Master Thesis - atlas.kek.jp · CHAPTER 1. INTRODUCTION 2 tracking. Hadronic interaction For the...

Master Thesis

Measurement of the material in the ATLAS Inner Detector usinghadronic interactions for an improvement in the track reconstruction

Department of Physics, Tokyo Institute of Technology

Tsubasa Kanai

March 7, 2013

Abstract

The ATLAS is a high energy physics experiment at the Large Hadron Collider (LHC). Themain purpose of this experiment is a discovery of the new particles and new phenomena. Inthe experiment, the inner detector plays a crucial role in the track reconstruction of chargedparticles, and it is essential to reconstruct tracks precisely since the accuracy of the trackreconstruction strongly affects physics results. Since particles passing through the detectorare affected by the material, a precise description of the material in the detector is requiredfor the Monte Carlo simulation to obtain a good agreement in tracking between the data fromthe detector and the simulation. However, it is hardly possible to put an exact amount of thematerials in the simulation just from the design in the engineering point of view, thus data-driven method is adopted for the measurement of the detector materials. Although photonconversions are traditionally used for the material measurement, the method using hadronicinteractions is adopted for this analysis, and comparison of measured material in the innerdetector between data and simulation is performed.

The data used in this analysis were collected in March-June 2010 in proton-proton col-lisions at a center-of-mass energy of 7 TeV by the ATLAS detector. In this period, theintegrated luminosity was 19 nb−1. Since the fake vertices accidentally reconstructed fromthe irrelevant tracks are expected to increase in recent high-luminosity runs, these low lumi-nosity runs are intentionally used to retain the high purity of the reconstructed secondaryvertices.

The secondary vertices, which are decay points of primary particles generated in the colli-sions, are reconstructed from the secondary track candidates that are expected to emerge fromthe hadronic interactions with the detector material. Hence, it is necessary to reconstructmany secondary tracks which started at the points away from the proton-proton collisionpoints. However, the standard reconstruction system in the ATLAS is not optimised fortreating such secondary tracks, thus the retracking technique which retries the track recon-struction with the loose selection criteria is adopted.

The combination of the retracking and the secondary vertex reconstruction provides muchmore hadronic interaction vertices than the past analysis, and the structure of the outer lay-ers in the tracking system becomes clearly visible. On the other hand, as the purity of thereconstructed vertices decreases due to the combination of the irrelevant tracks, the study toimprove the purity after the retracking is also performed. As a result of the analysis, 5-6%material uncertainty is estimated under the current geometry in the simulation, while 10%uncertainty on the amount of the material is applied for any physics analysis.

In addition, the systematic uncertainty on the track reconstruction efficiency is evaluatedin the assumption where an improved description of the material is considered in the sim-ulation, and physics impacts are also investigated with the improved material estimation.This study indicates the possibility that the uncertainties on the jet energy scale and thefragmentation function would decrease by about 30% and 20%, respectively.

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Contents

Abstract ii

1 Introduction 11.1 Importance of the material measurement in the ATLAS inner detector . . . . 11.2 Material measurements using hadronic interactions . . . . . . . . . . . . . . . 11.3 The structure of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 LHC and ATLAS Experiment 42.1 LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 ATLAS Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Physics in the ATLAS Experiment . . . . . . . . . . . . . . . . . . . . 6

3 ATLAS Detector 93.1 Overview of the detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 The Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2.1 Pixel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2.2 SCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2.3 TRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2.4 Material distribution of the inner detector . . . . . . . . . . . . . . . . 16

3.3 Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Track Reconstruction in The ATLAS Inner Detector 214.1 Overview of tracking system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Inside-out track reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.2.1 Space Point creation in the silicon detector . . . . . . . . . . . . . . . 224.2.2 Space Point seeded track finding . . . . . . . . . . . . . . . . . . . . . 234.2.3 Ambiguity solving algorithm . . . . . . . . . . . . . . . . . . . . . . . 244.2.4 TRT extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.3 Outside-in track reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 254.3.1 TRT segment finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.3.2 Back tracking into the silicon detector . . . . . . . . . . . . . . . . . . 26

4.4 The track parameters and the requirements . . . . . . . . . . . . . . . . . . . 264.5 Retracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

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CONTENTS iv

5 Data Samples and Event Selection 295.1 Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.2 Minimum Bias Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295.3 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

6 Secondary Vertex Reconstruction 316.1 Secondary track candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316.2 2-track vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.3 Fake removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.4 Final selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6.4.1 Breakdown of true vertices . . . . . . . . . . . . . . . . . . . . . . . . 336.4.2 Removing backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . 33

6.5 Mapping of hadronic interactions . . . . . . . . . . . . . . . . . . . . . . . . . 37

7 Quality of Secondary Vertex 437.1 Vertex Resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437.2 Purity and efficiency for secondary vertices . . . . . . . . . . . . . . . . . . . 477.3 Study on improvement of purity . . . . . . . . . . . . . . . . . . . . . . . . . 477.4 Study using MC samples with extra material . . . . . . . . . . . . . . . . . . 52

8 Comparison in data and MC 538.1 Correction for primary tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . 538.2 Comparison of vertex yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538.3 pT and η distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

9 Systematic Uncertainty 639.1 Systematics due to selection criteria . . . . . . . . . . . . . . . . . . . . . . . 639.2 The closure test using distorted MC samples . . . . . . . . . . . . . . . . . . 639.3 Total systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

10 Results 6610.1 Numerical Comparison in data and MC . . . . . . . . . . . . . . . . . . . . . 6610.2 Systematic uncertainty on track reconstruction efficiency . . . . . . . . . . . . 6610.3 Areas which profit from the material uncertainty study . . . . . . . . . . . . . 67

11 Conclusion 70

Acknowledgements 71

A Details of Datasets and Software 74A.1 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74A.2 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Chapter 1

Introduction

1.1 Importance of the material measurement in the ATLASinner detector

The ATLAS experiment [1] is an experiment in high energy physics at the world-biggestaccelerator, Large Hadron Collider (LHC) [2], the purposes of which are the discovery ofnew particles such as Higgs Boson as well as new phenomena beyond the Standard Model(SM). The ATLAS detector is composed of several particle detectors: the Inner Detector(ID) plays a crucial role in the track reconstruction of the charged particles, high granularityliquid-argon (LAr) electromagnetic sampling calorimeters measures energy deposits includingtheir positions, the hadronic calorimeters take hold of the hadron showers and the MuonSpectrometer (MS) works on the measurement of the muon tracks which pass through theMS. It is essential to carry out tracking charged particles precisely since those tracks areused in physics analysis and could directly affect the physics results such as the jet energyscale and the fragmentation function. The more precise measurements are needed, the moreaccurate tracking is essential. The passage of the particles is affected by the material in thedetectors and support structures as a result of the multiple scatterings, the electro-magneticinteractions and the hadronic interactions. Therefore, a good description of the material inthe detectors are needed in the simulation to get a good agreement of tracking performancebetween the data from the detector and the Monte-Carlo (MC) simulation. However, it ishardly possible to put an exact amount of the materials in the simulation just from the designin the engineering point of view. Therefore, data-driven method is adopted for the precisemeasurement of the detector materials.

1.2 Material measurements using hadronic interactions

Photon conversions are traditionally used to measure materials in the ATLAS experiments aswell as other experiments in high energy physics [3]. In the ATLAS experiment, there are othermethods for the material measurements with Ks decays [4], SCT extension efficiency [5] andhadronic interactions [6]. Material measurements using hadronic interactions had alreadybeen done in terms of comparison between data and MC, however, there were rooms forimproving a description of the materials and for extending the study in the further outerlayers in the inner detector. In this thesis, these studies are presented by using MC sampleswith distorted material and applying new requirements after using an additional technique of

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CHAPTER 1. INTRODUCTION 2

tracking.

Hadronic interaction

For the inelastic process due to hadronic interactions, interaction length λ can be expressedby:

λ =A

ρNAσinel, (1.1)

where A is atomic weight [g/mole], NA is Avogadro’s number (6.02×1023/mole), ρ is density[g/cm3] and σinel is inelastic cross section [cm2]. The number of interactions, which is countedin this analysis, would be proportional to the number of nucleons which is followed by:

NAρ

A=

1λσinel

. (1.2)

thus it is important that the inelastic cross section σinel is almost independent on momenta ofparticles in GeV scale. Otherwise a correction for the momentum spectrum in the simulationis necessary to match the one in reality before comparing the vertex yields.

Advantage of the material measurement using hadronic interactions

There are some merits of the material measurement by the hadronic interactions. First,opening angle between secondary particles emerging after the hadronic interaction variesfrom 0◦ to 180◦ and is larger than the one between electron-positron pair by the photonconversion, while the latter is almost 0◦. Hence, spatial resolutions measured by the hadronicinteractions are very good and around 500 µm, which are about 10 times accurate as thosein the photon conversions. This advantage resulted from the large opening angle is brieflyexplained in figure 1.1.

Figure 1.1: Schematic drawings of hadronic intarction (top) and photon conversion (bottom).

CHAPTER 1. INTRODUCTION 3

Second, it is possible to directly measure the amount of the material in the detectorby counting the number of secondary hadronic interactions between primary particles andthe material. This is because the hadronic interaction length is almost independent on thecomponents of the material, while this is not applied to the radiation length.

1.3 The structure of this thesis

This thesis is organised as follows. The LHC and ATLAS experiment are explained in detailin chapter 2. The ATLAS detector, which has the most essential role in the experiment and iscomposed of several sub-detectors, is introduced in chapter 3, where the material distributionsin the inner detector are also described in terms of radiation length and interaction length.The method of the track reconstruction is summarised in chapter 4, including the techniqueof retracking, which is used to obtain the secondary tracks caused by hadronic interactionsat the outer region in the silicon detectors. Chapter 5 provides information on datasets forboth data and MC used in the analysis as well as event selections which are applied for theanalysis in order to efficiently compare data with MC. For the material measurements usinghadronic interactions, it is necessary to reconstruct the secondary vertices from the secondarytracks, chapter 6 and 7 summarise how to reconstruct the vertices and how to evaluate thequality of the ones. Measured materials in MC is compared with those in data to evaluate thedifferences between data and MC, which correspond to systematic uncertainties on materialdescriptions, and the results are presented in chapter 8. All possible systematic uncertaintiesare described in chapter 9 where MC studies in measurements of distorted materials areshown, results of which are used to evaluate confidence in the measurements in data. Thisstudy could improve the accuracy of track reconstruction, and chapter 10 provides physicsimpacts obtained from the results of this study as well as provides the summary of the results.Finally, the conclusion is presented in chapter 11.

Chapter 2

LHC and ATLAS Experiment

2.1 LHC

The LHC is a hadron accelerator and collider with two superconducting rings, installed in thelong circular tunnel (26.7 km) which was constructed for the CERN LEP machine between1984 and 1989. The motivation of the LHC is to derive the physics beyond the StandardModel with the center of mass energy

√s up to 14 TeV. The design of LHC depends on some

fundamental principles connected with contemporary technology. Since the LHC is a particle-particle collider, it needs two rings with counter-rotating beams, unlike particle-antiparticlecolliders which can share the same phase space for both beams in a single ring. The internaldiameter of the tunnel in the arcs is 3.7 m, and there are four interaction points between thetwo rings. Each detector of four different experiments, ATLAS [1], CMS [7], ALICE [8] andLHCb [9], is located at each interaction point (figure 2.1).

In the LHC rings, many bunches made of about 1011 protons each are circulated. Ac-cording to the LHC design, there are 2,808 bunches in each ring at the center of mass energy√

s = 14 TeV, with a bunch spacing 25 ns. The number of events1 per second is given by:

Nevent = Lσ, (2.1)

where the σ is the cross section for the event and the L is an instantaneous luminosity. Theinstantaneous luminosity depends only on the beam parameters and can be written by:

L =N 2

b nbfrevγr

4πεnβ∗F, (2.2)

where Nb is the number of protons per bunch, nb the number of bunches per beam, frev

the revolution frequency, γr the relativistic gamma factor, εn the normalised transverse beamemittance, β∗ the beta function at the collision point, and F the geometric luminosity reduc-tion factor depending on the crossing angle at the interaction point (quoted from the eq.(2.3)in [2]). As expressed in these equations, both the high beam energy and high beam intensityare required in the exploration of rare events.

The design luminosity of the LHC is 1034 cm−2s−1 and expected total cross section is 80mb, where an average number of proton-proton interactions per bunch crossing (denoted by<µ>) would be about 23. The designed parameters for the LHC are summarised in table 2.1.

1An event means one bunch crossing that as least one proton-proton collision per bunch crossing occur.

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CHAPTER 2. LHC AND ATLAS EXPERIMENT 5

Figure 2.1: Schematic layout of the LHC. Beam1 (red line) moves forward clockwise, and beam2(blue line) goes ahead anticlockwise.

Table 2.1: Designed parameters in the LHC.

Parameter ValueCircumference 26.7 km

Center of mass energy (√

s) 14 TeVInstantaneous luminosity (L) 1034 cm−2s−1

Total cross section (σtot) 80 mb (= 8 × 10−26 cm2)Number of protons per bunch 1.15 × 1011 (maximum limit)Number of bunches in the ring 2,808 (for each beam)

Bunch spacing 25 ns<µ> ∼ 23


The LHC have been running at√

s = 7 TeV from 2011 to 2012 and 8 TeV in 2012,respectively. The delivered luminosity during those periods, as well as related values, aredescribed in the next section.

2.2 ATLAS Experiment

The aims of the ATLAS (A Toroidal LHC ApparatuS) are searches and discoveries of theorigin of mass, unveiling of the fundamental symmetry, extra dimensions of space, unificationof fundamental forces, and evidence for dark matter candidates in the Universe. The ATLASdetector is optimised for the purpose, precisely explained in chapter 3. The LHC and AT-LAS have started the physics run in 2009 at

√s = 900 GeV in proton-proton collision, and

continued running with√

s up to 8 TeV in 2012 while putting the technical stop or wintershutdown within the term. Table 2.2 shows recorded luminosity at the ATLAS, including theluminosity delivered by the LHC, and other records related to the data-taking.

Table 2.2: Recorded luminosity and related values.

2010 2011 2012√

s 7 TeV 7 TeV 8 TeV

Integrated luminosity ATLAS recorded 45.0 pb−1 5.25 fb−1 21.7 fb−1

LHC delivered 48.1 pb−1 5.61 fb−1 23.3 fb−1

Data-taking efficiency at the ATLAS 93.6% 93.5% 93.5%Peak luminosity (cm−2s−1) 2.1 × 1032 3.65 × 1033 7.73 × 1033

<µ> < 1 11.6 2 20.7 3

2.2.1 Physics in the ATLAS Experiment

The ATLAS can measure the characterictics of the SM particles as well as can search for theexistence of the particles or phenomena beyond the SM. The Higgs boson is only focused onhere.

Higgs boson

The Higgs mechanism can describe the electroweak symmetry breaking and implies the ex-istence of the SM Higgs boson. In recent decades, searches for the Higgs boson have beenperformed at several accelerators such as the LEP and the Tevatron, as well as the LHC. InJuly 2012, two experiments at the LHC, ATLAS and CMS, announced the discovery of a newboson consistent with the SM Higgs boson. This section provides the characteristics of theSM Higgs boson.

Figure 2.2 shows the four types of the Higgs production processes which could occur at theenergy scale of the LHC. The gluon fusion process produces the Higgs boson via a top-quarkloop from two gluons, which is dominant of the four processes. For the vector-boson fusion,the Higgs boson is generated by the W or Z bosons and two quarks are scattered foward

2Before and after the technical stop in September 2011, the beta fuction at the interaction point (β∗) wasreduced from 1.5 m to 1.0 m. This is the value after the reduction of the β∗. For β∗ = 1.5 m, < µ >= 6.3 wasrecorded.

3This is the value for data taken until November 26th in 2012, corresponding to the integrated luminosityR

Ldt = 20.8 fb−1.


or backward directions which helps to identify this process. The Higgs boson can emergesfrom the virtual vector bosons W ∗ or Z∗ and then decays into a bottom quark pair. Thecontribution of the last process ttH is small, thus it is negligible for most of the analysis4.

(a) gluon fusion (b) vetor-boson fusion

(c) Higgs-strahlung (d) ttH

Figure 2.2: The Feynman diagrams of the Higgs production process which could occur at theLHC.

The Higgs boson itself cannot be detected as it decays immediately after the production.Hence, search for the Higgs boson is performed by considering its decay process. Figure 2.3shows the distributions of the branchig ratio and the cross section multiplied by the branchingratio as a function of the Higgs mass mH . In the ATLAS experiment, there are five decaychannels which are well analysed.

• H → ZZ(∗) → 4l: This process provides good sensitivity over as wide mass range(110-600 GeV) due to the excellent momentum resolution of the ATLAS.

• H → γγ : When analysing this channel, the understanding of the background such asSM diphoton production is crucial.

• H → WW (∗) → lνlν: The signature for this channel is two opposite-charge leptonswith large transverse momentum and large missing transeverse energy due to escapingneutrinos.

• H → ττ : The measurement of this decay rate provides a test of the SM prediction forthe τ Yukawa coupling [12].

• H → bb: Although gg → H → bb is the dominant production process, the large amountof background presents. Hence, H → bb channels in association with a vector bosonWH or ZH is well performed in the ATLAS experiment [13].

Since some analysis of these processes requires reconstructed leptons, the performance ofthe tracking is essential for searching the Higgs boson. Hence, the material measurement ofthe ATLAS ID profits the Higgs analysis.

4It is taken into account only in the H → γγ analysis


(a) Branching ratio (b) σ× branchig ratio

Figure 2.3: Distributions of the branchig ratio (left) and the cross section multiplied by thebranching ratio (right) as a function of the Higgs mass mH . Each decay process is shown inthe plots.

Chapter 3

ATLAS Detector

The ATLAS detector consists of several sub-detectors, and the solenoid and toroid magnetsbetween the sub-detectors. This chapter focuses on the explanation in such elements of theATLAS detector after showing the overview of the detector.

3.1 Overview of the detector

Since the coordinate system in the ATLAS is used repeatedly in the following sections andchapters throughout the thesis, the definition of the system is introduced first. The nominalinteraction point between the protons is defined as the origin of the coordinate system, thenthe direction of the beam defines z-axis and the x-y plane is a perpendicular plane to thez-axis. In fact, x- and y- axis point to the center of the LHC ring and upwards, respectively.The direction of the z- axis is defined such that the coordinate system leads to the righthand system. While the endcaps are put on both sides of the barrel which is the centerregion with cylindrical shape, the endcap with positive z is named the Side-A and the onewith negative z is the Side-C. When the cylindrical coordinate is used, the azimuthal angleφ is measured in the x-y plane vertical to the beam pipe, and the polar angle θ is the anglefrom the z-axis. For the direction of physics objects or the specific region in the detector, thepseudorapidity η defined as − ln tan θ/2 is often used. In order to identify the physics objects,there are other three variables defined: the transverse momentum pT mainly used for tracks,the transverse energy ET for jets, and the missing transverse energy Emiss

T for missing objectssuch as neutrinos.

Since many physics objects emerge from the proton-proton interactions, to detect themefficiently, there are several essential requirements for the detector:

• Electronics and sensor elements must have fast response and must be radiation-hard,to tolerate the extreme condition at the LHC and to reduce the effect of overlappingevent.

• Almost full coverage in azimuthal angle φ and as large acceptance in pseudorapidity ηas possible.

• Good momentum resolution and reconstruction efficiency for charged particles in theinner tracker.

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CHAPTER 3. ATLAS DETECTOR 10

• Good energy and spatial resolutions in the electromagnetic (EM) calorimetry for elec-tron and photon identification and reconstruction efficiency.

• Full-coverage hadronic calorimetry for accurate measurements of jets and EmissT .

• Good muon identification and momentum resolution, as well as the ability to determinethe charge of high-pT muons such that it is hard to measure in the inner tracker.

• Efficient triggering on low pT objects while rejecting background sufficiently.

The ATLAS detector have been designed and made so that it fulfilled all these requirements.Figure 3.1 shows the cut-away view of the ALTAS detector, which is 25 m in height and 44m in length. The weight of the whole detector is approximately 7000 tonnes. Its performancegoals in terms of resolution and coverage are summarised in table 3.1.

Figure 3.1: Overview of the ATLAS detector.

Table 3.1: Performance goals of the ATLAS detector.

Detector component Required resolutionCoverage

Measurement TriggeringTracking σpT /pT = 0.05% pT ⊕ 1% |η| < 2.5 −EM calorimetry σE/E = 10%/

√E ⊕ 0.7% |η| < 3.2 |η| < 2.5

Hadronic calorimetrybarrel and endcap σE/E = 50%/

√E ⊕ 3% |η| < 3.2 |η| < 3.2

forward σE/E = 100%/√

E ⊕ 10% 3.1 < |η| < 4.9 3.1 < |η| < 4.9Muon spectrometer σpT /pT = 10% at pT = 1 TeV |η| < 2.7 |η| < 2.4

The innermost component of the ATLAS detector is the inner detector which plays acrucial role in the track reconstruction. Since the inner detector is surrounded by a 2 Tsolenoidal field, it is possible to measure the momentum of a charged particle passing throughthe inner detector. The inner detector consists of three separated sub-detectors. First, par-ticles that emerge from the collisions pass through the Pixel which measure the position of a


hit by silicon pixels and the next one is the SemiConductor Tracker (SCT) which can detectcharged particles with silicon strips. The last sub-detector in the inner tracker is the Transi-tion Radiation Tracker (TRT), that identify electrons and pions from the ionization loss.

Outside the solenoid magnet, there is the high granularity liquid-argon (LAr) electromag-netic sampling calorimeters with the coverage |η| < 3.2. it is surrounded by the hadroniccalorimetry made of a scintillator-tile calorimeter, which is composed of a large barrel andsmaller extended barrel cylinders on both sides of the central barrel. The endcaps of thehadronic calorimeters is also base on the LAr technology and they cover |η| > 1.5. The LArforward calorimeters with the coverage up to |η| = 4.9 plays essential roles in the energymeasurements from both electromagnetic and hadronic points of view.

Outside the calorimeter, the toroidal magnet is located, which is separated into a longbarrel and two inserted endcap magnets. The three layers in the muon chamber can measurethe muon tracks with the excellent resolution.

3.2 The Inner Detector

Figure 3.2: Overview of the ATLAS inner detector

Since hundreds of particles are generated in each collision at the LHC, high-precisionmeasurements for the tracks under the large track density are required for the inner tracker.The ATLAS inner detector, which consists the Pixel, SCT and TRT, is designed for satisfyingsuch hard requirements. Figure 3.2 shows the cut-away view of the Inner Detector (ID). TheID is surrounded by a solenoid magnet with 2 T, which is over 5.3 m in length and 2.5 m indiameter.

The silicon detector (Pixel and SCT), in other words the precision tracking detector,covers the region |η| < 2.5. Its barrel region has cylindrical shape and is put around thebeam pipe. And the endcaps made of several disks, perpendicular to the beam axis, arelocated on both sides of the barrel. The total number of readout channels is approximately80.4 million (Pixel) and 6.3 million (SCT).

In the TRT, a large number of hits is provided by the straw tubes with 4 mm diameter,


which can carry out the tracking up to |η| = 2.0. The TRT can measure only R-φ positionswhich the tracks pass through, using the straw tubes parallel to the beam axis. The totalnumber of TRT readout channels is approximately 351,000.

The combination of these trackers provides very robust pattern recognition and highprecision in R, φ and z coordinates. Table 3.2 and 3.3 shows the basic parameters of theinner detector system, and intrinsic accuracies and the alignment tolerances for each sub-detector layer, respectively. The following subsections give the detailed characteristics andstructures of the Pixel and SCT, as well as the material distribution in the ID. Procedure forthe track reconstruction in the ATLAS ID is described in chapter 4

Table 3.2: Basic parameters of the inner detector.

Radial range (mm) Length in z (mm)The whole detector 0 < R < 1150 0 < |z| < 3512Beam pipe 29 < R < 36 −Pixel The whole region 45.5 < R < 242 0 < |z| < 30923 cylindrical layers barrel region 50.5 < R < 122.5 0 < |z| < 400.52 × 3 disks endcap region 88.8 < R < 149.6 495 < |z| < 650

SCT The whole region 255 < R < 549 (barrel) 0 < |z| < 805251 < R < 610 (endcap) 810 < |z| < 2797

4 cylindrical layers barrel region 299 < R < 514 0 < |z| < 7492 × 9 disks endcap region 275 < R < 560 839 < |z| < 2735

TRT The whole region 554 < R < 1082 (barrel) 0 < |z| < 780617 < R < 1106 (endcap) 827 < |z| < 2744

73 straw planes barrel 563 < R < 1066 0 < |z| < 712160 straw planes endcap 644 < R < 1004 848 < |z| < 2710

Table 3.3: Intrinsic accuracy and alignment precision for each detector element.

Intrinsic accuracyAlignment precision

(µm)(µm)

R z R-φPixel

B layer 10 (R-φ) 115 (z) 10 20 72nd and 3rd 10 (R-φ) 115 (z) 20 20 7Disks 10 (R-φ) 115 (z) 20 100 7

SCTBarrel 17 (R-φ) 580 (z) 100 50 12Disks 17 (R-φ) 580 (z) 50 200 12

TRT 130 − − 30

3.2.1 Pixel

The total number of the Pixel modules is 1,744. All modules are arranged in either threebarrel layers or two endcaps each with three disks. The basic parameters of the Pixel detector,


such as position in radius and the number of pixels, are listed in table 3.4. There are 112barrel staves and 48 endcap sectors (8 sectors each disk), moreover they are separated intomodules as shown in figure 3.3. The pixel module is composed of the front-end chips, bumpbonds, the sensor tile and a flexible polymide printed circuit board. There are 16 front-endchips thinned to 180 µm thickness and each chip has 2,880 electronic channels. Bump bondsconnect the electronics channels to the Pixel sensor elements. The size of the sensor tile is63.4 × 24.4 mm2 with about 250 µm thick. The circuit board has a module-control chipbonded to the flex-hybrid. Also, there is a polymide pig-tail with a connector or a wiremicro-cable glued to the flex-hybrid. In general, the minimum amount of material in front ofthe Pixel sensors, typically the flex-hybrid.

Table 3.4: Parameters of the Pixel detector.

Radius (mm) Staves Modules PixelsBarrel

B layer 50.5 22 286 13.2×106

2nd layer 88.5 38 494 22.8×106

3rd layer 122.5 52 676 31.2×106

z (mm) Sectors Modules PixelsEndcap (one side)

Disk 1 495 8 48 2.2×106

Disk 2 580 8 48 2.2×106

Disk 3 650 8 48 2.2×106

Total 1,744 80.4×106

3.2.2 SCT

The SCT consists of 4,088 modules, which are arranged to four barrel layers or to nineendcap disks at each side. Table 3.5 and 3.6 show the basic parameters of the SCT barrel andendcaps, respectively. A barrel SCT module has 80 µm pitch micro-strip sensors connectedto binary signal readout chips. The photograph and drawing of the barrel module are shownin figure 3.4. The two sensors, each on the top and bottom side, are rotated by ±20 mradaround the center of the sensors. In each side, a sensor consists of 770-strips (768 active)and it is 128 mm long along the strip direction. The nominal resolution of the module is 17µm in R-φ and 580 µm in z. There are 1976 modules in two endcaps, and they are classifiedinto three types: Outer, Middle and Inner. The parameters of each type are summarisedin table 3.5, and figure 3.5 shows the photographs of the modules and the drawing.


Figure 3.3: Schematic view of a barrel pixel module (top) with the pixel hybrid and sensor ele-ments, including the MCC (module-control chip), the front-end (FE) chips, the NTC thermistors, thehigh-voltage (HV) elements and the Type0 signal connector. The middle illustration is a plan viewdescribing the bump-bonding of the silicon pixel sensors to the polyimide electronics substrate. Thebottom photograph is a barrel pixel module.

Table 3.5: Parameters of the SCT barrel. The radii are those of the outer surface of the support.The average radii of active sensors are shown in brackets.

Barrel layer Radius (mm) Number of modules1st layer 284 (299) 3842nd layer 355 (371) 4803rd layer 427 (443) 5764th layer 498 (514) 672Total 2112

Table 3.6: Parameters of the SCT endcaps. The numbers for each endcap are shown and they arecommon in two endcaps.

Disk 1 2 3 4 5 6 7 8 9|z| (mm) 853.8 934.0 1091.5 1299.9 1399.7 1771.4 2115.2 2505.0 2720.2Outer 52Middle 40 −Inner − 40 −


Figure 3.4: Photograph (left) and drawing (right) of a barrel module, showing its components. Thethermal pyrolytic graphite (TPG) base-board provides a high thermal conductivity path between thecoolant and the sensors.

Figure 3.5: The upper photograph shows the three SCT end-cap module types (outer, middle andinner from left to right). The lower drawing shows a view of the different components for a middlemodule, including the high thermal conductivity spine, the polyimide hybrid and the ABCD readoutASIC ’s.


3.2.3 TRT

The TRT is also composed of the barrel and two endcaps. In the barrel, there are up to 73layers of straws interleaved with fibres, on the other hand, 160 straw planes interleaved withfoils in each endcap. They can identify electrons using transition radiation. It is designedsuch that all charged tracks with pT > 0.5 GeV and |η| < 2.0 traverse at least 36 straws,while the barrel-endcap region (0.8 < |η| < 1.0) is the exception.

In the barrel, there are 32 modules in each of three rings and each module is made of acarbon-fibre. Figure 3.6 shows a quarter of the TRT barrel.

The TRT end-caps consist of two sets of wheels in each side. The set closer to the centerof the ATLAS detector contains 12 wheels, each with eight layers spaced 8 mm apart. Theouter set of wheels contains eight wheels, with eight straw layers but spaced 15 mm apart.Each layer contains 768 radially oriented straws of 37 cm length.

Figure 3.6: Photograph of a quadrant of the barrel TRT. The shapes of one outer, one middle and oneinner TRT module are highlighted. The triangular sub-structures correspond to the barrels supportstructure space-frame.

3.2.4 Material distribution of the inner detector

Since the ATLAS detector must tolerate the harsh environment and the pile-up from multipleinteractions per bunch crossing, it has a high granularity and good mechanical stability interms of electronics, readout and cooling services. This is why the inner detector consists ofmuch larger material than those of previous tracking detectors. Such large material causesthe following problems:

• Electrons may lose most of the energies by bremsstrahlung in front of the electromag-netic calorimeter.

• About 40% of photons convert into an electron-positron pair in front of the LAr cryostatand the electromagnetic calorimeter.

• Many hadrons may decay due to inelastic hadronic interactions inside the inner detectorvolume, even in case of low-energy charged pions.


Hence, in order to avoid the mismodelling of such processes, it is crucial to implement theID material in MC simulations precisely. Figure 3.7 shows a map of photon conversion verticesin the ID, using a data sample with 500,000 events at a collection rate of 200 Hz. Electronswith pT > 0.5 GeV resulted from photon conversions in minimum-bias events (section 5.2) areused. This study indicates that photon conversions can happen in many structural elements,such as the end-plates of both the barrel and endcaps.

Figure 3.7: Mapping of photon conversions as a function of z and R, integrated over φ, in the innerdetector. 500,000 minimum bias events (About 40 minutes of data-taking at a collection rate of 200Hz) are used. This includes about 90,000 conversion electrons with pT > 0.5GeV originating from thephotons in the π0/η decays.

Figure 3.8 and 3.9 show the integrated radiation length X0 and interaction length λ, as afunction of |η| at the exit of the ID envelope. The most striking features correspond to non-active servies such as cooling connections, electrical connections and barrel services extendingto the cryostat. Since high-η tracks pass through longer distances inside the beam pipe, thedistributions for the beam pipe rise to the right. Table 3.7 shows the integrated radiationlength X0 and interaction length λ from the interaction point, estimated as a function ofradius for |η| = 0 and 1.8. The detailed description of the ID material is used in the MCsimulation.


Figure 3.8: Material distribution (X0, λ) at the exit of the ID envelope, including the services andthermal enclosures. The distribution is shown as a function of |η| and averaged over φ. The breakdownindicates the contributions of external services and of individual sub-detectors, including services intheir active volume.

Figure 3.9: Material distribution (X0, λ) at the exit of the ID envelope, including the services andthermal enclosures. The distribution is shown as a function of |η| and averaged over φ. The breakdownshows the contributions of different ID components, independent of the sub-detector.

Table 3.7: Integrated radiation length (X0 from an interaction point to given radius.

|η| = 0 |η| = 1.8Radius range (mm) X0 Radius range (mm) X0

Exit beam pipe 0 - 36 0.0045 0 - 36 0.014Exit B layer 0 - 57 0.037 0 - 57 0.105Exit Pixel 3rd layer 0 - 172 0.108 0 - 172 0.442Entry SCT 0 - 253 0.119 0 - 253 0.561Entry TRT 0 - 552 0.205 0 - 621 0.907Exit TRT 0 - 1081 0.469 0 - 907 1.126


3.3 Calorimeter

The whole calorimeter system covers the range |η| < 4.9, and adopts different techniquesoptimised for widely varying physics requirements and for the radiation environment. Fig-ure 3.10 shows the cut-away view of the sampling calorimeters. Over the η range matchedto the inner detector, the fine granularity of the EM calorimeter is appropriate for precisionmeasurements of electrons and photons. The granularity in the other region is fine enoughfor the jet reconstruction and Emiss

T measurements.The calorimeter thickness must be determined carefully in both terms of energy measure-

ments and connection to the muon spectrometer. The EM calorimeter has its total thicknessgreater than 22 X0 in the barrel and greater than 24 X0 in the endcaps. For high energyjets, it provides approximate 9.7 λ in the barrel (10 λ in the endcaps). The total thicknessat η = 0 is 11 λ (including 1.3 λ in the outer support), which is sufficient to reduce pionpunch-through below the irreducible level. Both the large coverage and sufficient thicknessprovide good Emiss

T measurement.

Figure 3.10: Cut-away view of the ATLAS calorimeter system.

3.4 Muon Spectrometer

The muon system is based on the behaviour of muon tracks in the superconducting air-core toroid magnets, which are installed with trigger and high-precision tracking chambers.Figure 3.11 shows the cut-away view of the muon spectrometer and it indicates that themuon system consists of four separate muon chambers as well as the toroidal magnets. TheMonitored Drift Tubes (MDT’s) provides a precision measurement of the track coordinates onthe basis of bending direction in the magnetic field. The Cathode Strip Chambers (CSC’s),which cover large pseudorapidities η, can withstand the demanding rate and backgroundconditions. For the trigger system, the Resistive Plate Chambers (RPC’s) in the barrel andthe Thin Gap Chambers (TGC’s) in the endcaps are used. The main parameters of thesemuon chambers are listed in table 3.8.


The toroidal magnetic field is generated by the three air-core toroids, one barrel toroidand two endcap toroids, while the two endcap toroids are inserted in the barrel toroid at eachend. Each of the three toroids is composed of eight coils symmetrically around the beam axis.

Figure 3.11: Cut-away view of the ATLAS muon system.

Table 3.8: Basic parameters of the muon spectrometer.

MDT (Monitored Drift Tubes)Coverage |η| < 2.7 (< 2.0 for the innermost layer)

Number of chambers 1,150Number of channels 354,000

Function Precision trackingCSC (Cathode Strip Chambers)

Coverage 2.0 < |η| < 2.7Number of chambers 32Number of channels 31,000

Function Precision trackingRPC (Resistive Plate Chambers)

Coverage |η| < 1.05Number of chambers 606Number of channels 373,000

Function Triggering and second coordinateTGC (Thin Gap Chambers)

Coverage 1.05 < |η| < 2.7 (< 2.4 for triggering)Number of chambers 3,588Number of channels 318,000

Function Triggering and second coordinate

Chapter 4

Track Reconstruction in TheATLAS Inner Detector

4.1 Overview of tracking system

The algorithm of the track reconstruction usually has two steps, one is pattern finding ofall possible combinations on hits in the detector and the other is track fitting which makestrajectories of the track candidates. In the modern track reconstruction strategies, however,there is no clear border between the pattern finding module and track fitting module [14].This is because many pattern finding strategies (contrary to a classical histogram basedapproach) include two stage patterns, which are a global pattern search and a local patternrecognition where the track fitting is already involved. On the other hand, the combinatorialKalman filter [15] and the deterministic annealing filter [16] incorporate an intrinsic patternrecognition in the fitting process. Therefore, the full chain of pattern recognition and trackfitting is treated as a single unit.

There are two sequences of the ID New Tracking (NEWT) which is the current algorithmfor the track reconstruction in the ATLAS experiment, one is inside-out reconstruction andthe other is outside-in tracking. The former is mainly used in the reconstruction and the latteris consecutive tracking. The pattern search concepts for both sequences have also been usedin the old type of the ATLAS ID reconstruction program, however, these two sequences wereintegrated and accomplished by additional components in the ID NEWT approach. Anothersequence, the second stage pattern recognition for finding vertices, kink objects caused bybremsstrahlung and their associated tracks is adopted in the NEWT. Section 4.2 and 4.3describe the methods of the track reconstruction for the inside-out tracks and the outside-intracks, respectively. Figure 4.1 shows the flow-chart of the tracking system.

In addition to the sequences during the reconstruction mentioned above, there is a specialtechnique of the track reconstruction to reconstruct many secondary tracks which emerge faraway from the position of the primary vertex. The technique is named ”retracking” since itcarries out the track reconstruction again after the usual reconstruction. The procedure ofthe retracking and its characteristics are described in section 4.5.

4.2 Inside-out track reconstruction

The inside-out tracking is the main sequence of the track reconstruction in the ATLAS. Thealgorithm starts with creating space points which is the three dimensional positions of hits

21

CHAPTER 4. TRACK RECONSTRUCTION IN THE ATLAS INNER DETECTOR 22

Si Space Points

SiSPSeeded

Tracks

Resolved

Tracks

Extended

Tracks

Pattern

Recognition

Ambiguity

Solving

TRT

Extension

Inside-out tracking

TRT Segments

Inward

Extension?

TRT Seeded

Tracks

Resolved TRT

Tracks

Track

Fitting

Succeeded

Ambiguity

Solving

Outside-in tracking

Failed

TRT Standalone

Tracks

Figure 4.1: Flow-chart of the tracking algorithm. Inside-out tracking is illustrated in the left rectan-gular, and the right one shows the reconstruction by the outside-in tracking.

in the silicon tracker. The combinations of the space points are fitted as track trajectories,then an ambiguity solving algorithm works to retain only tracks which have good quality.The TRT extension is a final step of the inside-out track reconstruction, which means thatthe tracks created by only space points in the silicon tracker are extended to the TRT afterthe proper test described in the following subsections. Figure 4.2 shows the flow-chart of theinside-out tracking algorithm including the simple drawings.

4.2.1 Space Point creation in the silicon detector

The space point creation is the first step of the inside-out tracking, and is carried out inthe silicon detector. There are two silicon detectors in the inner detector, the Pixel andSCT. In the case of the Pixel detector, it is very simple to form the space points. ThePixel detector measures hit positions in η and φ coordinates and its positions in radius isdetermined during the installation of the detector. That is how three dimensional position oneach hit is measured. On the other hand, the sensors in the SCT have only one dimensionalinformation orthogonal to the direction of the silicon strips. However, since a SCT modulehave two sensors which are put close to each other and rotated by a stereo angle with respectto another, the SCT module composed of a sensor-pair can measure the two dimensionalpositions on the hits in the plane orthogonal to radius at the intersections of silicon strips.The radius positions of hits in the SCT are determined in a similar way to the Pixel, duringthe installation of the detector.


Figure 4.2: Flow-chart of the inside-out tracking algorithm including the simple drawings. Inside-outtracking starts with the space point creation and the created space points are used in the patternrecognition to reconstruct the first set of track candidates. Then ambiguous candidates are removedand the rest are attempted to extend from the silicon detector to the TRT.

4.2.2 Space Point seeded track finding

The sets of space points filled in the previous step move to the next process, that is seedingthe track candidate in the inner detector. The process is divided into two different tasks, thetrack seed finding and the creation of track candidates. Both tasks are based on the seedsfound in the step of space point creation.

Track seed finding

Concerning the track seed search, there are two ways in the ATLAS ID. Here, both ways areintroduced while one is an obsolete way in the latest ATLAS software.

• Seed finding with constraint of z position of the vertex - This finding methoduses pairs of the space points from only the Pixel detector in its first step. z coordinateof the vertex for each pair of the space points is built by a vertex maker. The vertexinformation for each pair is stored, with keeping each seed compatible with a givenmomentum and range of its transverse impact parameter. After the fast primary vertexsearch is performed, the primary vertex is adopted to constrain the seeds with three ormore space points. The tolerance region for the vertices created from the track seedsdetermines a cut parameter which can restrict the qualities of tracks and vertices.

• Unconstrained seed finding - This is the track seed search performed without thegiven z vertex constraint, which needs a higher number of initial track seeds. Although


the unconstrained seed finding requires more computing resources than the constrainedfinding, This is more efficient to find tracks in events with loosely constraint primaryvertices, such as H → γγ events or pile-up events which have non-physical single tracks.

The constrained seed finding was mainly used in the past ATLAS software, and the uncon-strained finding method is the default in the NEWT track reconstruction.

Track candidate creation

The trajectory building process starts after the space point seeds are found as mentionedabove. The given track seeds have already enough information to search further hits associatedwith one track candidate. This leads to the local part of the silicon pattern recognition, wherethe space point objects are dissolved into the cluster objects built originally. This is becausethe track fitting is involved in the track candidate creation. Although the sets of the clustersare allowed to contain clusters which have not been used to make space points, those clusterslocated on the detector elements to build the trajectory can be used for the track candidatecreation. In general, a silicon detector element has more than one hit per event, thus themost likely extension of the trajectory is chosen as a track candidate. It is found that onlyabout 10 % of the space point seed objects are successfully extended to the track candidates.There is a possibility to find more than one track candidate from a given seed, but this isa rare case in the ATLAS ID track reconstruction. The track candidates created here areassigned as SiSPSeeded Tracks.

4.2.3 Ambiguity solving algorithm

The ambiguity of created track candidates have to be resolved before they are extended to theTRT which is the most outer sub-detector in ID. The biggest problem on the track candidatesat this stage is that they could share hits, i.e. multiple track candidates could have a commonhit in the silicon detector, and some of them might be fake tracks which would not correspondto any charged particles. Therefore, track candidates are ranked in their likelihood. Sincethe fit χ2 divided by the degrees of freedom is not appropriate to decide whether a trackis well reconstructed or it is a fake track 1 , the ”track scoring” strategy [17] is adopted inthe NEWT. In the strategy, different characteristics of tracks are represented by a beneficialor penalty track score. In general, the measurements of different sub-detectors are weightedwith different scores. Table 4.1 shows the summary of the track characteristics with effectson the track scores. After assessing these scores for the track candidates found in the spacepoint seeded track search, hits shared in multiple tracks are assigned to the track with higherscore. Then the remaining tracks are refitted without the formerly shared hit 2.The refitted tracks are scored again, and then are added to the list of the tracks. The trackswith the highest score remain in the list during the iterative steps, while tracks that fell atthis step are removed in the list and are not treated in further process. The remaing trackafter all these steps are named Resolved Tracks.

1A track which corresponds to a real charged particle can have a large χ2.2In the current strategy, shared hits between multiple tracks are allowed if the track fulfills dedicated quality

criteria.3Hole means an expected hit that has not been found


Table 4.1: Track characteristics and their effects on the track scores

Track characteristics Detector Effect on track scoreHole 3 in the B layer Pixel strong penalty

Hole in the Pixel 2nd or 3rd layer Pixel penaltyOverlap hit Pixel, SCT strong benefit

Hole in the SCT sensor SCT weak penaltyHole in the SCT layer (module) SCT strong penalty

4.2.4 TRT extension

At the next stage in the tracking procedure, silicon-only tracks are extended from the silicondetector into the TRT. In this process, the tracks that passed through all the steps above areused as an input to find compatible sets of the TRT measurements.

There are two TRT extension tools in the ATLAS software: one is the main tool usedin the standard implementation and the other is optimised for very high hit densities. Here,only the standard one is introduced because the latter is not used in the analysis. The toolstarts with finding a trajectory through the track extrapolation of the silicon-only tracks. Itcarry out a line fit to evaluate whether the TRT hit, which is expressed in r − φ coordinatesin the barrel and in r−z coordinates in the endcaps, is compatible with the silicon-only trackor not. If the extension is successfully found, the extended track is refitted and scored in asimilar way to the silicon-only tracks. Since the refitting allows the initial silicon-only trackto change, the score of the silicon-only track can be higher than the one of the extended track.In this case, the silicon-only track is kept in the list of the tracks. The extended track passingthrough all these steps is assigned as Extended Tracks.

4.3 Outside-in track reconstruction

The outside-in track sequence is prepared for the case where initial track seeds are not foundor do not exist. There are three patterns in the case as follows:

• Ambiguous hits can interfere with the track seed in the silicon detector and prevent thescore of the seeded track from surviving the ambiguity solving process.

• Tracks coming from secondary decay vertices inside the ID volume (e.g. K0S and Λ

decays) or from photon conversions may not have any or only insufficient silicon hits tocreate the track seed in the inside-out sequence.

• Substantial energy loss, of electrons in most cases, at outer radii of the silicon seededtracks may cause that the TRT extension tool follows a wrong direction, such thatcorresponding TRT hits would not be found.

In order to carry out the track reconstruction even in these cases, the NEWT establishesthe outside-in tracking sequence after the inside-out tracking. There are two steps in theoutside-in tracking sequence, TRT segment finding and back tracking the segments into thesilicon detector.


4.3.1 TRT segment finding

The algorithm of the TRT segment finding starts with a global pattern search and then followsa local pattern recognition for building an intrinsic track segment. Since the TRT drift tubemeasurements do not include any information on the coordinate parallel to the straw direction,no space point objects can be created in the TRT. Therefore, the r − φ planes in the barreland the r−z planes in the endcaps are chosen to create the track segments. In order to reduceoverlaying track segments, these two dimensional track segments are investigated by η slicesof the TRT. Since the missing hit in the slice could exist, the hits have to be considered inseveral slices. That is how the track segment candidates are resolved and they become TRTStandalone Tracks.

4.3.2 Back tracking into the silicon detector

TRT Standalone tracks need to be extended to the silicon detector. This process decideswhether the extrapolation of the TRT-only tracks are compatible with dedicated silicon hitsor not. If a TRT Standalone tracks pass through the process successfully, the track is assignedas Resolved TRT Tracks. This type of tracks is crucial for secondary tracks which are usedduring the secondary vertex reconstruction at the outer radii in the silicon detector.

4.4 The track parameters and the requirements

A trajectory of the fitted track is determined by the following five parameters:

• q/p: Charge of the track divided by the momentum.

• d0: Transverse impact parameter.

• z0: Longitudinal impact parameter.

• φ: Azimuthal angle of the track direction at the point of the closest approach to thecollision point.

• θ: Polar angle of the track direction at the point of the closest approach to the collisionpoint.

The definitions of these parameters are also shown in figure 4.3, where the point P correspondsto the perigee of a given track. The impact parameter of a track is the distance betweenthe origin and the track trajectory. Two impact parameters d0 and z0 correspond to theprojection to transverse and longitudinal directions, respectively. Usually, impact parametersare measured with respect to the origin, but in this analysis the impact parameters withrespect to the primary vertex positions or to the secondary vertex positions are used. Inorder to prevent confusions due to the difference of the definitions, each impact parameter isdenoted by:

• dPV0 , zPV

0 : impact parameters with respect the primary vertex position.

• dSV0 , zSV

0 : impact parameters with respect the secondary vertex position.

When investigating the quality or the characteristics of the track, pseudorapidity η calculatedfrom the θ is usually used during the analysis. These track parameters not only identify a tracktrajectory but also are used for quality cuts of the track. In addition to the five parameters,the track fit χ2 also plays a essential role in assessing the track quality.


(a) (b)

Figure 4.3: Drawings to describe the definitions of the track parameters. (a)Projection of a track tox-y plane including the perigee which is the closest approach of the track to the origin in the plane.(b)Projection of a track to R-z plane including the perigee.

Selection criteria

Selection criteria for the reconstructed tracks are summarised in table 4.2. These criteria areapplied to the minimum bias events, which are described in section 5.2. The secondary vertexreconstruction in this analysis starts with the tracks after applying these selection cuts. Thedifinitions of several variables in the table are as follows:

• NSiHits: The total number of hits in the silicon detector for a given track.

• NNotShared: The number of silicon hits not shared by tracks other than a given track.

• NShared: The number of silicon hits shared by tracks other than a given track.

• NTrkShareHit: The number of tracks which share a given hit.

• NPixelHole: The number of holes in the Pixel.

• NSCTHole: The number of holes in the SCT.

• NSiHole = NPixelHole + NSCTHole .

• NDoubleHole: The number of pairs of 2 consecutive holes 4.

4For example, a pair of holes on SCT 1st and 2nd layers.5In fact, this depends on types of the silicon seeds. The silicon seeds are made of three space points, and

there are three types of the silicon seeds: Three Pixel space points, two Pixel and one SCT space points, andthree SCT space points. They require |d0| < 10 mm, 1.7 mm, and no cut, respectively.


Table 4.2: Selection criteria during the stan-dard reconstruction.

Selection criteriapT > 100 MeVd0 < 10 mm 5

z0 < 250 mm|η| < 2.7

NSiHits ≥ 7NNotShared ≥ 6NShared ≤ 1

NTrkShareHit ≤ 2NPixelHole ≤ 2NSCTHole ≤ 2NSiHole ≤ 3

NDoubleHole ≤ 1

Table 4.3: Selection criteria for the retrack-ing.

Selection criteriapT > 100 MeVd0 < 300 mmz0 < 1500 mm

|η| < 2.7NSiHits ≥ 7

NNotShared ≥ 5NShared ≤ 2

NTrkShareHit ≤ 2NPixelHole ≤ 2NSCTHole ≤ 2NSiHole ≤ 3

NDoubleHole ≤ 1

4.5 Retracking

The previous section described the standard selection cuts for reconstructed tracks in theminimum bias events. In the selection criteria, impact parameters are limited as they shouldbe small enough. However, since this study needs many secondary tracks which emerge fromthe detector layers due to hadronic interactions, tracks with large impact parameters haveto be reconstructed. The retracking makes it possible to retry the track reconstruction whileloosening the selection criteria [18]. Originally, this technique has been developed for theanalysis of some models searching for the physics beyond the standard model, which predictfinal states including charged particles with large impact parameters resulting from the decayof long-lived or heavy neutral particles [19, 20]. The retracking solves the problem such thattracking efficiency for those tracks with large impact parameters is very poor in the standardtrack reconstruction.

The study in the note [18] provides selection criteria optimised in order to make trackingefficiency increase as well as to keep the fake rate 6 of the reconstructed tracks low. Table 4.3shows the selection cuts in the retracking. Four values of the selection cuts are changed anddisplayed in bold type. In the analysis described in the following chapters, the tracks passingall the requiremetns are used.

6The fake rate is the ratio of reconstructed tracks not matching to any truth tracks in MC truth record.

Chapter 5

Data Samples and Event Selection

5.1 Data Samples

The data used in this analysis were collected in March-June 2010 in proton-proton collisionsat a center-of-mass energy of 7 TeV. In this period, the instantaneous luminosity rangedfrom 1027 to 1029 cm−2s−1, and the integrated luminosity was 19 nb−1. Since the fakevertices accidentally reconstructed from the irrelevant tracks are expected to increase in highluminosity runs, these low luminosity runs are intentionally used to retain the high purity ofthe reconstructed vertices. The data were collected by the minimum bias trigger, while theone in the ATLAS collects 3 types of events: single-, double- and non-diffractive events. Thelast ones are dominant in the events by the minimum bias trigger in the ATLAS.

To compare with data, non-diffractive MC is used. Since the purpose of this analysisis to measure the material of the detector, it is required to select non-diffractive events indata. Details of the selection cuts on those events are described in section 5.3. MC eventswere generated using PYTHIA6 [24] with the AMBT1 (ATLAS Minimum Bias Tune 1) [25],simulated with GEANT4 [26], and processed with the reconstruction software which is thesame as used in data. Detailed descriptions of the ATLAS simulation infrastructure can befound in [27]. Other MC datasets are used to evaluate the systematic uncertainty due tohadronic interactions, those are explained in chapter 9.

5.2 Minimum Bias Events

The ’Minimum bias’ event usually means the one associated with the non-single-diffractive(NSD) inelastic collision [21]. They are mostly caused by soft interactions, with low track/particlemultiplicities and low transverse momentum (pT ). During low-luminosity running at LHC,when the number of proton-proton collisions per bunch crossing is ≤ 1, minimum bias eventswere well studied [22]. The minimum bias events are major backgrounds in physics analysisat high-luminosities, and the average number of minimum bias interactions per bunch cross-ing is around 23 at the LHC design luminosity [1]. Therefore, it is crucial to have a precisemodelling of minimum bias for all other high-pT physics measurements.

Minimum Bias Trigger

A minimum bias trigger is required to select the inelastic interactions with small bias. TheATLAS detector has a three-level trigger system: Level 1 (L1), Level 2 (L2) and Event Filter

29

CHAPTER 5. DATA SAMPLES AND EVENT SELECTION 30

(EF). The Minimum Bias Trigger Scintillators are mounted at both ends of the detectorin front of the liquid-argon end-cap calorimeter cryostats at z = ±3.56m [23]. They aresegmented into eight sectors in azimuthal direction and two rings in pseudorapidity η (2.09 <|η| < 2.82 and 2.82 < |η| < 3.84).

5.3 Event Selection

In order to compare data with MC efficiently, single- and double-diffractive events are removedfrom the data and the remaining events are compared with MC non-diffractive events. Thisis achieved by requiring a large number of track multiplicities at the primary vertex. Thisapproach works well when the additional number of pp interactions per event (pile-up) issmall, thus only the low-luminosity runs are used in this study.

To make this approach work correctly, it is required that there be exactly one reconstructedprimary vertex per event, and that it should have at least 11 associated tracks. The remainingevents are expected to have only less than 1% of single- and double-diffractive events thatare originally generated, while about 68% of non-diffractive events are left. After these eventselections, the remaining numbers of events are 40.9 million in data and 13.5 million in MC.

Figure 5.1 shows the z-coordinate distributions of the primary vertex. The distribution forMC is wider than the one in data and the mean of the distribution has a little offset comparedto data. The vertical lines in the plot correspond to the mean values of the distributions,which were fitted with the Gaussian function, those values for data and MC are -0.25mmand -4.97mm, respectively. Therefore MC events are weighted such that the mean and widthof the distribution match data. What being done on the weighting is to divide a number ofentries in each bin for data by the one for MC, and to multiply the ratio to all variables inthe MC event. This weighting technique is applied to all results below.

PVZ [mm]

-200 -150 -100 -50 0 50 100 150 2000

0.002

0.004

0.006

0.008

0.01

0.012

0.014ATLAS Work In Progress

= 7 TeVs

Data 2010MC

Figure 5.1: Distributions of primary vertex z-coordinates for data (black solid line) and MC (filledhistogram) normalised to unity. Red and yellow vertical lines correspond to the means of the distri-butions for data and MC, respectively.

Chapter 6

Secondary Vertex Reconstruction

The method of the track reconstruction and requirements for the tracks are mentioned inchapter 4. There are several steps for the secondary vertex reconstruction, thus each step inthe reconstruction is explained in this chapter.

6.1 Secondary track candidates

A secondary track emerges from the decay or interaction where is away from the proton-protoninteraction point. The remaining tracks after removing the primary tracks are assigned as thesecondary track candidates. While tracks with pT greater than 100 MeV are reconstructed,the tracks with such small pT may have bad quality, therefore pT > 300 MeV is required forsecondary track candidates. Since some reconstructed tracks are primary ones and other onesare secondaries, it is required to distinguish the secondaries from the primaries. The primarytracks are expected to have small impact parameters, thus in order to remove the primaries,the selection cut on the transverse impact parameter d0 ≥ 5mm are applied to the selectingout the secondary track candidates. From the MC study, it is found that this requirementremoves about 99% of the primaries. For the track fit quality, χ2/ndf < 5 is also applied asthe selection cut in order to use well reconstructed tracks.

In addition to requirements above, the number of hits in each sub-detector is restricted.Since this study focuses on the secondary vertices located from the beam pipe to the SCT 2ndlayer in the Barrel region, secondary tracks which emerge from such vertices should have someSCT hits. Thus it is required that the secondary track candidates have at least 1 SCT hit,while there is no requirement for the number of Pixel hit at this stage. These requirementsfor the secondary track candidates are summarised in table 6.1.

Table 6.1: Requirements for the secondary track candidates.

pT > 300MeVd0 > 5mmχ2/ndf < 5

# SCT hit ≥ 1no requirement for # Pixel hit

31

CHAPTER 6. SECONDARY VERTEX RECONSTRUCTION 32

6.2 2-track vertices

A universal vertex finder, which is designed to find all vertices in the event, is adopted in thisanalysis. The first step of the algorithm is to find all possible intersections of selected trackpairs. These two secondary tracks in each pair are assumed to come from a single point, andthen the vertex position is determined. During this process, the track parameters are modifiedif necessary, then the vertex fit χ2 is determined from the differences between the measuredtrack parameters and the re-calculated ones. Figure 6.1 shows the χ2 distributions withcomparison in data and MC, before (figure 6.1 (a)) and after (figure 6.1 (b)) the retracking.Shapes of the distributions with and without the retracking are almost the same, althoughthe means of the distributions with the retracking are a little larger than the ones withoutthe retracking. The χ2 is used to remove fake vertices in the next section 6.3.

2χ

0 2 4 6 8 10 12 14 16 18 20

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ctio

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(a)

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ctio

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= 7 TeVs

Data 2010MC

With Retracking

(b)

Figure 6.1: Distributions of χ2 for all 2-track vertices in data (black lines with points) and in MC(filled histograms). (a)Left and (b)right plots correspond to distributions before and after executingthe retracking, respectively. These are normalised to unity in the displayed range.

6.3 Fake removal

2-track vertices as mentioned in the previous section 6.2 could include many fake vertices,such as combinatorial background. It is required that vertex χ2 should be less than 4.5. MCstudies indicate that this selection removes about 85% of random pairings and more than83% of hadronic interaction vertices are kept.

Then, for the secondary tracks at the reconstructed vertices, the number of hits in eachdetector layer is restricted. This is because the secondary tracks should not have any hitin the inner layer than the position of the vertex, and should have some hits in the outerlayer than the position. This fake removal method depends on the radius of the vertex, andrequirement for each radius region is summarised in table 6.2. The definitions of the wordsand variables in the table are as follows:


B Layer: the first Pixel layer in the BarrelAirGap1: between the beam pipe and the B LayerAirGap2: between the B Layer and the 2nd Pixel layerN”layer”: the number of hits in the ”layer” associated with the trackNPix: the total number of Pixel hits associated with the track.

Table 6.2: Fake removal on the number of hits in each detector layer.Radius of SV Region Requirements on Pixel hits for both of tracks

R ≥ 47.7 mm inside of B Layer NBLayer ≥ 147.7 mm < R ≤ 54.4 mm B Layer NPix ≥ 154.4 mm < R ≤ 92.2 mm AirGap1 OR Pixel 2nd layer NBLayer = 0 AND NPix ≥ 192.2 mm < R ≤ 119.3 mm AirGap2 NBLayer = 0 AND NPix2nd = 0 AND NPix3rd ≥ 1119.3 mm < R ≤ 126.1 mm Pixel 3rd layer NBLayer = 0 AND NPix2nd = 0

R > 126.1 mm outside of Pixel 3rd layer NPix = 0

According to MC studies, It is found that this fake removal method, which depends onradius of the vertex, removes half to two-thirds of the initial set of 2-track vertices. However,a reduction in efficiency for reconstructing hadronic interaction vertices is only 2-10%.

6.4 Final selection

In the vertex finding procedure described in section 6.2 and 6.3, only 2-track vertices aretreated. To finalize the vertex finding, the 2-track vertices which are close to each otherneed to be merged. Since any track can be assigned in multiple 2-track vertices, such tracksmust be identified correctly and be resolved so that all track-vertex associations are unique.The algorithm performs an iterative process of cleaning the set of vertices, which is basedon an incompatibility-graph approach [28]. At each step it identifies two close vertices andmerges them, or finds the worst association of track-vertex for those multiplex associationsand breaks it. The iterations finish when no close vertices or multiply-assigned tracks areleft. This algorithm successfully works on events with track multiplicity up to ∼200, which issignificantly lager than the average multiplicty in events in this analysis (. 50 tracks/eventwithout the retracking and . 100 tracks/event with the retracking).

6.4.1 Breakdown of true vertices

All steps of secondary vertex reconstruction are already mentioned as above. By usinggenerated-particle information in MC, which is stored during the detector simulation byGeant4, it is possible to understand what types of the primary particles would produce thesecondary vertices. Table 6.3 shows breakdown of the primary particles. The ratio of eachkind of particles to all kinds of particles are also shown. The ratio in generated particles maybe different from the ratio in the reconstructed ones, and it is impossible to retain all nu-clear interactions and to remove backgrounds completely. In this analysis, some backgroundparticles are removed successfully as shown below.

6.4.2 Removing backgrounds

A proton-proton collision event may have decays of short lived particles, K0S and Λ decays,

and photon conversions. Since reconstructed secondary vertices include them and they arebackgrounds for hadronic interactions, it is essential to remove those backgrounds in some


Table 6.3: Breakdown of primary particles and the ratio.particle the ratio (%)

γ 16.6π± 46.5

proton 8.7neutron 5.6

K0S 7.4

K0L 1.8

K± 4.7other strange mesons 0.3

strange baryons 3.9charm mesons & baryons 0.7

way. Three sources of backgrounds, K0S , Λ and photon, can be eliminated from the set of

reconstructed vertices by assessing the distributions of their invariant mass. Since all thethree particles are neutral and decay into two charged particles in the most dominant decaychannels, it is enough to investigate the vertices which are neutral and have two tracks.

(a) K0S

K0S mainly decays into two neutral pions or two charged pions with opposite charge to each

other. The branching ratio for each decay mode is 30.7% (K0S → π0π0) and 69.2% (K0

S →π+π−), respectively [29]. Since only the latter decay mode can be reconstructed in the rangeof the inner detector, it is enough to look into the invariant mass of K0

S which decayed intotwo charged pions.

Figure 6.2 shows the invariant mass of the two charged tracks in data after the retracking,in the assumption where sources of all neutral 2-track vertices decayed into two charged pions.The most left peak at ∼ 250 MeV is caused by photon conversions, and the peak is shifteddue to the assumption in the mass of the tracks. Many K0

S provoke the largest peak at about500 MeV in the histogram, while the nominal mass of K0

S is 497.6 MeV [29]. In order toremove the decays of K0

S , the following selection cut for the invariant mass (mππ) is applied:

|mππ − 500 [MeV]| > 35 [MeV]. (6.1)

(b) Λ

There are two decay modes, for Λ particle, one is Λ → pπ− and the other is Λ → nπ0. Thebranching ratio of the former is about 64%, for the latter it is about 36%, respectively. Insimilar to the case of K0

S , the decay mode to nπ0 does not need to be considered since onlycharged particles are reconstructed. Figure 6.3 shows the invariant mass (mpπ−), which isthe mass of reconstructed neutral vertices with two tracks assumed to decay into proton andpion with negative charge, in data with the retracking.

The peak in the plot corresponds to Λ particles which decayed into proton and π−. Theselection cut for removing Λ is following:

|mpπ− − 1115 [MeV]| > 15 [MeV]. (6.2)


[MeV]ππm

0 1000 2000 3000 4000 5000 6000 7000 8000

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of V

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es /

40 M

eV

310

410

510

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710

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Data 2010

With Retracking

Figure 6.2: Invariant mass of reconstructed vertices in data with the retracking. Reconstructedneutral vertices wth two tracks are assumed to be associated with π+π−, and the vertices with |z| < 700mm are used.

MeV-πpm950 1000 1050 1100 1150 1200 1250

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ATLAS Work In Progress = 7 TeVs

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With Retracking

Figure 6.3: Invariant mass of reconstructed vertices in data with the retracking. Reconstructedneutral vertices with two tracks are assumed to be associated with pπ−, and the vertices with |z| < 700mm are used.


(c) photon

In the case of removing photon candidates, it is necessary to look into the invariant massassociated with positron and electron. In figure 6.4, the invariant mass (mee) are shown, inthe same way as two cases above, in the assumption where all reconstructed vertices decayedinto positron and electron. The highest peak around 400 MeV, which is shifted due to theassumption, correspond to K0

S . Since photon is massless particle and dominant in the peakat ∼ 0 MeV, vertices which have the mass close to zero are rejected:

mee > 50 [MeV] (6.3)

[MeV]eem

0 500 1000 1500 2000 2500 3000

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of V

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es /

40 M

eV

410

510

610


Data 2010

With Retracking

Figure 6.4: Invariant mass of reconstructed vertices in data with the retracking. Reconstructedneutral vertices with two tracks are assumed to be associated with e+e−, and the vertices with |z| < 700mm are used.

All steps for reconstruction and background removal are finished and it should be impor-tant to compare the number of vertices between data and MC, with/without the retracking.Table 6.4 shows the number of reconstructed vertices per selected event for each reconstruc-tion step, after all selections including background removal, with comparing data with MCbefore/after the retracking. During the reconstruction and analysis, reconstructed verticesare separated into three types: i) neutral ones with two tracks, ii) charged ones with twotracks and iii) ones with three or more tracks. Table 6.5, therefore, shows the number of re-constructed vertices per selected event for each type, comparing data with MC, before/afterbackground removal, with/without the retracking. In both of the tables, number of recon-structed vertices in data is greater than the one in MC, at any step or any type. This is mainlybecause primary particle multiplicity in data is ∼ 6-10 % higher than that in MC. Therefore,the correction factor to match MC to data is applied for results in MC (section 8.1).

As shown in the two tables, the fake removal method reduces reconstructed vertices by ∼90 %, which indicates that most of 2-track vertices reconstructed at the first step seem to befake vertices. Another important thing is that the retracking with large impact parameters


Table 6.4: Number of reconstructed secondary vertices per selected event at each step.

Before the retracking After the retrackingdata MC data MC

all 2-track vertices 3.58 2.94 61.4 49.6after fake removal 0.107 0.0932 1.86 1.52after final selection 0.0984 0.0859 1.22 1.07

after background removal 0.0471 0.0422 0.987 0.854

Table 6.5: Number of reconstructed secondary vertices per selected event for each type after allselections.

Before the retracking After the retrackingdata MC data MC

2-track neutral(before masscut) 0.0725 0.0635 0.641 0.5732-track neutral(after) 0.0212 0.0197 0.410 0.370

2-track charged 0.0234 0.0204 0.477 0.4033 or more tracks 0.00241 0.00205 0.101 0.0813

brings about 10 times more vertices than before, at any reconstructions steps. Vertex recon-struction efficiency, which is defined and looked into in section 7.2, goes significantly up andthis fact enables the hadronic interaction study to extend to outer layers.

There are much less vertices with three or more tracks than 2-track vertices, this meansthat most of primary particles might decay into two particles after nuclear interactions withmaterial in the detector.

6.5 Mapping of hadronic interactions

It is possible to look at 2-D map of the detector using results of the reconstruction. In thissection, therefore, some maps of the detector after all selections above are shown. Figure 6.5and 6.6 show the 2-D maps of the reconstructed vertices with |z| < 700 mm in x − y plane,figure 6.5 displays the region from the beam pipe to the SCT 2nd layer and figure 6.6 showsan enlarged map within the Pixel. As a result of the retracking, the modules and its supportsin the SCT 1st and 2nd layer are clearly visible along φ direction, which are located in R ∼300 mm and 371 mm, respectively. The number of modules along φ direction in each layer canbe confirmed, in fact there are 32 and 40 modules in the SCT 1st and 2nd layers, respectively.In addition, figure 6.5 gives an appearance of the Pixel octagonal support frame at R ∼ 200mm, as well as of the Pixel support tube which is the clear circle at R ∼ 220 mm and whichsurrounds the octagonal support. At the beam pipe and Pixel layers, although there were aplenty number of reconstructed vertices in the past study before the retracking [6], figure 6.6shows clearer distribution of the material in the detector, support and cooling pipe. Sincethis plot also reflects the φ structure of the modules, one can count the number of modulesin each layer, which is 22, 38, 52 in the 1st, 2nd and 3rd layers, respectively. The left plot in


figure 6.7 provides the distribution in the limited range around the SCT modules of the 1stlayer, a corresponding schematic drawing is put at right hand side. One can understand theSCT modules are put on the cylindrical support when looking carefully at those two figures.

X [mm]-400 -300 -200 -100 0 100 200 300 400

Y [m

m]

-400

-300

-200

-100

0

100

200

300

400

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410ATLAS Work In Progress = 7 TeVs

Data

With Retracking

Figure 6.5: The y vs. x distribution of secondary vertices reconstructed in data with the retracking.Secondary vertices with |z| < 700 mm, after all selections, have been used. Vertices from the beampipe to SCT 2nd layer are shown. Only bins with 8 or more entries are displayed.

The next several figures 6.8, 6.9 and 6.10 provide R vs. z distributions of the verticesintegrated over φ. The first figure 6.8 shows the entire Pixel detector including its endcapslocated in 450 mm < |z| < 700 mm, as well as the inner two layers in the SCT. Two rectangularregions with |z| > 410 mm and R < 200 mm contains many fake vertices since the fake removalmethod using the Pixel barrel hits does not work in the regions. In addition, MC studiesindicate that reconstructed vertices inside the beam pipe and in the gaps between the materiallayers are dominated by fake vertices such as combinatorial background. However, a smallfraction of the vertices in the area are due to hadronic interactions with the gases in the gapsmainly filled with N2. For the SCT region, 12 modules along z direction for each layer areclearly visible with their supports. Figure 6.9 presents the vertex positions in only the beampipe and the Pixel. The horizontal bands at R ∼ 47, 85, 120 mm correspond to the Pixeldetector modules, and the bands at R ∼ 65, 70, 105, 110 mm reflect supports, cables andservices. Various vertical bands are the supports. In similar to the case of y−x distributions,the vertex map and design picture in R− z plane focused on the SCT layers are presented infigure 6.10.

The third type of the vertex maps is φ vs. R distribution. Figure 6.11 shows the mapin φ − R plane integrated over z from −300 mm to 300 mm. This helps to investigate the φstructure in each layer, and the map focused on the beam pipe and B layer indicate that thestructure of the beam pipe appears to be broad (figure 6.12 (a)). Although this structure areseen for only data, this is because the beam pipe is not strictly centered around the origin inreality. To resolve this sinusoidal behaviour of the beam pipe, φ profile of the reconstructed


X [mm]-150 -100 -50 0 50 100 150

Y [m

m]

-150

-100

-50

0

50

100

150

310

410ATLAS Work In Progress

= 7 TeVsData

With Retracking

Figure 6.6: The y vs. x distribution of secondary vertices, within Pixel region, reconstructed indata with the retracking. Secondary vertices with |z| < 700 mm, after all selections, have been used.Minimum entries in each bin is 130.

X [mm]-20 0 20 40 60 80 100 120

Y [m

m]

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240

260

280

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320

340

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ATLAS Work In Progress

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(a) (b)

Figure 6.7: Secondary vertex distribution in x-y plane (left) and design geometry (right) for SCTmodules in SCT 1st layer. Secondary vertices with |z| < 700 mm, after all selections, have been used.Minimum entries in each bin is 5.


Z [mm]-600 -400 -200 0 200 400 600

R [m

m]

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250

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350

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With Retracking

Figure 6.8: The R vs. Z distribution of secondary vertices reconstructed in data with the retracking.Vertices from the beam pipe to SCT 2nd layer are shown. Only bins with 30 or more entries aredisplayed.

Z [mm]-400 -300 -200 -100 0 100 200 300 400

R [m

m]

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With Retracking

Figure 6.9: The R vs. Z distribution of secondary vertices reconstructed in data with the retracking.Vertices inside Pixel detector are shown. Only bins with 80 or more entries are displayed.


Z [mm]-600 -400 -200 0 200 400 600

R [m

m]

260

280

300

320

340

360

380

400

420

50

100

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With Retracking

(a)

BottomBracket

(b)

Figure 6.10: The R vs. Z distribution of Secondary vertices in SCT 1st and 2nd layer (left) anddesign geometry for SCT 1st layer with positive-z (right). (a) Minimum entries in each bin is 30.

vertices in the beam pipe (26 mm ≤ R < 39 mm) are fitted with the following function:

p0 + p1 cos (φ − p2), (6.4)

where p0 - p2 are the fit parameters. Figure 6.12 (b) shows the φ profile as well as the line offitted function. The fitting results in (p0, p1, p2) = (30.62 ± 0.00, −1.877 ± 0.002, 1.458 ±0.001), which shows only statistical uncertainties from the fitting. From this result, it isfound that the cernter of the beam pipe is located on (p1 cos p2, p1 sin p2) = (−0.211 ±0.002, −1.865 ± 0.003). Using the same procedure, it is possible to calculate the coordinatesof the centers for the 1st and 2nd pixel layers, but they are negligible because of very smallcontributions. These values are used for the comparison of the reconstructed vertices in thebeam pipe between data and MC (chapter 8).


R [mm]0 100 200 300 400 500

[rad

]φ

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Figure 6.11: The φ vs. R distribution of secondary vertices reconstructed in data with the retracking.Vertices with |z| < 300 mm are shown. Only bins with 20 or more entries are displayed.

R [mm]0 10 20 30 40 50 60 70

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]φ

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rage

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32


= 7 TeVs

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With Retracking

(b)

Figure 6.12: (a) The φ vs. R distribution of reconstructed vertices in the beam pipe and the Pixel1st layer, with |z| < 300 mm. The bin width is 1 mm in R, and 0.1 in φ. Minimum entries of each binis 300. (b) A fit to the φ profile of reconstructed vertices. The y-axis is the mean radius in the rangearound the beam pipe (26 ≤ R < 39 mm) for each φ bin. The bin width is 0.1 in φ.

Chapter 7

Quality of Secondary Vertex

In the previous chapter, the method of secondary vertex reconstruction and the result ofthe reconstruction are described. It is very important to evaluate the quality of the verticessince the set of the vertices may have many fakes regardless of applying some backgroundremovals. MC have been mainly used in the study in this chapter, as true information duringthe detector simulation is essential to calculate various quantities.

7.1 Vertex Resolutions

Evaluation of the quality starts with investigating the vertex resolution. The resolution canbe evaluated to measure the difference between the position of the reconstructed vertex andthe position of the true vertex. The position of the vertex is described in three dimensions,thus it is possible to get the resolution in each coordinate, while this section shows resolutionsonly in R and z coordinates. Figure 7.1 shows the distributions of ∆Z and ∆R in the beampipe (28 mm ≤ R < 36mm) after the retracking, which are defined as follows:

∆Z = Zreco − Ztruth, ∆R = Rreco − Rtruth, (7.1)

where Zreco and Rreco are the position of the reconstructed vertex, and Ztruth and Rtruth arethe position of the true vertex. These distributions are fitted with the following function:

p0 exp{−(x − p1)2

2p 22

}+ p3 exp

{−(x − p1)2

2p 24

}+ p5x + p6, (7.2)

where the first two Gaussian functions with a common mean represent the signal and thefirst-order polynomial reflects the background, p0 - p6 are the fit parameters. The resolusionis defined as the width of the core in the distribution, that is the fit parameter p2 (< p4).The resolution distributions for other layers are shown in figure 7.2 and figure 7.3, while zand R resolutions are put next to each other. Table 7.1 shows the summary of the resolutionsresulting from the fitting, with comparing before and after the retracking. For the SCT 2ndlayer, the resolutions before the retracking are not displayed due to lack of statistics in theregion. Hadronic interactions give great resolutions for both z and R directions, which variesfrom 100 µm to 1 mm, depending on radius.

43

CHAPTER 7. QUALITY OF SECONDARY VERTEX 44

[mm]truth Z− recoZ = Z∆

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Ent

ries

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mm

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MC

Fit

With Retracking

(a) Beam pipe R < 36 mm)≤(28 mm

/ndf = 28.61622χ

[mm]truth R− recoR = R∆

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2E

ntrie

s / 0

.1 m

m0

20

40

60

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100

310×


MC

Fit

With Retracking

(b) Beam pipe R < 36 mm)≤(28 mm

/ndf = 72.50372χ

Figure 7.1: (a)z and (b)R resolutions for vertices reconstructed in the beam pipe. The range of radiusfor the vertices is displayed in each plot. MC have been used with retracking. Red lines show fittedfunctions described in the text. Fit χ2 divided by number of degrees of freedom is also displayed.

Table 7.1: Summary of the z and R resolutions in each layer with or without retracking

before the retracking after the retrackingin z (µm) in R (µm) in z (µm) in R (µm)

Beam pipe 179±2 137±1 199±1 151±1B layer 190±3 172±2 206±1 161±1Pixel 2nd layer 179±4 175±6 190±2 165±2Pixel 3rd layer 250±14 704±38 292±6 345±5Pixel support tube 1143±26 1604±61 871±22 680±15SCT 1st layer 981±42 837±170 583±8 295±5SCT 2nd layer − − 573±20 386±14



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Fit

With Retracking

(c) B layer R < 72 mm)≤(47 mm

/ndf = 37.98922χ


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With Retracking


/ndf = 119.1312χ


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With Retracking

(e) Pixel 2nd layer R < 110 mm)≤(85 mm

/ndf = 16.36332χ


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Fit

With Retracking

(f) Pixel 2nd layer R < 110 mm)≤(85 mm

/ndf = 39.48162χ


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mm

2

4

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10

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MC

Fit

With Retracking

(g) Pixel 3rd layer R < 145 mm)≤(119 mm

/ndf = 7.51092χ


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4

6

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14310×


MC

Fit

With Retracking

(h) Pixel 3rd layer R < 145 mm)≤(119 mm

/ndf = 15.10182χ

Figure 7.2: z (left) and R (right) resolutions for vertices reconstructed in the B layer (top), in thePixel 2nd layer (middle) and in the Pixel 3rd layer (bottom). The range of radius for the vertices isdisplayed in each plot. MC have been used with retracking. Red lines show fitted functions describedin the text. Fit χ2 divided by number of degrees of freedom is also displayed.



-4 -2 0 2 4

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/ 0.2

mm

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4

5

6

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9

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MC

Fit

With Retracking

(i) Pixel support tube R < 240 mm)≤(180 mm

/ndf = 1.088112χ


-4 -2 0 2 4

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ries

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mm

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MC

Fit

With Retracking

(j) Pixel support tube R < 240 mm)≤(180 mm

/ndf = 3.418622χ


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MC

Fit

With Retracking

(k) SCT 1st layer R < 320 mm)≤(275 mm

/ndf = 1.701722χ


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ries

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MC

Fit

With Retracking

) SCT 1st layerl( R < 320 mm)≤(275 mm

/ndf = 15.98432χ


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ries

/ 0.2

mm

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0.8

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1.2

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MC

Fit

With Retracking

(m) SCT 2nd layer R < 391 mm)≤(351 mm

/ndf = 0.7231962χ


-4 -2 0 2 4

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ries

/ 0.2

mm

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0.6

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1.2

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1.6

310×


MC

Fit

With Retracking

(n) SCT 2nd layer R < 391 mm)≤(351 mm

/ndf = 2.861392χ

Figure 7.3: z (left) and R (right) resolutions for vertices reconstructed in the Pixel support tube(top), in the SCT 1st layer (middle) and in the SCT 2nd layer (bottom). The range of radius for thevertices is displayed in each plot. MC have been used with retracking. Red lines show fitted functionsdescribed in the text. Fit χ2 divided by number of degrees of freedom is also displayed.


7.2 Purity and efficiency for secondary vertices

Additional variables to evaluate the quality of the reconstructed vertices are purity and effi-ciency. Purity (p) is defined as the fraction of the reconstructed vertices matched to the trueones, and efficiency (ε) is the fraction of the true vertices matched to the reconstructed ones:

p =Nmatch

Nrec, (7.3)

ε =Nmatch

Ntrue, (7.4)

where Nrec is the number of reconstructed vertices, Ntrue is the number of true vertices,and Nmatch is the number of reconstructed vertices matched to true ones. The match, here,requires some restrictions. The first requirement is that the reconstructed vertices must bewithin the region which have 95 % of the vertices at the center of each resolution distribution.The next is that at least two tracks in the reconstructed vertex must match tracks in the truevertex. This match between the tracks is that the reconstructed tracks have ”matchingprobabilities” (Pmatch) greater than 80 %, expressed by:

Pmatch =10 · N common

Pix + 5 · N commonSCT + 1 · N common

TRT

10 · N trackPix + 5 · N track

SCT + 1 · N trackTRT

, (7.5)

where N commonSubDet is the number of common hits among the reconstructed and true tracks in

the sub-detector, and N trackSubDet is the number of hits which the reconstructed track has in

the sub-detector. Since both the average number of hits per track and the contribution ofthe hit to the reconstructed track parameters varies significantly between the different sub-detectors, the hits for each sub-detector are weighted as described in the formula. This hitbased matching probability and other method are shown in [30], with the result of trackreconstruction efficiency in each method.

Purity and efficiency have been calculated, following the definitions above, in each detectorlayer with comparing them between before and after the retracking. Table 7.2 shows the resultof the purity and efficiency for the secondary vertices with |z| < 300 mm. It is found thatthe retracking which allows large impact parameters raise secondary vertex reconstructionefficiency significantly while keeping the degradation of the purity small by around 10%.

7.3 Study on improvement of purity

As pointed out in the previous section, the purity decreases as a result of the retracking.Therefore, in this section, the study to improve the purity after the retracking is performed,although the reconstruction efficiency is sacrificed.

One of the causes of low purity is that the retracking allows many irrelevant tracks. Thisproduces a certain amount of combinatorial background from the random combination ofthe tracks. In order to resolve this problem, it is helpful to investigate the track parameterscarefully, and the impact parameter is focused in this study. The impact parameter is usuallymeasured with respect to the interaction point of protons or the position of reconstructedprimary vertex. However, if it is measured with respect to the position of the secondary vertexwhich have the track, the new impact parameter helps to evaluate the quality of the secondaryvertices. Therefore, the new impact parameters denoted by dSV

0 and zSV0 are calculated with


Table 7.2: Purity and efficiency for reconstructed vertices in each layer.

Resolution criteria Before the retracking After the retracking2-track, >2-track p (%) ε (%) p (%) ε (%)

Beam pipe |∆Z| < 1.0, 0.6 mm 82.1±0.1 4.77±0.01 78.93±0.04 31.17±0.03|∆R| < 1.0, 0.6 mm

B layer |∆Z| < 2.0, 1.0 mm 73.5±0.1 2.63±0.01 72.04±0.03 25.02±0.02|∆R| < 2.0, 1.0 mm

Pixel 2nd layer |∆Z| < 4.5, 3.0 mm 78.3±0.2 1.43±0.01 79.08±0.06 17.02±0.02|∆R| < 4.5, 3.0 mm

Pixel 3rd layer |∆Z| < 6.0, 5.0 mm 45.9±0.3 0.770±0.007 40.90±0.06 15.99±0.03|∆R| < 6.0, 5.0 mm

Pixel support tube |∆Z| < 6.0, 5.0 mm 51.0±0.7 0.713±0.014 26.92±0.08 22.48±0.07|∆R| < 6.0, 5.0 mm

SCT 1st layer |∆Z| < 6.0, 5.0 mm 49.4±0.9 0.292±0.008 38.39±0.13 11.71±0.05|∆R| < 6.0, 5.0 mm

SCT 2nd layer |∆Z| < 6.0, 5.0 mm 20.4±1.1 0.0698±0.0042 16.48±0.15 2.457±0.025|∆R| < 6.0, 6.0 mm

respect to the secondary vertex and are assessed. Figure 7.4 shows the distributions of thedSV

0 and zSV0 for all the socondary vertices after selection cuts mentioned in chapter 6. The

plots compare the data against MC, and integral of each histogram is normalised to unity.

[mm]0SVd

-1.5 -1 -0.5 0 0.5 1 1.5

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ber

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es /

even

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0

0.02

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= 7 TeVs

Data 2010MC

With Retracking

(a)

[mm]0SVz

-2 -1 0 1 2

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even

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0

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0.1 ATLAS Work In Progress= 7 TeVs

Data 2010MC

With Retracking

(b)

Figure 7.4: Distributions of dSV0 (left) and zSV

0 (right) for the reconstructed secondary vertices afterall cuts mentioned in chapter6, in data (black lines with points) and MC (filled histograms). Allhistograms are normalised to unity.

Figure 7.5 shows the purity and efficiency as a function of the maximum dSV0 (left) and

zSV0 (right), for the reconstructed secondary vertices and the secondary tracks at the vertices.

Figure 7.6 and 7.7 presents the same plots for other layers from the B layer to the SCT 2ndlayer. The tighter cuts on the impact parameters are set, the higher the purity becomes forall the layers, especially for the outer layers, with the sacrifice of the efficiency.

To keep the efficiency relatively high, the selection cuts on the impact parameters aredecided to be set as follows:

|dSV0 | < 1 mm, |zSV

0 | < 2 mm. (7.6)


Table 7.3 summarise the purity and the efficiency for each layer after the new cuts on theimpact parameters with respect to the secondary vertex positions. The result values areseparated into three types depending on which cut are applied: only |dSV

0 | < 1 mm, only|zSV

0 | < 2 mm, and both of them.

| [mm] (wrt SV)0

max |d

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Pur

ity

0.75

0.76

0.77

0.78

0.79

0.8

0.81

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0.83

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Eff

icie

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0

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Purity

Efficiency

With Retracking

(a) Beam pipe R < 36 mm)≤(28 mm

| [mm] (wrt SV)0

max |z

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Pur

ity

0.76

0.77

0.78

0.79

0.8

0.81

0.82

0.83

Eff

icie

ncy

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45


Purity

Efficiency

With Retracking

(b) Beam pipe R < 36 mm)≤(28 mm

Figure 7.5: Purity and efficiency for vertices reconstructed in the beam pipe, as functions of themaximum of |dSV

0 | (left) and of |zSV0 | (right) in MC. The range of radius for the vertices is displayed

in each plot and the vertices with |z| < 300 mm have been used with retracking. Values of the purity(black) and the efficiency (red) correspond to the left and right vertical axes, respectively.

Table 7.3: Purity and efficiency with impact parameters cuts after the retracking.

|dSV0 | < 1 mm |zSV

0 | < 2 mm|dSV

0 | < 1 mm &|zSV

0 | < 2 mmp (%) ε (%) p (%) ε (%) p (%) ε (%)

Beam pipe 79.34±0.04 30.78±0.03 79.61±0.04 30.78±0.03 79.84±0.04 30.42±0.03B layer 74.00±0.04 24.15±0.02 73.73±0.03 24.60±0.02 75.01±0.04 23.83±0.02Pixel 2nd layer 80.45±0.06 16.46±0.02 80.44±0.06 16.70±0.02 81.15±0.06 16.21±0.02Pixel 3rd layer 58.69±0.09 12.36±0.03 54.67±0.09 11.35±0.03 61.61±0.10 9.879±0.024Pixel support tube 52.52±0.13 19.30±0.06 44.61±0.13 18.40±0.06 57.53±0.15 16.87±0.06SCT 1st layer 60.05±0.17 10.46±0.04 50.81±0.16 10.73±0.04 63.25±0.17 9.983±0.043SCT 2nd layer 33.00±0.30 2.092±0.023 24.24±0.22 2.294±0.024 37.14±0.33 2.031±0.023

These new requirements helps to resolve a bad agreement in the number of the verticesbetween data and MC due to the retracking, as well as efficient removal of many fake vertices.The results for the comparison between data and MC are shown and discussed in the nextchapter.


| [mm] (wrt SV)0

max |d

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Pur

ity

0.7

0.71

0.72

0.73

0.74

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0.76

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0.8

Eff

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0

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0.35


Purity

Efficiency

With Retracking


| [mm] (wrt SV)0

max |z

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Pur

ity

0.7

0.71

0.72

0.73

0.74

0.75

0.76

0.77

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0.79

0.8

Eff

icie

ncy

0

0.05

0.1

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0.3

0.35


Purity

Efficiency

With Retracking

(d) B layer R < 72 mm)≤(47 mm

| [mm] (wrt SV)0

max |d

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Pur

ity

0.76

0.78

0.8

0.82

0.84

0.86

0.88

0.9

Eff

icie

ncy

0

0.05

0.1

0.15

0.2


Purity

Efficiency

With Retracking

(e) Pixel 2nd layer R < 110 mm)≤(85 mm

| [mm] (wrt SV)0

max |z

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Pur

ity

0.75

0.76

0.77

0.78

0.79

0.8

0.81

0.82

0.83

0.84

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Eff

icie

ncy

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0.11

0.12

0.13

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0.15

0.16

0.17

0.18

0.19


Purity

Efficiency

With Retracking

(f) Pixel 2nd layer R < 110 mm)≤(85 mm

| [mm] (wrt SV)0

max |d

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

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ity

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0.5

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1

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0.18


Purity

Efficiency

With Retracking

(g) Pixel 3rd layer R < 145 mm)≤(119 mm

| [mm] (wrt SV)0

max |z

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Pur

ity

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Eff

icie

ncy

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18


Purity

Efficiency

With Retracking

(h) Pixel 3rd layer R < 145 mm)≤(119 mm

Figure 7.6: Purity and efficiency for vertices reconstructed in the B layer (top), in the Pixel 2ndlayer (middle) and in the Pixel 3rd layer (bottom), as functions of the maximum of |dSV

0 | (left) and of|zSV

0 | (right) in MC. The range of radius for the vertices is displayed in each plot and the vertices with|z| < 300 mm have been used with retracking. Values of the purity (black) and the efficiency (red)correspond to the left and right vertical axes, respectively.


| [mm] (wrt SV)0

max |d

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Pur

ity

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

Eff

icie

ncy

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0.05

0.1

0.15

0.2

0.25


Purity

Efficiency

With Retracking

(i) Pixel support tube R < 240 mm)≤(180 mm

| [mm] (wrt SV)0

max |z

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Pur

ity

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Purity

Efficiency

With Retracking

(j) Pixel support tube R < 240 mm)≤(180 mm

| [mm] (wrt SV)0

max |d

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

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ity

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Purity

Efficiency

With Retracking

(k) SCT 1st layer R < 320 mm)≤(275 mm

| [mm] (wrt SV)0

max |z

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Pur

ity

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0.45

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Eff

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0.04

0.06

0.08

0.1

0.12

0.14ATLAS Work In ProgressPurity

Efficiency

With Retracking

) SCT 1st layerl( R < 320 mm)≤(275 mm

| [mm] (wrt SV)0

max |d

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Pur

ity

0

0.1

0.2

0.3

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ncy

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0.005

0.01

0.015

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0.03

0.035

0.04

0.045


Purity

Efficiency

With Retracking

(m) SCT 2nd layer R < 391 mm)≤(351 mm

| [mm] (wrt SV)0

max |z

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Pur

ity

0

0.05

0.1

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0.015

0.02

0.025

0.03

0.035


Purity

Efficiency

With Retracking

(n) SCT 2nd layer R < 391 mm)≤(351 mm

Figure 7.7: Purity and efficiency for vertices reconstructed in the Pixel support tube (top), in theSCT 1st layer (middle) and in the SCT 2nd layer (bottom), as functions of the maximum of |dSV

0 |(left) and of |zSV

0 | (right) in MC. The range of radius for the vertices is displayed in each plot andthe vertices with |z| < 300 mm have been used with retracking. Values of the purity (black) and theefficiency (red) correspond to the left and right vertical axes, respectively.


7.4 Study using MC samples with extra material

In order to evaluate the effect on increase of the material in the detector, the MC sampleswhich have the material distorted uniformly in the whole ID are used, with the retracking.Table 9.1 shows the characteristics of their samples as well as the nominal MC which is thesame MC as treated above. These samples with distorted material are also used in chapter 9to assess the systematic uncertainty on the measurement.

Table 7.4: Characteristics of MC samples distorted in the whole ID.

Name Characteristics Number of eventsnominal The default geometry 19989200distort1 +5% material in the whole ID 4999689distort2 +10% material in the whole ID 4998681

Using these 3 samples, the same analysis described up to the previous section is performed.Table 7.5 summarises the purity and efficiency for the secondary vertices in each layer afterthe cuts on the dSV

0 and zSV0 expressed by equation (7.6). The purity hardly depend on the

extra material, in fact the change is within a few percent. On the other hand, as predicted,the efficiency of the secondary vertex reconstruction strongly depends on the material. Asthe material increases by 5-10%, the efficiency goes down by 3-10%. This is due to reductionof the tracking efficiency for the secondary tracks which pass through the detector with extramaterial.

Table 7.5: Comparison of purity and efficiency between the nominal and distorted MC samples.

nominal distort1 (+5%) distort2 (+10%)p (%) ε (%) p (%) ε (%) p (%) ε (%)

Beam pipe 79.84±0.04 30.42±0.03 79.84±0.08 29.41±0.05 79.41±0.08 28.60±0.05B layer 75.01±0.04 23.83±0.02 75.01±0.07 22.75±0.04 74.65±0.07 22.10±0.04Pixel 2nd layer 81.15±0.06 16.21±0.02 81.23±0.11 15.40±0.04 81.05±0.11 14.94±0.04Pixel 3rd layer 61.61±0.10 9.879±0.024 61.59±0.20 9.456±0.046 60.76±0.20 8.961±0.044Pixel support tube 57.53±0.15 16.87±0.06 58.21±0.29 16.24±0.11 57.91±0.29 15.67±0.11SCT 1st layer 63.25±0.17 9.983±0.043 63.92±0.34 9.546±0.081 62.97±0.34 9.345±0.079SCT 2nd layer 37.14±0.33 2.031±0.023 38.63±0.66 1.980±0.043 37.78±0.65 1.924±0.042

Chapter 8

Comparison in data and MC

Since the major goal of the study is to evaluate the difference of the material in the detectorbetween data and MC, it is essential to compare the vertex yields in data with the yields inMC. Therefore, in this chapter, the comparison of the distributions for vertex yields in eachlayer is performed after proper corrections. The results only after the retracking are shownand discussed since the results before the retracking are already described in [6].

8.1 Correction for primary tracks

The number of nuclear interactions between primary particles and the material in the detec-tor should be proportional to the number of primary particles passing through the detector.Although the number of primary tracks in MC must agree with the number in data, thereis some disagreement [23]. Figure 8.1 shows momentum distributions of primary tracks in-tersecting the beam pipe at |z| < 300 mm, comparing data with MC. The two distributionsagree well, while there is a little differences in the low momentum region. According to [6],the correction for these differences, which means reweighting the MC momentum spectrum tomatch the data, did not change the result significantly. Hence, the ratio of the total numberof the tracks in data and MC is used as the correction factor in this analysis.

Thus, the number of primaries in MC needs to be corrected such that it amounts to thesame number as the number in data. To determine this correction, all reconstructed primarytracks are extrapolated to find their intersections with layers in the inner detector, and trackswhich intersect a layer with |z| < 300, 700 mm are considered further. Since primary tracksproduced at small polar angles θ travel through more material and this results in a higherinteraction probability, each track is weighted by 1/ sin θ. The ratio of the weighted sum ofthe number of the tracks in data and MC gives average correction factors. Table 8.1 showsthe correction factors in each layer, for the vertices with |z| < 300, 700 mm. These factorsare applied for the distributions of the vertex yields in MC, below.

8.2 Comparison of vertex yields

R distributions

In order to enable the comparison between data and MC, several histograms are prepared.Figure 8.2 and 8.3 shows the radius distributions of the reconstructed secondary verticesintegrated over φ and z, comparing data with MC. The two figures include the vertices with

53

CHAPTER 8. COMPARISON IN DATA AND MC 54

p [GeV]

0 2 4 6 8 10 12 14

Fra

ctio

n / 0

.2 G

eV

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14


Data 2010MC

With Retracking

Figure 8.1: Momentum spectrum of primary tracks intersecting the beam pipe at |z| < 300 mm indata (points) and MC (filled histogram). Both spectra are normalised to unity in the displayed range.

Table 8.1: Summary of the correction factors for the primary tracks in each layer.

factors factors|z| < 300 mm |z| < 700 mm

Beam pipe 1.074 1.074B layer 1.073 1.074Pixel 2nd layer 1.067 1.074Pixel 3rd layer 1.065 1.073SCT 1st layer 1.063 1.064SCT 2nd layer 1.062 1.063


|z| < 300, 700 mm, respectively. Each peak corresponds to either layer with the modules orsupport structure as follows:

• R ∼ 30 mm: the beam pipe.

• R ∼ 50 mm: the B layer including its modules.

• R ∼ 70 mm: support of the B layer.

• R ∼ 90 mm: the Pixel 2nd layer including its modules.

• R ∼ 110 mm: support of the Pixel 2nd layer.

• R ∼ 130 mm: the Pixel 3rd layer including its modules.

• R ∼ 200 mm: the octagonal Pixel support frame.

• R ∼ 230 mm: the Pixel support tube.

• R ∼ 260 mm: the support between the Pixel and SCT.

• R ∼ 280 mm: the support of the SCT 1st layer.

• R ∼ 300 mm: the SCT 1st layer including its modules.

• R ∼ 355 mm: the support of the SCT 2nd layer.

• R ∼ 445 mm: the SCT 3rd layer including its modules.

For the SCT 3rd layer or outers, it is impossible to distinguish the layer itself from the supportstructure. This is because the track reconstruction efficiency for the track starting at largerradii than the SCT 2nd layer is very low, due to the requirement of the track having at least4 silicon hits. In the outer region with R greater than 150 mm, non-negligible discrepancybetween data and MC is observed.

Although the cause of this discrepancy is attributed to the reconstruction of the manyirrelevant tracks as a result of the retracking, this can be resolved by looking carefully into thetrack parameters for the secondary tracks. The method of the cuts on the impact parameterswith respect to the secondary vertex positions, dSV

0 and zSV0 , is adopted in this analysis.

Figure 8.4 and 8.5 shows the same distributions but after the selection cuts, |dSV0 | < 1 mm

and |zSV0 | < 2 mm, described in section 7.3. Those cuts successfully removes many fake

vertices, especially between the Pixel and SCT, as well as makes the discrepancy in data andMC smaller. Since the purity increased after the cuts, the structure of the detector becomesmore clearly visible.

z distributions

It is also effective to study z distributions of the vertices in each layer. Figure 8.6 and 8.7shows the number of the secondary vertices per selected event as a function of z in each layer.The integrated range in R for each layer is displayed in each plot. The distribution for thebeam pipe (figure 8.6 (a)) is drawn after the center of the beam pipe in data is corrected by themethod described in section 6.5. Only for the beam pipe, since it is difficult to distinguish fakevertices into true vertices under the environment of the high track density around the beampipe after the retracking, the distribution without the retracking is used. As the particles


R [mm]

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ATLAS Work In ProgressData 2010MC

With Retracking|z| < 300 mm

Figure 8.2: Radius distributions of reconstructed secondary vertices with |z| < 300 mm in data(points) and MC (filled histogram) after applying the corrections and selection cuts including back-ground removals.

R [mm]

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-110ATLAS Work In Progress

Data 2010MC

With Retracking|z| < 700 mm

Figure 8.3: Radius distributions of reconstructed secondary vertices with |z| < 700 mm in data(points) and MC (filled histogram) after applying the corrections and selection cuts including back-ground removals.


R [mm]

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| < 1 mmwrtSV

0|d

| < 2 mmwrtSV

0|z

|z| < 300 mm

Figure 8.4: Comparison of radius distributions of reconstructed secondary vertices with |z| < 300 mmbetween data (points) and MC (filled histogram) after the cuts for impact parameters with respect tothe secondary vertex positions.

R [mm]

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With Retracking

| < 1 mmwrtSV

0|d

| < 2 mmwrtSV

0|z

|z| < 700 mm

Figure 8.5: Comparison of radius distributions of reconstructed secondary vertices with |z| < 700 mmbetween data (points) and MC (filled histogram) after the cuts for impact parameters with respect tothe secondary vertex positions.


with larger η travel through longer distance in the material, the number of reconstructedvertices around z = 0 are fewer than the one at larger z. There is an asymmetric feature inthe MC though, this is due to the symmetric cuts on the longitudinal impact parameter zPV

0

for the secondary tracks (table 6.1), in spite of z asymmetry in the primary vertex positionsshown in figure 5.1. For other layers, this effect does not appear because the wide enoughrange of the longitudinal impact parameter zPV

0 is used during the retracking.For the pixel layers (figure 8.6 (a-c)), there are several sharp peaks, which represent the

silicon sensors in the module. Most of the ’spikes’ are sharper in the MC, two reasons areconsidered: the MC has a simplified geometry for some detector elements, and misalignmentsin data can cause broadening, despite of the fact that the distribution for each layer in datais in very good agreement with the one in MC.

In the distributions of the Pixel support tube (figure 8.7 (a)), the peaks correspondingto the structure of the octagonal support frame are well seen. The number of yields in eachbin changes greatly at |z| = 400 mm, this is because the fake removal using the hits of thebarrel Pixel layers works for the vertices with |z| < 400 mm, in this radial region. The restof the distributions in figure 8.7 are for the SCT 1st and 2nd layers. The retracking alsoprovides the visibility of the SCT structure. In both of the distributions, the peaks due tohybrid assembly, which is attached to the SCT sensors and has the highest density in theSCT modules, are visible. The number of the vertex yields in data and MC agrees well forthe SCT 1st layer, however the data has more vertices for the 2nd layer than the MC.

Table 8.2 shows the number of the vertex yields with |z| < 300 and 700 mm in each layerafter all the corrections and selections including the cuts on dSV

0 and zSV0 , comparing data

with MC. Only statistical uncertainties are presented in the table, and the systematic effectsare considered in chapter9. For all the layers except for the SCT 2nd layer, the differencesof the vertex yields between data and MC are within about 10%. Whereas there is about15% larger number of the yields at the SCT 2nd layer in data than in MC, the cause of thisdifference have not been resolved yet. Some possibilities are considered for the problem, oneis that more bad tracks were reconstructed in data than in MC as a result of the retracking,and another is that more material exists in reality than estimated.

Table 8.2: Number of the vertex yields in data and MC.

|z| < 300 mm |z| < 700 mmdata MC data MC

Beam pipe * (1.328 ± 0.018) × 10−2 (1.278 ± 0.032) × 10−2 (1.331 ± 0.018) × 10−2 (1.280 ± 0.032) × 10−2

B layer (1.116 ± 0.001) × 10−1 (1.191 ± 0.001) × 10−1 (1.491 ± 0.001) × 10−1 (1.559 ± 0.001) × 10−1

Pixel 2nd layer (3.472 ± 0.003) × 10−2 (3.829 ± 0.005) × 10−3 (5.996 ± 0.004) × 10−2 (6.331 ± 0.007) × 10−2

Pixel 3rd layer (1.750 ± 0.002) × 10−2 (1.899 ± 0.004) × 10−2 (3.621 ± 0.003) × 10−2 (3.842 ± 0.006) × 10−2

Pixel support tube (9.000 ± 0.015) × 10−3 (8.758 ± 0.026) × 10−3 (2.333 ± 0.002) × 10−2 (2.254 ± 0.004) × 10−2

SCT 1st layer (5.950 ± 0.012) × 10−3 (5.957 ± 0.022) × 10−3 (1.329 ± 0.002) × 10−2 (1.311 ± 0.003) × 10−2

SCT 2nd layer (1.909 ± 0.007) × 10−3 (1.660 ± 0.011) × 10−3 (4.302 ± 0.010) × 10−3 (3.725 ± 0.017) × 10−3

* For the beam pipe, the values without the retracking are displayed.


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Figure 8.7: Comparison of the z distributions of the secondary vertices in each layer from (a)thePixel support tube to (c)the SCT 2nd layer between data (points) and MC (filled histograms). Theradius range in each layer is displayed in each plot. The vertical axes correspond to the number ofsecondary vertices per selected event. These plots show all vertices after all the selections includingthe cuts for impact parameters with respect to the secondary vertex positons.


8.3 pT and η distributions

The radius distributions and z distributions for each layer are useful when investigating thestructure of the material. On the other hand, when the effects on the tracking efficiency areconsidered, the uncertainty as a function of η and pT are used [23] in general. In addition, whilethe radiation length and interaction length are well understood in η distributions (figure 3.8,3.9), in order to evaluate the material uncertainty which affects the uncertainty on the trackingefficiency, it is essential to assess the number of vertex yields due to hadronic interactions asa function of η as well as pT .

Figure 8.8 shows the η distribution for the positions of reconstructed vertices after allthe selection cuts, comparing data with MC. Their distributions agree well except for highη region (|η| >2.5). In this high η region, there should be few true vertices due to lack ofthe material outside of the beam pipe, therefore fake vertices are dominant and the retrackigmay cause the difference between data and MC. Figure 8.9 presents another distribution forthe secondary vertices, it is the distribution of pT which is transverse projection of the sumof momenta for all the secondary tracks which happened in the vertex. Although the vertexyields around 0.8 MeV in data are a few percent more than the one in MC, the distributionsagree reasonably well.

According to [23], the material uncertainty strongly depends on the η and pT . Therefore,the number of the vertices as a function of both η and pT are investigated. The inelasticcross section of the hadronic interaction depends a little on momenta of interaction particles.Hence, the number of vertices should be corrected for the number of primary particles passingthough the detector among each pT and η bin. As NSV (ηi, pTj , pk) expresses the number ofsecondary vertices within bins of three variables ηi, pTj , pk, the ratio of the number of thevertices in data and MC after the correction for the number of the primary tracks is givenby:

r(ηi, pTj ) =Ndata

SV (ηi, pTj )∑k NMC

SV (ηi, pTj , pk) ·Ndata

PrimTrk(ηi, pTj, pk)

NMCPrimTrk(ηi, pTj

, pk)

, (8.1)

where NPrimTrk means the number of primary tracks. The ratio r as a function of pT and η issummarised in table 8.3. In the table, pT and η are separated into 9 and 5 bins, respectively.The difference between data and MC varies from about 1% to 10%. The ratios integratedover one variable are also shown in the table, and the distances of them to unity are around5%. This result indicates that the material uncertainty, which means the difference of thematerial in the ID between the reality and the simulation, is about 5% in terms of thematerial measurement using hadronic interactions. The physics impacts which profit fromthis are discussed in section 10.3.


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Table 8.3: Ratio of secondary vertex yields in data and MC as a function of pT and η.

pT bin [MeV] |η| < 1.3 1.3 ≤ |η| < 1.9 1.9 ≤ |η| < 2.1 2.1 ≤ |η| < 2.3 2.3 ≤ |η| < 2.5 all η bins100 < pT ≤ 150 1.098±0.007 0.919±0.005 0.944±0.007 0.956±0.007 0.912±0.006 0.964±0.003150 < pT ≤ 200 1.115±0.006 0.969±0.005 0.930±0.006 0.954±0.006 0.924±0.006 0.981±0.003200 < pT ≤ 250 1.118±0.006 0.978±0.004 0.928±0.006 0.976±0.006 0.935±0.005 0.990±0.002250 < pT ≤ 300 1.114±0.005 0.968±0.004 0.955±0.006 1.004±0.006 0.967±0.005 1.002±0.002300 < pT ≤ 350 1.141±0.005 0.999±0.004 0.968±0.006 1.043±0.006 0.993±0.005 1.029±0.002350 < pT ≤ 400 1.113±0.005 1.013±0.004 0.971±0.005 1.072±0.006 1.014±0.005 1.037±0.002400 < pT ≤ 450 1.111±0.005 1.014±0.004 0.990±0.005 1.093±0.006 1.037±0.005 1.047±0.002450 < pT ≤ 500 1.095±0.005 1.031±0.004 0.991±0.005 1.112±0.006 1.046±0.005 1.054±0.002500 < pT 1.042±0.001 1.068±0.001 1.047±0.001 1.155±0.001 1.082±0.001 1.070±0.004all pT bins 1.054±0.001 1.052±0.001 1.026±0.001 1.122±0.001 1.054±0.001 1.0587±0.0004

Chapter 9

Systematic Uncertainty

Since results above included only statistical uncertainty, systematic uncertainty needs to beconsidered. In this chapter, possible uncertainties are discussed for various sources.

9.1 Systematics due to selection criteria

Various selection cuts are applied for the secondary vertices during the track and vertexreconstruction. Hence, if cut values change, it could happen that the results such as thenumber of vertices change. Since the estimation for such effects from various cuts havealready been performed in [6], the same uncertainties can be applied to the results in thisanalysis.

The systematic uncertainties due to this source are determined by varying criteria to:

• merge vertices close to each other,

• uniquely assign tracks to a single vertex,

• and change the allowed range of χ2 for two-track vertices.

After varying the values for selection criteria in data and MC for each case, it was found thatthe difference between data and MC is less than 1%. Therefore, 1% systematic uncertaintydue to these sources is assigned.

9.2 The closure test using distorted MC samples

Although this study looks at reconstructed secondary vertices, the number of them is affectedby track reconstruction efficiency which is a little sensitive to an increase/decrease in thematerial. In fact, there are two effects for the number of the reconstructed secondary verticeswhen the material increases/decreases. If the material increases,

• primary particles interact with the material more often,

• on the other hand, track reconstruction efficiency for secondary tracks decreases.

The former makes the number of the reconstructed vertices go up. In contrast the numberof the reconstructed vertices decreases due to the latter, due to decrease in the number ofreconstructed secondary tracks. It is very hard to decouple and evaluate these two effects

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CHAPTER 9. SYSTEMATIC UNCERTAINTY 64

correctly because track reconstruction efficiency cannot be calculated in data in which thereis no true information. In order to estimate the systematic uncertainty on the track recon-struction efficiency, the MC-only study is adopted. This is called ”the closure test” whichattempts to assess the possibility of measuring known material distortions between severalMC samples, as well as to evaluate the difference of the reconstruction efficiency between theirsamples. This study is performed by using MC samples which have an increase/decrease ofthe material in the detector.

The closure test uses the MC samples which have the material distorted uniformly in thewhole ID, with the retracking. Table 9.1 shows the characteristics of their samples as wellas the nominal MC which is the same as the MC sample used in the analysis during thecomparison between data and MC.

Table 9.1: Characteristics of MC samples distorted in the whole ID.

Name Characteristics Number of eventsnominal The default geometry 19989200distort1 +5% material in the whole ID 4999689distort2 +10% material in the whole ID 4998681

Using these 3 samples, the same analysis described up to the previous chapter are per-formed. Figure 9.1 shows the results of the analysis, in which the vertical axes correspond tothe ratio defined as Ndistort/Nnominal, where the Ndistort is the number of the reconstructedsecondary vertices in the distorted MC and Nnominal is the same number for the nominal MC.The left and right plots use only vertices with |z| < 300 and 700 mm, respectively. Table 9.2summarise the ratio in each layer. For all layers from the B layer to the SCT 2nd layer, thenumber of reconstructed vertices reflects the increase in the material, although the ratio is alittle fewer than the ratio of the material amount due to the tracking efficiency going down.The ratio in the most left bin shown in figure 9.1, which corresponds to the beam pipe, isless than 1.0 for both plots. This is because the material in the beam pipe have not beendistorted and only effect on the tracking efficiency works.

Table 9.2: The ratio of the number of vertices in distorted and nominal MC.|z| < 300 mm |z| < 700 mm

distort1/nominal distort2/nominal distort1/nominal distort2/nominal

Beam pipe 0.988±0.002 0.980±0.002 0.986±0.002 0.975±0.002B layer 1.024±0.002 1.051±0.002 1.024±0.002 1.050±0.002Pixel 2nd layer 1.020±0.003 1.036±0.003 1.024±0.003 1.049±0.003Pixel 3rd layer 1.035±0.005 1.042±0.005 1.037±0.003 1.056±0.003Pixel support tube 1.039±0.007 1.066±0.007 1.035±0.004 1.064±0.004SCT 1st layer 1.037±0.008 1.066±0.009 1.035±0.006 1.065±0.006SCT 2nd layer 1.033±0.016 1.061±0.016 1.048±0.011 1.069±0.011

If there is no effect on the track reconstruction efficiency, it is predicted that the ratioin distorted and nominal MC should be the ratio of the material, i.e. the ratio should be1.05 and 1.10 for the distort1 and distort2, respectively. Therefore, the differences betweenthese predicted ratios and the measured ratios are the systematic effects on the trackingefficiency. For each layer, the larger one out of the differences for two distorted samples,including their statistical uncertainties, are assigned as the systematics. Table 10.2 shows the

CHAPTER 9. SYSTEMATIC UNCERTAINTY 65

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Figure 9.1: The ratio of the number of the vertices in the distorted MC to the one in the nominal MCas a function of radius. Used distorted samples have extra 5% (red) and 10% (blue) material in thewhole ID. Reconstructed vertices with |z| < 300 mm (left) and 700 mm (right) are used and the cutsfor impact parameters with respect to secondary vertex positions are applied. Each bin correspondsto each layer, and the width of each bin is the range of each layer.

systematic uncertainty for each layer and for each range in z. Since the uncertainty on thetracking efficiency depends on a length of the track, which indirectly connected to where thetrack starts, the uncertainty is separated into the layer. For the beam pipe, because of nodistortion in the area, the difference from 1.0 is assigned as the systematic uncertainty.

Table 9.3: The systematic uncertainty due to the track reconstruction efficiency.

|z| < 300 mm |z| < 700 mm(%) (%)

Beam pipe 2.4 2.7B layer 5.1 5.2Pixel 2nd layer 6.7 5.4Pixel 3rd layer 6.3 4.9Pixel support tube 4.1 4.0SCT 1st layer 4.3 4.1SCT 2nd layer 5.5 4.2

9.3 Total systematic uncertainty

The total systematic uncertainty is the sum of all the uncertainty mentioned above. Therefore,1 % systematic due to the selection criteria and the systematic resulted from the closure testfor each layer are applied to the final results in section 10.1.

Chapter 10

Results

10.1 Numerical Comparison in data and MC

The number of the secondary vertex yields in each layer is already evaluated in chapter 8 andthe corresponding systematic uncertainties are described in chapter 9. The combination ofthem provides the final results on the vertex yields located in each layer. Table 10.1 showsthe ratio of the vertex yields inside each layer in data and MC. Two values for each layercorrespond to the ranges in z of secondary vertex positions, |z| < 300 or 700 mm.

Most of the ratios with |z| < 300 mm is different from unity even if the systematicuncertainties are considered. There are three possible candidates of the causes as follows:

• Amount of the material implemented in the MC may be several percent from the onein the reality.

• Mismodelling of the tracking. Due to the retracking, a large number of the irrelevant orbad reconstructed tracks affects the secondary vertex reconstruction. A certain rate ofvertices that contain such bad tracks is removed as described in chapter 7, neverthelessthose vertices could retain.

• Since the selected range of the vertices does not cover the whole barrel region, if there iseven a little disagreement in the ’spikes’ expressing large quantities of material betweendata and MC, the number of vertex yields could be different between them.

On the other hand, except for the SCT 2nd layer, the number of the vertex yields with|z| < 700 mm inside each layer agrees between data and MC in the range of statistical andsystematic uncertainties. Hence, the total amount of the material and the effect on thetracking can be well described in the range of the whole barrel. For the SCT 2nd layer,however, there is a non-negligible discrepancy in data and MC. This indicates that the badtracks with large impact parameters are reconstructed more often in data than in MC, andalso the more material in data could be placed in the SCT 2nd layer.

10.2 Systematic uncertainty on track reconstruction efficiency

The major goal of reducing the material uncertainty is to decrease the systematic uncertaintyon the track reconstruction efficiency. According to [23, 31], the systematic uncertainty on thetrack reconstruction efficiency strongly depends on pT and η of the tracks. Table 10.2 showsthe systematic uncertainty for given pT and η. It varies from ±2% to ±15%, which decreases

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CHAPTER 10. RESULTS 67

Table 10.1: The ratio of number of the vertex yields in data and MC.

|z| < 300 mm |z| < 700 mmBeam pipe * 1.040±0.003±0.035 1.040±0.003±0.038B layer 0.937±0.001±0.057 0.956±0.001±0.059Pixel 2nd layer 0.907±0.002±0.070 0.947±0.001±0.061Pixel 3rd layer 0.921±0.002±0.067 0.942±0.002±0.056Pixel support tube 1.028±0.004±0.052 1.035±0.002±0.052SCT 1st layer 0.999±0.004±0.053 1.014±0.003±0.052SCT 2nd layer 1.150±0.009±0.075 1.155±0.006±0.060

* For the beam pipe, the values without the retracking are displayed.

with pT and increases with |η|. These values are currently used as the ATLAS standard andinclude 10% uncertainty in the whole ID and 30% uncertainty on material between Pixel andSCT. On the other hand, the analysis described in chapter 8 provided about 5% materialuncertainty as a result of the rough estimation. Therefore, this rough uncertainty can reducethe systematics on the tracking efficiency by half1. Under the assumption that the systematicson the tracking efficiency decreased by the half for all the bins shown in 10.2, the impacts onthe physics results from this improvements are studied in the next section.

Table 10.2: Summary of the tracking efficiency systematics due to the material uncertainty for givenpT and η.

pT bin [MeV] |η| < 1.3 1.3 ≤ |η| < 1.9 1.9 ≤ |η| < 2.1 2.1 ≤ |η| < 2.3 2.3 ≤ |η| < 2.5100 < pT ≤ 150 8% 8% 10% 10% 15%150 < pT ≤ 200 4% 6% 7% 9% 13%200 < pT ≤ 250 3% 5% 6% 7% 12%250 < pT ≤ 300 2% 4% 6% 6% 11%300 < pT ≤ 350 2% 4% 5% 6% 9%350 < pT ≤ 400 2% 4% 5% 5% 8%400 < pT ≤ 450 2% 3% 4% 5% 8%450 < pT ≤ 500 2% 3% 4% 4% 7%500 < pT 2% 3% 4% 4% 7%

10.3 Areas which profit from the material uncertainty study

Many physics analysis requires well reconstructed charged tracks, thus reduction of the sys-tematic uncertainty on the track reconstruction efficiency should profit precision measure-ments of various phenomena. As examples of many possibilities, in this thesis, Jet energyscale (JES) and fragmentation function are introduced.

1This is also rough estimation because the systematics on the tracking efficiency may not have a linearcorrelation with the material uncertainty.


Jet energy scale

The jet energy measurement is crucial for many areas of physics analysis and the high accuracyis also required. The uncertainty in the jet energy measurement, however, is the dominantexperimental uncertainty for numerous physics results, for example the cross-section measure-ment of inclusive jets, dijets or multi-jets as well as of vector bosons accompanied by jets, andnew physics searches with jets in the final state [32]. A reduced uncertainty on the jet energyscale is based on the increased knowledge of the detector performance. The performance ofthe track reconstruction efficiency is one of the important contributions to the jet energymeasurements.

Figure 10.1 shows the systematic uncertainty on the jet energy scale as a function of thejet pT . The plot also provides the breakdown of the total systematic uncertainty. Over thefull pT region shown in the plot, material description in the calorimeter is the dominant con-tribution to the systematics. However, in high-pT region, the total systematic uncertainty isdominated by the systematics on the tracking efficiency in jet core. The systematic uncer-tainty on the tracking efficiency is 3.6% of 4.3% (total) at pT = 900 GeV. If the systematicuncertainty on the tracking efficiency can be reduced by the half under the assumption in theprevious section, it should change into 1.8% and the total uncertainty will become 3.0%.

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Figure 10.1: The systematic uncertainty on the jet energy scale as a function of jet pT . Thebreakdown of the total uncertainty is also shown.


Fragmentation function F (z)

The fragmentation function is defined as the probability that a hadron carries longitudinalmomentum fraction z. The fragmentation function is the jet property which can be mea-sured in the ATLAS experiment [33]. During the analysis on the jet fragmentation, chargedparticles measured in the ID are then associated with the jets using a geometry definition.Since these associated particles give the structure of jets, the understanding of such tracksbehaviour is essential for the measurement of the fragmentation function.

First, fragmentation have to associate the outgoing partons with the rest of the event asthe jet contains colourless hadrons while the initial parton carries colour. Second, the processincludes the production of hadrons and occur at an energy scale where the QCD couplingconstant is large and perturbation theory cannot be used. The fragmentation is thereforedescribed using a QCD-motivated model in which parameters must be determined from ex-periments.

The fragmentation function and its systematic uncertainty depend on the jet pT . Fig-ure 10.2 shows the systematic uncertainty of the fragmentation function F (z) as a functionof the longitudinal momentum fraction z. The total uncertainty rises to the right mainly dueto the uncertainty on the jet energy scale. For the range of small z, there are two dominantuncertainties. one is the uncertainty on the tracking efficiency and the other is the one on theresponse matrix, which provides a mapping between reconstructed objects and those obtainedfrom event generator. Similarly to the case of the JES, if the uncertainty on the trackingefficiency goes down by the half, it will become about 1% from 2% in the most z region shownin the plot. At the same time, the total uncertainty will reduce to about 2.4% from 3%.

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Figure 10.2: The systematic uncertainty on the fragmentation function F (z) as a function ofthe longitudinal momentum fraction z. The breakdown of the systematics is also displayedin the plot.

Chapter 11

Conclusion

The ATLAS experiment is an experiment in high energy physics at the LHC, the purposesof which are the discovery of new particles such as Higgs Boson as well as new phenomenabeyond the Standard Model (SM). Material measurements in the ATLAS ID are essentialto ensure the excellent performance of the track reconstruction and photon conversions havetraditionally been used for the measurement. In this analysis, the measurement of the mate-rial in the ID using hadronic interactions is performed.

The data collected during the first half of 2010 and the corresponding minimum bias MChave been used for the comparison of the secondary vertex yields. In order to obtain plenty ofstatistics of the hadronic interactions, the retracking technique, which reconstructs the trackswith large impact parameters, was used and it provided the good reconstruction efficiency forthe secondary vertices compared to the past results.

Since the reconstructed secondary vertices include many fake vertices due to contributionsof the photon conversions and decays of long-lived particles such as Λ and K0

S , those verticeswere removed by investigating the distributions of their invariant mass. The reconstructedvertices successfully showed the maps of the detector structure including the services andsupports. The retarcking profited the appearance of the SCT module structure, whereas thepast study did not provide the clear mapping for the material outside the Pixel detector.

Although the number of irrelevant tracks increased as a result of the retracking, this pro-voked many fake vertices. The problem was resolved by applying the stringent cut on theimpact parameters with respect to the secondary vertex positions.

The comparison between the MC samples with extra material and the nominal MC pro-vides effects on the tracking efficiency, which was applied to the data-MC comparison as thesystematic uncertainty on this measurement. The results indicate that the number of vertexyields with |z| < 700 mm in each layer agrees well between data and MC except for the SCT2nd layer, which could be strongly affected by the vertices reconstructed from the bad tracks.The vertex distribution as a function of pT and η was also compared between data and MC.This suggested that the material uncertainty, in other words the difference of the material inthe reality and the simulation, was about 5%.

This result gives the rough estimation of the systematic uncertainty on the tracking effi-ciency, and in the assumption where it can be reduced by half, the effects for the jet energyscale and the fragmentation function were studied. The uncertainty on the JES will decreasefrom 4.3% to 3.0% at the jet pT = 800 GeV and the uncertainty on the fragmentation functionwill decrease from 3.0% to 2.4% in the region of the longitudinal momentum fraction fromz ∼ 10−2 to z ∼ 10−1.

70

Acknowledgements

First of all, I am really grateful to my supervisor Osamu Jinnouchi for giving me the op-portunity to participate in the ATLAS experiment. He also gave me great suggestions andcomments for my study regardless his busyness, which helped me to make progress in thereasearch to the appropriate direction.

My deep thanks also to the ATLAS Collaboration, especially SCT and ID material work-ing group. Members of the SCT group, in particlular, Stephen Mcmahon who is the projectleader of the SCT, Patricia Ward and Junji Tojo have spent much time disscussing with meon my research and I managed to succeed the SCT extension of the hadronic interactionstudy thanks to advices I received from them. Thijs Cornelissen and Krisztian Peters, whoare conveners of the ID material group, have supported me in both terms of the materialmeasurements and the tracking. Vivek Jain, who was an analyser in the hadronic interactionstudy before I joined, teached me the detail of the past study and the future possibility fromthe good knowledge and the experience. Without his cordial support I could not obtain theresults described in the master thesis. I am really thankful to all members in the ATLASexperiment as well as them.

I also appreciate members of Jinnouchi laboratory in Tokyo Institute of Technology. Inparticlular, Ryo Nagai and Tomonori Kubota thought seriously about the solution of prob-lems which happened to me. I would like to thank to them for their kindness.

Finally, I am pleased to be given the opportunity to express my reaserch as the masterthesis.

71

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Appendix A

Details of Datasets and Software

In the analysis, several datasets collected and stored in the ATLAS are used. And thereconstruction, which is mainly the retracking and the reconstruction of the secondary vertex,are conducted by the ATLAS software. Hence, their technical details are described in thisappendix.

A.1 Datasets

As described in chapter refchap-datasample, the data collected from March to June in 2010are used. The names of the datasets including the MC samples are the following:

• data10 7TeV.periodA.physics MinBias.PhysCont.ESD.repro05 v02/

• data10 7TeV.periodB.physics MinBias.PhysCont.ESD.repro05 v02/

• data10 7TeV.periodC.physics MinBias.PhysCont.ESD.repro05 v02/

• mc10 7TeV.105001.pythia minbias.recon.ESD.e574 s932 s946 r1649/ (nominal MC, ATLAS-GEO-16-00-00)

• mc10 7TeV.105001.pythia minbias.recon.ESD.e577 s1024 s946 r1926/ (+5% material inID, ATLAS-GEO-16-02-00)

• mc10 7TeV.105001.pythia minbias.recon.ESD.e577 s1025 s946 r1926/ (+10% materialin ID, ATLAS-GEO-16-03-00)

While the AOD datasets are useful for many physics analysis, they cannot be used forthe retracking which requires more detector information. Therefore, the study in this thesisneeds these ESD datasets above. For the data, moreover, the following GRL (Good RunsList) is applied in the event selection:

• data10 7TeV.pro05.merged LBSUMM minbias 7TeV.xml

A.2 Software

ATLAS release 17.0.5.6 is used during the reconstruction step using the datasets above. Forthe retracking and the secondary vertex reconstruction, several softwares are adopted:

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APPENDIX A. DETAILS OF DATASETS AND SOFTWARE 75

• Reconstruction/VKalVrt/VrtSecInclusive

• InnerDetector/InDetExample/InDetRecExample

• InnerDetector/InDetRecTools/SiSpacePointsSeedTool xk

List of Figures

1.1 Schematic drawings of hadronic intarction (top) and photon conversion (bottom). 2

2.1 Schematic layout of the LHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 The Feynman diagrams of the Higgs production process which could occur at

the LHC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Branchig ratio and cross section multiplied by branching ratio as a function of

mH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1 Overview of the ATLAS detector. . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2 Overview of the ATLAS inner detector . . . . . . . . . . . . . . . . . . . . . . . . 113.3 Schematic view of a barrel pixel module. . . . . . . . . . . . . . . . . . . . . . 143.4 Photograph and drawing of a barrel module . . . . . . . . . . . . . . . . . . . 153.5 Photograph of the three SCT end-cap modules. . . . . . . . . . . . . . . . . . 153.6 sct-endcap-module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.7 Mapping of photon conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . 173.8 Material distribution (X0, λ) breaking down services and individual sub-detectors. 183.9 Material distribution (X0, λ) breaking down different ID components. . . . . 183.10 Cut-away view of the ATLAS calorimeter system. . . . . . . . . . . . . . . . . . . 193.11 Cut-away view of the ATLAS muon system. . . . . . . . . . . . . . . . . . . . . . 20

4.1 Flow-chart of the tracking algorithm. . . . . . . . . . . . . . . . . . . . . . . . 224.2 Flow-chart of the inside-out tracking algorithm including the simple drawings. 234.3 Drawings to describe the definitions of the track parameters. . . . . . . . . . 27

5.1 Distributions of primary vertex z-coordinates for data and MC . . . . . . . . 30

6.1 Distributions of χ2 for all 2-track vertices. . . . . . . . . . . . . . . . . . . . . 326.2 Invariant mass of reconstructed vertices associated with π+π− in data with the

retracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356.3 Invariant mass of reconstructed vertices associated with pπ− in data with the

retracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356.4 Invariant mass of reconstructed vertices associated with e+e− in data with the

retracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366.5 The y vs. x distribution of secondary vertices in data. . . . . . . . . . . . . . 386.6 The y vs. x distribution of secondary vertices in data within Pixel detector. . 396.7 Secondary vertex distribution in x-y plane and design geometry for SCT modules. 396.8 The R vs. Z distribution of secondary vertices in data. . . . . . . . . . . . . . 406.9 The R vs. Z distribution of secondary vertices in data within Pixel detector. 40

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LIST OF FIGURES 77

6.10 Secondary vertex distribution in R-Z plane and design geometry for SCT mod-ules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6.11 The φ vs. R distribution of secondary vertices in data . . . . . . . . . . . . . 426.12 The φ vs. R distribution of secondary vertices and the φ profile of reconstructed

vertices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

7.1 z and R resolutions for vertices reconstructed in the beam pipe. . . . . . . . . 447.2 z and R resolutions for vertices reconstructed in the Pixel layers. . . . . . . . 457.3 z and R resolutions for vertices reconstructed in the Pixel support or SCT layers. 467.4 Distributions of dSV

0 and zSV0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

7.5 Purity and efficiency as functions of the maximum of |dSV0 | and |zSV

0 | in thebeam pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49


0 | in thePixel layers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50


0 | in thePixel support or in the SCT layers. . . . . . . . . . . . . . . . . . . . . . . . . 51

8.1 Momentum spectrum of primary tracks intersecting the beam pipe at |z| < 300mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

8.2 Radius distributions of reconstructed secondary vertices with |z| < 300 mm. . 568.3 Radius distributions of reconstructed secondary vertices with |z| < 700 mm. . 568.4 Comparison of radius distributions within |z| < 300 mm with impact parame-

ters cuts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578.5 Comparison of radius distributions within |z| < 700 mm with impact parame-

ters cuts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578.6 z distributions of the secondary vertices in the beam pipe or in the Pixel detector. 598.7 z distributions of the secondary vertices in the PST or SCT layers. . . . . . . 608.8 η distributions of reconstructed secondary vertices per event. . . . . . . . . . 628.9 pT distributions of reconstructed secondary vertices per event. . . . . . . . . . 62

9.1 The ratio of the number of vertices in the distorted (+5/10%) and the nominalMC as a function of radius. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

10.1 The systematic uncertainty on the jet energy scale as a function of jet pT . . . 6810.2 The systematic uncertainty on the fragmentation function F (z). . . . . . . . 69

List of Tables

2.1 Designed parameters in the LHC. . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Recorded luminosity and related values. . . . . . . . . . . . . . . . . . . . . . . . 6

3.1 Performance goals of the ATLAS detector. . . . . . . . . . . . . . . . . . . . . . . 103.2 Basic parameters of the inner detector. . . . . . . . . . . . . . . . . . . . . . . . . 123.3 Intrinsic accuracy and alignment precision for each detector element. . . . . . . . . 123.4 Parameters of the Pixel detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.5 Parameters of the SCT barrel. . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.6 Parameters of the SCT endcaps. . . . . . . . . . . . . . . . . . . . . . . . . . 143.7 Integrated radiation length (X0 from an interaction point to given radius. . . . . . . 183.8 Basic parameters of the muon spectrometer. . . . . . . . . . . . . . . . . . . . . . 20

4.1 Track characteristics and their effects on the track scores . . . . . . . . . . . . . . 254.2 Selection criteria during the standard reconstruction. . . . . . . . . . . . . . . . . 284.3 Selection criteria for the retracking. . . . . . . . . . . . . . . . . . . . . . . . . . 28

6.1 Requirements for the secondary track candidates. . . . . . . . . . . . . . . . . . . 316.2 Fake removal on the number of hits in each detector layer. . . . . . . . . . . . . . . 336.3 Breakdown of primary particles and the ratio. . . . . . . . . . . . . . . . . . . . . 346.4 Number of reconstructed SV per event at each step. . . . . . . . . . . . . . . 376.5 Number of reconstructed SV per event for each type. . . . . . . . . . . . . . . 37

7.1 Summary of the z and R resolutions in each layer with or without retracking . . . . 447.2 Purity and efficiency for reconstructed vertices in each layer. . . . . . . . . . . . . 487.3 Purity and efficiency with impact parameters cuts after the retracking. . . . . . . . 497.4 Characteristics of MC samples distorted in the whole ID. . . . . . . . . . . . . . . 527.5 Comparison of purity and efficiency between the nominal and distorted MC samples. 52

8.1 Summary of the correction factors for the primary tracks in each layer. . . . . . . . 548.2 Number of the vertex yields in data and MC. . . . . . . . . . . . . . . . . . . . . 588.3 Ratio of secondary vertex yields in data and MC as a function of pT and η. . . . . . 62

9.1 Characteristics of MC samples distorted in the whole ID. . . . . . . . . . . . . . . 649.2 The ratio of the number of vertices in distorted and nominal MC. . . . . . . . . . . 649.3 The systematic uncertainty due to the track reconstruction efficiency. . . . . . . . . 65

10.1 The ratio of number of the vertex yields in data and MC. . . . . . . . . . . . . . . 6710.2 Summary of the tracking efficiency systematics due to the material uncertainty for

given pT and η. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

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