution with a small contribution from E

miss,soft

possible for ΣET > 50GeV. This component is on average about 60% of pZ

, and subject to the stochastic

fluctuations further discussed below.

The increase of Z → µµ + 1 jet topologies in the Z → µµ sample leads to an additional source of

fluctuations affecting RMS

miss

x(y)

(ΣET) for 70GeV < ΣET ≲ 180GeV. In general the Z → µµ sample

collected for this study covers p

≲ 140GeV with relevant statistics. At this limit it is expected that

the hadronic recoil contains two reconstructed jets, with the onset of this contribution at ΣET of about

180GeV. The corresponding change of the dominant final state composition for ΣET > 180GeV leads to a

7 This lower boundary of this range is given by the muon selection with p

> 25 GeV, as described in Section 5.1, assuming no

other hard-scatter vertex tracks, i.e. E

miss,soft

= 0. The upper boundary indicates the lower limit of ΣET to accommodate at

least one jet with p

jet

> 20 GeV in addition the two muons (for the jet selection see Section 3.3.5).

Page 27

(a)

(b)

(c)

(d)

Figure 8: The Emiss

resolution RMS

miss

x(y) determined for (a) an exclusive Z → µµ sample without jets with pT >

20 GeV (Njet = 0) and for (b) an exclusive sample with at least one jet above this threshold (Njet ≥ 1), as a function

of ΣET in data and MC simulations. The dependence of RMS

miss

x(y) on the pile-up activity, as measured by NPV, 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.

change of shape of RMS

miss

x(y)

(ΣET), as the transverse momentum of the individual jets rises and the number

of contributing jets slowly increases. The expected RMS

miss

x(y)

(ΣET

) ∝

√

ΣET scaling driven by the jet-pT

resolution [44] therefore dominates RMS

miss

x(y) at these higher ΣET. The MC predictions for RMS

miss

x(y)

(ΣET

)

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 ΣET > 200GeV.

Page 28

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-pT measurement. The dependence of RMS

miss

x(y) on the

pile-up activity measured by NPV is shown in Fig. 7(b). Data show a less steep slope of RMS

miss

x(y)

(NPV

)

than MC simulations, but with about 10% worse resolution in the low pile-up region of NPV ≲ 5. The

resolution in data is better than in MC simulations by about 10% for the region of higher pile-up activity

at NPV≈ 20.

The differences between data and MC simulations seen in RMS

miss

x(y)

(ΣET) for the inclusive Z → µµ

sample can be further analysed by splitting the sample according to the value of Njet. Figure 8(a)

shows the dependence of RMS

miss

x(y) on ΣET for Z → µµ events with Njet = 0. The dominant source of

fluctuations other than the muon-pT resolution is in this case introduced by the incomplete reconstruction

of the hadronic recoil. These fluctuations increase with increasing p

, which in turn means higher overall

event activity measured by ΣET. 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 ΣET.

The exclusive Njet≥ 1 samples extracted from Z → µµ data and MC simulations show the expected

RMS

miss

x(y)

∝

√

ΣET 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 ΣET 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 NPV shown in Fig. 8(c) indicates that the Emiss

resolution is basically

independent of pile-up, for the Njet = 0 sample. This is expected from the exclusive Emiss

composition

comprising the (track-based) E

miss,µ

and E

miss,soft

terms only. Data and MC simulations compare well

within a few percent, and without any observable dependence on NPV. Figure 8(d) shows the NPV

dependence of RMS

miss

x(y) for the Njet≥ 1 sample. Comparing this result to Fig. 7(b) confirms that all

pile-up dependence of the Emiss

resolution is arising from the jet term. Both trend and magnitude of the

data-to-MC comparison follow the observation from the inclusive analysis.

6.2.5 Emiss

resolution in final states with neutrinos

The Emiss

resolution for final states with E

miss,true

> 0 is measured by RMSmiss

x(y) according to Eq. (12)

and evaluated using dedicated inclusive W → eν and W → µν samples from MC simulations, and the

inclusive t¯t MC sample defined in Section 5.3. For these samples, RMS

miss

x(y) can be determined as a

function of E

miss,true

= pν

. 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 Emiss

-based and the mT-based

selections.

Figure 9 shows RMS

miss

x(y) evaluated as a function of E

miss,true

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 pT resolutions of the electrons and muons, yield a very similar Emiss

resolution for W → eν

and W → µν final states. Generally, poorer resolution is observed in t¯t final states. The deviation

from the expected RMS

miss

x(y)

∝

√

(Emiss,true

) scaling behaviour for W → lν at lower Emiss,true

reflects the

kinematic features of the W boson and its decay. Events with low p

, and therefore small hadronic

Page 29

Figure 9: The Emiss

resolution measured by RMS

miss

x(y) as a function of the true missing transverse momentum E

miss,true

for the W → eν, W → µν, and t¯t samples from MC simulations.

recoil, lie predominantly in the region 25GeV ≲ p

≲ 50GeV. Since the hadronic recoil is generally the

poorly measured component of an event and the reconstructed Emiss

is dominated by the lepton pT in this

region, the Emiss

resolution tends to be better here than for events with larger hadronic recoil populating

≲ 25GeV and p

≳ 50GeV.

6.3 Emiss

tails

Large reconstructed Emiss

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 Emiss

components for final states with well-known

expectation values for Emiss

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 Emiss

constituents. Even for a well-defined final state, event-

by-event fluctuations in terms of which particles, jets, and soft tracks enter the Emiss

reconstruction, and

with which pT, lead to deviations from a normally distributed (Emiss

,Emiss

) response.

Figure 10 shows the combined (Emiss

,Emiss

) 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 Emiss

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 Emiss

resolution, rather than using any of the widths measured

by fitting Gauss functions in selected ranges of the distribution.

Page 30

Figure 10: The combined distribution of Emiss

and Emiss

for an inclusive Z → µµ from simulation. Gaussian fits

limited to the ±1 × RMS and ±2 × RMS 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 Emiss

itself and can be estimated by measuring

the fraction of events with Emiss

> Emiss,threshold

ftail = 1

∞

Emiss,threshold

h(Emiss

)dEmiss

, with H =

∞

h(Emiss

)dEmiss

(13)

Here h(Emiss

) is the Emiss

distribution for a given event sample, and E

miss,threshold

is a threshold set to

estimate tails. Any decrease of ftail at a fixed integral H indicates an improvement of the Emiss

resolution,

and is more sensitive to particular improvements than e.g. RMS

miss

x(y). For example, improving the E

miss,soft

reconstruction by rejecting ID tracks from the hard-scatter vertex with poor reconstruction quality yields

a significantly smaller ftail for the same event sample.

The tails in the Emiss

distributions for the final states considered for this study are quantified by the fraction

of events above a certain Emiss

threshold using MC simulations. Figure 11(a) shows that the Z → ll

events (l = e or l = µ) with E

miss,true

= 0 have significantly reduced tails when compared to W → lν

and t¯t 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

such that the fraction of events with |Emiss

− Emiss,true

| above a given

threshold is determined, shows the universality of the hadronic recoil in Z → ll and W → lν, as can be

seen in Fig. 11(b).

Another finding of this study is that the tail in the |Emiss

− Emiss,true

| distribution for the higher ΣEjet

t¯t

sample is considerably larger than for the low-ΣE

jet

samples with Z → ll or W → lν final states. As

can be seen in Fig. 11(c), the tails are much more consistent between Z → µµ and t¯t samples when the

distribution for the Z → µµ sample is reweighted such that it follows the same ΣE

jet

distribution as the

t¯t sample. The enhanced tails are thus likely introduced by the jet response and multiplicity, which has a

residual sensitivity to pile-up.

Page 31

(a)

(b)

(c)

Figure 11: In (a) the integral tail fraction ftail given in Eq. (13) is shown as a function of the integration threshold

Emiss,threshold

, for MC simulations of Z → ll, W → lν, and t¯t final states. The tail fraction in terms of a threshold

applied to |Emiss

− Emiss,true

|, the distance between the reconstructed (Emiss

) and the expected (Emiss,true

) vectors, is

shown in (b) for all considered final states. The same fraction is shown in (c) for the Emiss

distributions for Z → µµ

before and after a reweighting following the ΣET distribution for t¯t is applied, together with ftail from the t¯t final

state.

7 Systematic uncertainties

The systematic uncertainties associated with the measurement of Emiss

are provided for the response

(Emiss

scale) as well as for the resolution. They depend on the composition of the hard terms and on

Page 32

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 Emiss

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 Emiss

reconstruction are uncorrelated.

The determination of the Emiss

scale and resolution uncertainties arising from the soft term E

miss,soft

described in this section.

7.1 Methodology

The extraction of the systematic uncertainties for the reconstructed Emiss

is based on data-to-MC compar-

isons of spectra of observables measuring the contribution of E

miss,soft

to the overall Emiss

7.1.1 Observables

The vector sum of the transverse momentum vectors of all particles and jets emerging from a hard-scatter

interaction (pHS

) is given by

pHS

T =

T +

pjet

pobs

(observable)

pinv

T (not observable)

Here p

generally represents the transverse momenta of non-observable particles, which are summed up

to form pinv

. All other transverse momenta are carried by particles that are observable in principle, and

sum up to pobs

. Momentum conservation dictates pHS

= |pHS

| = 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 (phard

) for the observable-particle contribution

pobs

can be measured. The reconstructed hard final-state objects entering Emiss

as described in Section 3.2

are used to measure phard

phard

contributing

electrons

T +

contributing

photons

contributing

τ-leptons

τhad

contributing

muons

contributing

jets

pjet

The expectation is that phard

= |phard

| > 0 and phard

pobs

. Adding psoft

= −Emiss,soft

, with Emiss,soft

defined in Eq. (6), to phard

yields an improved estimate of the net transverse momentum carried by

undetectable particles, as some of the experimental inefficiencies are mitigated.8

In the Z → µµ final state without genuine missing transverse momentum the expectation is that Emiss

−(phard

+ psoft

) = 0. While this expectation does not hold due to the experimental inefficiencies, it

nevertheless raises the expectation that for events without jets psoft

points into the direction of the hadronic

recoil, i.e. opposite to phard

in the transverse-momentum plane. The deviation from this expectation is

8 As discussed in Section 3.4, the soft term represents only charged particles with pT > 400 MeV not associated with fully

identified and reconstructed particles or jets. Therefore, including psoft

can only recover a part of the actual soft pT-flow of

the interaction.

Page 33

𝒫∥

𝐩T

soft

𝒫⊥

𝐄T

miss

𝐩T

hard = 𝐩T

𝑍

(a) Z + 0 jet topology

𝐩T

soft

𝐩T

𝑍

𝐄T

miss

𝐩

jet

𝐩T

𝑍

𝐩

jet

𝒫∥

𝒫⊥

𝐩T

hard = 𝐩T

𝑍 + 𝐩

jet

𝐄T

miss

𝐩T

soft

(b) Z + 1 jet topology

Figure 12: Schematic view of the parallel (P ) and perpendicular (P⊥) projections of psoft

on phard

for Z → µµ

events without genuine Emiss

, for (a) a final state without any jets and (b) a final state with one jet. The expectation

values for a perfect Emiss

reconstruction are E[P ] = p

T for Njet = 0 and E[P ] = phard

for Njet ≥ 1, with E[P⊥] = 0

in all cases.

measured in terms of the parallel (P ) and perpendicular (P⊥) projections of psoft

onto phard

. Figure 12

schematically shows these projections for Z + 0-jet and Z + 1-jet topologies.

The average 〈P 〉 in a given bin k of phase space defined by phard

measures the E

miss,soft

response, with

〈P 〉 = 〈phard

〉k indicating a perfect response in this bin. The Emiss

resolution contribution from E

miss,soft

reconstruction is measured by two components, the fluctuations in response (RMS

) and the fluctuations

of the (transverse) angular deflection around the phard

axis, measured by RMS

⊥. These fluctuations are

expressed in terms of variances, with

RMS

2 = 〈(P )2〉 − 〈P 〉2

and

RMS

⊥ = 〈(P⊥)2〉 .

7.1.2 Procedures

The extraction of the systematic uncertainties introduced into the Emiss

measurement by the E

miss,soft

term

is based on data-to-MC-simulations comparisons of 〈P 〉(phard

) for the response, and of RMS2(phard

) and

RMS

⊥(phard

) 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

on Emiss

, the exclusive Z → µµ selection with Njet = 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. phard

= pZ

as shown in Fig. 12(a).

Page 34

> [GeV]

Powheg+Pythia MC

MadGraph+Pythia MC

Data 2015

Data uncertainty

ATLAS

μμ→

-1

= 13 TeV, 3.2 fb

0 Jets

[GeV]

hard

10 20 30

40 50 60

70 80 90 100

MC/Data

0.8

0.9

1.1

1.2

(a)

[GeV

RMS

100

120

140

Powheg+Pythia MC

MadGraph+Pythia MC

Data 2015

Data uncertainty

ATLAS

μμ→

-1

= 13 TeV, 3.2 fb

0 Jets

[GeV]

hard

10 20 30

40 50 60

70 80 90 100

MC/Data

0.8

0.9

1.1

1.2

(b)

[GeV

RMS

Powheg+Pythia MC

MadGraph+Pythia MC

Data 2015

Data uncertainty

ATLAS

μμ→

-1

= 13 TeV, 3.2 fb

0 Jets

[GeV]

hard

10 20 30

40 50 60

70 80 90 100

MC/Data

0.8

0.9

1.1

1.2

(c)

Figure 13: The (a) average value of the longitudinal projection 〈P 〉 and the (b) variance RMS

of the longitudinal

projection P of psoft

onto phard

for Z → µµ event with Njet = 0, for data and two different MC simulations, shown

as a function of phard

. The variance RMS

⊥ of the perpendicular projection P⊥ is shown in (c) for the same event

samples. The shaded band indicates the systematic uncertainties derived as described in the text.

The uncertainties are determined by comparing P and P⊥ spectra from data and MC simulations, in bins

of phard

. 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 Emiss,soft

Page 35

relative to the direction of phard

. To account for differences in response between data and simulation, the

longitudinal component of Emiss,soft

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.

7.2 Systematic uncertainties in Emiss

response and resolution

The result for the systematic uncertainty of the Emiss

scale, determined as discussed in the previous section,

is summarised in Fig. 13. The average longitudinal projection of psoft

onto phard

, 〈P 〉, as a function of

phard

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 phard

range.

The systematic uncertainty for the Emiss

resolution is extracted from the variances of the parallel (RMS

)

and perpendicular (RMS

⊥) projections of Emiss

onto phard

defined in Section 7.1.2. Figure 13(b) shows

the phard

dependence of RMS

measured for the exclusive Z → µµ sample (Njet = 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

(RMS2)MC/(RMS2)data is shown as a function of phard

. The results of the evaluation of the variances

RMS

⊥ of the perpendicular projections as a function of phard

are shown in Fig. 13(c), together with the

resulting phard

dependence of the ratio (RMS

⊥)MC/(RMS2

⊥)data. The systematic uncertainties of the data

cover all differences to MC simulations.

8 Missing transverse momentum reconstruction variants

8.1 Calorimeter-based Emiss

The Emiss

soft term from the calorimeter E

miss,soft,calo

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 E

miss,soft,calo

is calculated from topo-clusters calibrated at the LCW

scale. Only topo-clusters with a calibrated energy ELCW

clus

> 0, not contributing to the reconstruction of

the hard objects used to calculate the hard term given in Eq. (6), are considered for E

miss,soft,calo

. In

addition, topo-clusters that are formed at the same location as the hard object signals are not considered

for E

miss,soft,calo

even if their signals are not directly contributing to the reconstruction of the hard objects.

The fully reconstructed Emiss

using E

miss,soft,calo

is E

miss,calo

Page 36

Compared to the reference Emiss

and ΣET, E

miss,calo

and ΣEcalo

have an enhanced dependence on pile-

up, mostly introduced by the soft term. To partly compensate for the irreducible contribution of pT-

flow reconstructed from topo-clusters generated by pile-up to E

miss,calo

, 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 pT > 20GeV. The contribution

of these jets to E

miss,calo

and ΣEcalo

, defined in terms of momentum components (px, py), depends on the

overlap with already accepted reconstructed particles,

(px, py) =

{ (0, 0)

κE ≥ 50% (large overlap)

(1 − κE)×(pjet

x , pjet

y ) κE < 50% (small or no overlap)

(14)

The overlap fraction κE is given in Eq. (8). Jets with κE ≥ 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

reconstruction. The transverse momentum contribution of groups of clusters representing a jet-like pT-

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-pT threshold applied in Emiss

reconstruction, is reduced if all jets and jet fragments, including those

from pile-up, are included.

8.2 Emiss

from tracks

The reference track-based soft term E

miss,soft

is largely insensitive to pile-up, as indicated by the dependence

of the Emiss

resolution RMS

miss

x(y) on NPV in the exclusive Z → µµ sample (Njet = 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 Emiss

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 (pmiss

) all jets and reconstructed particles are ignored, i.e. the pmiss

reconstruction

does not include any calorimeter or MS signals. The pmiss

resolution is then inherently immune to pile-up,

while the pmiss

response is low as all neutral pT-flow in |η| < 2.5 as well as all pT-flow outside of this

region is excluded.

8.3 Performance evaluations for Emiss

variants

The main motivation to study Emiss

-reconstruction variants is to improve some combination of the

Emiss

resolution, scale, and stability against pile-up. As with the composition of objects entering Emiss

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

Emiss,calo

and pmiss

to the corresponding measurements using the reference Emiss

illustrates their principal

features for the Z → µµ and t¯t production final state.

Page 37

Figure 14: Comparison of the reference Emiss

resolution with the resolutions of the track-only-based variant pmiss

described in Section 8.2, and the reconstruction variant E

miss,calo

employing a calorimeter-based soft term, as

discussed in Section 8.1. The resolutions are determined as described in Section 6.2.3 and shown as a function of

the ΣET. For consistency, for all three variants, the ΣET value is taken from Emiss

8.3.1 Comparisons of Emiss

resolution

Figure 14 compares the E

miss,calo

and pmiss

resolutions with the one obtained from the reference Emiss

, for

the inclusive Z → µµ sample in data. Each is shown as a function of ΣET corresponding to the reference

Emiss

, giving an estimate of the total hard-scatter activity. The low-ΣET region is dominated by events

with Njet = 0, where the contribution of Emiss,soft,calo

in E

miss,calo

yields a poorer resolution than for Emiss

and where Emiss

and pmiss

have identical performance. The high-ΣET region is dominated by events with

higher jet multiplicity, where pmiss

resolution is degraded relative to the reference Emiss

by the incomplete

measurement of jets.

Figure 15(a) compares the E

miss,calo

and pmiss

resolution as functions of the pile-up activity measured by

NPV, with the one obtained from the reference Emiss

for the exclusive Z → µµ samples with Njet = 0

in data. The E

miss,calo

resolution is dominated by pile-up and shows significantly degraded performance

relative to pmiss

and the reference Emiss

. The exclusive use of only tracks from the hard-scatter vertex for

both pmiss

and Emiss

yields the same stability against pile-up.

In events with jet activity, the degraded pmiss

resolution is observable, especially outside the region of

highest pile-up activity, as seen in Fig. 15(b) for the Emiss

resolution obtained with the inclusive Z → µµ

sample in data for NPV ≲ 15. This is even more obvious in final states with relatively high jet multiplicity

and genuine missing transverse momentum, like for the t¯t-production sample from MC simulations. As

shown in Fig. 15(c) for this final state, both the reference Emiss

and the calorimeter-based E

miss,calo

have

a significantly better resolution than pmiss

, at the price of some sensitivity to pile-up, which is absent for

pmiss

. The NPV dependence of the resolution is enhanced in E

miss,calo

, due to the increased contribution

from soft calorimeter signals without pile-up suppression at higher NPV.

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(a)

(b)

(c)

Figure 15: Comparison of the reference Emiss

resolution with the resolutions of the track-only-based variant pmiss

described in Section 8.2, and the reconstruction variant E

miss,calo

employing a calorimeter-based soft term, as

discussed in Section 8.1. The resolutions are determined as described in Section 6.2.3 and shown as a function of

the pile-up activity measured in terms of the number of reconstructed vertices NPV for (a) an exclusive Z → µµ

sample without jets with pT > 20 GeV and (b) an inclusive Z → µµ sample, both selected from data. In (c), the

resolution of the Emiss

reconstruction-variants in a final state with significant jet activity and p

T> 0 is compared

using MC simulations of t¯t production.

Page 39

(a)

(b)

(c)

Figure 16: Comparison of the reference Emiss

, the calorimeter-based E

miss,calo

and track-only-based pmiss

response

in an (a) exclusive and an (b) inclusive Z → µµ sample from data. The projections of the respective Emiss

, Emiss,calo

and pmiss

onto the direction of pZ

T , calculated according to Eqs. (9) and (10), are shown as a function of p

T . In

(c), the linearity of the reference Emiss

, E

miss,calo

, and pmiss

scales, calculated according to Eq. (11), is shown as a

function of the true E

miss,true

for the t¯t-production MC simulation sample.

8.3.2 Comparisons of Emiss

scale

Following the description in Section 6.2.1, the Emiss

response is evaluated for the reference Emiss

, E

miss,calo

and pmiss

using the respective projections of Emiss

, Emiss,calo

, and pmiss

onto the direction of pZ

, according

Page 40

to Eqs. (9) and (10). Figure 16(a) shows the average projection as a function of p