Pile-up Correction in Missing Transverse Momentum Reconstruction in the ATLAS Experiment in Proton-Proton Collisions at √

ATLAS-CONF-2014-019 19/05/2014

ATLAS NOTE

ATLAS-CONF-2014-019

May 19, 2014

Pile-up Correction in Missing Transverse Momentum Reconstruction in the ATLAS Experiment in Proton-Proton Collisions at √

s = 8 TeV

The ATLAS Collaboration

Abstract

The ATLAS experiment recorded proton–proton collision data at

√

s =

8 TeV at the LHC in 2012 corresponding to an integrated luminosity of about 20 fb

⁻¹

. The high instanta- neous luminosity achieved (up to 8

·10³³

cm

⁻²

s

⁻¹

), combined with bunch crossings every 50 ns, led to unprecedented backgrounds (pile-up) from additional proton–proton collisions oc- curring at the same bunch crossing as the triggered collision of interest, and from remnants of electronic signals from previous bunch crossings in the detectors. Typical run conditions were characterised by an average of 21 pile-up interactions, increasing to 35 by the end of the data taking. This pile-up led to a significant deterioration of the missing transverse momentum reconstruction performance. Both the hard part of the recorded event, which is comprised of identified leptons, photons, and reconstructed jets, and the soft part contain- ing detector signals from the underlying event, are a

ff

ected by these pile-up contributions.

While the objects contributing to the hard part are fully calibrated and corrected for pile- up, the signals from the ATLAS calorimeters and tracking detectors contributing to the soft part are typically not. Several correction methods for this soft part have been developed in ATLAS to mitigate the effect of pile-up on the missing transverse momentum reconstruc- tion performance. In this note, these methods as well as relevant features of their respective inputs are described. In addition, performance improvements for various final states are evaluated and systematic uncertainties arising from the application of these corrections are presented.

c

Copyright 2014 CERN for the benefit of the ATLAS Collaboration.

Reproduction of this article or parts of it is allowed as specified in the CC-BY-3.0 license.

1 Introduction

The reconstruction of any proton–proton hard-scatter interaction with the ATLAS [1] detector at the LHC is challenged by the presence of pile-up. This pile-up is introduced by multiple proton–proton interac- tions occurring during the same bunch crossing, and the remnants of electronic signals from previous bunch crossings in the detectors. The high luminosity operation of the LHC in 2012 routinely provided peak luminosities up to 8

·

10

³³

cm

⁻²

s

⁻¹

. This, in combination with the high inelastic proton–proton cross section at

√

s

=

8 TeV, led to run periods with on average

µ =

35 additional proton–proton col- lisions per bunch crossing, and an overall annual average of approximately 21 collisions for 2012 data taking.

Reconstructed kinematic event features and variables like the missing transverse momentum (E

^miss_T

) must be corrected for the contribution of this pile-up, to ensure a physics reconstruction performance comparable to the one achieved at low luminosity (µ

≈

0). While fully calibrated and thus pile-up corrected objects like leptons, photons, and jets provide the hard signal contribution to E

^miss_T

, the soft signals contributing to E

^miss_T

are not corrected a priori. The various methods described in this note primarily address the corrections of this soft-signal contribution.

This note is organised as follows. In Section

2, the relevant features of the ATLAS experiment are

presented and the general challenges associated with E

^miss_T

reconstruction are discussed. In Section

3,

several methods for correcting the soft signal contribution are described, and the corresponding recon- structed quantities used to determine these corrections are shown. The validation of E

^miss_T

reconstruction after applying these pile-up corrections is presented in Section

4. The systematic uncertainties introduced

by the various correction methods are summarised in Section

5. Section6

concludes this note by sum- marising the performance of the pile-up corrections for E

_T^miss

. A glossary of terms is given in Addendum

I, followed by a brief schematic overview of the default signal contributions to

E

_T^miss

in Addendum

II.

A full evaluation of the E

^miss_T

reconstruction performance for ATLAS in 2012 can be found in Ref. [2].

It includes the e

ff

ects of pile-up corrections for various final states, and the full derivation of systematic uncertainties. In this note the focus is on the presentation of the correction methods studied for this data, and the investigation of the expected performance improvements supporting the choices made to obtain the results shown in Ref. [2].

2 Missing transverse momentum reconstruction and pile-up

In this section, the general effects of pile-up on those detector signals that are relevant for E

^miss_T

recon- struction are briefly summarised, together with a brief recall of the basics of E

^miss_T

reconstruction in ATLAS. This is preceded by a short overview of the ATLAS detector and the data and Monte Carlo simulation samples used in this note.

2.1 The ATLAS detector

The ATLAS experiment features a multi-purpose detector system with a forward-backward symmetric cylindrical geometry and a solid angle coverage close to 4π. The detector closest to the proton–proton collision vertex is the inner tracking detector (ID), which covers the pseudorapidity

¹

range

|η|<

2.5. It consists of a silicon pixel detector, a silicon microstrip detector (SCT), and, for

|η| <

2.0, a straw-tube

1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and thez-axis along the beam pipe. Thex-axis points from the IP to the centre of the LHC ring, and they-axis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane,φbeing the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angleθasη=−ln tan(θ/2).

transition radiation tracker (TRT). The ID is surrounded by a thin superconducting solenoid generating a 2 T axial magnetic field.

A highly granular electromagnetic lead/liquid-argon (LAr) sampling calorimeter provides precision energy measurements for photons and electrons up to

|η| <

3.2. Hadronic coverage is provided by an iron

/

scintillator-tile calorimeter within

|η| <

1.7, and by a copper

/

LAr calorimeter in the end-cap region 1.5

< |η|<

3.2. The forward calorimeter employs copper/LAr and tungsten/LAr devices for both electromagnetic and hadronic energy measurements up to

|η|<

4.9.

The muon spectrometer surrounds the calorimeters. It consists of three large air-core superconduct- ing toroid systems, with precision tracking chambers providing accurate muon momentum measurements up to

|η|<

2.7. Additional detectors for muon triggering are incorporated in the region

|η|<

2.4.

2.2 Collision data

ATLAS collected proton–proton collision data during 2012 corresponding to an integrated luminosity of about 20 fb

⁻¹

. Data used for the development of soft-signal pile-up correction techniques and the validation and performance evaluations include minimum bias events, final states without genuine

²

E

_T^miss

, such as Z

→

e

⁺

e

⁻

(µ

⁺µ⁻

), and events with genuine E

_T^miss

, like W

→

e(µ)ν

_e(µ)

. All data events are required to pass the ATLAS data quality selection. This suppresses instrumental contributions to E

_T^miss

and avoids the inclusion of non-collision events such as cosmic-rays and beam-induced backgrounds in the samples.

The event samples above are collected by triggers having the lowest sensitivity to the actual pile- up conditions during data taking. Minimum bias events are extracted from a zero-bias trigger stream collecting events weighted by luminosity, without a detector signal requirement. In the o

ffl

ine event selection, the minimum bias events are required to have at least one reconstructed primary vertex with at least five good tracks with p

_T >

500 MeV. The single lepton triggers are used to collect the samples with W and Z bosons. These are stable against pile-up, as they are either based on tracks (muon final states) or on very dense and compact calorimeter signals with a very small catchment area for pile-up (electron final states). A requirement of at least one reconstructed hard-scatter vertex with at least three tracks with p

_T >

500 MeV is imposed on all events in the samples used.

2.3 Monte Carlo simulations

Monte Carlo (MC) simulated events modelling the final states considered in this analysis are generated to a stable particle level and processed using a G

eant

4 [3] based full simulation of the ATLAS detector.

To model pile-up, simulated minimum bias events are superimposed onto the simulated signal events.

For each event, an average number of interactions

µ

is selected from the distribution observed in data in 2012. The actual number of overlaid minimum bias events is then selected from a Poisson distribution around

µ. The eff

ects of pile-up interactions from previous bunch crossings are also taken into account, including a complete modelling of the corresponding calorimeter signal history discussed in Section

2.4.

The proton bunch position in the LHC bunch train and the bunch-to-bunch proton intensity variations are sources of response variations especially in the ATLAS LAr calorimeter [4]. In 2012, the LAr signals are corrected for this in data and MC simulations, with small remaining effects. Therefore it is not required to have a detailed modelling of the varying LHC bunch structure and fill patterns in the simulation.

PYTHIA8 [5] with the MSTW2008 leading order (LO) parton density function (PDF) [6] and the ATLAS AM2 [7] underlying event and multiple parton interaction tune is used to model the minimum bias collisions. For Z and W production the next-to-leading order (NLO) POWHEG [8] model is used,

2GenuineE_T^missis true missing transverse momentum generated by non-interacting particles, for example by neutrinos with transverse momentum p^ν_T (E_T^miss,True = p^ν_T). Accordingly, proton–proton interactions without genuineE^miss_T have a final state exclusively comprising of fully detectable particles.

with the final state partons showered by PYTHIA8 using the CT10 NLO PDF [9] and the ATLAS AU2 tune [10].

2.4 Pile-up in the ATLAS calorimeters

The ATLAS calorimeters and their read-out systems are designed to cope with the LHC bunch cross- ing frequency and the resulting high proton–proton interaction rate. While the particular emphasis of all employed detector technologies is on signal stability and operational survival in this high radiation environment, the effect of signal pile-up is suppressed to a large degree by signal shaping. In particular the LAr calorimeters, with charge collection times around 400 ns, feature shaping amplifiers that provide a bi-polar pulse with a net zero integral. The basic calorimeter signal extraction algorithm, on the other hand, clusters calorimeter cell signals into three-dimensional signal objects following spatial signal sig- nificance patterns. This topological clustering is very e

ff

ective in suppressing noise but tends to increase the likelihood of survival for pile-up signals in the presence of large signals from the hard-scatter process.

Relevant details of these features are discussed in Ref. [11].

There are two qualitatively di

ff

erent pile-up signal contributions in ATLAS. First, the additional proton–proton interactions occurring in the same bunch crossing as the collision of interest lead to in- time pile-up signal contributions. The principal experimental observable sensitive to the actual number of additional interactions is the number of primary vertices N

_PV

reconstructed by the ATLAS ID.

Second, due to the long charge collection time and the specific choice of signal shaping in the LAr calorimeters, the calorimeter signal is sensitive to between 9 and 15 bunch crossings at 50 ns LHC bunch crossing intervals, depending on the calorimeter region. Due to the bi-polar LAr pulse shape, the integral e

ff

ect of this out-of-time pile-up is the reduction of the contribution from the in-time pile-up. However, residual contributions are observable in the calorimeter signal. The average number of collisions

µ

is a sensitive observable for the signal e

ff

ects introduced by out-of-time pile-up. It is reconstructed in a time window of about 60 s around the recorded event from the dedicated forward detectors providing the luminosity measurements in ATLAS [12]:

µ=

L

×σ_inel

N

_bunch×

f

_LHC.

(1)

Here L is the measured instantaneous luminosity,

σ_inel

is the total inelastic proton–proton cross section, N

_bunch

is the number of bunches in LHC, and f

_LHC

is the LHC revolution frequency.

The central hadronic scintillating tile calorimeter in ATLAS has a faster signal collection time, thus is much less sensitive to the bunch-crossing signal history. Also, its location behind the electromagnetic calorimeters shields it against the low energy particles di

ff

usely scattered by the predominantly soft additional proton–proton interactions. Thus the e

ff

ect of out-of-time pile-up on the signal in the tile calorimeter is generally small [13].

2.5 Missing transverse momentum reconstruction

The missing transverse momentum is an event-level observable with two principal contributions man- ifested in a hard term and a soft term. The hard term (E

miss,HardTerm

T

) represents the hard-event signal contribution comprised of selected fully reconstructed particles and jets. The soft term (E

miss,SoftTerm

T

)

is reconstructed from the soft-event signal contribution. The definitions of both the hard and the soft

event in the context of E

^miss_T

reconstruction are given in Addendum

I. In addition to

E

_T^miss

, which is the

magnitude of a vector with components E

^miss_x(y)

in the transverse event plane, the scalar sum of transverse

momenta

Σ

E

_T

is reconstructed as a measure of the total activity from the hard-scatter collision. The

observables are defined as

E

^miss_x(y) =

E

miss,HardTerm

x(y) +

E

miss,SoftTerm

x(y) =− X

hard objects

p

_x(y)− X

soft signals

p

_x(y),

(2)

E^miss_T =

E

^miss_x ,

E

^miss_y

,

(3)

E

^miss_T = E^miss_T

= q

(E

^missx

)

²+

(E

^miss_y

)

²,

(4)

Σ

E

_T= Σ

E

^HardTerm_T + Σ

E

^SoftTerm_T = X

hard objects

p

_T+ X

soft signals

p

_T.

(5)

Further details of the reconstruction of E

miss,HardTerm

T

and E

miss,SoftTerm

T

are discussed in Refs. [2,

14].

An overview of the default E

_T^miss

composition and the corresponding reconstruction sequence is given in Addendum

II, in TableA

for the hard and in Table

B

for the soft term contributions.

The important point for the studies presented here is that all contributions to E

miss,HardTerm

T

are already

corrected for pile-up, and are only considered when reconstructing E

_T^miss

if the corresponding signal quality and kinematic selections are passed. One exception is the E

_T^miss

contribution from hard jets with 20 GeV

<

p

_T <

50 GeV after pile-up corrections. In this case an additional condition is applied, requiring the contributing jets to be associated with the primary vertex (for details, see discussion in Section

3.2).

Pile-up contributions to signals entering E

miss,SoftTerm

T

, on the other hand, are not a priori corrected.

Such a correction is not straight forward because E

miss,SoftTerm

T

is reconstructed from tracks and calorime- ter cell clusters signals not associated with the hard objects entering the E

miss,HardTerm

T

reconstruction.

³

While the track p

_T

provides a well measured kinematic representation of a charged particle above the reconstruction threshold, the cluster signals lack a universal calibration reference (i.e., a universal in-situ kinematic constraint or MC truth reference).

The transverse momentum of neutral particles, and all particles outside of the ATLAS ID acceptance

|η|<

2.5, is reconstructed from the calorimeter cell cluster signals. To first order these signals represent the locally deposited energy, together with some compensation for signal losses due to clustering cuts and for energy losses in inactive material close to their location [15]. Even when not considering the signal modulations introduced by out-of-time pile-up in the ATLAS LAr calorimeters, these signals are at best only a fair representation of the true p

_T

of incoming particles, as shown in Ref. [16]. The larger context provided by the full E

_T^miss

reconstruction provides a basis for the development and validation of pile-up correction techniques for E

miss,SoftTerm

T

. The expectations for the “true” overall E

_T^miss

for selected final states in both data and MC simulations establish calibration references for these techniques.

3 Pile-up suppression in E

^miss

T

reconstruction

Pile-up has a significant effect on the reconstruction of E

^miss_T

and

Σ

E

_T

. This can be seen from the example in Figure

1, which shows the average hΣ

E

_Ti

and

hE_T^missi

increasing with in-time pile-up in different detector regions for Z

→ µµ

events without jets with p

_T >

20 GeV. The muon contribution to E

^miss_T

and

Σ

E

_T

, which is limited to the regions

|η| <

2.7, is independent of N

_PV

. It is indicated by an offset

hΣ

E

_Ti(NPV =

1)

>

0 in Figure

1(a). The offset is largest within |η| <

1.5, reduced due to limited muon detector coverage and the reduced muon p

_T

flow at higher

η

in 1.5

< |η| <

3.2, and vanishes for 3.2

<|η|<

4.9 due to lack of muon detector coverage. The di

ff

erent shapes of

hΣ

E

_Ti(N_PV

) in the three

η

3The reconstructed tracks and calorimeter cell clusters contributing toEmiss,SoftTerm

T are protected from overlapping with each other and thus form an unambiguous signal for the soft part of the event.

regions reflect features of the ATLAS calorimeters, in particular with respect to the signal formation in the presence of pile-up (see Section

3.3.1

for related discussions).

The dependence of

hE^miss_T i

from the various detector regions on N

_PV

shown in Figure

1(b)

is biased by the incomplete capture of the hadronic recoil balancing the Z-boson p

_T

in any of the detector re- gions. This leads to a significant o

ff

set in the regional

hE_T^missi

reconstructed from calorimeter signals in the regions

|η| <

1.5 and 1.5

< |η| <

3.2, respectively. This offset is to first order independent of N

_PV

. Increasing fluctuations in the calorimeter response due to increasing pile-up, together with second order e

ff

ects related to the increasing survival of valid contributions from the hadronic recoil with increasing N

_PV

, lead to the observed N

_PV

dependence of the regional

hE_T^missi

. The non-linear rise of

hE^miss_T i

cal- culated from calorimeter signals from the region 3.2

< |η| <

4.9 with increasing N

_PV

is dominated by resolution e

ff

ects. In this region there are only insignificant contributions to the hadronic recoil of the more centrally produced Z bosons.

The major challenge in developing pile-up suppression methods for E

_T^miss

reconstruction lies in the correction of the soft-event contribution measured by E

miss,SoftTerm

T

. The soft event associated with the hard scatter can have a significant contribution to the E

^miss_T

reconstruction performance, especially to resolution and linearity in final states where E

miss,SoftTerm

T

has a large contribution to E

_T^miss

. The additional di

ff

use transverse momentum flow from pile-up adds significant fluctuations to E

miss,SoftTerm

T

. It thus

deteriorates the E

_T^miss

resolution and a

ff

ects the E

^miss_T

scale, as those are coupled by the E

^miss_T

observation bias.

⁴

Therefore, the pile-up contributions require corrections, especially in low multiplicity final states with significant E

miss,SoftTerm

T

.

Unfortunately, the reconstructed p

_T

flow patterns, especially from in-time pile-up, are very similar to the soft event p

_T

flow associated with the hard-scatter process. This limits the spectrum of useful cor- rections to three approaches. First, the pile-up corrections can be based on signals which can safely be associated with the hard-scatter vertex of the event. For the soft event, this is so far only possible for re- constructed charged particle tracks. Second, a more stochastic approach based on transverse momentum densities from the soft event, as measured using the calorimeter, can be used as a scale for suppress- ing contributions to E

^miss_T

reconstruction. Finally, a combination of the correction using the transverse momentum density and the track-based filtering can be applied. These three approaches are reflected in the four methods – one track-based, one calorimeter-based, and two configurations for the combined approach – for pile-up suppression presented in this note.

3.1 Methods considered for pile-up suppression

As stated above, the pile-up corrections considered here are predominantly applied to the soft term component of E

_T^miss

and

Σ

E

_T

. The exception is the method that modifies the hard term by requiring jets to be associated with the hard scatter (see description below).

As mentioned in Section

2.5, the soft event reconstructed in ATLAS consists of charged-particle

tracks and calorimeter cell clusters which are not associated with fully reconstructed hard objects in the event. Any spatial signal overlap between clusters and tracks is removed by giving preference to the track momentum and direction, if the nominal transverse momentum resolution of the track is better than the corresponding resolution for the cluster. This is the case for tracks with p

_T<

100 GeV. The approach reflects the higher reconstruction quality of the track kinematics, especially for the lower-p

T

tracks found in the soft event. The details of the overlap resolution between clusters and tracks are described in Refs.

[2,

14]. The following summary lists the correction methods applied to suppress pile-up contributions to

E

^miss_T

and

Σ

E

_T

.

4By construction,E_T^miss>0 even for final states without genuine missing transverse momentum in the presence of a finite resolution, as indicated in Eq. (4).

NPV

0 5 10 15 20 25 30 35

[GeV]〉T EΣ〈

0 100 200 300 400 500 600 700

|<1.5 η

|

|<3.2 η 1.5<|

|<4.9 η 3.2<|

ATLAS Preliminary = 8 TeV s

-1 Ldt=20 fb

∫

Data 2012 > 20 GeV

T

0 jets p µ µ

→ Z

(a)hΣETi(NPV)

NPV

0 5 10 15 20 25 30 35

[GeV]〉miss TE〈

0 5 10 15 20 25 30 35 40

|<1.5 η

|

|<3.2 η 1.5<|

|<4.9 η 3.2<|

ATLAS Preliminary = 8 TeV s

-1 Ldt=20 fb

∫

Data 2012 > 20 GeV

T

0 jets p µ µ

→ Z

(b)hE^miss_T i(NPV)

Figure 1: Effect of pile-up on

(a)

the average

hΣ

E

_Ti

and

(b)

the average

hE^miss_T i, reconstructed in

Z

→µµ

events without jets with p

_T>

20 GeV. Both are measured in data in terms of N

_PV

, for di

ff

erent ranges of

η. No pile-up corrections are applied to the

E

^miss_T

and

Σ

E

_T

soft terms of the data shown.

Tracking-based pile-up corrections (STVF and JVF): The “Soft-Term Vertex-Fraction” (STVF)

method employs the ratio of the (scalar) sum of soft-event track- p

_T

associated with the hard- scatter vertex to the sum of all soft-event track-p

T

in the event. This ratio is used to scale all soft-event contributions to E

^miss_T

and

Σ

E

_T

in a given event. In addition, the “Jet Vertex-Fraction”

(JVF) [17,

18,19] is used to filter jets contributing to the hard term in

E

_T^miss

and

Σ

E

_T

. It uses a similar ratio as STVF, but is restricted to tracks associated with a given jet. The details of the STVF scaling and the determination of STVF are presented in Section

3.2.1. The JVF-based jet

filter is discussed in Section

3.2.2. An overview on the contributions to

E

^miss_T

and

Σ

E

_T

affected by these corrections is given in Tables

A

and

B

of Addendum

II.

Jet-area-based pile-up suppression (EJA, EJAF, JAF): The common aspect of these methods is the

use of an event-by-event estimator for the transverse momentum density of the soft event. The corresponding p

_T

-thresholds are employed to remove signal contributions from the soft term in E

^miss_T

and

Σ

E

_T

. This is an extension of the pile-up suppression for hard jets suggested in Ref. [17]

and of the corresponding ATLAS implementation [19]. It involves the decomposition of the soft event into soft jets with p

_T ≥

0, with typically two different definitions for these jets: one for the measurement of the transverse momentum density (ρ-jets), and another as a signal base for applying the p

_T

-threshold (filter-jets). The details of this approach and the common aspects of the transverse momentum density determination are described in Section

3.3, and details of theρ-jet

and filter-jet configurations are given in Section

3.4.

1.

EJA:

The “Extrapolated Jet Area” (EJA) method measures the p

_T

-density using the soft event only in the central part of ATLAS (approximately

|η|<

2). This density is then extrapolated to the forward region using p

_T

-flow profiles derived from minimum bias data. Details of the extrapolation are described in Section

3.3.3.

2.

EJAF:

The “Extrapolated Jet Area with Filter” method (EJAF) uses the same approach as EJA to measure the p

_T

-density, including the extrapolation. In addition, a JVF-based selec- tion [19] is applied to the filter-jets.

3.

JAF:

The “Jet Area with Filter” (JAF) method uses a p

_T

-density calculated from the soft-

event signals within

|η|<

4.9 without extrapolation. It also applies a JVF-based selection on

the filter-jets.

3.2 Tracking-based pile-up corrections

Reconstructed charged-particle tracks provide useful handles for correcting pile-up, not only for the soft term of E

^miss_T

, but also for removing jets generated by pile-up from the hard term.

3.2.1 Soft-term vertex-fraction

The tracking-based pile-up correction for the soft term uses charged-particle tracks that are not associ- ated with physics objects (soft-event tracks), but come from either the hard-scatter vertex or any of the reconstructed pile-up vertices. Only tracks with more than six hits in the ATLAS silicon pixel and SCT detectors (combined), or with more than ten hits in the silicon pixel, the SCT, and the TRT (combined), and reconstructed with 500 MeV

<

p

_T <

100 GeV within

|η|<

2.5 are considered for this correction.

The ratio of the (scalar) p

_T

-sum of all soft-event tracks from the hard-scatter vertex V

_HS

to that from all k

=

1

. . .

N

_PV

primary vertices V

_k

(including V

_HS

) provides a useful measure of the pile-up activity within an event:

STVF

=

PN_trk(VHS)

i=1

p

^trk_T,i

(V

_HS

)

PN_PV

k=1

PN_trk(Vk)

i=1

p

^trk_T,i

(V

k

)

.

(6)

Here p

^trk_T,i

(V

k

) is the p

_T

of the soft-event track i coming from vertex V

k

, and N

_trk

(V

k

) is the total number of reconstructed tracks not associated with any hard object from this vertex. Tracks are assigned to a primary vertex requiring a perpendicular impact parameter

|d₀| <

2 mm and a longitudinal impact parameter z

₀

with

|z₀

sin

θ|<

2 mm. Here

θ

is the polar angle of the track.

A track is considered to be associated with a hard object when (a) it is the source of the kinematics of a reconstructed particle, (b) it is used for particle identification, or (c) it generally overlaps with calorimeter signals representing the particle. In addition, tracks can be associated by spatial overlap with jets, e.g. for the determination of JVF in Section

3.2.2.

The pile-up correction is then applied by scaling the E

miss,SoftTerm

T

components by STVF, with 0

≤

STVF

≤

1:

E

miss,SoftTerm

x(y),corr =

STVF

·

E

miss,SoftTerm

x(y) ,

(7)

E

miss,SoftTerm

T,corr =

STVF

·

E

miss,SoftTerm

T ,

(8)

Σ

E

^SoftTerm_T,corr =

STVF

·Σ

E

^SoftTerm_T .

(9)

Figure

2

shows the STVF distribution for Z

→µµ

production without and with hard jets (p

T >

20 GeV).

Data and MC simulations are in good agreement when STVF is small, but this agreement deteriorates at larger STVF. This is due to mis-modeling of the track activity in MC simulations when fewer pile- up interactions are present. At low STVF (large pile-up activity) the overall spatial track distribution and the overall track-p

T

spectrum agree more with data due to mixing of many individually simulated interactions in one event. The di

ff

erences between simulated and measured track distributions are more enhanced for individual proton–proton interactions. The corrected E

_T^miss

components are re-summed following Eqs. (2), (4), and (5), but using the scaled E

miss,SoftTerm

x(y),corr

and

Σ

E

^SoftTerm_T,corr

from Eqs. (7) and (9) for the soft term, respectively.

3.2.2 Filtering based on the jet vertex-fraction

Additional performance improvements are achieved by requiring that jets contributing to E

miss,HardTerm T

are associated with the hard-scatter vertex. These jets are already corrected for pile-up, following the

strategies outlined in Ref. [19], but no requirement concerning their vertex association is applied. For

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Events / 0.01

1 10 102

103

104

105

106

Data 2012 µ µ

→ MC Z MC ttbar MC WZ MC ZZ MC WW Ldt=20 fb-1

∫

= 8 TeV s

> 20 GeV 0 jets pT

ATLASPreliminary

〉 STVF weight

0.1 0.2 0.3 0.4 0.5 0.6 0.7 〈0.8 0.9 1

Data / MC 0.750.80.850.90.9511.051.1

(a) No jets withpT>20 GeV

0 0.2 0.4 0.6 0.8 1

Events / 0.01

10 102

103

104

105

µ µ

→ Z

Ldt=20 fb-1

∫

s= 8 TeV ATLAS Preliminary

Data inclusive MC inclusive Data 0 jet MC 0 jet Data at least 1 jet MC at least 1 jet

〉 STVF weight

0 0.2 0.4 0.6 〈0.8 1

Data/MC

0.750.8 0.850.9 0.951 1.051.1

(b) Inclusive and exclusive

Figure 2: Comparison of the soft-term vertex-fraction (STVF), as defined in Eq. (6), in

(a)

for an exclusive Z

→µµ

sample without any jets with p

_T >

20 GeV, and in

(b)

for the inclusive and an another exclusive sample with at least one jet with p

_T>

20 GeV from the same final state.

E

^miss_T

reconstruction, jets not associated with the hard-scatter vertex can be safely interpreted as originat- ing from one of the additional pile-up interactions and are therefore completely excluded.

⁵

This approach avoids generating fake E

^miss_T

when all other contributions, including E

miss,SoftTerm

T

, are corrected for pile- up.

The filter applied to the accepted jets is based on the jet vertex-fraction JVF. It measures the summed p

_T

carried by reconstructed tracks associated with the jet and coming from the hard-scatter vertex V

_HS

relative to the summed p

_T

carried by all tracks associated with the jet. The track-to-jet association is established using the ghost association technique [17,

19].

The JVF reconstruction is very similar to the STVF reconstruction in Eq. (6), only now applied to tracks associated with a given jet instead of the soft event:

JVF

= P^N

jet trk(VHS)

i=1

p

^jet_T,trk,i

(V

HS

)

PN_PV

k=1

P^N

jet trk(Vk)

i=1

p

^jet_T,trk,i

(V

k

)

.

(10)

Here N

_trk^jet

(V

k

) is the number of tracks from vertex V

_k

associated with the jet, and p

^jet_T,trk,i

(V

k

) is the p

_T

of track i associated with vertex V

k

and associated with the jet.

The quantity JVF is assigned jet by jet. It can only be calculated for jets well within the ID acceptance (|η

jet|<

2.4), and for jets with associated tracks:

JVF

=

( −1

no tracks associated with jet

0

. . .

1 all central jets with tracks

.

(11)

Jets within

|η_jet|<

2.4 and with 20 GeV

<

p

_T <

50 GeV are accepted only if JVF

,

0 (weak association with V

_HS

). Otherwise their signals are completely excluded from the E

_T^miss

and

Σ

E

_T

reconstruction. Jets with larger p

_T

or with

|η_jet| >

2.4 always contribute to E

_T^miss

and

Σ

E

_T

. This filter e

ffi

ciently selects jets from the hard scatter, while providing significant rejection of jets produced by pile-up collisions [19].

The jet contribution to E

miss,HardTerm

T

is re-summed using only the jets passing the JVF-based filter.

5The calorimeter signals associated with these jets are completely removed from the final state signals extracted forE^miss_T . Specifically, they are not added to the soft term ofE_T^miss.

3.3 Jet-area-based method

The track-based pile-up correction discussed in the previous section has the advantage of using very clean and stable measures from the central detector region to scale E

miss,SoftTerm

T

. However, it relies on the correlation between the central and forward p

_T

-flow, and the identification of the actual hard-scatter vertex in a given event. To use more direct measures of the p

_T

-flow across the full ATLAS detector acceptance (|η|

<

4.9), an alternative approach exploiting calorimeter signals from the soft event was developed. It is based on the p

_T

-density of the soft event, in a variation of the pile-up suppression strategy suggested in Ref. [17] and its application to jets in ATLAS discussed in Ref. [19].

3.3.1 Determination of the transverse momentum density

In the method outlined in Ref. [17], all particles within the full detector acceptance are clustered into narrow jets using a recursive recombination algorithm like k

_t

[20,

21] or Cambridge-Aachen [22, 23],

both with small (e.g., R

=

0.4) distance parameters. All jets with p

_T ≥

0 are formed and their catchment (active) area A

_jet

[24] is calculated. Here jets with p

_T =

0 are not actually clustered, rather they reflect the partitioning of the area void of signals in the rapidity

/

azimuth (y, φ) plane (

∆y×∆φ ≈

10

·

2π for an approximate

y-range of|y| <

5 in ATLAS) after all jets with p

_T >

0 are removed. The number of p

_T =

0 jets is this area divided by the most probable jet area A

_jet

(p

T =

0)

≈ πR²/2 for the

k

t

algorithm, if no particles are present (active ghost area [24]). The calculation of A

_jet

allows the measurement of a transverse momentum density

ρjet,i

for any jet i with p

^jet_T,i

and A

_jet,i

,

ρjet,i =

p

^jet_T,i

A

_jet,i .

(12)

The median p

_T

-density

ρ^med_evt

for all N

_jets

found within a given range

⁶η_min< η_jet < η_max

can be calculated as

ρ^med_evt =

median

n ρjet,io

for i

=

1

. . .

N

_jets

in

η_min< η_jet< η_max.

(13) The evaluation range [η

_min, η_max

] for

ρ^med_evt

can be the full detector acceptance or any restricted region of sufficient size. The use of the median

ρ^med_evt

in any given

η-region emphasises the contribution of the

soft-event signals to the event p

_T

-density, which is most sensitive to pile-up.

In the context of a pile-up correction for E

miss,SoftTerm

T

and

Σ

E

^SoftTerm_T

, only soft-event signals are used to build the

ρ-jets. This results in a slightly lowerρ^med_evt

than using all signals in the event for sparsely populated final states, but avoids biases in

ρ^med_evt

introduced by the larger signals from hard objects in hard-scatter final states with higher multiplicities. The contributions to E

miss,SoftTerm

T

from the hard-scatter vertex as well as from pile-up are typically generated by smaller signals. The lower density estimate

ρ^med_evt

therefore provides a more appropriate scale to evaluate these signals with respect to their likelihood to be generated by pile-up, as it avoids excessive losses of valid soft contributions from the hard-scatter interaction.

Studies of pile-up suppression for jets in ATLAS found that

ρ^med_evt

is an appropriate estimator of the in- time pile-up activity. It is also sensitive to the out-of-time pile-up contribution, especially if determined using the region

|η| <

2 [19]. Including the

|η| >

2 region into the

ρ^med_evt

reconstruction yields a smaller estimate of the pile-up activity than that obtained from the central region. This is mostly due to the particular geometry of the ATLAS calorimeters and their cluster reconstruction algorithms.

The readout granularity in the forward regions of the calorimeter system is significantly reduced, leading to a more sparsely populated event plane in terms of kinematic four-vectors reconstructed from

6ρ-jets and filter-jets are formed in (y, φ) space, whileρ^med_evt is calculated using theρ-jets pointing to a given detector region specified in terms ofη. This relates regional detector signal characteristics with the reconstructedρ^med_evt .

the calorimeter signals. The lateral distribution of the incoming particle energy over a larger number of cells by electromagnetic or hadronic showers leads to an inadvertently increased merging of several particle showers into the same group of cells. This reduces the efficiency of the topological cell-clustering algorithm in the reconstruction of the incoming particle-flow patterns. The clustering algorithm still needs to be applied in the forward region to reduce local signal fluctuations to acceptable levels, but it inadvertently accumulates the calorimeter signals into only a few kinematic four-vectors.

Extending the use of narrow k

t

-jets with p

_T ≥

0 as

ρ-jets to these sparsely populated signal regions

increases the number of

ρ-jets withρ_jet=

0 contributing to

ρ^med_evt

. Consequently,

ρ^med_evt

for the whole event decreases significantly, in some events down to

ρ^med_evt =

0. While some decrease is expected from the lower p

_T

-densities generated by the particle flow at higher

y

[25], the observed drop is much steeper due to the instrumental e

ff

ects. It can be moderated by increasing the

ρ-jet size, therefore increasing the

signal catchment area. This reduces the area void of signals, decreases the number of

ρ-jets withρ_jet=

0, and leads to a larger and more appropriate

⁷ρ^med_evt

. The specific choices of

ρ-jet sizes used for the studies

presented in this note are discussed in Section

3.4.

3.3.2 Application of the jet-area-based filter

The pile-up corrections based on the jet area implemented for E

miss,SoftTerm

T

employ both

ρ-jets and

filter-jets built from the soft-event tracks and calorimeter cell clusters with the k

t

algorithm implemented in FastJet [25,

27]. The contribution of the

N

_filter-jet

filter-jets (with transverse momentum p

^filter-jet_T

, area A

^filter-jet

, and at direction

η^filter-jet

) is defined as

E

miss,SoftTerm

x(y) =−

N_filter-jet

X

i=1

p

^jet_x(y),i,

(14)

and, with p

^jet_T,i =|

( p

^jet_x,i,

p

^jet_y,i

)

|

, the following filter applied:

p

^jet_T,i=











0 p

^filter-jet_T,i < ρ^med_evt

(η

^filter-jet_i

)

·

A

^filter-jet_i

p

^filter-jet_T,i −ρ^med_evt

(η

^filter-jet_i

)

·

A

^filter-jet_i

p

^filter-jet_T,i ≥ρ^med_evt

(η

^filter-jet_i

)

·

A

^filter-jet_i

.

(15)

The median transverse momentum density

ρ^med_evt

(η) is determined from

ρ-jets, with the various config-

urations described in Section

3.4. To avoid the already discussed occupancy issues for |η| >

2, it is determined event by event within

|η|<

2, and then extrapolated to higher

η.

3.3.3 Extrapolation of the transverse momentum density into the forward regions

The extrapolation function is measured with minimum bias events using a sliding window of total width

∆η=

1.6. The mean

hp_Ti(η) at any directionη∈

[−5, 5] is the average of the event-by-event summed p

_T

from calorimeter cell clusters located inside this window (η

−∆η/2, η+ ∆η/2).⁸

This p

_T

is reconstructed from the cluster signals after the application of the local hadronic calibration [15,

28]. The window is

moved in small steps

δη =

0.1, and the average p

_T

-sum is determined at each new

η

position. This procedure generates smooth density profiles with a typical correlation length of

∆η/2, and avoids biases

due to the use of the median.

7ThepT-density generated by the underlying event in proton–proton collisions at√

s =7 TeV was measured by ATLAS [26]. Extrapolating this measurement to √

s=8 TeV yieldsρ^med_evt up to 2 GeV per unit area in (y, φ)-space.

8The sliding window does not exceed the|η|<4.9 boundary of ATLAS. If the absolute distance betweenηand the lower or upper boundary is smaller than∆η/2, the total window size is reduced accordingly. The minimum window width is slightly less than∆η/2 at the boundary. This avoids the possibly large fluctuations introduced by very small integration areas at the boundaries.

The average amount of energy scattered into the

∆η

window at a given position

η

by the minimum bias events depends on the number of proton–proton collisions in the recorded event. The corresponding calorimeter signal is in addition affected by the out-of-time pile-up (see Section

2.4). Thus, hp_Ti

(η) depends on both the in-time and out-of-time pile-up, and must be determined as a function of N

_PV

and

µ.

This is done by collecting

hp_Ti

profiles in bins of N

_PV

(width

∆

N

_PV =

1) and

µ

(

∆µ=

2) and converting them to average density profiles

hρi

(η, N

_PV, µ).

As

ρ^med_evt

determined in the central region is a sensitive event-by-event estimator of the pile-up signal activity, the

hρi(η,

N

_PV, µ) profiles have been normalised such that

P

^ρ

(η, N

_PV, µ)= hρi(η,

N

_PV, µ)

hρi_central

(N

_PV, µ).

(16)

By calculating the average within

|η| < η_plateau

, where [−η

_plateau,+η_plateau

] defines the range where

ρ^med_evt

is approximately constant for any given (N

PV, µ),

hρi_central

(N

PV, µ)=

1 2η

_plateau

Z ₊ηplateau

−ηplateau

hρi(η,

N

_PV, µ)

dη . (17) The normalisation scale 1/hρi

_central

(N

_PV, µ) in Eq. (16) then only depends on

N

_PV

and

µ. For the nor-

malised profiles this means that P

^ρ

(η, N

_PV, µ) ≈

1 for

|η| < η_plateau

, regardless of the pile-up condition reflected by (N

PV, µ). For simplicity, and supported by experimental observations,

P

^ρ

(η, N

_PV, µ) can

safely be assumed to be symmetric around

η=

0.

The normalised transverse p

_T

-density profile P

^ρ

(η, N

_PV, µ) starts to decrease for |η| > η_plateau

, as expected from the physics and detector effects discussed in Section

3.3.1. The shape of this drop is

well described by two one-sided Gaussian functions with width

σ_center

, and respective means

η_plateau

and

−η_plateau

for the two

η-hemispheres. Beyond the plateau and the Gaussian shaped slopes is a wide base-

line, again following a Gaussian functional form. It is constrained by the measured averaged densities at high

|η|, with a mean ofη=

0, a width

σ_base

, and a peak amplitude

A_base

. The sum of the central (G

_center

) and base (G

_base

) shapes is normalised such that the total amplitude is equal to 1 at

η = ±η_plateau

. This results in a smoothly connected function described by

P

^ρ_fct

(η, N

_PV, µ)=

(

1

|η|< η_plateau

(1

−

G

_base

(η

_plateau

))

·

G

_center

(η)

+

G

_base

(η)

|η| ≥η_plateau .

(18) The Gaussian shapes in P

^ρ_fct

are defined as

G

_center

(η)

=











exp

h

−(η−η_plateau

)

²/(2σ²_center

)

i

η≥η_plateau

exp

h

−(η+η_plateau

)

²/(2σ²_center

)

i

η≤ −η_plateau ,

(19)

G

_base

(η)

= A_base·

exp

h

−η²/(2σ²_base

)

i

.

(20)

Empirical fitting of the functional form P

^ρ_fct

(η, N

_PV, µ) from Eq. (18) to all measured

P

^ρ

(η, N

_PV, µ) shapes

in all available (N

_PV, µ) bins, with a basic polynomial ansatz for the

N

_PV

and

µ

dependencies of the parameters in G

_base

and G

_center

, yields

η_plateau

(N

_PV, µ) =

1.8

,

σ_center

(N

PV, µ) = σ_center

(N

_PV

)

= α₀+α₁

N

_PV+α₂

N

_PV² , A_base

(N

_PV, µ) = A_base

(N

PV

)

= β₀+β₁

N

_PV+β₂

N

_PV² ,

σ_base

(N

_PV, µ) = γ₀

(N

_PV

)

+γ₁

(N

_PV

)

µ+γ₂

(N

_PV

)

µ²

= γ_0,0

1

+γ_0,1

exp(γ

_0,2

N

_PV

)

+γ_0,3

exp(γ

_0,4

N

_PV²

)

+ γ_1,0

1

+γ_1,1

N

_PVµ

+ γ_2,0

1

+γ_2,1

N

_PVµ².

(21)

All

µ-dependence of

P

^ρ_fct

(η, N

_PV, µ) can be collected in σ_base

(N

PV, µ), reflecting that in general the µ-

dependence of the calorimeter signal is largest in the ATLAS forward calorimeters [19], the region which provides the strongest constraint for

σ_base

. The final set of 16 parameters

{η_plateau, αi, βi, γ_i,k}

is universal for the 2012 data-taking period. It was derived from data, and it has been verified that the resulting profiles P

^ρ

(η, N

_PV, µ) agree with MC simulations within the statistical uncertainties. This is expected as

these profiles are dominated by the well simulated detector effects discussed in Section

3.3.1. They are

therefore universal and used for pile-up suppression in both data and MC simulations. The

η,

N

_PV

and

µ

dependent median p

_T

-density is then

ρ^med_evt

(η)

=ρ^med_evt ·

P

^ρ_fct

(η, N

_PV, µ),

(22)

where

ρ^med_evt

is determined as given in Eq. (13), with

η_min = −η_plateau

and

η_max = η_plateau

. It is derived using

ρ-jets with the two diff

erent sizes discussed below. This is expected to be a good representation of the pile-up activity and the e

ff

ect on the soft-event calorimeter signals for any pile-up condition during ATLAS data-taking in 2012. The normalised shapes P

^ρ_fct

(η, N

_PV, µ) for selected pile-up conditions are

shown in Figure

3.

3.4 Pile-up correction configurations using the jet area

To apply pile-up suppression to the soft-event contribution to E

_T^miss

, the E

miss,SoftTerm

T

components are re- summed using only the filter-jets passing the cut in Eq. (15), based on the (possibly extrapolated)

ρ^med_evt

(η).

As the set of filter-jets in a given event represents the measurement of the soft event including pile-up, filter-jets from the set not passing this cut are completely dropped from E

^miss_T

and

Σ

E

_T

reconstruction.

Various configurations for jet area based pile-up corrections are considered in this note:

Extrapolated Jet Area EJA ρ^med_evt

(η

_jet

) is measured and extrapolated as explained in Section

3.3.3. The ρ-jets and filter-jets are identical, and formed with the

k

t

algorithm with R

=

0.4. This particular choice is motivated by previous studies using 2011 ATLAS data [29].

Extrapolated Jet Area Filtered EJAF ρ^med_evt

(η

_jet

) is measured and extrapolated as explained in Section

3.3.3. The ρ-jets and the filter-jets are

k

t

jets with R

=

0.6. After being selected according to Eq. (15), the surviving filter-jets with

|η| <

2.4 are subjected to an additional filter by requiring JVF

>

0.25. The filter-jets passing this cut, and all filter-jets with

|η| >

2.4, then contribute to E

miss,SoftTerm

T

. The larger value for R is used to reduce the number of

ρ-jets with

p

_T =

0 in the central detector region.

Jet Area Filtered JAF ρ^med_evt

(η

_jet

)

= ρ^med_evt

is determined within

|η| <

5 with anti-k

t

jets with R

=

0.8.

In this case, the large jet size is applied to mitigate the detector e

ff

ects on the median transverse momentum density discussed in Section

3.3.1. The

k

t

jet algorithm with R

=

0.4 is used for the filter-jets, which are also subjected to the selection given in Eq. (15). They are then additionally filtered by requiring JVF

>

0.25 for those filter-jets within

|η| <

2.4. The surviving filter-jets, including those with

|η|>

2.4, contribute to E

miss,SoftTerm

T

.

The filter-jets used for defining the pile-up corrected signal contribution to E

miss,SoftTerm

T

do not necessar- ily need to be constructed by the same jet definition (algorithm and algorithm parameters) as the

ρ-jets

used to measure

ρ^med_evt

. Any jet definition using the soft-event signals as input and providing a consistent jet-area measurement can be used.

3.5 Transverse momentum density in data and MC

The median transverse momentum density

ρ^med_evt

is the basic observable for the jet-area-based pile-up cor-

rections of the soft-event contribution to E

_T^miss

. It is measured for the three

ρ-jet sizes (R=

0.4, 0.6, and