study of the 2004 end-cap beam tests of the...

STUDY OF THE 2004 END-CAP BEAM TESTS OF THE

ATLAS DETECTOR

by

Marco Bieri

B.Sc., University of Calgary, 2003

THESIS SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

IN THE DEPARTMENT

OF

PHYSICS

c© Marco Bieri 2006SIMON FRASER UNIVERSITY

Spring 2006

All rights reserved. This work may not bereproduced in whole or in part, by photocopy

or other means, without permission of the author.

APPROVAL

Name: Marco Bieri

Degree: Master of Science

Title of Thesis: Study of the 2004 End-Cap beam tests of the ATLAS detector

Examining Committee: Dr. K. Kavanagh (Chair)

Dr. M. Vetterli, Professor, Senior Supervisor

Department of Physics, SFU/TRIUMF

Dr. D. O’Neil, Professor

Department of Physics, SFU

Dr. D. Broun, Professor

Department of Physics, SFU

Dr. C. Oram, Senior Research Scientist

TRIUMF

Date Approved: April 13, 2006

ii

SIMON FRASER URWEM~W~ i brary

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Abstract

The ATLAS detector is an all-purpose detector to study high-energy proton–proton colli-

sions. ATLAS is located at the LHC (Large Hadron Collider) at CERN in Geneva, Switzer-

land. Before first data taking, many beam tests have been carried out in order to fully

understand each detector component. The studies in this thesis will concentrate on the

2004 beam test of the entire combined end-cap calorimeter system. The first section of this

thesis outlines particle selection in the incoming test beam, eliminating contamination in

order to have an accurate calibration environment. The remainder of the thesis focuses on

detector calibration and performance studies, including signal-to-energy calibration con-

stant determination, and various detector energy summation methods studying their effect

on response. Overall detector energy sharing characteristics including the response of dead

detector regions is also presented.

iii

I would like to dedicate this thesis to my family all over the

globe, especially Mami and Papi.

iv

Acknowledgments

I of course will start this list with my FAMILY (Mami, Papi and Milena), for support in

pretty much anything I have ever done. They are the biggest reason why I am even writing

this thank you list today. Also many cheers to my overseas relatives (Grossmami’s, Gotti,

and all Bieri’s/Gisler’s in California, Switzerland etc.) who have hosted me on my MANY

trips to CERN, or Europe in general in the past few years, showing up at their door with a

backpack/guitar and a laptop.

Many CHEERS to all my good friends, The GeoffLukeIanMyself Project gang, or

pretty much whoever has been part of my music in general, letting me beat up the drums

after a rough day of fighting c++. Dr. OJ, for showing me around the old Vancouver,

Ian who has been watching me do this since second year, we beat undergrad together!!

Apartment 522, for making one of my hardest, one of the most fun years of MY LIFE

!!! The Calgary undergrad crew (Pat, who convinced me to go to grad school). Tim for

triggering my calculus/algebra competitiveness.

All the awesome people up at SFU, especially our HEP group: Mike (my boss and

also the guy who introduced me to particle physics), Ingemar, Yann (HUGE thanks here),

Dugan, Dr. Walker, Sir Douglas (aka c++ god) , etc. Our amazing physics staff, Candida,

who I owe much $$ to courtesy of all those papers she “reminded” me to fill out, Sada for

my travel advances and phone bills, Mehrdatovich nicest guy ever, EM-quantum soul mate

HOFF, enjoy the mice !! The Hayden Lab, all FIFTEEN OF YOU and yes you too Marti.

For a more complete list, go to the grad student wall, practically everyone is awesome.

Thanks to all my teachers over the years.

MANY CHEERS to all the great people I was fortunate to work with on ATLAS, Warren

“Got Ramps?”, Malachi “YOU ARE THE FCAL!!”, this list can go on forever but just some

quick names, Manuella, Rob, the many Peters etc ...

v

ACKNOWLEDGMENTS vi

Last and not least ... drum roll ... CHELSEA EVANGELINE ROONEY, who has joined

me on this particle journey the past few years, actually caring when the occasional word

like “uA/MeV” or “Y scan” came up in between “GLIM this .. snowboarding that ..”. Also

thanks to her for making sure to start what one finishes, along with many other things like

reading this thesis. Where is the CAT !! Meeting her also proved that creative writing and

particle physics has a large overlap.

Contents

Approval ii

Abstract iii

Dedication iv

Acknowledgments v

Contents vii

List of Tables x

List of Figures xi

1 Introduction 1

1.1 Physics Motivation of ATLAS . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Higgs Boson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.2 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Reaction Rate, Luminosity and Interaction Cross

Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3.1 Proton–Proton collisions . . . . . . . . . . . . . . . . . . . . . . . 9

1.3.2 Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Calorimetry 12

2.1 Particle Showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

vii

CONTENTS viii

2.1.1 Electromagnetic Showers . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.2 Hadronic Showers . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Energy Deposition in Matter . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3 Sampling Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4 Calorimeter Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5 Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3 The ATLAS detector 26

3.1 ATLAS Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2 ATLAS Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2.1 Hadronic End-Cap Calorimeter . . . . . . . . . . . . . . . . . . . 32

3.2.2 Electromagnetic End-Cap Calorimeter . . . . . . . . . . . . . . . . 33

3.2.3 Forward Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 ATLAS Muon System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 CBT-EC2 Beam Tests 37

4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2 Triggering and Event Timing . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.3 Energy Signal Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 43

4.4 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.4.1 Digitization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.4.2 Peak Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.5 Detector Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.6 ADC→MeV conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.6.1 HEC Pulse Calibration . . . . . . . . . . . . . . . . . . . . . . . . 47

5 Beam Quality 53

5.1 Multiple Hits Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.2 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.2.1 Muon Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.2.2 EM Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

CONTENTS ix

6 End-Cap Calorimeter Response and Resolution 72

6.1 HEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.1.1 Optimal Filtering vs Cubic Fit . . . . . . . . . . . . . . . . . . . . 72

6.1.2 Energy Response . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.1.3 X scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.2 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.2.1 Topological Clustering . . . . . . . . . . . . . . . . . . . . . . . . 79

6.3 End-Cap Y scans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.3.1 Positrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.3.2 Pions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

7 Conclusion and Outlook 92

Bibliography 94

A CBT-EC2 Setup Diagrams 96

A.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

A.2 Run I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

A.3 Run II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

List of Tables

2.1 Hadronic shower composition . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Calorimeter parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1 ATLAS inner detector parameters . . . . . . . . . . . . . . . . . . . . . . 28

3.2 ATLAS calorimeter details . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3 FCAL in numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.1 MeV/µA values for end-cap detectors . . . . . . . . . . . . . . . . . . . . 47

5.1 119 GeV narrow e+: multiple hits cut statistics . . . . . . . . . . . . . . . 59

5.2 119 GeV e+: scintillator cut statistics . . . . . . . . . . . . . . . . . . . . 61

5.3 60 GeV e+: multiple hit cut statistics . . . . . . . . . . . . . . . . . . . . . 63

5.4 Multiple hit elimination cut values for various particle beams . . . . . . . . 65

5.5 193 GeV e−: muon cut statistics . . . . . . . . . . . . . . . . . . . . . . . 69

x

List of Figures

1.1 Feynman diagrams of Higgs production channels . . . . . . . . . . . . . . 3

1.2 Higgs branching ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Number of events at LHC in first year . . . . . . . . . . . . . . . . . . . . 6

1.4 LHC injector complex . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 LHC overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.6 Proton-Proton collision . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1 Photon interaction cross section for various processes . . . . . . . . . . . . 14

2.2 Electron energy loss in lead . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Heitler EM shower model . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Hadronic shower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5 Particle energy deposition in copper . . . . . . . . . . . . . . . . . . . . . 20

2.6 LAr sampling calorimeter readout . . . . . . . . . . . . . . . . . . . . . . 21

3.1 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2 ATLAS calorimetry system . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Calorimeter end-cap system . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.4 Structure of the HEC readout gap . . . . . . . . . . . . . . . . . . . . . . . 32

3.5 EM accordion structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.6 FCAL cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.7 Muon System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.1 CBT-EC2: top view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2 CBT-EC2: side view, Run II . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3 CBT-EC2: side view, FCAL region . . . . . . . . . . . . . . . . . . . . . . 39

xi

LIST OF FIGURES xii

4.4 CBT-EC2: front view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.5 CBT-EC2: 3D image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.6 ATLAS signal readout shapes . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.7 CBT-EC2: Noise rms values . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.8 HEC calibration chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.9 HEC calibration current pulse . . . . . . . . . . . . . . . . . . . . . . . . 48

4.10 Ionization vs calibration current . . . . . . . . . . . . . . . . . . . . . . . 49

4.11 DAC vs ADC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.12 Run I: DAC/ADCcalib comparison . . . . . . . . . . . . . . . . . . . . . . 51

4.13 Run II: DAC/ADCcalib comparison . . . . . . . . . . . . . . . . . . . . . . 52

5.1 193 GeV e+: EMEC reco, including beam contamination signatures . . . . 54

5.2 BPC hits scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.3 119 GeV narrow e+ : scintillator TDC multiple hit signatures . . . . . . . . 56

5.4 119 GeV narrow e+ : scintillator ADC multiple hit signatures . . . . . . . . 57

5.5 119 GeV narrow e+: S2 vs B2 ADC counts . . . . . . . . . . . . . . . . . 58

5.6 119 GeV narrow e+: S2 scint ADC with B2 cut . . . . . . . . . . . . . . . 59

5.7 119 GeV narrow e+: reference scint’s before and after cut . . . . . . . . . . 60

5.8 119 GeV e+: scint before/after cut . . . . . . . . . . . . . . . . . . . . . . 62

5.9 60 GeV e+: missing scintillator events . . . . . . . . . . . . . . . . . . . . 63

5.10 60 GeV wide e+: reference scint’s before and after cut . . . . . . . . . . . 64

5.11 193 GeV wide e−: reference scint’s before and after cut . . . . . . . . . . . 66

5.12 193 GeV e+: HEC vs EMEC, before beam quality event selection . . . . . 67

5.13 193 GeV e−: before and after muon elimination . . . . . . . . . . . . . . . 68

5.14 193 GeV e+: reco HEC and EMEC, various EMEC/HEC fractions . . . . . 70

5.15 193 GeV e+: total Reco, various EMEC/HEC fractions . . . . . . . . . . . 71

6.1 80 GeV e+: Comparing CF and OF signal reconstruction . . . . . . . . . . 73

6.2 e+: HEC energy scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

6.3 π+: HEC energy scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.4 200 GeV π+: HEC response using various EMEC/HEC deposition event

selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.5 HEC: X scan of e+ and π+ . . . . . . . . . . . . . . . . . . . . . . . . . . 78

LIST OF FIGURES xiii

6.6 Gaussian Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.7 π+: HEC response for various topo clustering . . . . . . . . . . . . . . . . 816.8 e+: EMEC response for various topo clustering . . . . . . . . . . . . . . . 82

6.9 Y scan: reco fit examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.10 Y scan at X=0 mm, e+ 193 GeV. . . . . . . . . . . . . . . . . . . . . . . . 84

6.11 60 GeV e+: Various Y scans . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.12 e+: various Y scan resolution . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.13 π+ : Y scan at X= 0 mm . . . . . . . . . . . . . . . . . . . . . . . . . . . 886.14 π+: Y scan at x= –60 mm and x= –120 mm . . . . . . . . . . . . . . . . . 896.15 π+: Y scan resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

A.1 Front view: HEC and EMEC . . . . . . . . . . . . . . . . . . . . . . . . . 96

A.2 Front view: real, HEC and EMEC . . . . . . . . . . . . . . . . . . . . . . 97

A.3 Side view: real, HEC, EMEC and FCAL . . . . . . . . . . . . . . . . . . . 98

A.4 Front view: FCAL cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

A.5 Run I: interaction points . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

A.6 CBT-EC2 RunI: Side view . . . . . . . . . . . . . . . . . . . . . . . . . . 101

A.7 CBT-EC2 RunI: Layer 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 102





A.12 CBT-EC2 RunI: Layer 6, phi section of CTC . . . . . . . . . . . . . . . . 107

A.13 CBT-EC2 RunI: Layer 6, eta section of CTC . . . . . . . . . . . . . . . . . 108

A.14 Run II: interaction points . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

A.15 CBT-EC2 RunII: Side view . . . . . . . . . . . . . . . . . . . . . . . . . . 110

A.16 CBT-EC2 RunII: Layer 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 111





A.21 CBT-EC2 RunII: Layer 6, phi section of CTC . . . . . . . . . . . . . . . . 116

LIST OF FIGURES xiv

A.22 CBT-EC2 RunII: Layer 6, eta section of CTC . . . . . . . . . . . . . . . . 117

Chapter 1

Introduction

The ATLAS (A Toroidal LHC Apparatus) experiment located at CERN is an all-purpose

detector that will study the highest energy and luminosity1 proton–proton collisions created

by man to date. The protons are accelerated by the Large Hadron Collider (LHC) and first

collisions will be recorded as early as the summer of 2007. The high energy and luminos-

ity of the LHC beams will create a high radiation and event multiplicity environment for

ATLAS, that enforces many constraints on the detector, making it an extremely complicated

multi-part apparatus. The complexity of the detector also forces the use of mass computing

to process and store the huge amount of data produced by the collisions. It is predicted that

the first year of running will produce ≈ 2000 Terabytes of data.After years of planning, the detector is now in the installation phase as research facil-

ities and universities from all over the globe install their contributions in the ATLAS pit

100 m underground at the Swiss-French border. In order to understand the apparatus before

the first data are read out, there have been many tests looking at the response of individual

components. The study of interest in this thesis is part of one of two final beam test series

before collisions in 2007. The Combined End Cap Calorimeter (CBT-EC2) test phase took

place over two run periods, in the summer of 2004, at the H6 beam line at the Prevessin

CERN site in France. This test studied the combination of the entire end-cap calorimeter

system for the first time, along with reconfirming previous test results which were ob-

tained between 1998 and 2003. Details of previously performed beam tests can be found

in Refs. [1], [2], and [3]. The end-cap system consists of the Hadronic Endcap Calorime-

1Luminosity will be discussed in section 1.1.2.

1

CHAPTER 1. INTRODUCTION 2

ter (HEC), the Electromagnetic Endcap Calorimeter (EMEC) and the Forward Calorimeter

(FCAL), which will be discussed in detail in section 2.2.

This thesis presents two main studies. The first half concerns work to assure that only

particles of a certain type are considered in the incoming beam. The main task of the beam

quality studies is to eliminate muons, multiple hits per recorded event and “simply” elimi-

nating beam contamination by applying specific conditions on certain parameters. Once a

clean beam sample is achieved, the thesis concentrates on the calculations of some beam

test specific calibration constants in order to understand the electronics. The second part

of the thesis consists of the study of energy reconstruction in different subdetectors. The

main interest of this test period is to understand the energy sharing between the detectors,

especially studying the dead region at the interface of the three end-cap systems. In order

to study these effects, various position and energy scans spanning all sub-detectors were

done to show uniformity in response. The individual and complete detector energy resolu-

tion with varying clustering methods is also studied. The layout of this thesis is as follows.

The remainder of this chapter gives a brief introduction to some accelerator quantities and

features, along with some LHC details and ATLAS specific quantities. The following two

chapters describe general details about calorimetry and particle interactions with matter,

along with discussing components of the entire ATLAS detector, putting emphasis on the

end-cap calorimeter system. The remaining chapters give details of the CBT-EC2 setup and

outline the studies that were performed, including results.

1.1 Physics Motivation of ATLAS

The ATLAS detector will be the latest experiment putting constraints on the Standard Model

(SM) as it is known today. The high luminosity of the LHC will allow the verification, in

a matter of days, of previously measured properties such as the top quark mass, the study

of b-quark physics, and accumulation of data with excellent statistical precision for many

other SM measurements. The detector will also continue the search for the Higgs boson

in order to confirm the existence of the Higgs field which is postulated to be responsible

for particle mass. The new energy frontier of the LHC will also allow us to push beyond

the Standard Model and search for Supersymmetric sparticles that are undetected to date.

The richness of ATLAS physics is a particle physicist’s playground and is only described


briefly in the following sections, concentrating on the Higgs boson and giving a very brief

introduction to Supersymmetry.

1.1.1 Higgs Boson

The Higgs boson is the last particle in the Standard Model that remains undetected. Its

discovery would therefore be a huge triumph. The Higgs mechanism is the underlying

process giving matter mass by postulating the existence of a Higgs field. The way to verify

this theory is to discover the Higgs boson. The creation of this boson can occur through

various production channels as illustrated in Figure 1.1.

g

tH

W,Z

qq

q

W,ZH

t

g

qW,Z

W,Z

H

g

g

t

t

t

t

H

(b)(a)

(c) (d)

t

Figure 1.1: Feynman diagrams for Higgs production channels. (a) gluon-gluon fusion , (b)tt̄ fusion, (c) ZZ and WW fusion, (d) W and Z bremsstrahlung [1].

Once Higgs bosons are created, various decays can occur depending on the mass of

the particle. Figure 1.2 shows the branching ratios2 for different mass values of the Higgs

boson. The dark gray region in this figure corresponds to an experimentally ruled out Higgs

mass region of less than 114 GeV with a 95 % Confidence Level, obtained by experiments

performed at LEP and the Tevatron. The center yellow region is the most probable Higgs

mass that fits current models.2Branching ratio is the probability of a decay to occur with respect to all other possible processes.


Figure 1.2: Higgs branching ratios for different decay channels. LEP and the Tevatronexcluded the Higgs mass below 114 GeV at a 95 % CL as shown by the grey region [1].

1.1.2 Supersymmetry

Supersymmetry is a theory that has the potential to solve many of the Standard Model’s

problems that exist today. If verified, a Grand Unified Theory (GUT) can be formulated

that would cause the electroweak and the strong coupling constants to converge at energies

of about 1016 GeV. Supersymmetry also addresses the mass hierarchy problem, and unlike

the Standard Model has the possibility to be extended to the Plank scale. The theory is

based on a new symmetry between fermions and bosons. It predicts that each particle has

a supersymmetric partner (called a sparticle) that has identical mass and quantum numbers

except for spin. The spins are such that each fermion has a bosonic superpartner and vice

versa 3. These supersymmetric particles have never been observed, which shows that if this

symmetry exists, it must be broken. This symmetry breaking causes the sparticles to have a

mass that is larger than any experiment has been able to probe to date, and hence they have

not been detected. ATLAS opens the window and has the potential to detect these sparticles

for the first time, if they exist.

3Fermions have half integer spin, and bosons have integer spin.


1.2 Reaction Rate, Luminosity and Interaction Cross

Section

In order to be able to predict the number of interesting events created in a specific time by

collisions of particles, the concept of reaction rate is used. The reaction rate R is a property

in units of events/second of a specific reaction and can be expressed as:

R = L σ (1.1)

where L is the instantaneous luminosity and σ is the reaction cross-section. L is a prop-erty that depends entirely on the characteristics of the accelerator. The luminosity in units

of s−1 · cm−2 for a collision of two beam bunches of N1 and N2 particles, with a machinebunch crossing frequency f and a cross-sectional overlap area of the beams denoted by A

is [9]:

L =N1N2 f

A. (1.2)

The LHC design luminosity values will be discussed in the following section. The second

term in equation 1.1 is a pure physics term and is related to the probability of the occurrence

of the particle production of interest. The reaction cross section has units of cm2. This can

be understood by picturing the probability of a specific reaction occurring in terms of the

overlapping colliding particle area. The size of this area corresponds to the probability of

the interaction between the two particles4. Therefore, the units on the right hand side of

equation 1.1 are:

eventss∗ cm2 ∗ cm

2 =events

s(1.3)

as expected for the reaction rate. It is evident from equation 1.1, that in order to obtain better

statistics by studying more events, a higher luminosity or reaction cross section is needed.

Since the interaction cross section is a physical property of a reaction, the luminosity is

the only term that can be improved to increase the observed reaction rate to obtain a better

4In the simplest case, imagine the scattering of two billiard balls. The probability of interaction is relatedto the size of the overlapping area of both balls.


statistical certainty.

In order to determine the number of events observed over a complete run period, the

concept of integrated luminosity is used. Assuming 230 days of operation and an instan-

taneous luminosity of 2.0 ×1033cm−2s−1, an integrated luminosity of 40 fb−1 (1 barn =10−24cm2) will be produced by the LHC in the first year.

Figure 1.3: The expected number of events for various interactions, in the first year of LHCoperation [4].

Figure 1.3 shows the number of expected events produced in the first year of LHC operation

assuming the above expected integrated luminosity. Comparing the number of Higgs events

to the total inelastic interactions shows how difficult a process it will be to select events of

interest.

1.3 LHC

The Large Hadron Collider will be the largest accelerator in the world with a circumference

of 27 km located in the old LEP (Large-Electron-Positron) tunnel, spanning the French-


Figure 1.4: LHC with injector complex. The injection stage is as follows: linac (50 MeV),PS booster (1.4 GeV), PS (26 GeV), SPS (450 GeV). CBT-EC2 data taking took place atthe Prevessin site, off the SPS ring [3].

Swiss border at CERN. What makes this accelerator the first of its kind is not the physical

size but the energies and luminosities that will be achieved. It will also be the largest

proton–proton collider. The LHC will collide 7 TeV on 7 TeV protons giving a center of

mass energy of 14 TeV with a design luminosity of 1.0 ×1034cm−2s−1 [15]. In order toemphasize the size of this accelerator, it is appropriate to state that the circumference of

the Tevatron at Fermilab in Chicago is 6.3 km, creating a CM energy of 1.96 GeV, with a

maximum luminosity of 1.15 ×1032cm−2s−1. The Tevatron is the largest functioning ac-celerator today. A reason that the LHC is a hadron collider is that a broad energy range can

be studied due to the nature of proton–proton interactions as outlined in section 1.3.1. This

broad energy distribution enables the search for particles with an unknown mass, such as

the Higgs boson. The high luminosity of the LHC will be achieved by having a 25ns bunch

crossing5. Each bunch crossing will have an estimated 23 collisions producing an interac-

tion frequency of 9.2×108 Hz. The proton velocity in the LHC will be only 9.69 km/h lessthan the speed of light, reconstructing an environment similar to 1× 10−12 s after the BigBang [1].

The acceleration of particles prior to injection into the LHC ring occurs in multiple

5Particles are grouped in bunches around the LHC ring as is illustrated in Figure 1.6.


Figure 1.5: LHC ring with experiments, ATLAS, CMS, LHC-B and ALICE [5].

stages (Figure 1.4) in order to reach the center of mass energy of 14 TeV. The acceleration

begins at a 50 MeV linear accelerator. The particles are then transferred to the 1.4 GeV

Proton Synchrotron (PS) booster, to the 26 GeV PS, and then to the 450 GeV Super Proton

Synchrotron (SPS) ring before being injected into the LHC. The CBT-EC2 apparatus of

interest in this thesis is located at the CERN H6 beamline, off the SPS ring. In order to

maximize the use of the LHC, four experiments are currently in construction around the

ring. The experiments consist of the multi-purpose detectors ATLAS and CMS, along with

LHC-B that will concentrate on b-quark physics. The fourth experiment, ALICE, will study

heavy-ion collisions since the LHC will also be used as a Pb-Pb collider with a CM energy

of 1150 TeV . The detector of interest in this thesis is ATLAS, and therefore CMS, ALICE

and the LHC-B will not be discussed further. The layout of the LHC and its detectors can

be seen in Figure 1.5.


1.3.1 Proton–Proton collisions

Protons are not fundamental particles, but are a combination of bound states of partons.

Partons are fundamental particles such as quarks and gluons. The partons making up pro-

tons are three valence (uud) quarks, and many gluons and sea quarks6. Since the energy of

the proton collisions is extremely high, individual parton interactions are what is observed,

not proton-on-proton as the name implies. The momentum fraction of a proton that a sin-

gle parton carries can be calculated via a parton distribution function. There are two types

of parton scattering, hard and soft. Hard scattering events are “golden events” that have a

high transverse energy, which are selected by the trigger system. Soft scattering events are

also known as minimum bias events and are responsible for a large signal background in

the detector. An ideal event is the hard scattering of two partons with a small minimum

bias event background. The high luminosity of the LHC introduces the concept of pile-up.

Pile-up in the ATLAS detector corresponds to energy in the detector that does not origi-

nate from the reaction of interest, in turn altering results. There are two main components

to pile-up. The first component relates to the high collision frequency that causes events

from more than one bunch crossing to be present in the detector at the same time. The

second pile-up component originates from the soft scattering events discussed above from

the same bunch. Developing algorithms that select physics processes of interest over the

pile-up effects will be another difficult task at ATLAS. Figure 1.6 shows a schematic of

proton–proton scattering.

1.3.2 Coordinate System

The LHC beam line is defined to be the z axis with a right-handed x coordinate, pointing to-

wards the center of the LHC ring, while the positive y axis is pointing upwards. The analysis

of data from ATLAS uses the usual spherical coordinate system for collider experiments.

There are two angles describing the system, θ and φ being the polar and azimuthal anglerespectively. In order to describe particles in inclusively measured reactions, a Lorentz

invariant variable known as the rapidity (y) is defined as:

6See any introductory particle physics book such as Ref. [7] for an explanation of proton composition.


Figure 1.6: Example of a proton–proton collision [5].


y =12

logE + pLE − pL

(1.4)

where pL is the longitudinal momentum along the interaction axis and E is the particle

energy. The above equation can also be written as:

tanh(y) =pLE

(1.5)

Equation 1.5 is valid for particles with mass m. The pseudo-rapidity, η, is the rapidity formassless particles and can be related to the polar angle θ in the following way:

η = − ln(

tanθ2

)

. (1.6)

The above relation is used to describe the region of interactions in ATLAS. The advantage

of the pseudo-rapidity over the polar angle θ is related to the concept of reference frameboosting. Since the collisions studied by ATLAS are in the proton-proton CM system, in-

dividual interacting partons have unequal momentum since quarks carry only a fraction of

the proton momentum. Due to this momentum imbalance, the detector is not in the center

of mass (CM) frame of the collision. Therefore, in order to obtain more easily interpretable

results, all measurements must be Lorentz boosted into the CM frame. Defining the az-

imuthal direction in terms of a Lorentz invariant variable eliminates the need to navigate

between reference frames. Another characteristic of pseudorapidity is that the particle rate

per unit area is equal for all η regions.

Chapter 2

Calorimetry

Calorimeters are a major component of modern particle physics experiments. One of the

most valuable properties of a calorimeter is that the resolution improves with the incident

particle energy, in contrast to detectors that depend on the bending of the particle path

in a magnetic field to determine its momentum. Furthermore, using magnetic fields is a

problem in detectors since neutral particle paths are unaltered. Calorimeters, on the other

hand, enable the energy measurement of neutral and charged particles.

There are two different types of calorimeters: sampling and homogeneous. The entire

detector volume of homogeneous calorimeters contributes to the response. The medium

used in homogeneous calorimeters must therefore be able to absorb the incident particles,

as well as produce signals corresponding to the particle energy, making it ideal for low

energy particle measurements1. This type of detector is usually composed of lead glass,

which creates a particle shower initiated by the incoming particle. The shower particles that

exceed the speed of light in the lead glass emit Cerenkov radiation, which is then detected

by surrounding photo-multiplier tubes (PMT). Another style of a homogeneous calorimeter

is the scintillator detector. The incident particle excites the medium and scintillating light

is emitted once the atoms return to the ground state. These photons are again detected by

the use of PMTs.

Sampling calorimeters are composed of layers of two materials including an active and

a passive medium. The passive material triggers showering of the incident particle, while

1Ideally homogeneous calorimeters are used since they detect most of the deposited particle energy. Spaceand cost constraints put a limit on the use of these detectors.

12

CHAPTER 2. CALORIMETRY 13

the active volume provides the readout. Sampling calorimeters will be discussed in section

2.3 since that is the detector design used throughout the ATLAS calorimetry system.

This chapter will start out with a review of particle shower properties for electromagnetic

and hadronic showers, and will then present the concept of sampling calorimetry. The

final sections will discuss two important calorimeter properties: compensation and energy

resolution. For a more detailed discussion of calorimetry one can read Refs. [8] and [9]

where most of the material from this chapter was obtained.

2.1 Particle Showers

Particles that pass through matter will lose energy by interacting with the surrounding

medium. There are many different processes varying from interactions that ionize the sur-

rounding matter, to simple vibrational excitation mechanisms. Particle interaction processes

can be electromagnetic or hadronic depending on the type of particle, resulting in different

shower criteria that are discussed in the upcoming section.

2.1.1 Electromagnetic Showers

This section will begin by discussing the quantum of the electromagnetic (EM) force, the

photon. Photons can interact with matter by four processes: the photoelectric effect, Comp-

ton scattering, Rayleigh scattering, or electron–positron pair production. The photoelectric

effect occurs when a photon is absorbed by an atom, which then ejects an electron. This

process dominates for low energy photons [8]. Compton scattering is similar to a two body

“billiard ball” scattering where the photon “bounces” off the atomic electrons while ex-

changing energy. Rayleigh scattering is unique since no energy of the photon is lost, but

the trajectory is altered affecting the position measurement resolution. Finally, electron–

positron production is a process where photons with sufficient energy create e+e− pairs

from the interaction with the nucleus or the atomic electrons. Figure 2.1 shows a plot of the

cross sections for the above interactions of photons in lead, as a function of energy. As can

be seen, e+e− pair production is dominant for high energy photons. This feature is the un-

derlying mechanism for EM showers and will be explained in detail below. More details of

the photon interaction processes discussed above can be found in any introductory particle


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��

��

��

�� !� � ��"#�$� ��%"&� �

' (*)+ ��,*- 'Z = .*/ )

− 02143507698;:!02=$?A@ σB9CDBσE>F G9F

κ H

IKJLMMMNOPQ LRS TKUJRMV UP LWX

σ Y[Z�\*]_^9` a5b

σ c[d9egfih�dkj

κ jkl�m

Figure 2.1: Photon interaction cross-section contributions in lead. σp.e. = photoelectric ef-fect, σRayleigh = Rayleigh scattering, σCompton = Compton scattering, Knue = pair productionoff the nucleus, Ke = pair production off atomic electron [5].

physics textbook, or in Ref. [1].

Electrons can lose energy via processes like ionization, bremsstrahlung, Moller scattering

or positron annihilation [9]. Before discussing electron energy losses any further, it is

important to introduce the concept of radiation length. By definition, the radiation length

is the distance an electron travels on average in a certain medium to reduce its energy by

a factor of 1/e as stated in Equation 2.1, where E0 is the incident energy, x is the distance

traveled, and X0 is the radiation length.

E = E0e− xX0 (2.1)

An estimate of the electron radiation length in a medium in terms of the atomic weight A,

the atomic number Z and the material density ρ is given by [9]:


X0 ≈ 180AZ2

ρ (2.2)

After considering the longitudinal scale it is important to measure the transverse shower

size that is characterized by ρm, the Molière radius, which can be written as [9]:

ρm =21MeV

EcX0, (2.3)

where Ec is the critical energy and X0 is the radiation length. Ec is defined as the energy

where the ionization energy loss is equal to the bremsstrahlung energy loss. Typically one

can assume the shower to be 95 % contained in a cone with twice the Molière radius [9].

26. Passage of particles through matter

��

Lead (Z = 82)��

��

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e−(��)��*&

e+(

��+��

1.0

0.5

0.20

0.15

0.10

0.05

,.-/021

−

3 4

E (MeV)1

010 100 1000

5 E−

dE

dx

, X

6−

3 4

Figure 2.2: Electron energy loss per radiation length in Lead [5].

The various processes discussed above dominate in different energy regimes as can be

seen in Figure 2.2. This figure shows that high energy electrons lose energy primarily

due to bremsstrahlung. Most of these bremsstrahlung photons are low in energy and are

absorbed in the medium via the photoelectric effect or Compton scattering, while high

energy photons create electron-positron pairs as discussed above (Figure 2.1). The electrons

and positrons created again emit photons via bremsstrahlung and the cycle goes on until the


Figure 2.3: Simple em shower model. A bremsstrahlung photon or positron electron pair isproduced every X0 for electrons/positrons and photons respectively.

electrons have an energy lower than Ec, where ionization starts to be the dominant source of

energy loss (≈10 MeV for lead in Figure 2.2). This process of electron multiplication viaphoton pair production and bremsstrahlung is what makes up an electromagnetic shower.

Heitler developed a quantitative EM shower model that is outlined in Figure 2.3. The main

component of this model is that electrons and photons both travel a distance of one radiation

length before bremsstrahlung photons are emitted or electron–positron pairs are created.

The shower starts with one electron of energy much larger than the critical energy. This

electron will travel one interaction length before emitting a bremsstrahlung photon with

half the incident electron’s energy. At that stage there is a photon and one electron, each

with energy equal to half the initial electron energy. The electron will continue and again

emit a photon after a distance X0 while the photon emits a positron-electron pair after one

radiation length. The particle multiplicity increases until the shower electrons are below

the critical energy and start to lose the remaining energy by ionization and excitations of

vibrations in the medium. It is important to note that this is a very simplified model in order

to help visualize a EM shower process. In order to get an accurate understanding of EM

shower behavior the use of proper Monte Carlo simulation is essential. Heitler’s EM shower

model assumes that above the critical energy all losses are primarily due to bremsstrahlung.

The number of electrons can therefore be written as:


N(t) = 2t (2.4)

where t is the number of interaction lengths. More discussion on electron multiplication

can be found in Ref. [9].

To sum up the electromagnetic shower discussion, it is important to note that these showers

are well understood since eventually all the incoming electron energy is used to ionize the

interaction medium. Therefore all the energy is accounted for, giving calorimeters accurate

measurements of the incoming electrons.

2.1.2 Hadronic Showers

Hadronic showers are much more complicated than EM showers due to the underlying

strong interaction component with the absorbing medium. This strong component enables

many more underlying processes in the particle–medium interaction and introduces the

concept of missing energy in the calorimeter. Missing energy is dissipated particle energy

in a medium that is fundamentally undetectable [8]. The nature of the strong interaction

can be explained no better than with an example given by Wigmans [8]. Assume that an

incoming hadron ionizes the surrounding medium, freeing electrons which are detected via

an EM shower as discussed in the previous section. But at the same time the hadron can

interact strongly with a nucleus in the medium. This is the heart of the shower fluctuation

since this strong process can cause the incoming hadron to turn into a number of other

hadrons, emit photons, or it can excite the atomic nucleus, which in turn causes vibrational

modes which are undetected in a calorimeter.

Energy Type Example Fraction ≈Electro Magnetic π0 → γγ O(50%)Visible non-EM π±, n O(25%)

Invisible non-EM nuclear excitation and breakup O(25%)Escape Energy ν, Shower leakage O(2%)

Table 2.1: Hadronic shower composition [10].

As one can readily see, there are many different components of a hadronic shower as is

summarized in Table 2.1. It is important to note that the above table only gives estimates of


the shower fraction and that there are large fluctuations present event by event. Fluctuations

in the detected energy component are also observed making hadronic shower reconstruction

more difficult. A diagram of a hadronic shower example is shown in Figure 2.4.

Figure 2.4: Hadronic shower example.

Before going any further, it is again important to look at the distance scales of a hadronic

shower as was discussed for the EM case above. The hadronic interaction probability of a

particle traveling a distance x is given by:

P(x) = 1− e−x

λ0 , (2.5)

where λ0 is the longitudinal hadronic shower distance scale called the nuclear interactionlength. The total interaction cross section σtot can be written in terms of the nuclear inter-action length as follows:

σtot =A

NAλ0. (2.6)

In the above equation, A is the atomic number, NA is Avogadro’s number and λ0 is expressedin units of g·cm−2. Looking at the dimensions of cross section [L]2 one can see that λ0 must


be proportional to A1/3 since the nuclear volume [L]3 scales with A. Experimentally λ0 canbe approximated as:

λ0 ≈ 35A1/3

ρ(2.7)

where ρ is the density of the medium. The radius of a hadronic shower is much broaderthan the Molière radius of an EM shower and ranges around one nuclear interaction length,

independent of the hadronic incident energy [3].

Having discussed the length scale of a hadronic shower, it is appropriate to look at the

theoretical framework behind individual processes. Since EM showers are the best under-

stood processes, as outlined in the previous section, the EM fraction term of a hadronic

shower is now discussed. The energy dependent EM fraction of a hadronic shower is given

by Gabriel [11] as:

fem = 1−(

EEav

)(k−1), (2.8)

where Eav is a scale factor that is related to the average energy needed to produce one pion

(assumed to be 1 GeV), and the exponent (k-1) is related to the multiplicity of the reac-

tion and the fraction of π0s produced per interaction. The value of k has been determinedexperimentally [8] to be between 0.8 and 0.84.

As outlined above, the hadronic sector of the shower is complicated due to the fact that over

300 processes are responsible for energy loss each accounting for at least 0.1 % [8]. Since

there is no concrete quantum chromodynamics (QCD) theory accounting for all processes,

a phenomenological model under the name of spallation has been developed [8]. Spalla-

tion is described as a two stage process: a fast internuclear cascade, followed by a slow

evaporative stage. The fast stage occurs on a time scale of ≈10−22 seconds. In this stage, ahadron interacts via quasi-free collisions with the nucleons inside the struck nucleus. These

struck nuclei can then create other unstable hadrons if the energy is sufficient, or simply

redistribute the kinetic energy, exciting the nucleus. Once the nucleus is excited and full of

unstable hadrons the second stage of spallation begins. This stage is the de-excitation of

the nucleus via the release of particles or γ rays. The released particles are mostly neutrons,but α’s and other particles can also emerge [8].


2.2 Energy Deposition in Matter

The amount of energy deposited in the detector is the quantity of interest for the design of

an efficient detector, instead of single particle interactions as was discussed in the previous

section. This section will therefore focus on the energy deposition scales of entire particle

showers in materials. The energy deposited in a detector is proportional to the number of

particles in the shower. The number of particles in an EM shower increases with depth

until the average energy per shower particle is below the multiplication threshold. Once the

shower maximum is reached the number of particles decreases as they are absorbed by the

medium. This effect can be seen in Figure 2.5, where the energy deposition of a shower is

shown as a function of depth.

Figure 2.5: The energy deposited as a function of depth for various energy electrons incopper . All curves have been normalized to compare the energy deposition profile. EGS4simulations were used for this plot [5].

The integral of the curves in Figure 2.5 gives the percentage of the incident energy

deposited in the detector in a given depth of the material. An interesting effect to note is


that near a shower maximum, small changes in thickness cause a large increase in energy

deposition with respect to a similar depth near the beginning or end of the shower. More

details on this subject can be found in [8].

2.3 Sampling Calorimeters

Sampling calorimeters contain hadronic and electromagnetic showers in a reasonable de-

tector depth by using more than one material to trap and measure the energy, as is the case

for homogeneous detectors. All calorimeters in ATLAS are of this type. The basis of op-

eration for this detector is to take samples of the shower by having an array of successive

active and passive media. The passive (absorber) medium has high density and initiates the

particle shower, while the active medium provides the readout. The readout scheme varies

with the choice of active medium. If a scintillator is chosen (as in the tile barrel), PMTs de-

tect emitted light from the excited scintillator atoms. If a liquid or gas medium is used, the

charged shower particles ionize the active medium and a current is measured. This method

is used in both of the end-caps and the EM barrel calorimeter in ATLAS, where Liquid

Figure 2.6: LAr type sampling calorimeter readout. The shower particles ionize the LArcreating a current which is measured. It is important to note that the showering processinside the absorber is not included in the drawing for simplicity.


Argon (LAr) is used as the active medium. Figure 2.6 illustrates the liquid active medium

method. The incoming particle enters from the bottom, creating a shower that ionizes the

LAr, creating free electrons. When under an electric field these electrons begin to travel to

the positive voltage terminal, creating a current which can then be read out. The ionization

current is proportional to the number of free electrons in the LAr gap and hence to the initial

energy of the incident particle. The geometry of the ATLAS LAr sampling calorimeters is

composed of consecutive rectangular readout structures as shown in Figure 2.6, except for

the EMEC, which uses the same idea with a different geometry2.

Sampling calorimeters have two important design parameters: the sampling fraction and

frequency. The sampling fraction is defined as the energy deposited by minimum ionizing

particles in the active calorimeter layers, measured relative to the total energy deposited in

the detector [8]. The sampling frequency describes the number of samples per unit depth.

The choice of material for the passive and active media depends on the physical charac-

teristics of the shower development, material availability, detector size constraints, and of

course, as in anything, cost. Liquid active media are usually chosen to be composed of a

liquified noble gas. The reason for this choice is that these elements have full outer electron

shells, minimizing re-absorption of ionized electrons3. The same liquid active medium is

usually used for different detector components to simplify the apparatus4. Scintillator ac-

tive media must have detailed and stable excitation levels in a strong magnetic and radiation

environment. The absorption component varies with the particles of interest. In the case

of EM calorimeters, a high Z material is chosen to quickly contain the shower, while for

a hadronic calorimeter, small interaction length materials are chosen to fully obtain a de-

tailed shower structure in order to identify the EM and hadronic shower components. The

choice of media for the ATLAS calorimeters, as well as the structural details, are discussed

in section 3.2. A list of various active and passive media and their properties is given in

Table 2.3.2See section 3.2.2 for more details.3Electronegative contamination in active media reabsorbs ionization electrons, altering the response.4All ATLAS calorimeters except for the tile use LAr as the active medium.


Density Ec X0 ρM λintPassive Material Z (g cm−3) (MeV) (mm) (mm) (mm)

C 6 2.27 83 188 48 381Al 13 2.70 43 89 44 390Fe 26 7.87 22 17.6 16.9 168Cu 29 8.96 20 14.3 15.2 151Sn 50 7.31 12 12.1 21.6 223W 74 19.3 8.0 3.5 9.3 96Pb 82 11.3 7.4 5.6 16.0 170

238U 92 18.95 6.8 3.2 10.0 105Concrete - 2.5 55 107 41 400

Glass - 2.23 51 127 53 438Marble - 2.93 56 96 36 362

Density Ec X0 ρM λintActive Material Z (g cm−3) (MeV) (mm) (mm) (mm)

Si 14 2.33 41 93.6 48 455Ar (liquid) 18 1.40 37 140 80 837Kr (liquid) 36 2.41 18 47 55 607Xe (liquid) 54 2.95 12 24.0 42 572Polystyrene - 1.032 94 424 96 795

Plexiglas - 1.18 86 344 85 708Quartz - 2.32 51 117 49 428

Lead-glass - 4.06 15 25.1 35 330Air 20o,1 atm - 0.0012 87 304 m 74 m 747 m

Water - 1.00 83 361 92 849

Table 2.2: Detector–medium interaction properties including the critical energy (Ec), theradiation length (X0), the Molière radius (ρM), and the nuclear interaction length (λint) [8].


2.4 Calorimeter Compensation

As was discussed in previous sections, hadronic and electromagnetic showers of the same

incident energy are not measured to the same precision. The EM shower energy is fully

reconstructed, in an accurately calibrated calorimeter, while hadronic showers are not, due

to missing energy and large shower fluctuations. This feature can be expressed as e/h > 1

where e and h are the EM and hadronic response respectively. An ideal calorimeter would

not react differently to each particle type and give a uniform response, acting as a compen-

sating calorimeter. As this is not the case for most calorimeters, one must compensate in

hardware or software and attempt to create an e/h ratio of 1. To fix this in hardware, active

and passive media must be chosen to suppress EM showers and enhance the hadronic com-

ponent. This method was chosen for detectors like D /0 at the Tevatron where the e/h valueis close to 1. Compensating calorimeters can use uranium absorber plates due to its high-Z

content and large fission probability, which produces many more neutrons than other media.

The many neutrons can then be detected by a proton rich scintillator [3]. The second way to

correct for the hadronic missing energy is to use software. This will be the method applied

by ATLAS since e/h is approximately 1.43. In order for software to perform this task, the

different hadronic shower components must be studied accurately, separating the EM frac-

tion from the hadronic fraction by studying the detector energy deposition density. After

the separation of the two processes, corresponding weights can reduce the EM component

while increasing the hadronic showers in order to obtain e/h ≈1.

2.5 Energy Resolution

The energy resolution measures the precision with which a calorimeter can determine the

incident particle’s energy. It is defined to be the width divided by the mean of the nor-

mal energy distribution5. This resolution can be parametrized in the following three term

expression for a sampling calorimeter.

σE

=A√E0

⊕B⊕ CE

(2.9)

5A fully contained particle shower follows a Gaussian distribution.


The terms in the above equation add in quadrature. E0 denotes the true particle energy and

E is the measured energy. A, B and C are constants for EM showers, but A is a function of E

for hadrons. The first term is the sampling term. It is determined by the sampling fraction

and frequency of the detector. This term can be understood by looking at EM showers.

The sampling calorimeter electron number N, which is proportional to the incident particle

energy, follows a Poisson distribution [1] with variance√

N. Writing the resolution in terms

of a Poisson distribution, expression 2.10 is obtained:

σE

∝√

NN

=1√N

∝1√E0

. (2.10)

Therefore the first term in equation 2.9 is related to EM showers via the sampling fraction

and frequency, and the shower EM content (fluctuation) in hadronic showers. The second

term of Equation 2.9 is called the constant term due to imperfect shower containment and

mechanical imperfections such as read out cables, cracks, etc. The third term is proportional

to the electronic noise but quickly becomes insignificant with increasing particle energy.

It is important to note that in the real ATLAS environment E0 will be an unknown and the

above parametrization will be written in terms of the measured energy only. However for

the beam tests described in this thesis, equation 2.10 is valid.

Chapter 3

The ATLAS detector

The ATLAS detector will be the largest of its kind having a width of 44 m, a diameter

of 22 m, and weighing over 7000 tons. A schematic of the detector can be seen in Fig-

ure 3.1. As with many other multi-purpose detectors, ATLAS is composed of many sub-

components which can be broken into three classes; the inner detector, the muon system,

and the calorimetry system. Combining the three systems makes ATLAS ideal for tagging b

quarks, jets, particle ID, etc., but most importantly for the discovery of the Higgs Boson as

described in previous chapters. The focus of this thesis is the end-cap calorimetry system.

For completeness, a brief outline of all the different main components is included. This

chapter describes the real ATLAS detector, not the beam test setup of interest in this thesis.

Complete details and design specifications can be found in the ATLAS Technical Design

Report [12].

3.1 ATLAS Inner Detector

The ATLAS inner detector (AIT) is the closest “barrel” region around the interaction point

and beam pipe. It consist of 3 sub-systems; semiconductor tracking (SCT) using pixel and

micro-strip detectors, and a straw tube tracker (TRT). The measurement properties include:

track reconstruction, momentum measurement, determination of the vertex position (colli-

sion point), and particle identification. The AIT is also part of an efficient trigger system

to pick out interesting events [12]. The pseudorapidity range of the AIT is between –2.5

to 2.5. The innermost detector uses the pixel SCT due to its high granularity. There are

26

CHAPTER 3. THE ATLAS DETECTOR 27

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140 million pixel detector elements with a size of 50 µm in the Rφ direction and 300 µmin z. The SCT microstrips are just outside the pixel region and consist of 8 layers of strips

containing 61 m2 of silicon, having 6.2 million readout channels. The ATLAS SCT is an

order of magnitude larger in surface than any previous silicon microstrip detector and must

also work in a radiation environment that alters the silicon wafers over time [12]. The ion-

izing radiation that the SCT must be able to withstand is over 300 kGy and over 5 ×1014

neutrons per cm2, in a operation period of 10 years. Outside the SCT microstrip, the straw

tube tracker is used for similar reconstruction to the SCT but is much less costly. The straw

tube tracker is also used for particle identification, by measuring transition radiation. This

radiation manifests itself as photons created when particles cross a material boundary with

different indices of refraction. A design parameter summary of the inner detector can be

seen in Table 3.1.

System Position Area Resolution Channels η coveragem2 σ(mum) (106)

Pixels 1 removable barrel layer 0.2 Rφ=12, z=66 16 ±2.52 barrel layers 1.4 Rφ=12, z=66 81 ±1.75 end-cap disks 0.7 Rφ=12, R=77 43 1.7-2.5on each side

Silicon strips 4 barrel layers 34.4 Rφ=16, z=580 3.2 ± 1.49 enc-cap wheels 26.7 Rφ=16, R=580 3.0 1.4-2.5on each side

TRT Axial barrel straws 170(per straw) 0.1 ±0.7Radial end-cap straws 170(per straw) 0.32 0.7-2.536 straws per track

Table 3.1: ATLAS Inner Detector design parameters, [12].

3.2 ATLAS Calorimeters

The ATLAS Calorimeter system is responsible for measuring the energy of electrons, jets,

and photons, along with determining the missing energy. Missing energy is calculated from

the lack of balance of the transverse momentum summation. It is also part of the event


trigger system and particle identification. A cross-sectional view of the calorimetry system

is shown in Figure 3.2.

Figure 3.2: The ATLAS calorimetry system [12].

The ATLAS calorimeter system is divided into two regions, barrel and end-cap. Two

different sampling calorimeter methods are used, LAr (liquid Argon) and tile. There are

three electromagnetic calorimeters including a barrel and two end-caps1. The pseudorapid-

ity coverage of the EM system is |η|< 1.475 for the barrel, while the end-caps cover 1.375< |η| < 3.2. All EM calorimeters are sampling LAr calorimeters and are composed of ac-cordion shaped kapton/copper electrodes and lead absorber plates. The accordion geometry

gives complete φ symmetry and minimizes the dead space [12]. The Hadronic Calorimetrysystem consists of a tile barrel and a LAr end-cap system. The tile calorimeter uses iron as

the absorption medium and scintillating tiles for the active material, giving a |η| coverageof less than 1.0. The hadronic end-caps (1.5 < |η| < 3.2) use LAr as the active region,with copper plates as the absorption medium. The Forward Calorimeter (FCAL) covers the

1The two end-caps are called A ( facing airport) and C. A is at positive z and C at negative z.


region 3.1 < |η|< 4.9 and is also a LAr detector using copper in the first layer and tungstenin the outer two layers as absorption media. The pseudorapidity and segmentation of the

different calorimeters can be seen in Table 3.2.

The end-cap calorimeter components (EMEC, HEC and FCAL) are all located in a

single cryostat as can be seen in Figure 3.3. The cryostat is composed of two vessels (cold

and warm) of aluminum alloy 5083 [13] separated by an evacuated region that contains

multilayer super-insulation. The EMEC is the first detector at the η region between 1.375and 3.2, followed by the HEC which is completely shielded by it. The FCAL sits inside

the hole of the EMEC and HEC wheels, 1.2 m behind the front face of the EMEC and only

provides coverage for high pseudorapidity. A diagram of the end-cap system is shown in

Figure 3.3.

Figure 3.3: Calorimeter end-cap system [12].


EM Calorimeter Barrel End-capCoverage |η| < 1.475 1.375 < |η| < 3.2Longitudinal segmentation 3 samplings 3 samplings 1.5 < |η| < 2.5

2 samplings 1.375 < |η| < 1.52.5 < |η| < 3.2

Granularity (∆η∆φ)Sampling 1 0.003 ×0.1 0.025 ×0.1 1.375 < |η| < 1.5

0.003 ×0.1 1.5 < |η| < 1.80.004 ×0.1 1.8 < |η| < 2.00.006 ×0.1 2.0 < |η| < 2.50.1 ×0.1 2.5 < |η| < 3.2

Sampling 2 0.025 ×0.025 0.025 ×0.025 1.375 < |η| < 2.50.1 ×0.1 2.5 < |η| < 3.2

Sampling 3 0.05 ×0.025 0.05 ×0.025 1.5 < |η| < 2.5Presampler Barrel End-capCoverage |η| < 1.52 1.5 < |η| < 1.8Longitudinal segmentation 1 sampling 1 samplingGranularity (∆η∆φ) 0.025 ×0.1 0.025 ×0.1Hadronic Tile Barrel Extended barrelCoverage |η| < 1.0 0.8 < |η| < 1.7Longitudinal segmentation 3 samplings 3 samplingsGranularity (∆η∆φ)Sampling 1 and 2 0.1×0.1 0.1×0.1Sampling 3 0.2×0.1 0.2×0.1Hardonic LAr End-capCoverage 1.5 < |η| < 3.2Longitudinal segmentation 4 samplingsGranularity (∆η∆φ) 0.1×0.1 1.5< |η| < 2.5

0.2×0.1 2.5< |η| < 3.2Forward Calorimeter ForwardCoverage 3.1< |η| < 4.9Longitudinal segmentation 2 samplingsGranularity (∆η∆φ) ≈ 0.2×0.2

Table 3.2: The ATLAS calorimeter system in numbers [12].


3.2.1 Hadronic End-Cap Calorimeter

The Hadronic End-Cap Calorimeter (HEC) is located at each end of the ATLAS detector,

covering the η region between 1.5 and 3.2 as can be seen in Figure 3.2. In order for thiscomponent to work efficiently it must have good radiation resistance, and cover a large

area.2 This sampling calorimeter consists of LAr and copper plates as the active and passive

medium respectively. The HEC is composed of two wheels, the inner wheel which is closer

to the beam interaction point and the outer. Both wheels consist of 32 pie-shaped modules

and are each read out in 2 longitudinal sections. The inner wheel has 25 copper plates all

with a thickness of 25 mm except for a 12.5 mm front plate all separated by 8.5 mm LAr

gaps. The outer wheel consists of 17 plates all with thickness 50 mm except for the front

plate which is 25 mm. The thicker plates were chosen in the outer wheel due to space

constraints in order to minimize shower leakage and cost. The HEC readout structure can

be seen in Figure 3.4.

Figure 3.4: Structure of the HEC readout gap [12].

2The HEC wheels extend 2 meters in radius from the beam line.


Each 8.5 mm LAr gap contains three read-out boards. The three-read-out-board struc-

ture is to minimize the ionization pileup, to help increase signal to noise, and to reduce

shorts and high-voltage sparks [12]. Only the centre electrode is read out. This setup will

give a readout segmentation of 2π/64 in φ and 0.05-0.1 in η for the two wheels respectively.

3.2.2 Electromagnetic End-Cap Calorimeter

The electromagnetic end-cap calorimeter is a sampling LAr calorimeter composed of two

wheels using accordion shaped kapton/copper electrodes and lead for the passive absorption

plates. The two wheels have a coverage of 1.4 to 2.5 and 2.5 to 3.2 respectively, for a total

coverage of 1.375 < |η| < 3.2. The accordion structure can be seen in Figure 3.5.

Figure 3.5: EM calorimeter accordion structure. Only three absorber plates are shown forclarity [12].

The accordion geometry causes an increase in LAr gap width, having a ratio of about 3:1

between outer and inner radius [13]. Therefore even though the lead absorption plates have

constant width, the LAr gaps increase with the wheel radius. Varying the high voltage with


Section FCAL1 FCAL2 FCAL3Material Copper Tungsten Tungsten

Acceptance 3.0 < η


Figure 3.6: FCAL cross section [12].

all sections use LAr as the active medium. The readout signal is transmitted by polyimide

insulated coaxial cables.

3.3 ATLAS Muon System

The ATLAS muon system is responsible for accurately tagging high energy muons and

measuring their momentum by deflecting them in a magnetic field. The muon chamber

layout can be seen in Figure 3.7 and features four detector types: thin gap chambers, resis-

tive plate chambers, cathode strip chambers and monitoring drift tube chambers. Details on

these detectors can be found in Refs. [12] or [14].

The bending magnet structure uses large, open, superconducting barrel, toroid magnets,

in order to reduce multiple scattering, along with two smaller end-cap magnets [12]. The

large barrel toroid is used in the |η| < 1.0 region, while 1.4 < η < 2.7 is affected by theend-cap magnets. There is an overlapping region (1.0 < η < 1.4) known as the transitionregion where the magnetic field is a mixture of the two fields [12].

The muon system uses the four components stated above to have an independent trigger

from the rest of ATLAS which is described in Ref. [14].


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Chapter 4

CBT-EC2 Beam Tests

The CBT-EC2 beam tests were performed over two run periods in the summer of 2004 at

the Prevessin site at CERN. This experiment includes, for the first time, the entire end-cap

calorimeter system consisting of the HEC, EMEC and FCAL, enabling the studies of dead

regions at the detector interfaces. This chapter features structural details such as the exper-

imental setup, trigger details, and also outlines the cell signal reconstruction. Calculations

of HEC calibration constants are also discussed.

W1, 2B1

BPC1, 2BPC3, 4BPC5, 6 H

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DOOR 166 DOOR 156 DOOR 146

S1

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Figure 4.1: Top view of the CBT-EC2 Setup including: beam position chambers (BPC),muon walls (M), multi wire proportional chambers (W) and various scintillators (S, B, V,and H) [16].

37

CHAPTER 4. CBT-EC2 BEAM TESTS 38

4.1 Setup

The experimental setup is similar to previous beam tests including beam monitoring tools

leading up to a cryostat. A top view of the setup can be seen in Figure 4.1 where the par-

ticles enter from the right. The beam monitoring tools consist of: multi-wire proportional

chambers (MWPC), beam position chambers (BPC), and various scintillators (Hole, Veto

etc). Details of beam instrumentation can be found in Refs. [21] and [22]. A Cerenkov de-

tector ( CEDAR ) is also present, but is not included in the previous figure; it is not used in

this analysis1. The main area of interest is the cryostat, which is illustrated as the open cir-

cle in Figure 4.1. The apparatus contained in the cryostat will be discussed in detail below.

A warm tail catcher2 (WTC) and an iron beam stop placed between two muon scintillator

veto walls are located behind the cryostat (to the left in the beam line schematic). Each

muon wall consists of an array of ten 20 cm × 200 cm scintillators, overlapping by ≈1 cm.A side view of the contents of the cryostat, along with the WTC and different incident target

heights for run II of the experiment3, is shown in Figure 4.2.

Figure 4.2: Run I side view of CBT-EC2, particles enter from the right. CTC is the cold tailcatcher [16].

1Technical problems prevented the Cerenkov detector from being useful.2The WTC is not used in this analysis.3The cryostat was moved up by 70cm for run II in order to access a deep FCAL region.


Figure 4.3: Side view of the FCAL and the Cold Tail Catcher (CTC), including the simu-lated FCAL cone [17].

The components of interest in Figure 4.2 are the HEC, EMEC and FCAL. These beam test

detectors are sub-sets of the entire end-cap system outlined in section 3.2, consisting of

components that have the same structure as the real ATLAS detector. The entire apparatus

is tilted in order to model the pointing geometry of ATLAS more accurately. A schematic

of the detector front face, including the location of standard impact points and scans, can

be seen in Figure 4.4. The EMEC test setup consists of two longitudinal samplings, a mid-

dle and a back layer, each including four pie-shaped wedges out of the 32 in the complete

ATLAS wheel. The HEC setup is composed of three samplings, the first two from the in-

ner wheel and the third from the outer wheel. Only eight wedges (1/4 of the entire wheel)

of each sampling are present. The FCAL test system includes the complete FCAL1 and

FCAL2 setup as described in section 3.2, along with a cold tail catcher (CTC4) instead of

FCAL3. Various support structures and LAr excluders are present, surrounding the CBT-

EC2 calorimeter setup. The LAr excluders, composed of Rohacell 71, occupy empty space

in the detector setup5. This prevents LAr from filling these regions, thus suppressing early

particle interactions. Figure 4.5 shows the EMEC-HEC component of the beam test, in-

4The cold tail catcher (CTC) is not used in the analysis.5Rohacell is a low density material with similar X0 to air, having low interaction properties with particles.


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cluding EMEC support structures and the HEC LAr excluder in green. In order to simulate

dead material in front of the FCAL in ATLAS, a large aluminum rod called the FCAL cone

is attached in the test detector as shown in Figure 4.3. Layer detailed diagrams of the beam

test setup can be found in Appendix A.

4.2 Triggering and Event Timing

Precise trigger and event timing properties are crucial in order to select proper events and

accurately reconstruct signals. An automatic event clock with a cycle frequency of 40.08

MHz (Period of 24.95 ns, which is the time between bunch crossings at LHC design lu-

minosity.) is used to clock the ADCs of the front-end boards (FEB)6. Accurate events are

obtained by the use of online trigger schemes along with offline event criteria selections.

The beam test trigger system is many orders of magnitude simpler than the real ATLAS

system. It is composed of a combination of scintillators whose output signals are input to

a level comparator, that produces a logic signal: “yes” or “no” (1/0), corresponding to the

presence of a particle, or not. The online trigger scheme is outlined in equation 4.1, and

consists of the coincidence of the S1,S2 and S3 scintillators whose location can be seen in

Figure 4.1. Three scintillators are used in order to minimize false events due to noise in the

scintillators.

S1 ·S2 ·S3 (4.1)

The above trigger scheme starts the event digitization and records the event time with re-

spect to the 24.95 ns event clock. The time offset between these two clocks is known as

the event phase and is measured using a Time to Digital Converter (TDC). Once events

are recorded, event selection criteria are applied. The event selection chain ensures that

the incident particles do not scatter away from the cryostat and miss the intended impact

position. The selection scheme is:

S1 ·S2 ·S3 ·VU ·VD ·VL ·VR ·HV ·EP ·LP (4.2)

where S1,S2 and S3 are simple scintillators ensuring a straight particle path towards the

6See section 4.4.1 for digitization details.


cryostat. VU,VD,VL and VR are veto counters (up, down, left, right) which eliminate

particles that scatter away from the main path. The hole veto (HV ) serves the same purpose

as the Veto counters. It is important to note that the above event selection only serves as

a simple event trigger, and does not ensure a clean event. Clean events and beam quality

methods are described in chapter 5.

4.3 Energy Signal Reconstruction

This section outlines the signal reconstruction process, originating from the triangular ion-

ization current in the active calorimeter medium7 to a measurement in units of MeV ( mil-

lion electron volts ) per calorimeter cell for each event. The technique used for this beam

test is the same as for the real ATLAS calorimeter.

4.4 Signal Processing

4.4.1 Digitization

The plot of ionization current vs time in the LAr has a triangular shape, as illustrated in

Figure 4.6. This shape is due to the variance of the charge distribution over time inside the

LAr gaps. Initially all ionization electrons move at a constant drift velocity under the ap-

plied electric field8. The overall charge displacement decreases once electrons arrive at the

positive voltage terminal. Therefore the number of moving electrons decreases linearly re-

sulting in a triangular ionization current distribution. The triangular current is transformed

by a readout chain, and then read out by digitizing the signal using an ADC in all three

sub-detectors. The shape of the read-out pulse is chosen to separate numerous events piled

up during the time interval of a single triangular current. The integrated readout signal area

is zero for single events. ADC counts are obtained every 25 ns using a 40 MHz digitization

clock, as is represented by the points in Figure 4.6. The maximum ADC peak is propor-

tional to the current amplitude and the area of the triangular current–time distribution. The

number of samples recorded varied between beam test periods. Run period I recorded 16

7See section 2.3 for details.8See section 2.3 for details.


Figure 4.6: Readout signal shape of ATLAS LAr calorimeters. The triangular solid lineshows the physics ionization current signal, while the points are the time samples after thereadout electronic chain [12].

time samples, while run period II recorded 7 time samples for the HEC, EMEC and FCAL.

ATLAS will use various time samples depending on the detector [13].

4.4.2 Peak Reconstruction

Various methods are applied to model the ADC digitization shape in Figure 4.6, in order

to determine the peak amplitude and time of the physics signal. The simplest method is

to fit a cubic function to the time sample with the maximum signal and its two neighbors.

This method does not reconstruct the full signal amplitude since the maximum time sample

does not always fall close to the ADC peak value. A more accurate determination of the

amplitude and time of the peak is obtained by the method of optimal filtering (OF). OF uses

predetermined weights in order to reconstruct a good fit to the digitization samples. The

reconstructed signal S, can be written as:

S =N

∑i=0

aisi (4.3)


where ai are the OF weights corresponding to the time sample si, and N is the number of

time samples. The weights are predetermined by using knowledge of the pulse shape, event

phase, and the time sample auto-correlation function of each cell. This auto-correlation

function takes into account the signal noise. The noise subtraction is the biggest advantage

of OF over other methods. Details of this method can be found in [20]. A comparison of

the cubic fit and OF signal reconstruction and resolution will be discussed in section 6.1.1.

The OF method is used throughout the analysis in this thesis.

4.5 Detector Noise

The pedestal value of a cell is the electronic signal present when no physics signals are in

the detector. Once this value is obtained for each cell, it is subtracted from physics signals

in order to exclude the noise in the signal amplitude. The pedestal value is calculated by

studying the 0th time sample of each cell. Variations of the pedestal mean and width for

each channel are small for each run period. Therefore, constant values are used for each

cell for run I and run II. Another important quantity is the rms of the detector noise. This

quantity takes into account noise fluctuations and is calculated as a function of the rms

of the pedestal. Figure 6.6 illustrates the rms noise values, in units of MeV, for each cell

(Run II) for the beam test sub-detectors. The same ADC→MeV conversion factors, to beoutlined in section 4.6, are used for noise and physics signals.

4.6 ADC→MeV conversionIn order to obtain energy deposition measurements per cell for each event, peak values have

to be converted from ADC counts to MeV. This process is broken down into numerous

components that take into account detailed calibration studies, along with previous beam

test results. This is the only component that connects this experiment to previous beam

tests. The calibration studies are performed before any real physics data are taken, in order

to understand the relationship between ioniza

study of the 2004 end-cap beam tests of the...

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