Energy resolution on trigger jets in the ATLAS experiment ... · electromagnetic and hadronic calorimeter. Calorimeter signals are used to reconstruct the jet using jet reconstruction

Energy resolution on trigger jets in the

ATLAS experiment at the Large Hadron

Collider

Katharine Woods

Master of Science

Department of Physics

McGill University

Montreal,Quebec

2011-08-08

A THESIS SUBMITTED TO MCGILL UNIVERSITY IN PARTIALFULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER

OF SCIENCE

c©Katharine S. Woods, 2011

DEDICATION

This document is dedicated to Doug Woods.

ii

ACKNOWLEDGEMENTS

I thank all those who had a helping hand in my education, and in writing this

document. Special thanks goes to my supervisor, Dr. Andreas Warburton. I’d like

to thank Malachi Schram, Pete Watson, Bertrand Chapleau and Jason Schwartz for

the various help and advice they’ve given me. I’m not sure if I should thank Rodger

Mantifel and Wesley Ernst for keeping me sane, or driving me crazy; I have yet to

decide. As well I’d like to thank my parents, and Mike Collicutt for the constant

support and encouragement.

iii

ABSTRACT

The most prominent high transverse-momentum products from proton-proton

collisions at the Large Hadron Collider are collimated jets of hadrons. These jets

are excellent probes for new physics at the LHC. This thesis presents a thorough

investigation of the ATLAS jet energy resolutions of offline reconstructed jets as well

as those of the high level trigger. The jet energy resolution is measured using a

dijet balancing technique on jets reconstructed with different algorithms (anti-kT ,

cone) in the pseudorapidity region |η| < 2.5. Results from detailed Monte Carlo

studies are compared with results from the collider data, based on up to 35 pb−1 of 7

TeV center-of-mass energy proton-proton collisions during the 2010 data taking run.

Results show that the jet energy resolution obtained from Monte Carlo simulations

agree with resolutions measured in data to within 10%.

iv

ABREGE

La majorite des produits a grande quantite de mouvement transverse resultants

des collision proton-proton au LHC sont les gerbes de particules, ou jets. Ces jets

sont d’excellentes sources pour sonder la nouvelle physique au LHC. La presente

these a pour objet l’etude approfondie de la resolution de l’energie des jets tel que

detectes par le detecteur de l’experience ATLAS, ainsi que pour ceux du systeme

de declenchement de haut niveau. La resolution de l’energie des jets est mesuree

en appliquant une technique d’equilibrage des jets dans la region de pseudorapidite

|η| < 2.5 et qui ont ete reconstruits avec des algorithmes differents. Les resultats

detailles d’une etude de simulation Monte Carlo sont compares aux donnees du col-

lisionneur prises au cours de l’annee 2010, cequi correspond a 35 pb−1 luminosite

integree provenant de collisions proton-proton a une energie de centre de masse de 7

TeV. Les resultats montrent que la resolution de l’energie des jets obtenue a partir

de simulations Monte Carlo est en accord avec celle mesuree a partir des donnees a

moins de 10%

v

TABLE OF CONTENTS

DEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

ABREGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 The LHC and the ATLAS Experiment . . . . . . . . . . . . . . . . . . . 5

2.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . 52.2 The ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Overall Concept . . . . . . . . . . . . . . . . . . . . . . . . 92.2.3 Magnet System . . . . . . . . . . . . . . . . . . . . . . . . 102.2.4 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.5 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.6 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . 16

3 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1 Level 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 High Level Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.1 Level 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2.2 Event Filter . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 ATLAS Jet Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . 24

vi

4 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1 Jet Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2 Jet Reconstruction Algorithms . . . . . . . . . . . . . . . . . . . . 31

4.2.1 Cone Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 324.2.2 kT and Anti-kT Algorithms . . . . . . . . . . . . . . . . . . 34

4.3 Jet Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . 35

5 Monte Carlo Samples and Analysis Procedure . . . . . . . . . . . . . . . 38

5.1 Monte Carlo Simulated Datasets . . . . . . . . . . . . . . . . . . . 385.2 ATLAS 2010 Data . . . . . . . . . . . . . . . . . . . . . . . . . . 405.3 Jet Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.3.1 Leading Jet Pseudorapidities . . . . . . . . . . . . . . . . . 405.3.2 Angle Between Leading Jets . . . . . . . . . . . . . . . . . 405.3.3 Third Jet’s Transverse Energy . . . . . . . . . . . . . . . . 425.3.4 Scaling according to Cross Section . . . . . . . . . . . . . . 435.3.5 Trigger Selection . . . . . . . . . . . . . . . . . . . . . . . . 435.3.6 Jet Selection in Data . . . . . . . . . . . . . . . . . . . . . 43

5.4 Dijet Balancing Method . . . . . . . . . . . . . . . . . . . . . . . 455.4.1 Measurement of Resolution from Asymmetry Variable . . . 455.4.2 Soft Radiation Correction . . . . . . . . . . . . . . . . . . . 46

6 Results and Resolution comparisons . . . . . . . . . . . . . . . . . . . . . 50

6.1 MC09 Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.1.1 Cone algorithm . . . . . . . . . . . . . . . . . . . . . . . . 536.1.2 Cone vs Anti-kT . . . . . . . . . . . . . . . . . . . . . . . . 536.1.3 Anti-kT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6.2 Comparisons with Data . . . . . . . . . . . . . . . . . . . . . . . . 596.3 A Few Extras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

A Non-fitted Asymmetry Variable Plots . . . . . . . . . . . . . . . . . . . . 72

B Sample ATLAS Event Display . . . . . . . . . . . . . . . . . . . . . . . . 74

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

vii

LIST OF TABLESTable page

3–1 Jet Transverse Energy Thresholds. . . . . . . . . . . . . . . . . . . . . 25

5–1 Monte Carlo (MC09) Simulated Datasets . . . . . . . . . . . . . . . . 39

5–2 Monte Carlo (MC10) Simulated Datasets . . . . . . . . . . . . . . . . 39

5–3 Trigger selection, here L1 J10 symbolizes a requirement for jets with atransverse energy of greater than 10 GeV. . . . . . . . . . . . . . . . 44

6–1 Offline cone jet reconstruction algorithm resolution parameters foundusing Monte Carlo simulated events. The uncertainties arise fromthe fitting process alone. . . . . . . . . . . . . . . . . . . . . . . . . 54

6–2 Anti-kT jet reconstruction algorithm resolution parameters in MonteCarlo. The uncertainties arise from the fitting process alone. . . . . 56

6–3 Anti-kT jet reconstruction algorithm resolution parameters in Data. . . 61

6–4 Anti-kT (4) jet reconstruction algorithm resolution parameters in Dataand Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6–5 Anti-kT (6) jet reconstruction algorithm resolution parameters in Dataand Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6–6 Event Filter jet reconstruction algorithm resolution parameters inData and Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . . . 64

6–7 Level 2 jet reconstruction algorithm resolution parameters in Data andMonte Carlo. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

viii

LIST OF FIGURESFigure page

1–1 The Standard Model of elementary particles. . . . . . . . . . . . . . . 4

1–2 Summary of interactions between SM particles. . . . . . . . . . . . . . 4

2–1 LHC Schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2–2 LHC Experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2–3 CERN Accelerator Complex . . . . . . . . . . . . . . . . . . . . . . . 7

2–4 Cut-away view of the ATLAS detector. . . . . . . . . . . . . . . . . . 8

2–5 ATLAS Magnet System. . . . . . . . . . . . . . . . . . . . . . . . . . 11

2–6 Cross Section of the barrel toroid. . . . . . . . . . . . . . . . . . . . . 12

2–7 Cut-away view of the ATLAS inner detector. . . . . . . . . . . . . . . 12

2–8 Cut-away view of the ATLAS Calorimeters. . . . . . . . . . . . . . . 14

2–9 Electromagnetic barrel calorimeter. . . . . . . . . . . . . . . . . . . . 15

2–10 Hadronic Tile Calorimeter. . . . . . . . . . . . . . . . . . . . . . . . . 16

2–11 Cut-away of the Muon spectrometer. . . . . . . . . . . . . . . . . . . 17

3–1 Overview of the ATLAS Trigger/DAQ System. . . . . . . . . . . . . . 20

3–2 ATLAS Level 1 Trigger System. . . . . . . . . . . . . . . . . . . . . . 21

3–3 ATLAS High Level Trigger. . . . . . . . . . . . . . . . . . . . . . . . 24

3–4 The efficiency for a jet reconstructed with the anti-kT reconstructionalgorithm with D = 0.4 to satisfy L1 as a function of the jet pT ,integrating over |η| < 2.8. Left to right, and top to bottom areefficiencies for the four lowest L1 thresholds: 5,10,15 and 30 GeV. . 26

ix

4–1 Evolution of Jet Formation. A parton from the pp collision radiatesand hadronizes to create a jet, which then deposits energy in theelectromagnetic and hadronic calorimeter. Calorimeter signals areused to reconstruct the jet using jet reconstruction algorithms. . . . 28

4–2 Schematic view of the reconstruction sequences for jets from calorime-ter towers (left), uncalibrated (center) and calibrated (right) topo-logical calorimeter cell clusters in ATLAS. The software domainsare indicated on the vertical scale. . . . . . . . . . . . . . . . . . . 30

4–3 Jet Reconstruction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5–1 Diagram showing the effect of the cut on η; only events that satisfy thecriteria |η| < 2.5 are used in the analysis. Monte Carlo simulateddata are reconstructed with an anti-kT (D = 0.4) jet algorithm. . . 41

5–2 Cut on the ∆φ of the two leading jets applied to Monte Carlo jetsreconstructed using the anti-kT algorithm with D = 0.4. Onlyevents that satisfy ∆φ1,2 > 2.8 are selected. . . . . . . . . . . . . . 42

5–3 Plot of the transverse energy of leading anti-kT (4) jets showing theeffect of weighting Monte Carlo samples by cross sections (see Table5–1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5–4 Monte Carlo resolution vs the cut made on the third jet ET for eightpT bins using the anti-kT jet reconstruction algorithm with D =0.4. The solid line corresponds to the linear fit while the dashedline shows the extrapolation to pT,3 = 0, which corresponds to anideal dijet sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5–5 Example of the soft radiation correction applied to Monte Carlo jetresolution using the anti-kT reconstruction with D = 0.4. Each binresolution is improved by roughly 10%. . . . . . . . . . . . . . . . 49

6–1 Example of fitted asymmetry variable plots for eight pT regions, usingMC09 simulated events with the anti-kT jet algorithm with distanceparameter D = 0.4. The two smaller Gaussians (coloured) representthe single Gaussian fits, while the top Gaussian (black) is the doubleGaussian described in Equation 6.2. As expected, in higher energybins the width of the Gaussians become smaller, corresponding toa better resolution in that energy region. . . . . . . . . . . . . . . . 52

x

6–2 Plot showing the accuracy of using a double Gaussian fit of theasymmetry variable in the pT bin 160-200 GeV. . . . . . . . . . . . 53

6–3 The same fit of the asymmetry variable in the pT bin 160-200 GeV isshown on a log scale. . . . . . . . . . . . . . . . . . . . . . . . . . . 53

6–4 Application of the Asymmetry Method to simulated events with 0 <η < 2.5. The resolution plot for Monte Carlo offline reconstructedjet energy using the anti-kT jet algorithm with a distance parameterof D = 0.4 is shown. The resolution parameters are extracted anddisplayed using the parameterization described in Equation 6.1. . . 54

6–5 Resolution plot for the cone offline jet algorithm with two differentcone sizes, R = 0.4 and R = 0.7, plotted alongside the Level IITrigger and the Event Filter resolutions. . . . . . . . . . . . . . . . 55

6–6 Resolution plot demonstrating the differences between different jetreconstruction algorithms (cone, anti-kT ), and different cone sizes(0.4, 0.6, 0.7) performed on offline Monte Carlo (MC09) simulatedevents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6–7 Resolution plot for the anti-kT offline jet algorithm with two differentdistance parameters, D = 0.4 and D = 0.6, plotted along with theLevel II Trigger and the Event Filter resolutions, using Monte Carlosimulated data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

6–8 An example of the asymmetry distribution for 0 < η < 2.5 and alow ET bin (60-80 GeV) determined from Monte Carlo simulation(gray) and compared with the result from data (black dots). . . . . 60

6–9 Resolution plot for the anti-kT offline jet algorithm with two differentdistance parameters, D = 0.4 and D = 0.6, plotted against the LevelII Trigger and the Event Filter resolutions, using ATLAS 2010 data. 61

6–10 Jet energy resolution data measurements, compared to MC foundusing the anti-kT jet algorithm with a distance parameter of D = 0.4. 62

6–11 Jet energy resolution data measurements, compared to MC foundusing the anti-kT jet algorithm with a distance parameter of D = 0.6 63

6–12 Jet energy resolution data measurements, compared to MC usingEvent Filter jet energy variables. . . . . . . . . . . . . . . . . . . . 64

xi

6–13 Jet energy resolution data measurements, compared to MC usingLevel 2 jet energy variables. . . . . . . . . . . . . . . . . . . . . . . 65

6–14 Jet energy resolution measurements found using simulated eventsfrom two different Monte Carlo tunings, MC09 and MC10. . . . . . 67

6–15 Jet energy resolution measurements found using two different inputs tothe jet reconstruction algorithm, topological towers and topologicalclusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

A–1 Example of non-fitted asymmetry variable plots for eight pT regions,using MC09 simulated events with the anti-kT jet algorithm withdistance parameter D = 0.4. . . . . . . . . . . . . . . . . . . . . . . 72

A–2 Example of non-fitted asymmetry variable plots for eight pT regions,using the 2010 full dataset with the anti-kT jet algorithm withdistance parameter D = 0.4. . . . . . . . . . . . . . . . . . . . . . . 73

B–1 A dijet event as seen by the ATLAS detector. . . . . . . . . . . . . . 74

xii

CHAPTER 1

Introduction

The Large Hadron Collider (LHC) at CERN, in Geneva, Switzerland promises

a major step forward for the field of particle physics. It is a proton-proton (pp)

accelerator designed to reach center-of-mass energies of up to 14 TeV in order to

recreate the first moments after the Big Bang. It’s the first accelerator to operate

at such high energies, which will enable it to explore a large fraction of energy

ranges not previously studied. It is expected that at these energies unknown physical

phenomena will not only occur, but also be observable. Among the particle debris

from the collisions may lie evidence for extra dimensions, dark matter, or the Higgs

boson, which gives mass to elementary particles. The design of the LHC, and that of

its two largest experiments, ATLAS [1] and CMS [2], has been tuned to enable the

full exploration of the Higgs mass range, searching for a broad variety of the Higgs

production and decay processes predicted by the Standard Model.

The Standard Model (SM) [3] has been used for over 30 years to describe all

properties of the interactions among fundamental particles such as quarks, leptons,

and the gauge bosons, and is, in fact, the most successful description of matter

at its most fundamental level. The SM includes 12 elementary particles of spin

1

2, known as fermions, that interact via spin 1 particles called bosons. Standard

Model fermions are classified according to how they interact and by the charges

they carry. There are 6 quarks which are subject to all forces (weak, strong, and

1

electromagnetic) and 6 leptons, which do not interact through the strong force. The

standard model particles and their properties are summarized in Figure 1–1, while

their interactions can be found in Figure 1–2. The SM relies on the existence of a

scalar field with a weak charge, the Higgs, H which gives rise to electroweak symmetry

breaking. This would explain the difference between the massless photon, which

mediates electromagnetism, and the massive W and Z bosons, which mediate the

weak force. The Higgs boson has not yet been discovered and therefore the SM has

yet to be verified experimentally. One of the main priorities of physics today is to

confirm the existence of the Higgs, or to discover what replaces it. Direct searches

at the Large Electron Positron (LEP) collider [4] e+e− collider have established a

lower limit mH > 114.4 GeV at the 95% confidence level, and important constraints

in the mass range around 170 GeV have been achieved by the Tevatron experiments

at the Fermi National Accelerator Laboratory [5].

The most prominent high transverse-momentum products from proton-proton

collisions at the LHC are collimated jets of hadrons. Jets are manifestations of

high-energy quarks or gluons, whereas hadrons are particles made of quarks, and

held together by the strong force. A precise knowledge of the jet energy and the

possible variation on this energy, the resolution, are necessary for the analysis of

events at ATLAS, as well as for many physics analyses such as the determination

of the top quark mass [6] and the reconstruction of dijet resonances [7]. Moreover,

this observable has a direct impact on the quality of the measurement of the missing

transverse energy, which will play an integral role in many searches for new physics,

in particular the search for a dark-matter candidate.

2

Due to the sheer volume of data coming from these proton-proton collisions it

is necessary for ATLAS to employ the use of a trigger system in order to reduce the

rate of collisions being recorded, while not rejecting any important, and potentially

important, physics events. In ATLAS, this is done using a three-level trigger system

based both on software and hardware. A complete understanding of the jet energy

resolution in the trigger is important not only to evaluate the performance of the

trigger, but also to confirm it isn’t degrading the final resolution.

This masters thesis presents a comparison of the resolution of the ATLAS jet

trigger and offline reconstruction algorithms for multiple jet reconstruction algo-

rithms.

The outline of this thesis is as follows. In Chapter 2, an overview of the Large

Hadron Collider is presented, along with the main features of the ATLAS detector.

Chapters 3 and 4 are devoted to the description of the ATLAS trigger system and

jets, respectively. Chapter 5 presents the data used in the analysis, both Monte

Carlo simulations and real data taken from the LHC, along with selection cuts used

in these studies. Chapter 6 presents the analysis in detail, as well as the results from

the resolution comparisons. Chapter 7 is devoted to the conclusions.

3

Figure 1–1: The Standard Model of elementary particles [8].

Figure 1–2: Summary of interactions between SM particles [9].

4

CHAPTER 2

The LHC and the ATLAS Experiment

2.1 The Large Hadron Collider

CERN, the European Organization for Nuclear Research, is one of the world’s

largest centers for physics research. CERN’s main area of research today is parti-

cle physics, the study of the fundamental constituents of matter. The collider is

contained in a circular tunnel formerly used to house the Large Electron-Positron

Collider [10]. The LHC tunnel has a circumference of 27 km and is at a depth ranging

from 50 to 175 m underground.

The Large Hadron Collider [11] will extend the frontiers of particle physics with

its unprecedented high energy and luminosity. Inside the LHC, bunches of up to

1011 protons collide 40 million times per second to provide 7 TeV1 proton-proton

collisions at a design luminosity of 1034 cm−2s−1. These values are higher by orders

of magnitude than what has been achieved by any previous accelerator. The high

interaction rates, radiation doses, particle multiplicities and energies, as well as the

requirements for precision measurements have set new standards for the design of

particle detectors. The LHC accelerates two counter-rotating beams of protons,

colliding them at four interaction points along the ring where detectors are located.

1 The full energy is expected to be 14 TeV.

5

These include the ATLAS detector at Point 1, the ALICE detector at Point 2, the

CMS detector at Point 5, and the LHCb detector at Point 8, as shown in Figures

2–1 and 2–2.

Figure 2–1: LHC Schematic [12] Figure 2–2: LHC Experiments [13]

A schematic of the LHC injector chain [14] can be found in Figure 2–3. The

first stage of the acceleration takes place in the Linac2, a linear accelerator with

an output proton energy of 50 MeV. The Proton Booster Synchrotron (PBS) then

increases the energy to 1.4 GeV, injecting into the Proton Synchrotron (PS). This

accelerates the beams to 26 GeV, and injects into the Super Proton Synchrotron

(SPS). The SPS accelerates the beam to 450 GeV, at which point they are injected

into the LHC for the start of the ramp up to a final energy of 7 TeV.

The beam is bent along the circular LHC ring by way of 1232 superconducting

dipoles and controlled and focused by another 600 smaller magnets. At the collision

6

Figure 2–3: CERN Accelerator Complex [12]

points of the two largest experiments the bunches are squeezed to a transverse size

of a few tens of µm, to achieve a maximum instantaneous luminosity up to 1034

cm−2s−1. At this luminosity, an average of about 23 proton-proton interactions are

expected to take place nearly simultaneously during the same bunch crossing, with

bunch crossings meeting at interaction points every 25ns. This correspoinds to over

900 million collisions per second. The amount of information that an LHC detector

outputs to describe a full event is about 1 MB, however the typical rate at which this

information can be written to storage is about 200 MB/s. Therefore only a fraction

on the order 10−5 of all events can be stored. This implies that very fast and efficient

triggers are a necessity to promptly analyze and select interesting events.

2.2 The ATLAS Detector

Two general purpose detectors, ATLAS (A Toroidal LHC ApparatuS) and CMS

(Compact Muon Solenoid) have been built for probing pp collisions. The ATLAS

7

Figure 2–4: Cut-away view of the ATLAS detector. [1]

detector, which is used for the study in this thesis, is located at point 1 on the LHC

ring, shown in Figure 2–1. The dimensions are 25 m in height and 44 m in length.

The overall weight of the detector is approximately 7000 tonnes. An example of an

ATLAS event display using real data from October 2010 is shown in Appendix B.

2.2.1 Nomenclature

The coordinate system and nomenclature used to describe the ATLAS detector

and also particles emerging from the collisions will be used repeatedly throughout

this thesis and thus will be summarized here. The beam direction defines the z-

axis. The x-y plane is transverse to the beam direction, and the interaction point

is defined as the origin of the three axes. The positive x-axis is defined as pointing

from the interaction point to the center of the LHC ring and the positive y-axis is

8

defined as pointing upwards. The azimuthal angle φ is, as usual, measured around

the beam axis. The polar angle θ is measured from the positive z direction, however

the pseudorapidity, η, is generally used instead. The pseudorapidity is defined as η =

−ln tan(θ/2) and is a massless approximation of the rapidity, a quantity defined as

y = 1

2ln[(E + pz)÷ (E − pz)]. It is a useful quantity due to the fact that the rapidity

difference of two particles is invariant under a boost in the z direction. The transverse

momentum pT , the transverse energy ET , and the missing transverse energy EmissT

are defined in the x-y plane, unless stated otherwise.

2.2.2 Overall Concept

The formidable LHC luminosity and resulting interaction rate are necessary be-

cause of the extremely small cross sections expected for many of the physics processes

the LHC was built to investigate. The inherent nature of proton-proton collisions

themselves impose another difficulty in the form of QCD jets. These cross sections

dominate over the rare processes the LHC will be searching for. Identifying such

final states for these rare processes imposes further demands on not only the neces-

sary integrated luminosity, but also on the particle identification capabilities of the

detectors on the LHC ring. Viewed in this context, these potential difficulties can

be turned into a set of general requirements for ATLAS and other LHC detectors.

These detectors require very fast and radiation hard electronics, as well as high

detector granularity in order to handle the particle fluxes and to reduce the influ-

ence of overlapping events. They also require good electromagnetic calorimetry for

electron and photon identification and measurement. It is also important to have

9

good muon identification abilities and momentum resolution over a wide range of

momenta.

High precision and acceptance are important in all parts of the detector. The

detector must provide essential signatures of events including electrons, photons,

muons, and jets. To meet these requirements, the detector is a complex of sub-

detectors that can roughly be divided into four systems:

• Magnet system for bending the trajectory of charged particles

• Tracking detectors for measurement of charged particles

• Calorimetry for energy measurement of electromagnetic and hadronic particles

• Muon chambers for measurement and identification of muons

2.2.3 Magnet System

The design of ATLAS is driven by the configuration of the magnet system [1],

which is a unique hybrid of four large superconducting magnets. It comprises a

superconducting solenoid surrounding the inner detector cavity, and three large su-

perconducting toroids (one barrel and two end-caps) arranged with an eight-fold

azimuthal symmetry around the calorimeters. It is 22 m in diameter and 26 m in

length, with a stored energy of 1.6 GJ. Figure 2–5 shows the layout of the system

that provides a magnetic field for a region with a volume of approximately 12,000

m3.

The solenoid magnet is placed inside the electromagnetic calorimeter and is

aligned on the beam axis. It is designed to provide a 2 T axial magnetic field in

the central tracking volume. To reduce material build-up the solenoid shares the

cryostat with the liquid argon calorimeter, and is cooled by helium to 4.5 K.

10

Figure 2–5: ATLAS Magnet System. [13]

The toroid magnet is divided into a barrel part and two forward regions. With

a toroid field, particles will cross the complete pseudorapidity range, nearly perpen-

dicular to the field. The field in the barrel region is 2 T and in the end caps from 4 T

to 8 T. The end cap toroids generate the magnetic field required for optimizing the

bending power in the forward regions of the muon spectrometer system. They are

supported by and can slide along the central rails, which facilitate the opening of the

detector for access and maintenance. Each end cap toroid consists of a single cold

mass built up from eight flat, square coil units and eight keystone wedges, bolted

and glued together into a rigid structure to withstand the Lorentz forces (see Figure

2–5). A photo of the barrel toroid is shown in Figure 2–6.

2.2.4 Inner Detector

The layout of the inner detector [1] is summarized in Figure 2–7. It is immersed

in a 2 T solenoidal field and is contained within a cylindrical envelope of length 6.2

m and of radius 2.1 m. Approximately 1000 particles will emerge from the collision

11

Figure 2–6: Cross Section of the barrel toroid. [13]

Figure 2–7: Cut-away view of the ATLAS inner detector. [13]

12

point every 25 ns within |η|<2.5, creating a very large track density for the detec-

tor. The inner detector consists of three independent sub-detectors. To achieve the

required pattern recognition, momentum measurement, and electron identification a

combination of discrete, high-resolution semiconductor pixel and silicon strip (SCT)

detectors are used in the inner part of the tracking volume. A transition radia-

tion tracker (TRT) is used in the outer part to provide continuous tracking in order

to improve momentum resolution over the region |η|<2.0. The transition radiation

tracker is the outermost component of the inner detector. It is a combination of a

straw tracker and a transition radiation detector. The detecting elements are straw

drift tubes, each four millimeters in diameter and up to 144 cm long.

2.2.5 Calorimetry

The ATLAS calorimeters constitute the subsystems that are most relevant to

this thesis. A calorimeter is usually divided into two separate parts, an electromag-

netic and a hadronic calorimeter [15]. This is possible because of the different inter-

actions with matter between electrons/photons, and hadrons. The ATLAS calorime-

ter [1], shown in Figure 2–8, is situated outside the solenoid magnet that surrounds

the inner detector. It consists of a liquid argon (LAr) electromagnetic calorime-

ter, which covers the pseudorapidity region |η|<3.2, a hadronic barrel calorimeter

covering the region |η|<1.7, a hadronic end-cap calorimeter covering 1.5 <|η|<3.2,

and forward calorimeters that provide both electromagnetic and hadronic energy

measurements in 3.1 <|η|<4.9, the region closest to the beam.

13

Figure 2–8: Cut-away view of the ATLAS Calorimeters. [1]

LAr Electromagnetic Calorimeter

The electromagnetic calorimeter is a lead-liquid argon sampling calorimeter with

accordion shape absorbers and electrodes, as shown in Figure 2–9. The lead sheets

initiate shower development with their short radiation length, and the secondary

electrons create ionization in the gaps of liquid argon. The ionization current is

proportional to the initial energy of the particles passing through the calorimeter.

The accordion geometry provides complete phi (φ) symmetry without azimuthal

cracks. It is divided into a barrel part (|η|<1.475) and two end-cap components (1.375

<|η|<3.2) with a crack region at 1.3<|η|<1.6, which has poor energy resolution. Each

end-cap calorimeter is divided into two coaxial wheels: an outer wheel covering the

region 1.375 <|η|<2.5 and an inner wheel covering 2.5 <|η|<3.2. These wheels are

LAr sampling calorimeters; however, they use copper plates instead of lead as their

passive medium.

14

Figure 2–9: Electromagnetic barrel calorimeter. [1]

Hadronic Calorimeter

The hadronic tile calorimeter is a sampling calorimeter consisting of a steel

absorber and plastic scintillator as the active medium. It is located in the central

rapidity region, reaching out to |η|<1.7 (where the LAr EM calorimeter takes over)

and is subdivided into a central barrel and two extended barrels. The orientation of

the scintillating tiles - radial and normal to the beam line - allows for almost full φ

coverage. The light created in the scintillators is read out with wavelength shifting

fibres to photomultipliers on the outside of the calorimeters. Figure 2–10 shows how

the mechanical assembly and optical readout are integrated together.

The very forward hadronic calorimeter with a coverage down to |η|= 4.9 is made

of copper/tungsten. The choice of these materials is necessary to limit the width and

depth of the showers from high energy jets close to the beam pipe, and to keep the

15

Figure 2–10: Hadronic Tile Calorimeter. [1]

background level low in the surrounding calorimeters from particles spraying out

from the forward region.

2.2.6 Muon Spectrometer

The muon spectrometer [1] forms the outer part of the ATLAS detector. The

overall layout of the spectrometer can be found in Figure 2–11. It is designed to detect

charged particles that have exited the calorimeters, to measure their momenta in a

pseudorapidity range up to |η|<2.7, and to trigger on particles in the region |η|<2.4.

It functions similarly to the inner detector, based on the magnetic deflection of muon

tracks so that their momentum can be measured, albeit with a different magnetic

field configuration.

The magnet configuration in the muon system provides an orthogonal field to the

muon trajectories that minimizes resolution degradation due to multiple scattering

effects. In the range |η|<1.4, magnetic bending is provided by the barrel toroid; for

16

Figure 2–11: Cut-away of the Muon spectrometer. [1]

1.6<|η|<2.7, two end-cap magnets are responsible for bending the muon tracks. In

the region between η = 1.4 and 1.6 (the transition region) the bending is done using

a combination of the two fields.

In the barrel part of the detector, precision-tracking chambers are placed be-

tween and on the eight coils of the superconducting barrel toroid magnet. In the

end-caps, where the toroid cryostat prevents chambers from being placed inside the

magnetic field, the chambers are placed in front of and behind the two end-cap mag-

nets. Here the muon momentum is measured from the difference in entry and exit

angle of the magnet.

Over most of the η range, the precision momentum measurement is performed

in the monitored drift tube chambers (MDTs). They cover a pseudorapidity range

|η|<2.7. These chambers consist of eight layers of drift tubes made out of aluminum

17

tubes with lengths ranging from 70 cm to 630 cm and a diameter of 30 mm each.

The tubes are placed transverse to the beam axis.

At high pseudorapidities (2<|η|<2.7) where the track density is larger, Cathode

Strip Chambers (CSCs) with higher granularity are used due to their higher rate

capability and time resolution. CSCs are multiwire proportional chambers segmented

into strips in orthogonal directions, which allows both coordinates to be measured.

An essential requirement of the muon system was the capability to trigger on

muon tracks. In addition to the precision-tracking chambers, a system of fast trigger

chambers have been added in the region |η|<2.4. Resistive Plate Chambers (RPCs)

are used in the barrel region (|η|<1.05) and Thin Gap Chambers (TGCs) are used

in the end cap region (1.05<|η|<2.4). These chambers measure both coordinates of

the track; in the bending plane (η) and in the non-bending plane (φ).

18

CHAPTER 3

Trigger

At nominal operating conditions, the LHC produces approximately 40 MHz of

proton-proton interactions. The ATLAS trigger system reduces this rate to about 200

Hz while keeping primarily the data that could contain interesting physics processes.

A smart trigger is therefore necessary in order to decide which events to select, and a

powerful data acquisition system is needed to provide the trigger with the necessary

information to make quick decisions and to keep selected events. ATLAS employs a

three-level system to keep the most interesting events while minimizing latency time.

This three-level system is shown schematically in Figure 3–1.

3.1 Level 1

The level 1 (L1) trigger [17] must make a decision in fewer than 2.5 µs, and has

an output rate of less than 100 kHz. An overview of the L1 trigger system is shown

in Fig 3–2.

The L1 system uses information on clusters and global energy in the calorimeters

and from tracks in dedicated muon trigger detectors. Both the calorimeter and

muon trigger processors provide trigger information to the Central Trigger Processor

(CTP), consisting of multiplicities for electrons/photons, taus/hadrons, jets, and

muons, and of flags for total transverse energy, total missing transverse energy, and

total jet transverse energy.

19

Figure 3–1: Overview of the ATLAS Trigger/DAQ System. [16]

20

Figure 3–2: ATLAS Level 1 Trigger System. [17]

The CTP forms the L1 accept decision (L1A) in under 100 ns on the basis of

lists of selection criteria, implemented as the trigger menu. The L1A signal then

gets distributed via the Trigger Timing and Control (TTC) system to all relevant

components. All triggers and their thresholds are programmable, and the CTP can

take into account up to 160 trigger inputs at any one time. The CTP generates

L1As derived from trigger inputs according to the L1 trigger menu which consists

of up to 256 trigger items. For example, L1 J10 symbolizes a requirement for jets

with a transverse energy of greater than 10 GeV. L1 2J10 would require that there

be at least two jets present above that threshold. 256 of these such conditions can

be combined to form a trigger item.

The CTP sends, at every L1A, information to the Region-of-Interest-Builder

(RoIB) in the Level 2 (L2) trigger, as well as to the Read-Out-System (ROS) of

21

the DAQ. L2 gets triggered by getting the information about the regions of interest

(ROI) generated by L1. The data sent to the ROS is a superset of the information

sent to the RoIB and can contain data for bunches before and after the triggering

bunch for debugging and monitoring purposes. The CTP provides an 8-bit trigger-

type word with each L1A that indicates the type of trigger and can be used to select

options in event data processing.

3.2 High Level Trigger

The role of the High Level Trigger(HLT) [18, 19] is to reduce the L1 trigger rate

to a rate compatible with writing the events to mass storage. This final rate is not so

much a technical limit, but is constrained by the availability of storage devices and

computing power for later analysis. The HLT system is shown in detail in Figure

3–3.

3.2.1 Level 2

Event data of accepted events are sent into the data acquisition system (DAQ)

via read-out drivers (RODs) and are made available to the High Level Trigger through

approximately 1600 read-out buffers (ROBs). In parallel with sending event data to

the DAQ system, the ROI information from the L1 trigger is transmitted to the L2

trigger via the ROI builder (ROIB). The ROIB processes the information from the L1

trigger and sends it to the L2 Supervisor (L2SV), which implements the first function

of the L2 trigger. The L2SV fans out the L1 result to one of the L2 processing units

(L2PU), which contain the event selection framework and are responsible for event

filtering.

22

Highly optimized algorithms run the L2PU applications and perform a selection

process that is broken down into a series of sequential processing steps. The first step

is simply to confirm the Level 1 trigger ROIs using full granularity event data from

the calorimeters and muon detectors. In subsequent steps, data corresponding to

the RoI are then requested from detectors not originally used by the L1 trigger and

analyzed. If the result is not consistent with any of the possible physics candidates,

it is rejected and no further processing occurs. For selected events, the L2 decision

is sent to the L2SV, and the detailed L2 result is sent to the pROS.

By looking only at the ROIs provided by the L1 trigger, it is possible to reduce

the amount of data transferred to the L2PUs to less than 2 percent of the total event

data. At L2, the total average processing time per event is expected to be about

10 ms. Events selected by the L2 trigger are built into complete events, which are

passed to the Event Filter for a further stage of event selection and classification using

offline algorithms. Both the L2 and event filter use offline-like software components

for doing event selection.

3.2.2 Event Filter

The third and final trigger level is called the Event Filter (EF) [20, 21]. The

total expected average processing time per event in the EF is about 1 s. After a L2

accept the full event data is assembled by computing nodes called subfarm inputs

(SFIs) and is redirected to processing farms where more elaborate filtering algorithms

are used. This level reduces the output rate to about 200 Hz.

The L2SV passes the L2 decisions to the event builder and the events accepted

by the L2 trigger are built. The complete events are then sent to the Event Filter

23

Figure 3–3: ATLAS High Level Trigger. [20]

Dataflow applications (EFDs), running in the Event Handler. The EFD then dis-

tributes the events to Processing Task applications (PTs), which run offline filtering

algorithms adapted for the EF. If the event is accepted it is recorded to permanent

storage via the subfarm output nodes (SFOs) for offline analysis. Events surviving

the EF selection are passed on for offline storage.

3.3 ATLAS Jet Trigger

The jet trigger system is fundamental for jet physics analyses, such as the study

presented in this thesis, since jet triggers are the primary means for selecting events

containing jets with high transverse momentum (pT ). The Level 1 jet trigger is based

on a sliding-window algorithm that selects high energy depositions in a square of size

0.4×0.4, 1.6×0.6, or 0.8×0.8 in ∆η × ∆φ and extends out to |η| = 3.2 [1]. Figure

24

Table 3–1: Jet Transverse Energy Thresholds in GeV at different trigger stages. Thesequence is such that the EF J20 signature is seeded by the L2 J15 signature. Figure3–4 shows the efficiencies for some of these triggers.

Level 1 Level 2 Event Filter

5 15 2010 25 3015 30 3530 45 5055 70 7575 90 90

3–4 shows the efficiencies for jets with an anti-kT reconstruction (discussed in the

next chapter) which satisfy L1, as a function of the jet pT .

During the 7 TeV pp data taking period of 2010, the Event Filter was running

the ATLAS cone jet reconstruction algorithm [22]. Since then ATLAS has moved

to adopt the anti-kT sequential combination algorithm as the algorithm to use for

physics analyses. In 2010 the Event Filter was running but not rejecting events,

instead allowing all events that passed the Level 2 Jet trigger and were processed by

the Event Filter to be written offline. This ensures measurements of events passing

the Level 2 trigger and reconstructed using the anti-kT jet algorithm are not biased

by the Event Filter itself. The jet transverse energy thresholds and corresponding

Level 1, Level 2 and Event Filter thresholds are shown in Table 3–1.

The L2 trigger is based on a basic cone algorithm (discussed in section 4.2.1)

limited to a maximum of three iterations to reconstruct a jet in the RoI provided by

L1. At the EF, offline-like reconstruction algorithms are used while only looking at

regions of interest provided by the L1 jet. Further details on the HLT triggers can

be found in Ref. [22].

25

Figure 3–4: The efficiency for a jet reconstructed with the anti-kT reconstructionalgorithm with D = 0.4 to satisfy L1 as a function of the jet pT , integrating over|η| < 2.8. Left to right, and top to bottom are efficiencies for the four lowest L1thresholds: 5,10,15 and 30 GeV. [23]

26

CHAPTER 4

Jets

High quality and efficient jet reconstruction is an important tool for most physics

analyses performed using the ATLAS detector. The jet energy resolution gives the

possible variance of the reconstructed jet energy and is an important tool in the

analysis of both signal and background events in ATLAS. A related and equally

important quantity is the jet energy scale (JES), which describes the relationship

between the observed energy of a reconstructed jet and the energy of the initial parton

which fragmented and created the jet. The principal apparatus for jet reconstruction

is the ATLAS calorimeter system. It provides near-hermetic coverage and is well

suited for high-quality jet reconstruction in the proton-proton collisions at the LHC.

The strongest force known today, aptly named the strong force [3], binds to-

gether quarks in order to create protons, neutrons, and all other hadrons. This

inter-quark force is so strong that it is nearly impossible to pull a single quark out

of a hadron. After high-energy parton-parton collisions in the LHC, free quarks and

gluons will hadronize, as they cannot exist individually on timescales longer than

10−23 s. In the Standard Model they are described as combining quarks and anti-

quarks spontaneously created from the vacuum. This process creates a collimated

shower of hadrons called a jet with the same direction as the initial parton. Figure

4–1 represents the stages of jet production and measurement.

27

Figure 4–1: Evolution of Jet Formation. A parton from the pp collision radiates andhadronizes to create a jet, which then deposits energy in the electromagnetic andhadronic calorimeter. Calorimeter signals are used to reconstruct the jet using jetreconstruction algorithms. [24]

28

4.1 Jet Inputs

In order to find jets in the ATLAS detector system, one must combine signals

from approximately 270 000 calorimeter cells into larger signal objects, which have

physically meaningful four-momenta. ATLAS uses two principal calorimeter signal

object definitions; calorimeter signal towers, and calorimeter topological cell clusters.

Figure 4–2 shows a schematic view of the jet reconstruction sequences.

Calorimeter signal towers are calorimeter cells in an η × φ window of 0.1×0.1,

projecting outwards from the interaction point. Projective calorimeter cells, which

completely fit inside a tower, will contribute their total energy to that tower signal,

whereas projective cells larger than the tower size contribute fractions of their signal

to different towers. Tower signals are a sum of weighted cell signals. Some towers

may have a negative tower signal due to fluctuations from noise in the electronics,

and in the physics due to pileup. Negative signal towers are combined with nearby

positive signal towers, resulting in a cancellation of some of the noise fluctuations.

Towers with physically valid four-momenta are then sent to the jet finder algorithm

as protojets.

Topological cell clusters (TopoClusters) are three-dimensional reconstructions of

energy representing the shower development of each particle entering the calorimeter.

They are then clustered together using seed cells that have a signal-to-noise ratio

(Ecell/σnoise, cell) above some threshold, S. Direct neighbour cells are then collected

into the cluster. Next-to-nearest cells are only absorbed by the cluster if they are

above a secondary threshold, N. Finally, a ring of ’guard’ cells are grouped into the

cluster if they are above a third threshold, P. In ATLAS, the default thresholds are S

29

Figure 4–2: Schematic view of the reconstruction sequences for jets from calorimetertowers (left), uncalibrated (center) and calibrated (right) topological calorimeter cellclusters in ATLAS. The software domains are indicated on the vertical scale. [22]

30

= 4, N = 2, and P = 0 [22]. After all initial clusters are built, a splitting algorithm

looks for multiple maxima in a cluster; if any are found the cluster is split between

the maxima.

There is a third calorimeter signal object, which can be formed from a combina-

tion of the two previous methods described, called the topological tower (TopoTower).

TopoTowers are built by first creating TopoClusters and using these to create pro-

jective towers. Since these are created using noise-suppressed clusters, they too are

noise-suppressed.

4.2 Jet Reconstruction Algorithms

In order to reconstruct a jet from information from the detector, and to compare

jets between trigger levels and between data and simulation, a precise definition of

a jet is required. This definition is presented in the form of a jet algorithm. Figure

4–3 shows the purpose of a jet algorithm. The signature of a jet is large energy

deposition in a localized group of calorimeter cells. Jet algorithms can be divided

into two groups: ones that cluster partons or calorimeter towers based on proximity

in coordinate space, like cone algorithms, and ones that cluster in momentum space,

as in kT algorithms. From a theoretical point of view, an ideal jet algorithm will

include the following features.

• Infrared safety - the presence or absence of soft particles between two particles

belonging to the same jet should not affect the recombination of these two

particles into a jet.

31

• Collinear safety - the reconstruction of a jet should not depend on the fact

that a certain amount of transverse momentum is carried by one lone particle,

or by two collinear particles.

• Invariance under boosts - the algorithm should be invariant under kinematic

boosts in the longitudinal direction.

• Boundary stability - the variables used to describe the jet must have kinematic

boundaries that are insensitive to the details of the final state.

• Order independence - the same jets should be found regardless of whether the

algorithm is looking at the parton, hadron, or detector level.

• Straightforward implementation - the algorithm should be straightforward to

implement in perturbative calculations.

From an experimental point of view, the quantity of computing resources needed,

for example cpu time, is an important factor when determining an ideal jet algorithm.

This of course is particularly important when it comes to the trigger system.

ATLAS supports a configurable and flexible jet reconstruction framework, which

can be adapted to accommodate new jet algorithms or signal definitions from the

detectors. The most commonly used jet algorithms in ATLAS are the seeded fixed-

cone finder with split and merge and the anti-kT algorithm, both with two different

parameters controlling the size of the reconstructed jet [22].

4.2.1 Cone Algorithm

A thorough description of the iterative seeded fixed-cone jet finder is given in

[22]. This algorithm takes as its input ’protojets’, and orders them in decreasing

transverse momentum, pT . If the highest pT object, or seed, is above the threshold

32

Figure 4–3: Jet Reconstruction. [16]

(typically >1 GeV), a cone of radius ∆R =√

∆η2 + ∆φ2 is built around the seed.

A new direction is then calculated from all the four-momenta inside the cone, and

a new cone of equal radius is centered around this new direction. Objects in this

new cone are then collected, and the direction is again calculated. This process is

repeated until a final, stable cone is found, which is then called a jet. Afterwards, the

next seed is taken from the list, and the procedure is repeated until no more seeds

are available. Narrow (Rcone = 0.4) and wide (Rcone = 0.7) cone jet finder algorithms

are used in ATLAS. This is due to the fact that there is no universal jet finder for

the final state in all topologies of interest. For example, wider jets are typically

preferred to capture the hard scattered parton kinematics for the measurement of

the inclusive QCD jet cross sections. On the other hand, narrow jets are preferred in

order to reconstruct a W boson decaying into two jets, or possible SUSY signatures.

The described procedure can lead to a final jet list where some of the jets overlap.

A split-and-merge procedure is used to separate or merge jets that overlap, depending

33

on whether the overlapping energy percentage is above or below some threshold (in

ATLAS, <0.5).

4.2.2 kT and Anti-kT Algorithms

The kT algorithm [25] is a sequential recombination algorithm used in ATLAS.

For each cluster the distance dij between pairs of ij initial objects is calculated using:

dij = min(p2

T i, p2

T j)(ηi − ηj)

2 + (φi − φj)2

D2. (4.1)

The algorithm also calculates di = p2T,i for each object. The minimum of all di

and dij is then calculated and labelled dmin. If dmin = dij, then those two objects are

merged into a new object k that is added to the list of objects, while i and j are

removed. If dmin = di, then object i is saved as a jet, and i is removed from the list.

This procedure is repeated until there are no objects left in the list. All the initial

objects in the list end up to be a jet, or part of a jet. The kT jet algorithm is, by

design, considered infrared and collinear safe. The distance parameter D allows some

control over jet size, which in ATLAS configurations can be defined to be either D

= 0.4 for narrow jets and D = 0.6 for wide jets.

An extension of the kT algorithm is the anti-kT algorithm [26]. Here the same

steps are involved, however the distance variables are calculated as follows:

dij = min(p−2

T i , p−2

T j )(ηi − ηj)

2 + (φi − φj)2

D2(4.2)

di = p−2

T,i. (4.3)

34

The difference in computing methods lets the anti-kT algorithm cluster hard and

soft jets together, whereas the kT algorithm tends to cluster soft particles together.

This is advantageous in the fact that the results from running the anti-kT algorithm

will change very little upon the addition of soft radiation. As well, the kT algorithm

requires lots of CPU resources and time, whereas the processing needs of the anti-kT

algorithm are comparable to those of the cone algorithms.

4.3 Jet Energy Resolution

The jet energy resolution is an important calorimeter parameter as it defines

the precision of the jet energy measurement. The absolute resolution can be defined

as the width of the distribution of the energies measured in the calorimeter. Most

of the fluctuations of these energy measurements will come from event–to–event

fluctuations, for instance in the ionization process or in the particle composition of

the jet. These fluctuations are ruled by Poisson statistics and therefore the relative

resolution based on these fluctuations can be defined as

σET

ET

=S√ET

, (4.4)

where ET is the energy of the jet measured in GeV, σ is the absolute energy

resolution, and S is the stochastic term. Other sources of fluctuation that will signif-

icantly affect the jet energy resolution can be characterized by additional terms and

added to the energy resolution expression in quadrature, if they are not statistically

correlated. These sources can be characterized by a noise term, which represents

the contribution from electronic noise in the calorimeter and will dominate in the

35

low energy regime, and a constant term, that includes fluctuations due to the detec-

tor. These can be calorimeter imperfections, non-compensation, or the presence of

cracks and dead material in the detector. This term typically dominates the energy

resolution at high jet energies.

With these additional terms the resolution expression (4.4) can be re-written as:

σET

ET

=N

ET

⊕ S√ET

⊕ C. (4.5)

In Monte Carlo simulated events the jet energy resolution due to detector effects

can easily be estimated by matching particle and calorimeter level jets in η - φ space

and looking at the width of the jet response distributions. This, however, cannot

be used in any data-taking scenarios. The dijet balance technique, described in the

next chapter, is a data driven technique and can be implemented with calorimeter

observables.

These factors, however, are related only to the detector performance. Other

factors influencing the reconstructed jet energy and therefore the resolution are con-

nected with the physics of the object. This is due to the jet algorithms themselves, as

they are not able to perfectly reconstruct the jet. A reconstructed jet may miss en-

ergy from the initial parton due to radiation that has radiated outside of the jet cone

size (out–of–cone radiation). It may also include energy in the jet that originated

from a source other than the initial parton due to underlying events (coming from

other interacting partons) or pileup (energy from particles coming from additional

minimum bias events in the detector). As well, very soft (low energy) tracks can

be swept away from the jet reconstruction cone by the 4 T magnetic field. A track

36

with a transverse energy of 1.6 GeV would be deflected from the original direction

by δφ = 0.5 radian when it reaches the electromagnetic calorimeter. Tracks with a

transverse energy of less than 0.8 GeV won’t make it to the barrel calorimeter at

all [27]. However, such low energy tracks will not affect the final measured value

of the jet energy resolution. The ATLAS JetEtMiss [28] group has developed a

useful tool to retrieve the jet energy resolution and its uncertanity for release 15

(REL 15), called the jet energy resolution provider [29]. It is a C++/ROOT class

to access the current estimate of the JER for anti-kT (D = 0.4, 0.6) reconstructed

jets in the regions between 0,0.8,1.2,2.1,2.8 to distinguish between different parts of

the detector.

37

CHAPTER 5

Monte Carlo Samples and Analysis Procedure

This chapter is dedicated to explaining in detail the steps followed in the anal-

ysis, as well as the Monte Carlo datasets used. The chapter begins with a brief

explanation of the MC simulated datasets, followed by a description of the event

selection performed, and the resolution calculation used in this analysis.

5.1 Monte Carlo Simulated Datasets

A successful way to produce hypothetical events with distributions predicted by

theory is through the use of event generators that produce Monte Carlo simulated

datasets. This study was performed on standard ATLAS Monte Carlo QCD dijet

samples using the MC09 tuning [30], as listed in Table 5–1, as well as on QCD dijet

samples using the MC10 tuning [31], as listed in Table 5–2. They were generated

using PYTHIA [32], a general purpose generator for hadronic events in high energy

colliders. All Monte Carlo events pass through a Geant 4 detector simulation with

a detailed description of all geometries and materials in ATLAS. Finally the Monte

Carlo events are reconstructed and analyzed with the same software as with ATLAS

data. Events are selected using hardware based Level 1 triggers from the calorimeter

and muon systems. The MC10 datasets are newer and based off of MC09 with

38

Table 5–1: Monte Carlo (MC09) Simulated Datasets

Sample pT range [Gev/c] Cross Section [pb] # of Events

J0 8-17 1.17×1010 99949J1 17-35 8.67×108 99851J2 35-70 5.60×107 100000J3 70-140 3.28×106 100000J4 140-280 1.52×105 97999J5 280-560 5.12×103 99750J6 560-1120 1.12×102 95995J7 1120-2240 1.075×100 84093

Table 5–2: Monte Carlo (MC10) Simulated Datasets

Sample pT range [Gev/c] Cross Section [pb] # of Events

J0 8-17 9.86×109 1118441J1 17-35 6.78×108 1098542J2 35-70 4.10×107 767994J3 70-140 2.19×106 689844J4 140-280 8.77×104 606997J5 280-560 2.35×103 621498J6 560-1120 3.36×101 553810J7 1120-2240 1.37×10−1 559375J8 2240+ 6.21×10−6 685077

improvements to the underlying event and pileup tunes based on early data. As

well, updated PDF’s1 were used in the production of MC10 events.

1 Parton Distribution Functions give the probability to find partons (quarks andgluons) in a hadron as a function of the fraction x of the hadron’s momentum carriedby the parton. Known parton distribution functions are obtained by using exper-imental data. They are the bridge between calculable two-parton interactions de-scribed by Feynman diagrams and the resulting observable cross sections in hadronicinteractions [33].

39

5.2 ATLAS 2010 Data

Beginning in March 2010, collision candidate events at a center-of-mass energy

of√

s = 7 TeV were recorded by the ATLAS detector. The data used in this thesis

corresponds to a total luminosity of 35 pb−1, collected during the 2010 data-taking

period. The same trigger and event selection criteria are applied to both the data

and Monte Carlo events.

5.3 Jet Selection

Offline jets are reconstructed using two jet algorithms, the anti-kT jet algorithm

with distance parameter of D = 0.4 and D = 0.6, as well as the cone algorithm with

radii of R = 0.4 and R = 0.7. Calorimeter topological clusters were used as inputs

to the jet finding. In order to enrich the purity of the sample, selection cuts were

made on the jets used in this analysis. These cuts are described in the following

subsections.

5.3.1 Leading Jet Pseudorapidities

It is necessary to ensure both jets are in the same eta region, where the resolu-

tions should be the same. Therefore, in this study only events that have two or more

jets that satisfy |η| < 2.5 are selected. The region |η| < 2.5 is devoted to precision

physics and excludes the forward calorimeter and lower granularity end cap region.

This cut on |η| is illustrated in Figure 5–1 using MC09 simulated datasets; jets were

reconstructed with an anti-kT (D = 0.4) jet reconstruction algorithm.

5.3.2 Angle Between Leading Jets

As required by the dijet balancing method, a cut on the ∆φ1,2 of > 2.8 of the

two most energetic jets in the event is required to ensure these jets are back-to-back.

40

Figure 5–1: Diagram showing the effect of the cut on η; only events that satisfythe criteria |η| < 2.5 are used in the analysis. Monte Carlo simulated data arereconstructed with an anti-kT (D = 0.4) jet algorithm.

41

Figure 5–2: Cut on the ∆φ of the two leading jets applied to Monte Carlo jetsreconstructed using the anti-kT algorithm with D = 0.4. Only events that satisfy∆φ1,2 > 2.8 are selected.

Ideally only events with ∆φ1,2 = π should be selected, however in practice this is not

practical since very few events possess this ideal requirement. The effect of this cut

is illustrated in Figure 5–2.

5.3.3 Third Jet’s Transverse Energy

A final cut is made on ET of the third most energetic jet in the event, such

that there are no third jets with an energy greater than 10 GeV. This cut plays an

important role when performing a soft radiation correction, which will be discussed

in section 5.4.2.

42

5.3.4 Scaling according to Cross Section

As shown in Tables 5–1 and 5–2, each JX (X = 0 - 8) MC sample is assigned

its own cross section. In order to use these samples together to perform any anal-

ysis, they must be first scaled to a common time-integrated luminosity, namely the

luminosity of the ATLAS data being used for this study.

The individual JX samples are scaled using Equation 5.1,where W = weight.

The results of which are shown in Figure 5–3. As seen in the legend the coloured

lines refer to the eight JX samples discussed in Table 5–1 and the solid black line is

the total, used in these studies.

W =σ

Nevents

∫

Ldt (5.1)

5.3.5 Trigger Selection

Events were selected only if the leading jet within the event passed a specific

trigger for its pT range. Table 5–3 describes the trigger selection used in this thesis.

In order not to suffer from a trigger bias, the resolution was studied only for jets

that had a transverse energy greater than 60 GeV. Different sets of triggers had to

be applied to the data taking periods A-F than to G-I since the high level trigger

was not running in earlier periods, but was present in period G and onwards. In

order to avoid a trigger bias, in these periods an EF trigger was used.

5.3.6 Jet Selection in Data

Additional jet cleaning cuts had to be made for the selection of 7 TeV collision

events in ATLAS; these were not applied to Monte Carlo since most of the cleaning

variables in the datasets were not very well modeled.

43

Figure 5–3: Plot of the transverse energy of leading anti-kT (4) jets showing the effectof weighting Monte Carlo samples by cross sections (see Table 5–1).

Table 5–3: Trigger selection, here L1 J10 symbolizes a requirement for jets with atransverse energy of greater than 10 GeV.

pT range Period A - Period F [GeV] Period G - Period I [GeV]

(60 - 80) L1 J10 EF J30 jetNoEF(80 - 110) L1 J15 EF J35 jetNoEF(110 - 160) L1 J30 EF J50 jetNoEF(160 - 210) L1 J55 EF J75 jetNoEF(210 - 260) L1 J55 EF J75 jetNoEF(260 - 310) L1 J75 EF J95 jetNoEF

44

The standard good runs list as used by the JetETMiss group was used in order

to ensure jets were selected when the ATLAS subdetectors were in proper working

condition. As well, only jets flagged as good (described in Ref. [34]) were used in this

study.

5.4 Dijet Balancing Method

The analysis method used to determine the jet energy resolution is the dijet

balancing method. It is based on momentum conservation in the transverse plane.

It was first used at the Tevatron experiments to measure jet energy resolutions using

dijet samples [35] and assumes the ideal case of only two jets in the event that

have the same particle ET . Due to effects mentioned in section 4.3, the energy of

the two jets will not always be equal in magnitude. This allows for the use of the

dijet balancing method in which the resolutions are derived from the width of the

asymmetry distribution between the two leading jets, described in Equation 5.2. A

second method to measure the jet energy resolution not used in this thesis is called the

bi-sector technique, and is based on the definition of an imbalance transverse vector

−→p T , which is defined as the vector sum of the two leading jets in the dijet event.

Using the bi-sector method the resolution can be expressed in terms of calorimeter

observables, as described in Ref. [36].

5.4.1 Measurement of Resolution from Asymmetry Variable

The asymmetry between the transverse energy of the two highest energy, or

leading, jets A(ET,1, ET,2) is defined as

A ≡ ET,1 − ET,2

ET,1 + ET,2

. (5.2)

45

The ET of the two leading jets is randomized in order to eliminate the bias due to

the first jet always having a higher energy than the second jet. The variance of this

variable is given by

σ2

A = (∂A

∂ET,1

)2σ2

ET,1+ (

∂A

∂ET,2

)2σ2

ET,2=

4

(ET,1 + ET,2)4(E2

T,2σ2

T,1 + E2

T,1σ2

T,2), (5.3)

taking ET,1 and ET,2 at their mean values (〈ET,1〉 and 〈ET,2〉) for a dijet event,

transverse momentum balance implies 〈ET,1〉 = 〈ET,2〉 = ET . Furthermore, since the

jets are required to be in the same η region, we can assume that σET,1= σET,2

= σET.

Using these two equalities we can simplify Equation 5.3 considerably, to find

σET

ET

=√

2σA. (5.4)

5.4.2 Soft Radiation Correction

In order to obtain the most accurate measurement of the JER using the dijet

balancing method, events have to be selected with exactly two back–to–back jets.

The selection cuts made were described in the preceding sections; however, it is also

important to account for the effects due to the presence of additional soft particle

jets not detected in the calorimeter.

To estimate the value of the asymmetry for a pure particle jet, σET/ET ≡

√2σA

is measured for a series of ET,3 threshold values starting from 12.5 GeV and up to

27.5 GeV in steps of 2.5 GeV. For each ET bin, the set of resolutions obtained from

the different thresholds is fitted with a straight line and extrapolated to ET,3 → 0.

This procedure is shown in Figure 5–4. This allows the resolution to be estimated on

what would be an ideal dijet sample. A soft radiation correction factor, Ksoft(ET ),

46

Figure 5–4: Monte Carlo resolution vs the cut made on the third jet ET for eightpT bins using the anti-kT jet reconstruction algorithm with D = 0.4. The solid linecorresponds to the linear fit while the dashed line shows the extrapolation to pT,3 =0, which corresponds to an ideal dijet sample.

47

is obtained from the ratio of the value of the linear fit at 0 GeV over the value at 10

GeV (which is the cut on the 3rd jet energy, discussed in section 5.3.3):

K(pT ) =(

σpT

pT)pT,3→0

(σpT

pT)pT,3=10GeV

. (5.5)

This correction factor is applied to the biased raw resolutions from the dijet

asymmetry variable in events that satisfy pT,3<10 GeV:

(σpT

pT

)corrected = K(pT ) · (σpT

pT

)pT,3<10GeV (5.6)

The beneficial effects of the soft radiation correction are shown graphically in

Figure 5–5. Studies showed the soft radiation correction was not necessary at the

trigger levels, and was therefore only performed on offline reconstructed jets.

The analysis method described in this section was used for both data and Monte

Carlo analysis at all processing levels. The results are discussed in the following

chapter.

48

Figure 5–5: Example of the soft radiation correction applied to Monte Carlo jetresolution using the anti-kT reconstruction with D = 0.4. Each bin resolution isimproved by roughly 10%.

49

CHAPTER 6

Results and Resolution comparisons

As was discussed in section 4.3, the fractional jet energy resolution σpT/pT , is

parameterized as

σET

ET

=N

ET

⊕ S√ET

⊕ C. (6.1)

There are many factors that can influence the jet energy resolution. Because

of this, the dijet balance method was applied to jets built with different algorithms,

sizes, and inputs. This study examines the differences between these.

The chapter begins with a study of Monte Carlo (MC09 tuning) jet energy

resolution. A first look is taken at the cone jet reconstruction algorithm, which was

only studied using Monte Carlo simulated data. A Monte Carlo comparison is then

made between the cone and anti-kT algorithms. The anti-kT algorithm is studied in

both Monte Carlo and ATLAS data. Section 6.1.3 presents the Monte Carlo results

and section 6.2 gives detailed comparisons between Monte Carlo and data, at the

offline, event filter and level 2 processing levels. Finally, section 6.3 presents a brief

investigation of the differences in measured jet energy resolution when using MC09

simulated data and MC10 simulated data, as well as a short study done on the effect

of different jet inputs (topological towers, topological clusters).

50

6.1 MC09 Studies

The Monte Carlo simulation result is fitted using Equation 6.1. The cone

algorithm was studied using strictly Monte Carlo simulations from the MC09 data

set. Originally, eight pT ranges were studied. However, the lowest energy bin was

eventually excluded due to trigger bias, and the highest bin was also excluded due

to a lack of statistics in data. The remaining six pT ranges were used to calculate

the asymmetry variable for the resolution measurement in these samples.

A double Gaussian fit (Equation 6.2) allows for an accurate representation of

not only the center peaks of the asymmetry variable, but the tails as well1 .

f(x) = p1e−

(x−p2)2

2p23 + p′1e

−

(x−p′2)2

2p′23 (6.2)

In fitting the double Gaussian there are six parameters to fit for: three for each

of the two Gaussians. The fitting was done by setting a minimum and maximum

value allowed for each parameter. These limits are loose and were estimated based

on the rms and mean values of the non fitted data (Appendix A).

The asymmetry variables were then fitted with this double Gaussian fit as shown

in Figures 6–1, 6–2, and 6–3. Using Equation 5.4, along with the variances taken

from each of the 6 fitted pT bins, (60-80, 80-110, 110-160, 160-210, 261-260, 260-

310), a plot of the resolution can be drawn and fitted with Equation 6.1, and the

three resolution parameters can be extracted. Figure 6–4 shows the resolution for

the offline anti-kT jet reconstruction algorithm with D = 0.4.

1 Another method is to fit only the center peaks with a single Gaussian function.

51

Figure 6–1: Example of fitted asymmetry variable plots for eight pT regions, us-ing MC09 simulated events with the anti-kT jet algorithm with distance parameterD = 0.4. The two smaller Gaussians (coloured) represent the single Gaussian fits,while the top Gaussian (black) is the double Gaussian described in Equation 6.2. Asexpected, in higher energy bins the width of the Gaussians become smaller, corre-sponding to a better resolution in that energy region.

52

Figure 6–2: Plot showing the accuracyof using a double Gaussian fit of theasymmetry variable in the pT bin 160-200 GeV.

Figure 6–3: The same fit of the asym-metry variable in the pT bin 160-200GeV is shown on a log scale.

6.1.1 Cone algorithm

The cone algorithm was studied using Monte Carlo events only. Figure 6–5

shows the difference in resolution between offline cone jets with R = 0.4 and R = 0.7

as well as the trigger variables. The offline cone jets with a radius of R = 0.7 behave as

expected, having much better resolution than the trigger jets. Table 6–1 documents

the fit parameters for the cone reconstruction algorithm. Here and throughout this

thesis, the uncertainties arise from the fitting process alone. In many cases the

resutls from the fits to the noise term are consistent with zero. This implies that the

data does not unequivocally demand these terms be fitted; however, to maintain the

integrity of the comparisons being made the term was kept throughout this thesis.

6.1.2 Cone vs Anti-kT

Figure 6–6 examines the differences in resolution between the two different jet

reconstruction algorithms studied in this thesis, with different cone sizes using Monte

Carlo simulated events. Jets built using the anti-kT algorithm perform better in terms

53

Figure 6–4: Application of the Asymmetry Method to simulated events with0 < η < 2.5. The resolution plot for Monte Carlo offline reconstructed jet en-ergy using the anti-kT jet algorithm with a distance parameter of D = 0.4 is shown.The resolution parameters are extracted and displayed using the parameterizationdescribed in Equation 6.1.

Table 6–1: Offline cone jet reconstruction algorithm resolution parameters foundusing Monte Carlo simulated events. The uncertainties arise from the fitting processalone.

Algorithm Stochastic term Noise Term Constant Term

Cone (R = 0.4) 2.01 ± 0.09 1×10−6 ± 5 0.093 ± 0.005Cone (R = 0.7) 1.68 ± 0.08 8.28×10−7 ± 1.41 0.076 ± 0.006

54

Figure 6–5: Resolution plot for the cone offline jet algorithm with two different conesizes, R = 0.4 and R = 0.7, plotted alongside the Level II Trigger and the EventFilter resolutions.

55

Table 6–2: Anti-kT jet reconstruction algorithm resolution parameters in MonteCarlo. The uncertainties arise from the fitting process alone.


Anti-kT (D = 0.4) 1.24 ± 0.75 9.84 ± 6.75 0.032 ± 0.078Anti-kT (D = 0.6) 1.08 ± 0.84 9.26 ± 7.15 0.032 ± 0.035

Event Filter 1.54 ± 0.14 1.17×10−4 ± 9.2 0.106 ± 0.012Level 2 1.54 ± 0.12 7.54×10−5 ± 9.1 0.163 ± 0.006

of resolution when compared to the cone algorithm, especially in high transverse

energy regions. Due to the fact that the analysis was only performed out to 300 GeV

for the anti-kT algorithm, the fit parameters (listed in Table 6–2) were extracted

and the resolution was extrapolated out to higher energies in order to compare with

the cone algorithm.

6.1.3 Anti-kT

The anti-kT algorithm was explored for distance parameters D = 0.4 and D =

0.6, Figure 6–7 illustrates the differences between the two and compared with the

high level trigger. Table 6–2 documents the fit parameters for each. In general,

using a wider cone size yields better resolutions than narrower cone sizes. This can

be explained by out-of-cone losses in the narrower jets. The effect is more noticeable

at lower energies due to the fact that higher energy jets tend to be narrower and

more collimated than lower energy jets. Overall the resolutions between the different

processing levels behave as expected, with the offline reconstruction giving the best,

followed by the event filter and the worst being the level 2. This is explained by the

steps and varying processing sophistication involved in each level’s jet reconstruction,

discussed in chapter 3.

56

Figure 6–6: Resolution plot demonstrating the differences between different jet recon-struction algorithms (cone, anti-kT ), and different cone sizes (0.4, 0.6, 0.7) performedon offline Monte Carlo (MC09) simulated events.

57

Figure 6–7: Resolution plot for the anti-kT offline jet algorithm with two differentdistance parameters, D = 0.4 and D = 0.6, plotted along with the Level II Triggerand the Event Filter resolutions, using Monte Carlo simulated data.

58

6.2 Comparisons with Data

An example showing the level of agreement between data and Monte Carlo of the

asymmetry distribution is given in Figure 6–8. Aside from a few noticible statistical

fluctuations in data at higher values of the asymmetry variable, it agrees well with

the Monte Carlo simulation. The final results using the full 2010 ATLAS dataset are

presented in Figure 6–9, and represent a best estimate of the jet energy resolution

in data. Corresponding resolution parameters can be found in Table 6–3. A close-

up comparison of data and Monte Carlo is shown for the anti-kT jet reconstruction

algorithm with a distance parameter of D = 0.4 and D = 0.6, as well as the Event

Filter and Level 2 resolution in Figures 6–10, 6–11, 6–12, 6–13, respectively. As

is expected, offline reconstructions perform better in terms of jet energy resolution

than the high level trigger. Within the high level trigger, the event filter provides

a better jet energy resolution than the 2nd trigger level. This is explained by the

fact that the level 2 reconstruction only looks in a region of interest specified by the

level 1 trigger. It does have access to the full granularity of all subdetectors, however

runs fast algorithms dedicated more to timing than resolution. The event filter

runs a more sophisticated algorithm in an offline-like environment, using full event

access (not just a ROI) so it is expected to provide a better jet energy resolution.

Offline reconstructions have much less time and processing restrictions, are equipped

with even more sophisticated algorithms, and have much more information, such as

calibration details, pertaining to the event.

The discrepancies between Monte Carlo and data decrease as the jet energy

increases. It can be seen that when comparing data to Monte Carlo, the simulated

59

Figure 6–8: An example of the asymmetry distribution for 0 < η < 2.5 and a lowET bin (60-80 GeV) determined from Monte Carlo simulation (gray) and comparedwith the result from data (black dots).

data describes ATLAS events with much more precision in the trigger (event filter

and level 2) than when using offline reconstructed jets. This could be explained

by factors that would affect offline jets much more, such as pileup and out-of-cone

radiation. This implies that the Monte Carlo used could be tuned differently in order

to better represent ATLAS data, which is in fact the case with MC10 simulated data,

discussed briefly in the previous chapter.

60

Figure 6–9: Resolution plot for the anti-kT offline jet algorithm with two differentdistance parameters, D = 0.4 and D = 0.6, plotted against the Level II Trigger andthe Event Filter resolutions, using ATLAS 2010 data.

Table 6–3: Anti-kT jet reconstruction algorithm resolution parameters in Data.


Anti-kT (D = 0.4) 1.66 ± 0.24 6.99 ± 6.42 1.40×10−7 ± 0.27Anti-kT (D = 0.6) 1.69 ± 0.16 1.28×10−4 ± 6.94 0.034 ± 0.049

Event Filter 0.667 ± 0.521 6.18×10−6 ± 18.8 0.154 ± 0.0169Level 2 1.88 ± 0.47 2.89×10−5 ± 45.8 0.137 ± 0.056

61

Figure 6–10: Jet energy resolution data measurements, compared to MC found usingthe anti-kT jet algorithm with a distance parameter of D = 0.4.

Table 6–4: Anti-kT (4) jet reconstruction algorithm resolution parameters in Dataand Monte Carlo.


Data 1.66 ± 0.24 6.99 ± 6.42 1.40×10−7 ± 0.27Monte Carlo 1.24 ± 0.75 9.84 ± 6.75 0.032 ± 0.078

62

Figure 6–11: Jet energy resolution data measurements, compared to MC found usingthe anti-kT jet algorithm with a distance parameter of D = 0.6

Table 6–5: Anti-kT (6) jet reconstruction algorithm resolution parameters in Dataand Monte Carlo.


Data 1.69 ± 0.16 1.28×10−4 ± 6.94 0.034 ± 0.049Monte Carlo 1.08 ± 0.84 9.26 ± 7.15 0.032 ± 0.035

63

Figure 6–12: Jet energy resolution data measurements, compared to MC using EventFilter jet energy variables.

Table 6–6: Event Filter jet reconstruction algorithm resolution parameters in Dataand Monte Carlo.


Data 0.667 ± 0.521 6.18×10−6 ± 18.8 0.154 ± 0.0169Monte Carlo 1.54 ± 0.14 1.17×10−4 ± 9.2 0.106 ± 0.012

64

Figure 6–13: Jet energy resolution data measurements, compared to MC using Level2 jet energy variables.

65

Table 6–7: Level 2 jet reconstruction algorithm resolution parameters in Data andMonte Carlo.


Data 1.88 ± 0.47 2.89×10−5 ± 45.8 0.137 ± 0.056Monte Carlo 1.54 ± 0.12 7.54×10−5 ± 9.1 0.163 ± 0.006

6.3 A Few Extras

The differences in Monte Carlo samples using the MC09 tuning (Table 5–1)

and the MC10 tuning (Table 5–2) were briefly investigated. Figure 6–14 displays

how they perform with respect to one another, using topological clusters as inputs,

and the anti-kT (4) jet reconstruction algorithm. The respective resolutions were

comparable in the low energy, however, as expected, the MC10 events had a better

resolution in the high-energy regime.

Two possible inputs to jet reconstruction are topological towers (tower) and

topological clusters (topo). When comparing jets using these inputs, all other vari-

ables remained the same (reconstruction algorithm, distance parameter). Figure

6–15 shows the difference in resolution between the two, and motivates the use of

topological clusters as inputs, as it displays a better energy resolution, especially as

it tends towards higher transverse jet energies.

This thesis has studied the jet energy resolution for multiple jet reconstruction

algorithms, with multiple cone sizes, as well as various reconstruction levels. In

general, when looking within a single reconstruction algorithm, a larger cone size

gave better results. The algorithms studied were the cone algorithm and the anti-kT

algorithm, which are explained in detail in Chapter 4. The anti-k−T algorithm was

found to perform better in terms of resolution than the cone algorithm, independent

66

Figure 6–14: Jet energy resolution measurements found using simulated events fromtwo different Monte Carlo tunings, MC09 and MC10.

67

Figure 6–15: Jet energy resolution measurements found using two different inputs tothe jet reconstruction algorithm, topological towers and topological clusters.

68

of the cone size chosen. The different levels of the ATLAS trigger (defined in Chapter

3) were also studied. Overall the offline reconstruction gave the best results in terms

of resolution, followed by the Event Filter, then the Level 2 trigger.

69

CHAPTER 7

Conclusions

This thesis has presented a detailed study of the ATLAS jet energy resolution,

both on offline reconstructed jets as well as trigger quantities. Monte Carlo simulated

events serve as a benchmark for comparisons to collision data from the ATLAS

detector. A total integrated luminosity of L = 35 pb−1 at√

s = 7 TeV was used in this

analysis. A dijet balance technique was used to measure the jet energy resolution for

different jet reconstruction algorithms (Cone and Anti-kT ), and different cone-sizes

(0.4,0.6,0.7). The high level trigger was also studied. Close agreement between data

and Monte Carlo events was observed in this analysis, indicating that the ATLAS

Monte Carlo machinery is satisfactorily tuned for physics studies involving jets, both

at the trigger and offline processing levels.

The studies presented in this thesis motivate the use of the anti-kT (D = 0.6)

jet reconstruction algorithm with topological clusters as input objects to be the

primary algorithm for physics analyses. This approach shows the best jet energy

resolution compared to other options, especially at high transverse momenta in the

pseudorapidity region 0 < η < 2.5. Overall, this is true when comparing wider jets

to narrower ones of the same reconstruction algorithm, which is most likely due to

out-of-cone losses in narrower jets, as discussed in section 4.3. The anti-kT algorithm

also allows for better trigger-offline agreement since the Event Filter now runs an

anti-kT like algorithm as well. The parameterization for the anti-kT algorithm using

70

D = 0.6 was found to be S = 1.07±0.84, B = 9.27±7.15, C = 0.032±0.034 in Monte

Carlo and S = 1.69± 0.16, N = 1.28× 10−4 ± 6.94, C = 0.034± 0.05 in data. These

results show that the resolution in data is described by the Monte Carlo simulation

to within 10%.

In future work, the technique should be utilized in order to study the effects of

pileup on the jet energy resolutions for the different algorithms, cone sizes, jet inputs,

and processing levels discussed in this thesis. As well, how the ATLAS jet energy

resolution changes upon the increase of center-of-mass energy should be studied, for

example at√

s = 14 TeV.

.

71

APPENDIX A

Non-fitted Asymmetry Variable Plots

Figure A–1: Example of non-fitted asymmetry variable plots for eight pT regions,using MC09 simulated events with the anti-kT jet algorithm with distance parameterD = 0.4.

72

Figure A–2: Example of non-fitted asymmetry variable plots for eight pT regions,using the 2010 full dataset with the anti-kT jet algorithm with distance parameterD = 0.4.

73

APPENDIX B

Sample ATLAS Event Display

Figure B–1: A dijet event as seen by the ATLAS detector.

The highest mass central dijet event and the highest-pT jet collected by the end

of October 2010: two central high-pT jets have an invariant mass of 2.6 TeV and the

highest pT jet has pT of 1.3 TeV.

• 1st jet (ordered by pT ): pT = 1.3 TeV, η = 0.2, φ = 2.8

• 2nd jet: pT = 1.2 TeV, η = 0.0, φ = -0.5

• Missing ET = 42 GeV, φ = 1.5

• Sum ET = 2.2 TeV

74

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