Analysis of the Hadronic Calibration of the ATLAS End-Cap Calorimeters using Test Beam Data

Analysis of the

Hadronic Calibration of the

ATLAS End-Cap Calorimeters using Test Beam Data

Diplomarbeit

vorgelegt von

Johannes Erdmann

angefertigt am

Max-Planck-Institut für Physik Prof. Dr. S. Bethke Fakultät für Physik

Ludwig-Maximilians-Universität München

9. Dezember 2008

Erstgutachter: Prof. Dr. Siegfried Bethke

Zweitgutachterin: Prof. Dr. Dorothee Schaile

Kurzfassung

Die Monte Carlo-basierte Kalibration der ATLAS Endkappen-Kalorimeter wird zum ers- ten Mal in einem Teststrahl-Aufbau mit Modulen aller Endkappen-Kalorimeter an Daten getestet. Auÿerdem wird das kohärente Rauschen im Elektromagnetischen Endkappen-Kalo- rimeter untersucht und der Einuss auf die Energiemessung diskutiert.

Zur Validierung der Simulation hadronischer Schauer mit den Schauermodellen QGSP und QGSP-BERTINI werden Daten und Monte Carlo für geladene Pion-Strahlen mit Energien von 40 bis 200 GeV und Elektron-Strahlen im Energiebereich von 6 bis 193 GeV verglichen.

Die Topologie rekonstruierter Teilchenschauer wird an Hand von Cluster-Momenten analy- siert. Es stellt sich heraus, dass die Monte Carlo-Simulation die rekonstruierte Energie gut beschreibt, aber für die Tiefe, Breite und Länge hadronischer Schauer zu kleine Werte vor- aussagt. Der genaue Auftrepunkt des Strahls sowie das Übersprechen der Elektronik haben einen starken Einuss auf Cluster-Momente.

Die Methode der Lokalen Hadronischen Kalibration wird mit den neuesten Korrekturfak- toren aus einer vollen ATLAS-Simulation an Pion- und Elektron-Daten getestet. Daten- und Monte Carlo-Ergebnisse werden verglichen. Nach Anwendung der Kalibration stimmt die rekonstruierte Energie von Pionen für Strahlenergien ab 120 GeV innerhalb von 1% für nied- rigere Energien innerhalb von 3% mit der Strahlenergie überein. Auÿerdem verbessert die Kalibration die Energie-Auösung. Die Übereinstimmung von Daten mit beiden Schauermo- dellen ist besser als 2%. Für den Auftrepunkt im Vorwärts-Kalorimeter ist die rekonstruierte Pion-Energie bis zu 7% niedriger als die Strahlenergie, was an der reduzierten lateralen Ak- zeptanz des Teststrahl-Aufbaus und einer leicht unterschiedlichen Verteilung des Materials vor dem Kalorimeter im Vergleich zum vollständigen ATLAS-Detektor liegt.

Abstract

The Monte Carlo based calibration of the ATLAS end-cap calorimeters is tested for the rst time in a test beam setup including modules from all end-cap calorimeters on data.

Moreover, coherent noise is studied in the Electromagnetic End-Cap Calorimeter and its impact on the energy measurement is discussed.

In order to validate the simulation of hadronic showers with the shower models QGSP and QGSP-BERTINI, data and Monte Carlo are compared for charged pion beams of energies from 40 to 200 GeV and for electron beams in the energy range from 6 to 193 GeV. The topology of reconstructed particle showers is studied by means of cluster moments. It turns out that the Monte Carlo describes well the reconstructed energy, but predicts values too low for the depth, width and length of hadronic showers. The exact impact point of the beam and cross-talk have a strong impact on cluster moments.

The method of local hadronic calibration is tested on pion and electron data with the latest

corrections from a full ATLAS simulation. The performances for data and Monte Carlo are

compared. After calibration, the reconstructed energy of pions agrees with the beam energy

within 1% for beam energies of 120 GeV and above for lower energies within 3% . Moreover,

the calibration improves the energy resolution. The agreement of data with both physics

lists is better than 2% . For the impact point in the Forward Calorimeter, the reconstructed

pion energy is up to 7% too low. This is due to the reduced lateral acceptance of the test

beam setup and a slightly dierent distribution of upstream material compared to the full

ATLAS setup.

Acknowledgements

First of all, I would like to thank Prof. Dr. Siegfried Bethke for being my academic supervisor and giving me the opportunity to do the research for my diploma thesis in the ATLAS group at the Max-Planck-Institut für Physik in Munich. I am grateful to him and Prof. Dr. Dorothee Schaile, the second reviewer of this thesis, for taking time and for a lot of good advice.

I am much obliged to Dr. Sven Menke and Dr. Peter Schacht for the guidance and supervi- sion of the research I have done this year. Their extraordinary support was encouraging and they have been open to questions and discussions at any time. I want to thank them as well for taking the time to read the drafts of this thesis.

I am grateful to Teresa, Paola, Andreas, Gena, Andrei and Emanuel from the HEC group at the MPI, who immediately welcomed me in the group and were always straightforward in oering me their help. Thanks for the excellent atmosphere and serious and non-serious discussions during lunch!

Special thanks go to Pavol Strizenec from Bratislava for the productive discussions and his eort to port the test beam software packages to the ATHENA release 14.0.0. In particular, I want to thank him for providing the test beam Monte Carlo.

Moreover, I would like to thank all other members of the LAr community, who have an- swered my questions and contributed to the progress of my work with their comments in the meetings.

Thanks to all those, who have helped to improve the drafts of this thesis by their comments:

Marina, Martin, Paola, Andreas, Andrei, Gena, Emanuel, Markus, Jonas and Gabi. Special thanks go to John Fraser, who took care of my English.

I am thankful to my oce mates from the theory group, Jochen, Marina, Patrick and

Clemens, for their good mood and the relaxed atmosphere in the oce. Last but not least I

want to thank my girlfriend Gabi and my parents, my sister Marion, my uncle Martin and

my grandmother Inge for the support during my time as a student and in particular all over

the last year.

Contents

Introduction 1

1. The ATLAS Experiment 3

1.1. Brief Summary of the Standard Model . . . . 3

1.2. The Large Hadron Collider . . . . 5

1.3. Physics at the Large Hadron Collider . . . . 6

1.4. The ATLAS Detector . . . . 6

1.4.1. ATLAS Coordinate System . . . . 8

1.4.2. Magnetic Field . . . . 8

1.4.3. The Inner Detector . . . . 9

1.4.4. The Calorimeters . . . . 9

1.4.5. The Muon Spectrometer . . . . 15

1.4.6. The Trigger and Data Acquisition System . . . . 15

2. Calorimetry and Interactions of Particles with Matter 16 2.1. Electromagnetic Interactions . . . . 16

2.1.1. Massive Charged Particles . . . . 16

2.1.2. Electrons and Photons . . . . 17

2.2. Strong Interactions . . . . 18

2.3. Particle Showers . . . . 19

2.3.1. Electromagnetic Showers . . . . 19

2.3.2. Hadronic Showers . . . . 20

2.4. Calorimetry . . . . 21

2.4.1. Homogeneous Calorimeters . . . . 22

2.4.2. Sampling Calorimeters . . . . 22

2.4.3. Hadronic Showers in High Energy Calorimeters . . . . 22

2.4.4. Energy Resolution in Calorimeters . . . . 23

3. The Combined End-Cap Calorimeter Beam Test 2004 24 3.1. Calorimeter Modules and Tail Catchers . . . . 24

3.2. Beam and Beam Instrumentation . . . . 26

3.3. Run Program . . . . 28

3.4. Signal Read-Out and Data Acquisition . . . . 28

4. Energy Reconstruction 29 4.1. From Ionisation to ADC Counts . . . . 29

4.2. Electronics Calibration . . . . 30

4.3. Noise . . . . 30

4.4. Oine Reconstruction - The ATHENA Framework . . . . 30

4.5. Topological Clustering . . . . 31

4.6. Cluster Moments . . . . 33

4.7. Hadronic Calibration . . . . 34

Contents

4.7.1. Global Method . . . . 35

4.7.2. Local Hadronic Calibration . . . . 35

5. Monte Carlo Simulation 39 5.1. Geant4 . . . . 39

5.2. Simulation of Hadronic Physics . . . . 39

5.3. Monte Carlo Simulation for the Combined End-Cap Beam Test 2004 . . . 41

6. Electronics Noise Studies 43 6.1. Width of the Electronics Noise Distribution . . . . 43

6.1.1. The CaloNoiseTool . . . . 43

6.1.2. Noise from Randomly Triggered Events . . . . 44

6.1.3. Impact of the Noise Estimate on Topological Clustering . . . . 44

6.2. Correlated Electronics Noise in the EMEC Inner Wheel . . . . 47

6.2.1. Test Beam . . . . 48

6.2.2. ATLAS Cosmics Run . . . . 53

6.2.3. Impact on Physics . . . . 53

6.3. Summary . . . . 55

7. Monte Carlo Validation on the Electromagnetic Scale 56 7.1. Electron Studies . . . . 56

7.1.1. Data Purication . . . . 56

7.1.2. Linearity and Resolution on the Electromagnetic Scale . . . . 59

7.1.3. Cluster Moments in the Forward Calorimeter Region . . . . 62

7.2. Charged Pion Studies . . . . 64

7.2.1. Data Purication . . . . 64

7.2.2. Linearity and Resolution on the Electromagnetic Scale . . . . 64

7.2.3. Cluster Moments in the Forward Calorimeter Region . . . . 68

7.3. Features in the Electromagnetic End-Cap Calorimeter Region . . . . 74

7.4. Summary . . . . 83

8. Monte Carlo Validation of Local Hadronic Calibration 87 8.1. Application of Local Hadronic Calibration to Charged Pions . . . . 87

8.1.1. Classication . . . . 93

8.1.2. Weighting . . . . 94

8.1.3. Out-Of-Cluster Corrections . . . . 95

8.1.4. Dead Material Corrections . . . . 96

8.2. Application of Local Hadronic Calibration to Electrons in the FCal Region . . 97

8.3. Summary . . . 102

9. Summary and Outlook 104

A. Cluster Moments Supplement 107

Bibliography 109

List of Figures 114

List of Tables 116

List of Abbreviations 117

Introduction

When the European Organization for Nuclear Research (CERN) in Geneva, Switzerland was founded in 1954 [1], the discovery of the so-called particle zoo a large variety of hadrons had just begun. Thanks to the achievements in the last 50 years, today we have a much more detailed understanding of the constituents of matter and the fundamental forces to which they are exposed. This knowledge is summarised in the well-established Standard Model of particle physics.

In September 2008, the Large Hadron Collider (LHC) at CERN began operation.

With a centre-of-mass energy of 14 TeV and a design luminosity of 10 ⁻³⁴ cm ⁻² s ⁻¹ , the LHC reaches new kinematic regions in high energy physics. It thus provides the capability to discover new physics beyond the Standard Model, which then could be studied in more detail with the planned luminosity upgrade of the LHC [2] or a future e ⁺ e ⁻ linear collider the ILC ¹ [3].

ATLAS is a general purpose detector at the LHC that is particularly designed for the discovery of new physics phenomena. For most of the important physics channels, the energy measurement of bundles of hadronic showers in the calorimeters, so-called jets, is crucial.

In the end-cap region, three dierent calorimeters are used: the Electromagnetic End-Cap Calorimeter (EMEC), the Hadronic End-Cap Calorimeter and the Forward Calorimeter. All of these are sampling calorimeters based on liquid argon (LAr) technology.

Since the response of the ATLAS calorimeters to hadronic showers is lower than to electro- magnetic showers, software compensation based on detailed Monte Carlo (MC) simulations is used to reconstruct the initial energy of hadrons. This procedure is crucial for a reliable jet energy scale. The compensation methods as well as the MC simulation itself need to be validated in beam tests before they will be used in the reconstruction of ATLAS data. For the validation in the end-cap region, only one single test beam (TB) setup including modules from all three calorimeters is available, the Combined End-Cap Calorimeter Beam Test 2004.

The beam test was carried out during summer 2004 at the H6 beam line of the Super Proton Synchrotron at CERN, which provided electron, charged pion, and muon beams with energies from 6 to 200 GeV .

Studies in the context of the validation of the local hadronic calibration a promising method for the software compensation of the lower response to hadronic showers are presented:

For the reconstruction of calorimeter signals, cells are grouped together to clusters on a geometrical basis by the topological clustering algorithm. Since this algorithm makes extensive use of the noise in the cells, the electronics noise in the TB modules is studied; in particular in the EMEC, the noise showed unknown deviations from the expected behaviour. The impact of such deviations on physics is discussed.

The characteristics of reconstructed particle showers can be described by cluster moments, which allows us to compare data with the predictions from MC simulations. Detailed results of such comparisons are presented for electromagnetic and hadronic showers in order to validate the simulation. The simulation of hadronic showers is a challenging task and greatly important for the reliability of MC based hadronic calibration methods. The simulation has been done

1 International Linear Collider

Introduction

with two shower models implemented in the simulation with Geant4 and steered by so- called physics list: QGSP (Quark Gluon String Precompound model) and its extension to QGSP-BERTINI with a Bertini-type intranuclear cascade model. The performance of the MC simulations is compared to data. Possible improvements achieved by the use of QGSP-BERTINI are discussed. Features found in the simulation of the EMEC module are analysed with respect to geometrical aspects and cross-talk.

The local hadronic calibration itself is tested on TB data with the latest corrections that have been extracted from MC simulations in the full ATLAS setup. The over-all perfor- mance, as well as the impact of the single steps of the calibration method, are discussed for charged pion and electron runs in the EMEC and Forward Calorimeter region. A detailed comparison of the performances on data and MC simulations is given.

This thesis is divided into nine chapters.

• Chapter 1 gives a brief introduction to the physics at the LHC and the ATLAS detector with a focus on the LAr calorimeters.

• In Chapter 2, interactions of particles with matter and the principles of calorimetry are reviewed.

• The TB setup is presented in Chapter 3.

• The energy reconstruction in the ATLAS LAr calorimeters, including topological clus- tering and hadronic calibration, are covered in Chapter 4.

• The MC simulation with Geant4 and, in particular, the simulation of hadronic physics with the physics lists QGSP and QGSP-BERTINI are introduced in Chapter 5.

• Chapter 6 presents the results of the EMEC noise studies.

• The validation of the MC simulation of electromagnetic and, especially, hadronic show- ers on the electromagnetic scale is discussed in Chapter 7, including the analysis of cluster moments. The impacts of alignment and cross-talk are discussed.

• Finally, the results of the validation of the local hadronic calibration are presented in Chapter 8.

• A summary of the results is given in Chapter 9, together with an outlook on the relevance of the results to the ATLAS experiment and further TB studies.

O

Natural units are used in this thesis, i.e. ~ = c = 1 , and hence masses, energies and mo-

menta are expressed in units of [GeV] . To avoid confusion, length and time are given in the

usual SI units [m] and [s] , because here they do not refer to subnuclear but to macroscopic

calorimeter quantities.

1. The ATLAS Experiment

The ATLAS experiment is located at the Large Hadron Collider (LHC) at CERN, the largest particle physics project ever built. This proton-proton ( pp ) collider began operation in September 2008 and will probably reach its planned centre-of-mass energy of 14 TeV in the year 2009. The high energy and luminosity available will allow for studies of new kinematic regions of particle physics and provide the potential to discover new phenomena.

In Section 1.1, a brief summary of the Standard Model is given. Section 1.2 describes the LHC. The main elds of study at the ATLAS experiment are presented in Section 1.3, and in Section 1.4, the ATLAS detector is described and its calorimeter system is detailed.

1.1. Brief Summary of the Standard Model

The Standard Model of particle physics [47] describes elementary particles and their interac- tions. Up to the present, it is in excellent agreement with data, although some shortcomings of the model are already known ¹ . For this reason, and due to profound unsolved questions (dark matter, number of free parameters, . . . ), it is widely believed that the Standard Model is just an eective theory, which is valid for energies below a certain threshold. As this threshold has not yet been reached with experiments, the Standard Model is the current theory of particle physics. Only a brief summary can be given here.

Table 1.1: Some properties of quarks and leptons [8]. For the denitions of the quoted quark mass values see Ref. [8].

Electric Mass Forces

charge strong em. weak

O ^{up quark ( u ) 2/3 e 1.5 − 3.3 MeV X X X}

O ^{down quark ( d ) −1/3 e 3.5 − 6.0 MeV X X X}

O strange quark ( s ) 2/3 e 104 ⁺²⁶ ₋₃₄ MeV X X X

O charm quark ( c ) −1/3 e 1.27 ^+0.07 _−0.11 GeV X X X

O ^{top quark ( t ) 2/3 e 171.2 ± 2.1 GeV X X X}

O bottom quark ( b ) −1/3 e 4.20 ^+0.17 _−0.07 GeV X X X

O ^{electron (e) −e} 0.510998910 - X X

O ±0.000000013 MeV

O electron neutrino ( ν _e ) 0 < 2 eV - - X

O ^{muon ( µ ) −e 105.658367 ±} 0.000004 MeV - X X

O muon neutrino (ν µ ) 0 < 0.19 MeV - - X

O ^{tau ( τ ) −e 1776.84 ± 0.17 MeV - X X}

O tau neutrino ( ν _τ ) 0 < 18.2 MeV - - X

1 E.g. neutrinos should be massless according to the Standard Model, but as neutrino oscillations have been

observed, it is concluded that neutrinos have non-zero masses. However, their values are still unknown [8].

Chapter 1. The ATLAS Experiment

In physics, there are four known fundamental forces: the electromagnetic force, the weak force, the strong force, and gravitation. However, gravitation is negligible in particle inter- actions, because on the scales of these interactions the other three forces are many orders of magnitude stronger.

All fermions in the Standard Model have spin ¹ ₂ and interact via the weak force. Those carrying an electric charge are also subject to the electromagnetic force. Six of the fermions, called quarks, interact strongly. The other six fermions are called leptons. Quarks as well as leptons are grouped into three generations, each of them consisting of a doublet (Table 1.1).

The lepton doublets contain one massive lepton with electric charge −e and an approxi- mately massless neutrino. Neutrinos do not carry any electric charge, and thus interact weakly only.

The quark doublets consist of one quark with electric charge ² ₃ e and one quark with electric charge − ¹ ₃ e . Quarks carry a colour quantum number for the strong interaction (similar to the electric charge for the electromagnetic interaction) and are conned to colourless hadrons.

In addition, there is for each fermion an anti-fermion of the same spin and mass, but with opposite additive quantum numbers (charge, lepton number, baryon number, strangeness, colour, etc.).

In the Standard Model, the forces are carried by so-called gauge bosons. The electromag- netic force is carried by the photon ( γ ), the weak force by the W ^± bosons and the Z boson, and the strong force by gluons (cf. Table 1.2); the latter exist in eight dierent colour com- binations.

The mathematical description of elementary particles within the Standard Model is done via quantum eld theories (QFT) [9], the combination of quantum mechanics and special relativity. Each fermion is associated with a quantised eld and its dynamics is described by equations of motion derived from a Lagrangian. Interactions between particles are introduced into the Lagrangian by requiring local gauge symmetries. While the electromagnetic force and the strong force can be described within such QFTs Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD), respectively it turns out that the electromagnetic and the weak force can be described consistently within one combined theory only, the so-called electroweak theory. As we observe separate electromagnetic and weak forces, the electroweak symmetry must be broken.

The favoured mechanism for giving masses to elementary particles is the Higgs mechanism, which breaks the electroweak symmetry spontaneously and gives masses to the quarks, the charged leptons, the W bosons, and the Z boson. The photon remains massless. Evidence for this mechanism and thus a success for the Standard Model would be the discovery of the Higgs boson, which has remained unobserved so far.

Table 1.2: Carriers of the four fundamental forces [8].

Force Carrier Mass [GeV] Spin

strong gluon 0 (theory) 1

electromagnetic photon < 1 · 10 ⁻¹⁸ eV 1

weak W bosons 80.398 ± 0.025 1

Z boson 91.1876 ± 0.0021 1

gravitation (graviton?) ( 0 ?) ( 2 ?)

1.2. The Large Hadron Collider

1.2. The Large Hadron Collider

The Large Hadron Collider (LHC) [10, 11] is a proton-proton collider, which was built in the former tunnel of the Large Electron-Positron Collider (LEP) at CERN in Geneva, Switzerland, and began operation in September 2008.

The circular LEP tunnel has a circumference of about 27 km . Pre-accelerated protons are injected in bunches into separate beam pipes that lead in both directions around the tunnel.

The bunches are accelerated with a system of radio frequency cavities to their nal energy of 7 TeV , i.e. a centre-of-mass energy of 14 TeV can be achieved. This is the highest centre- of-mass energy ever achieved in collider experiments about seven times higher than the current maximum energy at the TeVatron [12] at Fermilab. Each proton bunch consists of 10 ¹¹ particles at the start of a nominal ll. The bunch spacing is 25 ns and there are 2808 lled bunches in each ll. The design luminosity of pp collisions is 10 ⁻³⁴ cm ⁻² s ⁻¹ , which corresponds to about 23 inelastic collisions per bunch crossing [10]. To keep the particles on their circular track, superconducting NbTi magnets are used, which provide a magnetic eld of up to 8.33 T .

Figure 1.1: The LHC accelerator chain with the location of the experiments (not to scale!) [13].

The pre-acceleration of protons starts in the LINAC (LINear particle ACcelerator) which generates 50 MeV protons, which are then accelerated to 1.4 GeV in the Proton Synchroton Booster (PSB) and to 26 GeV in the Proton Synchroton (PS). Next, the protons enter the Super Proton Synchrotron (SPS), where they gain their nominal LHC injection energy of 450 GeV.

There are four main experiments conducted at the LHC (Fig. 1.1): ATLAS (A Toroidal

LHC ApparatuS) [14] and CMS (Compact Muon Solenoid) [15] are located at interaction

points of the two proton beams and are so-called general purpose detectors, designed to provide

Chapter 1. The ATLAS Experiment

physicists with miscellaneous information about the products of pp collisions (this requires nearly 4π coverage, information about particle tracks, momentum, energy, particle type, etc.).

These detectors are intended to study new physics in the elds of, for example, the Higgs boson search or Supersymmetry (see Section 1.3). The focus of this work is on the ATLAS detector, which is described in more detail in Section 1.4.

Lead nuclei can also be accelerated by the LHC. ALICE (A Large Ion Collider Experi- ment) [16] is intended to study their collisions and observe a possible quark-gluon plasma.

LHCb (Large Hadron Collider beauty experiment) [17] is dedicated to b quark physics and the measurement of CP violation in the b sector.

1.3. Physics at the Large Hadron Collider

At the LHC various aspects of particle physics will be studied. Just a short overview of the physics programs of the ATLAS and CMS experiments is given, both of which are searching for about the same physics in pp collisions.

The most well-known particle searched for at the LHC is probably the Higgs boson, which plays a crucial role in the Higgs mechanism of electroweak symmetry breaking. It is the currently favoured mechanism for giving masses to elementary particles within the Standard Model. Two decay channels are most promising at the LHC [18]:

• H → γγ for 100 GeV < m _H < 150 GeV

• H → ZZ ^(∗) → 4` for 120 GeV < m _H < 2 · m _Z

Ref. [18] comes to the conclusion that ATLAS has a large potential [...] for precision measurements of the Higgs-boson parameters

There are several elds of new physics that can be studied with the ATLAS and CMS experiments. One of these is the theory of Supersymmetry [19], which postulates superpartners for each Standard Model elementary particle. Such particles could be produced at the LHC, if Supersymmetry exists at the TeV scale. Moreover, the Lightest Supersymmetric Particle is stable in the case of R-parity conservation and thus would be a candidate for dark matter [18].

Other theories such as extra dimensions [20], Grand Unied Theories [21], composite- ness [22, 23], technicolor [24, 25], or the search for heavy gauge bosons, such as a Z ⁰ , will be tested. In addition, a main task of the ATLAS and CMS experiments are precision measure- ments of the parameters of the Standard Model. Examples of research in the top sector are the measurements of the top quark mass, the t ¯ t and the single top production cross section (and hence a measurement of the Cabibbo-Kobayashi-Maskawa matrix element |V _tb | ), and the W helicity in top quark decays [26].

1.4. The ATLAS Detector

Detectors at the LHC have to deal with two main diculties: The high luminosity needed to

observe such rare processes as mentioned in Section 1.3, and the short bunch spacing, which

leads to a huge particle ow causing a high strain on all detector components. Thus, fast and

radiation-hard electronics and sensor elements are needed as well as a sophisticated trigger

system. The second diculty is the nature of pp collisions. Since the partons (gluons and

quarks) of the accelerated protons take part in the hard scattering process, QCD processes

dominate the cross sections for most interesting processes. To identify the latter, it is necessary

that detectors at the LHC provide very good particle identication capabilities.

1.4. The ATLAS Detector

.

chamber tracking

calorimeter

electromagnetic hadronic

calorimeter chamber muon

photons electrons muons

pions

outermost layer

innermost layer _.

Figure 1.2: Schematic view of interactions of dierent particles in modern high energy general purpose particle detectors (following an illustration from Ref. [27]).

The structure of the ATLAS detector follows the typical principles of modern high energy general purpose detectors. Such detectors include an inner detector to track charged particles in a strong magnetic eld. External to this inner detector are electromagnetic and hadronic calorimeters, where photons, electrons and jets are absorbed to measure their energy. A muon detection system is placed around the whole. The main objectives are the measurement and detection of the following signatures (Fig. 1.2):

• As muons are charged, they leave a track in the inner detector. Moreover, they are compatible with minimum ionising particles (cf. Section 2.1) and, thus, they are mostly able to cross the inner detector and the calorimeters. Their momentum is then measured in the muon chambers (Section 1.4.5).

• Electrons (e ^± ) leave a track in the inner detector and are nally absorbed in the electromagnetic parts of the calorimeters.

• Photons are invisible in the inner detector. Their energy is absorbed in the electro- magnetic calorimeters.

• Jets are the signatures of quarks and gluons in the detector and consist, for example, of π ^± , π ⁰ , e ^± , γ , p, etc. They are tracked in the inner detector and lose their energy in the electromagnetic and hadronic parts of the calorimeter system.

• Particles that escape undetected because they interact via the weak force only (for example, neutrinos) give rise to a missing transverse momentum signal ( 6 p _T ). As the colliding partons within the proton (i.e. gluons or quarks) are approximately balanced in the transverse plane, the nal state is expected to have a transverse momentum ( p T ) close to zero.

The ATLAS detector is shown in Fig. 1.3. It consists of an inner detector, electromagnetic

and hadronic calorimeters, and a muon spectrometer. The inner detector is immersed in a

solenoidal magnetic eld, while muons are bent in a toroidal eld in the region of the muon

system. If not otherwise specied, the information in this section is taken from Ref. [14].

Chapter 1. The ATLAS Experiment

Figure 1.3: Cut-away view of the ATLAS detector [14].

1.4.1. ATLAS Coordinate System

The nominal interaction point is the origin of the ATLAS coordinate system [14]. The z -axis is dened as the beam axis. The x -axis is perpendicular to the beam axis and points to the centre of the LHC ring. The y -axis is perpendicular to the other two axes and points upwards. The positive z -direction is dened as side A, the negative z -direction as side C. The azimuthal angle φ is measured around the z -axis and the polar angle θ is the angle from the z -axis. In particle physics, the pseudorapidity

η = − ln tan θ 2

is often used, because in the limit of small masses compared to the energy of the parti- cle ( m E ) it is equal to the rapidity

y = 1

2 ln E + p _z E − p z

,

which is, in contrast to velocities, an additive quantity under Lorentz boosts.

1.4.2. Magnetic Field

The ATLAS magnetic system consists of four large superconducting magnets, which provide the solenoidal and toroidal elds: the central solenoid, the barrel toroid, and two end-cap toroids.

The central solenoid is located around the inner detector and provides a 2 T axial eld.

The barrel and end-cap toroids generate the magnetic eld for the bending of muons outside

the calorimeter system with a magnetic eld of ∼ 0.5 T in the central region and ∼ 1 T in

the end-cap regions.

1.4. The ATLAS Detector 1.4.3. The Inner Detector

The Inner Detector (ID) (Fig. 1.3) is placed in the 2 T solenoidal eld (Section 1.4.2) and measures the tracks of charged particles. High precision is needed to cope with the high track density in ATLAS in order to get excellent information on the momenta of high energy charged particles and the positions of primary as well as secondary vertices. The latter is a basic need for b -tagging and τ -identication. The performance goal for the tracking is

σ p T

p _T = 0.05% · p T [GeV ] ⊕ 1% , with p _T the transverse momentum and σ _{p T} its error.

The ID is about 7 m long and has a radius of 1150 mm covering an acceptance of |η| < 2.5.

It consists of three parts: The Pixel Detector is the innermost part of the ID and consists of silicon wafers. The microstrip Semi Conductor Tracker (SCT) surrounds the Pixel Detector.

Two silicon microstrip modules are arranged back-to-back with a stereo-angle of 40 mrad, allowing for a three dimensional measurement of the interaction point. The Transition Radi- ation Tracker (TRT) is located around the other two subdetectors and is comprised of straw tubes. It makes use of the eect of transition radiation (see Section 2.1.1) and thus can be used for particle identication purposes.

1.4.4. The Calorimeters

Calorimeters play a crucial role in most physics channels. The energies of electrons and photons are measured as well as those of hadrons. In particular, the energy of jets bundles of particles arising from quarks or gluons can be measured. Particles that leave the detector undetected (for example neutrinos) give rise to a missing transverse momentum signal ( 6 p _T ).

Thus, also the determination of 6 p T requires reliable calorimeter energy measurements.

The ATLAS calorimeter consists of a barrel and an end-cap part, each of which are com- posed of electromagnetic and hadronic calorimeters. All ATLAS calorimeters are sampling calorimeters (Section 2.4.2), but use two dierent techniques. The hadronic barrel calorimeter (Tile Calorimeter) uses steel for its absorbers, while scintillating tiles provide the active ma- terial. All other calorimeters (Electromagnetic Barrel Calorimeter, Electromagnetic End-Cap Calorimeter, Hadronic End-Cap Calorimeter, Forward Calorimeter) are Liquid Argon (LAr) calorimeters, which use dierent absorber materials and LAr as active material.

There are three main requirements for calorimeters:

• good containment of electromagnetic and hadronic showers,

• good energy resolution, and

• good hermiticity.

Good hermiticity is given, because the ATLAS calorimeters cover the range |η| < 4.9.

Containment of showers is achieved by a thickness of the electromagnetic calorimeters of 22 and 24 radiation lengths ( X ₀ ) in the barrel and end-cap regions, respectively, and by a total thickness of the calorimeters of approximately 10 interaction lengths (λ I ). The design values for the energy resolution are quoted in Table 1.3.

The dierent calorimeters are described in more detail in the next paragraphs. As the focus

of this work is on a combined beam test of the end-cap calorimeters, special emphasis is given

to the latter. Read-out and signal reconstruction in the LAr calorimeters are described in

Chapter 4.

Chapter 1. The ATLAS Experiment

Figure 1.4: The ATLAS Calorimeters [28].

Table 1.3: Design energy resolution of the ATLAS calorimeter system [14].

Detector component Energy resolution σ E /E EM calorimeters (electrons) 10%/ p

E[GeV] ⊕ 0.7%

hadronic calorimeters (jets)

barrel and end-cap 50%/ p

E[GeV] ⊕ 3%

forward calorimeter 100%/ p

E[GeV] ⊕ 10%

The Tile Calorimeter

The Tile Calorimeter (Tile) [29] is located behind the Electromagnetic Barrel Calorimeter (Fig. 1.4) and covers the region |η| < 1.7 . It uses steel for its absorbers and scintillators as active material. Its radial depth is approximately 7.4 interaction lengths. The Tile is divided into a central barrel part ( |η| < 1.0 ) and an extended barrel part ( 0.8 < |η| < 1.7 ), the latter covering the region between barrel and end-cap calorimeters.

The Electromagnetic Barrel Calorimeter

The Electromagnetic Barrel Calorimeter (EMB) [14, 30, 31] covers the region |η| < 1.475 . It is a LAr calorimeter with lead absorbers, which are separated by honey comb spacers (Fig. 1.6).

The spacers are lled with LAr, which is kept cold in the cryostat, in which the EMB is

placed. LAr sampling technology was chosen for its radiation resistance, long-term stability

and good energy resolution [31]. The read-out is performed by kapton electrodes in the gap

between the absorbers. The thickness of the EMB is at least 22 radiation lengths for all η

values.

1.4. The ATLAS Detector The whole geometry is folded into an accordion shape (Fig. 1.6), where the waves are axial and run in φ. This geometry naturally avoids azimuthal cracks. The folding angle needs to vary with the radius in order to keep the LAr gap constant (Fig. 1.5). Since particles coming from the interaction point traverse the calorimeter along the waves, the signal produced in dierent depths of the calorimeter layer is collected at the same electrodes. Thus, the accordion geometry provides built-in summing of the signal, which allows for a fast read-out.

An unfolded EMB electrode is shown with its division into cells in Fig. 1.7. In this way, three layers are formed: the rst layer has a very ne granularity along η , thus it provides a precise measurement of the η position of energy deposits. The granularity in the other two layers is coarser (see Fig. 1.5). A presampler with a LAr layer of thickness 11 mm is placed in front of the EMB to correct for energy loss in material upstream of the calorimeter. Electronics provide a division of the EMB in trigger towers with a granularity of ∆η × ∆φ = 0.1 × 0.1 for fast information to the level-1 trigger (Section 1.4.6).

The sampling fraction is dened as the energy deposited in LAr over the sum of energies deposited in LAr and the absorber material. In the EMB, the sampling fraction is of the order of 16 − 20% [32]. Due to the accordion geometry, the relative thickness of lead and LAr varies with φ . Consequently, also the sampling fraction is a function of φ .

The Electromagnetic End-Cap Calorimeter

The Electromagnetic End-Cap Calorimeter (EMEC) [14, 30, 31] covers the region 1.375 < |η| < 3.2 and is divided into two wheels with radii 330 mm and 2098 mm , respec- tively. Together with the Hadronic End-Cap Calorimeter (HEC) and the Forward Calorime- ter (FCal), it is placed in one common cryostat.

The EMEC uses the same LArlead technology with its accordion structure as the EMB.

But, in order to keep the summing capability of the accordion geometry, the waves are parallel to the radial direction and run axially (Fig. 1.8). This leads to a more complex geometry than in the EMB. The folding angles increase with increasing radius, in order to provide coverage in φ for all radii. The thickness of the absorbers is kept constant. Since the response is intended to be constant, the high voltage is required to vary with radius in order to compensate for the changing ratio of active to absorber material. Moreover, due to the constant absorber thickness, the depth of the calorimeter increases from 24X ₀ at |η| = 1.475 to 38X ₀ at |η| = 2.5 (outer wheel) and from 26X 0 to 38X 0 in the |η| region between 2.5 and 3.2 (inner wheel).

The sampling fraction in the EMEC is of the order of 7 − 10% [32]. Due to the same reason that causes the variation with φ of the sampling fraction in the EMB, the sampling fraction in the EMEC varies with η.

Since the material in front of the EMEC is several radiation lengths in size, another pre- sampler with a 5 mm thick LAr layer is installed in the region 1.5 < |η| < 1.8 . As precision physics is very dicult for |η| > 2.5, the granularity in η and φ is coarser than for smaller η values, and the longitudinal division is reduced to two layers.

The Hadronic End-Cap Calorimeter

The Hadronic End-Cap Calorimeter (HEC) [14, 30] is the only traditional LAr sampling calo- rimeter in the ATLAS detector. Copper plates are used for its absorber material. Consisting of two independent wheels and placed behind the EMEC, it covers the region 1.5 < |η| < 3.2 . The HEC gives small overlap regions with the Tile Calorimeter as well as with the FCal.

Each wheel is segmented longitudinally into two parts and consists of 32 identical wedge-

shaped modules (Fig. 1.9). The front wheels consist of 25 mm thick copper plates, while the

plates in the rear wheels are 50 mm thick. A honey comb structure of 8.5 mm size is lled

Chapter 1. The ATLAS Experiment

Figure 1.5: Sketch of a module of the EMB [30]. The dierent layers as well as the granularity in η and φ are shown.

Figure 1.6: Accordion structure of the electro- magnetic LAr calorimeters (EMB/EMEC): Ab- sorbers (grey), division of the electrodes into cells (coppery) and honey comb spacers are shown [33].

Figure 1.7: Electrode of the EMEC

outer wheel [30]. The division into

cells and layers are visible.

1.4. The ATLAS Detector

Figure 1.8: View of an EMEC wheel [30]. Only a few example absorbers are shown.

Figure 1.9: One of the 32 modules of the HEC [14].

Chapter 1. The ATLAS Experiment

with LAr. The LAr gap is equipped with three electrodes providing four independent drift zones of 1.8 mm width each. This division improves the uniformity of the electric elds and reduces the high voltage requirements.

The sampling fraction is constant in the HEC modules, and is given by 4.4% ( 2.2% ) in the HEC front (rear) wheel.

The read-out structure is pointing in φ and pseudo-pointing in η . Cold electronics based on GaAs is used to sum the signals from the dierent gaps. This choice provides a particularly low signal-to-noise ratio.

The Forward Calorimeter

The Forward Calorimeter (FCal) [14, 30] covers the region 3.1 < |η| < 4.9 (Fig. 1.10). It uses LAr technology and consists of one electromagnetic module with copper absorbers, and two hadronic modules with tungsten absorbers.

The forward region is exposed to very high particle uxes from minimum bias events ² . Thus, the forward calorimeters need to be very radiation hard, guarantee the containment of high energy particles, and provide a short charge collection time to avoid buildup of positive ions, which would distort the electric eld. Hence, a small LAr gap is needed. Dense absorber materials have been chosen. These ensure containment ( ∼ 10λ I ) and prevent spilling into the neighbouring calorimeters. The geometry of the electromagnetic (hadronic) FCal modules consists of a copper (tungsten) matrix with regularly spaced longitudinal channels. These channels are equipped with concentric rods and tubes parallel to the beam axis (Fig. 1.11).

The FCal geometry allows for an excellent control of the small LAr gap, which varies from 0.269 mm in the rst FCal module to 0.508 mm in the last module.

However, the extraction of sampling fractions in this unconventional geometry is a non- trivial task. The sampling fraction depends strongly on the incident angle of the particle. Its order of magnitude is 1% and is dierent for each module.

Figure 1.10: Schematic drawing showing the position of the FCal modules in the end-cap cryostat [34].

The dashed line indicates the transition region at

|η| ≈ 3.2 from the EMEC and HEC to the FCal.

Figure 1.11: Electrode structure of the rst FCal module [14]. The copper matrix as well as copper tubes and the rods with the LAr gaps are shown.

2 Minimum bias events appear when a very low amount of transverse momentum (p T ) is transferred between

the two interacting partons. These are the events most likely to occur in pp collisions.

1.4. The ATLAS Detector 1.4.5. The Muon Spectrometer

The inner detector and calorimeters are surrounded by the huge Muon Spectrometer (Fig. 1.3), which covers the region |η| < 2.7 . It is designed to detect charged particles exiting the calori- meter system (for instance muons with energies above ∼ 3 GeV ) and measure their momen- tum, i.e. the curvature in the toroidal magnetic eld (Section 1.4.2). The muon spectrometer consists of three layers in the barrel part and three end-cap wheels on each side.

The muon system provides high precision tracking chambers (Monitored Drift Tube and Cathode-Strip Chambers) as well as trigger chambers (Resistive Plate Chambers and Thin Gap Chambers). The performance goal is a resolution of 10% for 1 TeV muons in the central region.

For muons of ∼ 100 GeV, this translates into a resolution of the order of 2 − 3% [14, 35].

1.4.6. The Trigger and Data Acquisition System

With 40 million bunch crossings per second and an average of 23 inelastic scatterings per bunch crossing at design luminosity, the event rate of about 1 GHz has to be reduced to a manageable rate of about 200 Hz without loosing rare physics events, while providing a very eective reduction of minimum bias events. For this purpose, a three level Trigger and Data Acquisition system is used.

The rst level (L1) [36] is a hardware trigger reducing the event rate within a 2.5 µs decision

to about 75 kHz . It searches for high- p _T leptons, photons and jets, high missing transverse

momentum, and high total transverse energy. Information from the muon trigger chambers

and reduced-granularity information from the calorimeters is used. Regions-of-Interest (RoI)

are dened. This information is then passed to the high-level trigger, which consists of the

level-2 trigger (L2) and the event lter (EF). The L2 trigger reduces the event rate in about

40 ms to approximately 3.5 kHz . The Data Acquisition System (DAQ) receives and buers

the event data of the readout electronics of the subdetectors after the L1 trigger. For those

events that pass the L2 trigger, event-building is performed and the event is then moved

to the EF. The EF achieves the nal reduction to roughly 200 Hz by using oine analysis

procedures. Events passing the three trigger levels are written to permanent storage. One

event has an approximate size of 1.3 MB.

2. Calorimetry and Interactions of Particles with Matter

Calorimeters measure the energy of particles such as electrons, photons and hadrons. In addition, they provide the position of the deposited energy and thus information on the energies of jets and missing transverse energy.

The importance of calorimetry cannot be underestimated. A well-known example is the systematic error in the top quark mass measurements at the TeVatron, which is dominated by the error on the jet energy scale ¹ , i.e. by the energy resolution of the calorimeters [37].

In Sections 2.1 and 2.2, interactions of particles with matter which are of importance to calorimetry are reviewed. The phenomenon of particle showers is explained in Section 2.3.

Section 2.4 introduces the basic principles of calorimetry.

2.1. Electromagnetic Interactions

2.1.1. Massive Charged Particles

Heavy particles, i.e. particles with masses much greater than the electron mass, lose energy mainly through ionisation and atomic excitation. In a relatively wide range, this energy loss can be described on average by the Bethe-Bloch formula [38]:

− dE

dx = 4πN _A r _e ² m e c ² z ² Z A

1 β ²

ln

2m e c ² β ² I (1 − β ² )

− β ² − δ 2

(2.1) E energy of the incident particle

x distance propagated in the absorber material N A Avogadro's number

m e electron mass

r e classical electron radius ( e ² /(4πε 0 m e c ² ) , ε 0 : dielectric constant ) z charge of the incident particle in units of the elementary charge Z atomic number of the absorber material

A atomic mass number of the absorber material

β velocity of the incident particle in units of the speed of light

I characteristic ionisation constant (absorber dependent), I ≈ 16 · Z ^0.9 eV , Z > 1 δ density eect correction parameter (absorber dependent)

Fig. 2.1 shows the stopping power − ^dE _dx of positively charged muons on copper and gives an impression of the range of validity of the Bethe-Bloch formula. The stopping power function shows a broad minimum in an energy region of importance to high energy experiments. Par- ticles with losses close to the minimum (e.g. cosmic-ray muons) are referred to as minimum ionising particles or mips.

In addition to ionisation and atomic excitation, there are other possible processes for massive charged particles, but their contributions to the total energy loss is negligible. These processes

1 The jet energy scale is a correction factor applied to the energies of jets due to the uncertainties in calorimeter

calibration.

2.1. Electromagnetic Interactions

Muon momentum 1

10 100

Stopping power [MeV cm 2 /g] Lindhard- Scharff

Bethe-Bloch Radiative

Radiative effects reach 1%

µ ⁺ on Cu

Without δ Radiative

losses

0.001 0.01 0.1 1 10 βγ 100 1000 10 ⁴ 10 ⁵ 10 ⁶

[MeV/ c ] [GeV/ c ]

100 10

1

0.1 1 10 100 1 10 100

[TeV/ c ] Anderson-

Ziegler

Nuclear losses

Minimum ionization

E _{µ c} µ ⁻

Figure 2.1: Stopping power − ^dE _dx of positively charged muons in Cu as a function of their momen- tum [8]. Vertical bands indicate the boundaries between dierent approximations, the Bethe-Bloch approximation being valid in the central region.

are: bremsstrahlung (which is not negligible for light particles such as electrons it is, thus, discussed in Section 2.1.2), Cherenkov radiation, and transition radiation.

Charged particles radiate if their velocity is larger than the phase velocity of light in the medium. The radiation angle θ _c is specic for the velocity of the particle [8]:

tan θ c = p

β ² n ² − 1 ,

where n is the index of refraction of the medium. This eect is called Cherenkov radiation and can be used in homogeneous calorimeters (Section 2.4.1).

Transition radiation [39] occurs when a particle crosses the boundary between two media with dierent optical properties. This eect is not used in calorimetry, but, for example, in the Transition Radiation Tracker of the ATLAS detector (Section 1.4.3).

2.1.2. Electrons and Photons

Low energy electrons lose energy mainly by ionisation, as discussed in the previous section.

The energy loss of high energy electrons [8, 38] cannot be described by Eq. (2.1), because it is dominated by bremsstrahlung. High energy photons ² lose their energy in matter by e ⁺ e ⁻ pair production in the electric eld of nuclei. These two processes are naturally strongly correlated. The radiation length X 0 can be dened as the mean distance over which a high-energy electron loses all but 1/e of its energy by bremsstrahlung [8]. This is equal to

7

9 of the mean free path for pair production of high energy photons.

2 The energy loss of low energy photons (i.e. E γ ≤ 2m e ) is dominated by the photoelectric eect.

Chapter 2. Calorimetry and Interactions of Particles with Matter For high energies, the average energy loss is given by [38]:

− dE

dx = 4αN A

Z ² A z ²

1 4πε ₀ · e ²

mc ² 2

E · ln 183 Z ^1/3

E , x , N A , Z , A , z and ε 0 dened as in Section 2.1.1, α the ne structure constant and

m the mass of the incident particle.

Thus, the energy loss by bremsstrahlung is proportional to the particle energy and inversely proportional to the square of its mass. This is why bremsstrahlung is mainly relevant to electrons and not to heavier charged particles. The critical energy is dened as the energy where

− dE dx (E _c )

ionisation = − dE dx (E _c )

bremsstrahlung . An approximation [38] gives

E _c ^e ≈ 550 MeV

Z , Z ≥ 13 .

For muons, this leads to a critical energy of about E _c ^µ ≈ E _c ^e · _m

µ

m e

≈ 890 GeV . Hence, bremsstrahlung is negligible for muons below this energy.

The formation of electromagnetic particle showers via bremsstrahlung and pair production is described in Section 2.3.1.

2.2. Strong Interactions

In general, the strong interactions of hadrons with matter are described by Quantum Chro- modynamics (QCD); but, as the strong force diverges for low energies, perturbative QCD is limited to high energy hard scattering processes. Since hadronic multiparticle produc- tion processes are mostly non-perturbative [40], the description of such interactions relies on simulation methods, for example on Monte Carlo simulation (see Chapter 5).

The process most likely to occur in strong hadron-matter interactions is spallation [41].

For heavy elements, ssion is also possible. The process of spallation can be modelled in two stages [41]: a fast intranuclear cascade followed by a slower evaporation step. During the rst stage, the incoming particle makes quasi-free collisions with nucleons within the nucleus. A cascade of fast nucleons results, from which hadrons (mainly pions, protons and neutrons) can be produced. Particles reaching the nuclear boundary escape. During the second stage, the highly excited nucleus radiates free nucleons and photons. A variety of processes contributes to spallation. For illustrative purposes, an example is given [41]: In the interaction of a 2 GeV hadron with ²³⁸ U nuclei, there are about 300 processes that contribute more than 0.1% each to the total spallation cross section, while none of them dominates.

Since new high energy hadrons can be produced from hadronic interactions, hadronic show- ers occur, which are discussed in Section 2.3.2. However, without knowing the exact sequence of processes within hadronic interactions, a mean free path, the hadronic interaction length, λ _I , can be dened with the probability p(x) that a hadron travels a distance x without interaction [42]:

p(x) ∼ exp

− x λ _I

2.3. Particle Showers

Table 2.1: Radiation lengths X ₀ and hadronic interaction lengths λ _I for the absorbers and active material of the ATLAS LAr calorimeters [42].

Material X ₀ [ cm ] λ _I [ cm ] Cu 1 . 44 15 . 1 Pb 0 . 561 17 . 1

W 0 . 350 9 . 59

LAr 14 . 0 83 . 7

λ _I can be approximated by [42]:

λ _I ≈ 35 cm · A ^1/3 ρ [g/cm ³ ] ,

with A the atomic mass number of the absorber and ρ its density. Thus, λ _I is essentially energy-independent.

It needs to be noted that the hadronic interaction length λ _I is a much more approximate number than the radiation length X 0 . This is due to the variety of processes that can occur in strong interactions, as discussed above. Especially important is that the production of neutral pions leads to electromagnetic sub-showers (Section 2.3.2), which reduce the actual length of the hadronic shower depending on the energy of the π ⁰ .

Table 2.1 summarises values of radiation and hadronic interaction lengths for the active and absorber materials of the ATLAS liquid argon calorimeters. For these heavy nuclei, it can be seen that hadronic interaction lengths are typically one order of magnitude larger than radiation lengths.

2.3. Particle Showers

As discussed in Sections 2.1 and 2.2, new particles can be produced in interactions of high energy particles with matter. These secondary particles can again give rise to new particles and so on, so that a particle cascade or shower is started. It ceases when the energy of the newly produced particles is not high enough any more for particle production processes.

Showers originating from electrons or photons are called electromagnetic showers (Sec- tion 2.3.1), showers from hadrons hadronic showers (Section 2.3.2).

2.3.1. Electromagnetic Showers

In Section 2.1.2, bremsstrahlung as well as e ⁺ e ⁻ pair production from high energy electrons, positrons, and photons were discussed. As these processes can follow each other successively, an electromagnetic cascade arises (Fig. 2.2) [38].

Electromagnetic showers cease when either the energy of the e ^± falls below the critical energy E _c (see Section 2.1.2) and ionisation begins to dominate over bremsstrahlung, or the energies of the photon is below the threshold for e ⁺ e ⁻ production ( ≈ 2m e ). The depth of the shower is then given by the specic radiation length of the absorber: 98% of the energy of the incoming particle E ₀ is contained in a length of approximately [38]

L ≈ 2.5X ₀ · (ln (E ₀ /E _c ) + C _{γ ,e} ) , with C _γ = +0.5 and C _e = −0.5 .

Chapter 2. Calorimetry and Interactions of Particles with Matter

.

e+

e−

X 0

e+

e−

e+

e+ e−

e−

.

Figure 2.2: Sketch of an electromagnetic cascade initiated by a photon (blue wavy line) [43]. Electrons and positrons are represented by the red and green lines, respectively. The radiation length X ₀ is indicated.

Due to multiple scattering processes, the transverse size of electromagnetic showers is typ- ically non-zero. On average, it is given by the Molière radius R _m [38]:

R _m = 21 MeV E c

· X ₀

g/cm ² .

2.3.2. Hadronic Showers

As discussed in Section 2.2, inelastic hadron scattering o nuclei at high energies produces new hadrons, mainly pions, nucleons and kaons, and thus starts a hadronic cascade. The sketch in Fig. 2.3 shows that hadronic showers are much more inhomogeneous than electromagnetic showers.

.

escaped

electromagnetic invisible

visible non−em.

.

Figure 2.3: Sketch of a hadronic shower [38]. Examples of the dierent categories of energy deposits

as discussed in Section 2.4.3 are also shown.

2.4. Calorimetry Several eects contribute to this inhomogeneity and thus complicate the energy measure- ment in calorimeters [38, 39, 42].

• From isospin conservation it follows that each pion type ( π ⁺ , π ⁻ and π 0 ) is produced with a probability of 1/3 [44], i.e. one third of the pions are neutral pions. The energy fraction carried by the latter increases with energy, but is subject to large uctuations in all energy ranges. The dominant decay channel of neutral pions is π 0 → γγ with a lifetime of ∼ 10 ⁻¹⁶ s . This leads to electromagnetic sub-cascades (Section 2.3.1) within the hadronic shower.

• A large fraction of energy goes into binding energy losses such as nuclear excitation and nuclear break-up. To a large degree, this fraction is not measured in calorimeters, as discussed in Section 2.4.3.

• The de-excitation of nuclei can produce neutral long-lived or stable particles. Ex- amples are slow neutrons, K _L ⁰ and neutrinos.

• As the product of pion and kaon decays, muons can also occur. They can be described as mips (Section 2.1), and, thus, deposit only a part of their energy in the calorimeter.

A hadronic cascade ceases when the energy of the particles is no longer sucient to produce new particles. The characteristic length for the shower depth and transverse extension is the hadronic interaction length, λ _I , (Section 2.2). The depth L and radius R can be roughly approximated by [39]:

L ≈ h

0.6 ln (E/[GeV]) − 0.2 + 4 (E/[GeV]) ^0.15 i

· λ I

R ≈ λ I

When comparing electromagnetic and hadronic showers, two main dierences are obvious.

Firstly, in heavy absorber materials, the lateral and longitudinal extensions, determined by the radiation length X ₀ and the hadronic interaction length λ _I , are much smaller for elec- tromagnetic showers (Table 2.1). Secondly, the composition of both shower types is basically dierent, as discussed above. Consequently, electromagnetic and hadronic showers have dif- ferent responses in the calorimeter (Section 2.4.3). Simulated examples of showers generated by an electron and a charged pion of the same energy, absorbed in iron, are shown in Fig. 2.4.

2.4. Calorimetry

Calorimeters [8, 38, 39] absorb certain kinds of particles and reconstruct their energy by measurements of ionisation, scintillation light or Cherenkov radiation. Information about the position of the particle is obtained by segmenting calorimeters into cells.

As discussed in Sections 2.3.1 and 2.3.2, electrons, photons, and hadrons shower in calorime- ters and, thus, can be absorbed. In addition, the energy deposits of isolated muons can be measured, and information about neutrinos can be obtained by balancing events in the trans- verse plane, thus measuring the missing transverse momentum 6 p _T . A characteristic advantage of calorimeters is the possibility to measure neutral hadrons and photons in contrast to other detector parts.

There are mainly two types of calorimeters: homogeneous (Section 2.4.1) and sampling

calorimeters (Section 2.4.2). In Section 2.4.3, the diculties of measuring the energies of

hadronic showers are discussed; Section 2.4.4 comments on the energy resolution of calorime-

ters.

Chapter 2. Calorimetry and Interactions of Particles with Matter

a)

b)

Figure 2.4: Shower of a 50 GeV electron (a) and charged pion (b) in Fe [45].

2.4.1. Homogeneous Calorimeters

In homogeneous calorimeters [8], the whole absorber material is active, i.e. the signal is formed from the whole (measurable) energy deposited in the calorimeter. Absorber materials are either inorganic scintillating crystals such as BGO or PbWO 4 , Cherenkov radiators for example lead glass or liquid noble gases. The choice of material is, however, strongly limited.

2.4.2. Sampling Calorimeters

In sampling calorimeters [8, 39], passive absorber material is interspersed with an active medium, which is equipped with read-out. In the active medium, only a part of the energy that is deposited in the whole calorimeter is measured. The active material can be a scintillator, a liquid noble gas, a gas chamber, a semiconductor, or a Cherenkov counter.

The separation of absorption and read-out allows for an optimal choice of absorber mate- rials. Due to the large size of hadronic showers and the requirement of their containment, a certain thickness in terms of hadronic interaction lengths is needed in hadronic calorimeters.

Thus, they are often of the sampling type, which allows for a compact design and lower costs.

2.4.3. Hadronic Showers in High Energy Calorimeters

Parts of the energy of hadronic showers are not measured in the calorimeter (see Section 2.3.2).

Examples are neutrinos, which leave the detector without depositing energy; muons, which do not shower in the calorimeter; and nuclear de-excitation, which may result at least partially in (generally observable) particles, but their emission is likely to be out-of-time for the signal shaping (Section 4.1).

For this reason, the ratio of h/e, meaning the ratio of the responses for hadronic and electromagnetic showers, is typically < 1 [8]. In sampling calorimeters, there is the possibility of using passive material which provides a h/e -ratio of approximately 1 , for example depleted uranium, which compensates for the lower hadronic response by induced ssion processes.

However, the ATLAS LAr calorimeters are non-compensating.

2.4. Calorimetry Energy deposits in the ATLAS calorimeter can be classied following the convention of calibration hits [46] implemented in the simulation toolkit Geant4 (see Chapter 5, Ref. [47]):

(for examples see Fig. 2.3)

• visible electromagnetic energy:

− ^dE _dx from ionisation by electrons and positrons ( e ^± , γ → e ⁺ e ⁻ , π ₀ → γγ , etc.)

• visible non-electromagnetic energy:

− ^dE _dx from ionisation by other charged particles (π ^± , µ ^± , etc.)

• invisible energy:

energy released by non-ionising processes (e.g. nuclear break-up)

• escaped energy:

energy leaving the calorimeter volume by non-interacting particles (e.g. ν )

While the rst two categories lead to energy deposits measured directly in the calorimeter, invisible and escaped energy are the sources of the lower response to hadrons with respect to the response to electrons. Other sources of false energy measurements are leakage out of the calorimeters or energy loss in regions unequipped with read-out (dead material). All this underlines the need for a concept to assure reliable reconstruction of the energy of hadronic showers. Two dierent approaches are discussed in Section 4.7.

2.4.4. Energy Resolution in Calorimeters

The relative energy resolution of calorimeters σ _E /E , with σ _E the error of the energy mea- surement, is from now on simply referred to as resolution. It is given by [39]:

σ E

E = √ C S

E ⊕ C N

E ⊕ C C . (2.2)

⊕ denotes the quadratic sum and C _S , C _N , and C _C are characteristic constants for a given calorimeter and a certain shower type (electromagnetic/hadronic). Thus, the resolution of calorimeters improves with increasing energy.

The rst term in Eq. (2.2) is called the sampling term, which typically dominates the resolution in a wide range of energies. It is due to statistical uctuations which are ∼ 1/ √

N , with N the number of particles contained in the shower. Since N ∼ E , the quoted form of the term holds. Sampling constants for electromagnetic and hadronic showers dier strongly, because the latter are subject to huge uctuations in composition. Typical values for C S are 10% for electromagnetic and 50% for hadronic showers.

C _N /E is called the noise term, which is due to approximately energy-independent (σ E, noise ≈ const.) instrumental eects such as noise or pedestal shifts. The energy inde- pendence holds as long as the number of read-out channels does not vary with the energy, which is not the case for the topological clustering algorithm (Section 4.5).

The last term (C C ) is called the constant term. It collects eects such as calibration errors, non-linearities and non-uniformities of the detector. These contributions to the resolution σ _E /E are assumed to be about constant, because they are constant in factors that are applied to the energy.

The design resolution (without noise term) of the ATLAS calorimeters is quoted in Ta-

ble 1.3.