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Untersuchung zur E/p-Kalibrationdes Kalorimeter-Systemsam ATLAS Detektor

Bachelorarbeitzur Erlangung des Grades einesBachelor of Science in Physik

vorgelegt von

Carsten D. Burgardaus Denzlingen

Themenstellung: Prof. Dr. Karl Jakobs

Fakultät für Mathematik und PhysikAlbert-Ludwigs-Universität

Freiburg im Breisgau2011

CONTENTS iii

Contents

1 Abstract 1

1.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Zusammenfassung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Introduction 2

3 Experimental facilities 4

3.1 The LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.2 ALICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.3 LHCb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.4 CMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.5 ATLAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4 Measuring jets 9

4.1 How do particles interact with matter . . . . . . . . . . . . . . . . . . . . . 9

4.2 The calorimeter system of ATLAS . . . . . . . . . . . . . . . . . . . . . . . 11

4.3 Jet Energy Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.4 E/p measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.5 Background subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5 Improving the background subtraction 18

5.1 Definition of the terminology . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.2 Discussion of the central detector region . . . . . . . . . . . . . . . . . . . 20

5.3 Discussion of the forward and backward detector regions . . . . . . . . . . 23

6 The parametric approach 26

6.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

6.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

7 Results 39

7.1 Results on E/p measurements . . . . . . . . . . . . . . . . . . . . . . . . . 39

iv CONTENTS

7.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

7.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

References v

List of Figures vii

A The ATLAS coordinate system 43

B Monte Carlo Simulation 45

C Collection of all plots 46

C.1 Energy deposition density . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

C.2 Linear approximation of the energy deposition density . . . . . . . . . . . . 55

C.3 Linear approximation of the energy deposition as a function of track mo-mentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

C.4 Comparison of jet energy deposition density for wide and narrow jets (radialRMS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

C.5 Background estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

C.6 E/p plots, former correction factor . . . . . . . . . . . . . . . . . . . . . . 88

C.7 E/p plots, new correction factor . . . . . . . . . . . . . . . . . . . . . . . . 90

C.8 Comparison of background estimations for both correction factors . . . . . 92

1 ABSTRACT 1

1 Abstract

1.1 Abstract

The accurate knowledge of the Jet Energy Scale is a dominant factor for the vast majorityof precision measurements and new physics searches at the LHC. A key component forthis is the measurement of the single hadron response of the calorimeter, a problemusually adressed through E/p measurements. In this thesis, we critically review thisapproach, making use of

√s = 7TeV proton-proton collision data collected by the ATLAS

experiment in 2010. In the past, late showering hadron tracks were successfully used todirectly measure the background originating from neutral particles in the periphery ofthe track, assuming a constant contribution superimposed to the MIP track itself. Inthis thesis, we extrapolate the background contribution superimposed to the chargedhadron track by assuming a linear dependency of the energy deposition density of thedistance from the charged track. Concluding that, although the previously used estimationmethod does not agree with the actual deposition density measured, the assumption usedpreviously underestimates the background on the E/p observable by only 10% due togeometrical reasons.

1.2 Zusammenfassung

Die genaue Kenntnis der Jet Energy Scale des Kalorimeter-Systems ist ein bestimmenderFaktor für nahezu alle Präzisionsmessungen und Suchen nach neuer Physik an Hadronen-beschleunigern wie dem LHC. Eine Schlüsselrolle hierbei nimmt die Messung der singlehadron response des Kalorimeters ein. Hierzu ausgeführte E/p-Messungen werden im Hin-blick auf mögliche Fehler durch systematische Unterschätzung des durch neutrale Teilchenverursachten Untergrunds untersucht. Ereignisse, in denen geladene Hadronen erst spätelektromagnetische Schauer auslösen, werden verwendet, um den peripheren Untergrunddirekt zu messen. Die bisher zur Abschätzung des Untergrunds verwendete Annahme eineskonstanten Untergrunds im Bereich der geladenen Spur selbst wird untersucht. Als neueMethode der Abschätzung wird eine lineare Extrapolation der Energiedepositionsdichtevorgestellt. Obwohl die bisher verwendete Annahme die wahre Dichte der Energiedeposi-tion nicht gut wiedergibt, liefert auch die neue Extrapolationsmethode nur etwa um 10%höhere Abschätzungen des Untergrundes. Dies kann durch geometrische Überlegungenerklärt werden.

2 2 INTRODUCTION

2 Introduction

Ever since, mankind has tried to understand the forces of nature, that drive and holdtogether the world as we know it. Within the last century, however, this search hasadvanced vastly, which would not have been possible without the combination and closeinterplay of both theory and experiment. But the further this search continues, the morecomplex, elaborate and expensive the experiments become that are necessary to test thetheories proposed to explain the nature of matter and interactions.

One of the greatest successes in the course of this quest was the introduction of theStandard Model of particle physics, providing a consistent theory for particles and inter-actions and making predictions that could be verified experimentally to high precision.There are, however, hints that the standard model, although extremely successful, mightnot be the full picture. Many theories exist, trying to explain phenomena that cannotbe explained within the standard model, among which are fundamental questions likethe asymmetry of matter and antimatter observed in our universe, the nature of darkmatter and other, more involved phenomena. Experiments have to be planned and per-formed in order to test these theories and provide observations, eventually leading to theirverification or falsification.

State-of-the-art experiments in particle physics, designed to push the limits of ourunderstanding of the fundamental particles and their interactions further, are nowadays nolonger projects of single, brilliant scientists, but rather the outcome of large collaborationsof scientists and technicians, accurately designed and built over timescales of years anddecades.

Particle physics experiments can roughly be divided into two categories: Astro particlephysics experiments and collider experiments, the former looking for high-energy particlesfrom space, the latter trying to produce them with particle accelerators. Each of thesefields has its own unique advantages and disadvantages, and again only the combinationof all observations from both fields can provide a fully consistent picture. Astro particleexperiments benefit from the fact that, in cosmic events such as supernovae, particleswith energy ranges vastly exceeding the range of man-made accelerators are produced.The observation of such particles is, however, comparably rare, and since the productiondoes not happen under laboratory conditions, but many lightyears away from the earth,the aquisition of data sufficient to provide experimental proof for theories relies heavilyon a long time of observation and sometimes even on luck. Accelerator experiments, onthe other hand, have the advantage of producing high energy particles with a sufficientrate to provide large amounts of data. Furthermore, the observations can be made un-der reproducible conditions, ideally with a full coverage and observation of all producedparticles for the single event. Then, again, these experiments rely on accelerators, which

2 INTRODUCTION 3

are costly and limited in the range of accessible energy.

The ATLAS detector is one of the four main detector experiments at the LHC, theworld’s largest particle accelerator to date (2011), providing insight to energy regionspreviously unaccessible to collider physics. Its calorimeter system is complex, consistingof several layers and different modules. The design was optimized for high performanceprecision energy measurements of high energy particles emerging the collisions. Theproper calibration of this system requires detailed investigation of various effects as wellas the calculation and estimation of various backgrounds and correction factors.

One of the most challenging tasks in the calibration procedure is the determinationof the Jet Energy Scale (in the following JES), that is, the calorimeters response tohadronic jets. Jets are produced in great numbers at the LHC, since the cross sections forprocesses of the strong interaction are by far dominating all other possible interactions,and hadronic jets are the typical products of these interactions. A precise measurementof the jet energy is, however, difficult, as will be discussed in further detail in this thesis.Therefore, uncertainties on the JES are the dominant systematic uncertainties for manyprecision measurements and new physics searches at the ATLAS detector.

One way to measure the calorimeter JES and its uncertainty is to combine the meas-urements from the calorimeter with tracking information from the inner detector. Basedon the two corresponding quantities, the energy E measured by the calorimeter and thetrack momentum p measured by the inner detector, a calibration of the calorimeter re-sponse to single hadrons can be performed by considering their ratio E/p. The singleparticle response can then be convoluted with the predicted jet structure to derive theJES.

In this thesis, we will discuss and investigate estimation methods for the backgroundto measurements of the single hadron response, originating from neutral particles. Wewill also present a possible improvement of these methods based on measurements of theshape of this background. We propose an approach to parametrize this shape in a linearway, leading to new and slightly larger correction factors applied to the measured back-ground. We also present large-scale experiemtal results, demonstrating the advantages ofour method.

4 3 EXPERIMENTAL FACILITIES

3 Experimental facilities

3.1 The LHC

The Large Hadron Collider (LHC) is currently (as of 2011) the worlds largest and highest-energy particle collider. It is operated by the European Organization for Nuclear Re-search or CERN (Organisation Européenne pour la Recherche Nucléaire, formerly ConseilEuropéen pour la Recherche Nucléaire) and located in a particle physics laboratory north-west of Geneva, also often referred to as “CERN”. The LHC itself is a synchrotron, aspecial type of circular particle accelerator (as opposed to linear accelerators) and has acircumference of approximately 26.7 km. It was built underground in the tunnel of theformer Large Electron-Positron Collider (LEP), which was shut down and deconstructedin 2000 in order to make room for the LHC.

Figure 1: CERN overview and LHC tunnel

The LHC itself mainly consists of 1 232 superconducting dipole magnets with a nom-inal magnetic field strength of up to 8.3T. Two beams of protons counter-rotate in theLHC ring in opposite directions. Unlike particle-antiparticle colliders, where the oppositebeams can share one ring due to their opposite charge, the high design luminosity of1034 cm−2s−1 made the use of anti-protons impractical. Thus, also due to considerationof the limited space in the tunnel, a twin bore magnet (or “two-in-one”) design for thesuperconducting ring magnets was chosen.

Both beams are split into a great number of bunches (up to 2 808 each) of approxim-ately 1010 protons each. One of the main features of the LHC is the high kinetic energyof these protons. The collider was designed for a beam energy of 7TeV, and although thisenergy will not be reached until 2014, the current beam energy of 3.5TeV still makes theLHC the highest-energy man made particle accelerator ever built. The interested reader

3 EXPERIMENTAL FACILITIES 5

may, however, refer to [8] for more details on the LHC machine.

At four different places on the ring, the proton beams intersect. These intersectionpoints are located within large particle detectors, forming so-called “experiments”. Eachof these four experiments is operated by an international collaboration of scientists andtechnicians, and each of the detectors was designed in a unique way in order to fit theneeds of the special purpose of the particular experiment.

Two of these experiments, ATLAS and CMS, located on opposite sides of the ring, canbe viewed as omni-purpose detectors, whilst the other two, ALICE and LHCb, concen-trate on rather specialized fields of research. A number of other, much smaller experimentsis sharing the intersection points with the four mentioned above. The purpose and thedesign of all four main experiments will be briefly discussed in the following, althoughthere will be a strong focus on the design of the ATLAS detector, the details of whichwill become one of the main aspects of this thesis.

3.2 ALICE

Apart from the collision of protons, the LHC is also capable of accelerating heavy ions.The analysis of these collisions is the main research field of ALICE (A Large Ion ColliderExperiment), the only one of the four large LHC experiments designed specifically toadress the physics of strongly interacting matter, to investigate quantum chromo-dynamicsand especially to examine the physical properties of quark-gluon-plasma, a state of matterin which quarks and gluons behave as quasi-free objects.

The ALICE collaboration includes over 1 000 physicists and engineers from 105 insti-tutes in 30 countries. The ALICE detector itself has overall dimensions of 16×16×16m3

with a total weight of approximately 10 000 t and consists of two main parts. The firstone is the central barrel, which measures hadrons, electrons and photons and is embeddedin a large solenoid magnet reused from the LEP L3 experiment, while the other one isthe forward muon spectrometer.

From the inside out, the central barrel consists of an Inner Tracking System of sixplanes of high-resolution silicon pixel-, drift- and strip-detectors, a cylindrical Time-Projection Chamber, three particle identification arrays of Time-of-Flight, Ring ImagingCherenkov and Transition Radiation detectors, and two electromagnetic calorimeters.Detailed information on ALICE can be found in [9].

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3.3 LHCb

The main aim of the LHCb experiment is a precision analysis of the physics of heavyflavour hadrons, especially charmed c and beauty b hadrons (the latter accounting forthe experiments name). Rare decay modes of these and precise measurements of theirbranching ratios may be used to investigate the mechanism of CP violation and to cross-check the CKM-theory of this mechanism, which has, up to now, proven to hold withgreat precision [14, 15]. The standard model CP violation mechanism can, however, notexplain the imbalance of matter and antimatter observed in our universe, and so manybeyond-standard-model theories contain extensions of this mechanism.

Since the differential production cross section for heavy hadrons is largest in the for-ward and backward regions, the LHCb detector is essentially a single-arm spectrometerlocated in the forward region of the experimental site. It has highly flexible trigger systemsas well as superior vertex reconstruction capability in order to identify and investigatethe short-lived B-mesons with high precision. For this experiment, it is also possible toreduce the luminosity in order to reduce pile-up and improve the data quality by slightlydefocussing the beam at the LHCb collision point.

The LHCb collaboration consists of approximately 760 scientists and technicians from54 institutes, representing 14 countries. For further information, the reader may referto [10].

3.4 CMS

The CMS (Compact Muon Solenoid) experiment is one of the two omni-purpose detectorexperiments operating at the LHC. The spectrum of research objectives is wide andcontains amongst others the

• search for the Higgs boson and thus the verification (or falsification) of the Higgs-mechanism of electroweak symmetry breaking

• experimental check of the (mathematical) consistency of the Standard Model ofparticle physics at the TeV energy scale

• search for experimental groundings for different “beyond-Standard-Model” theoriessuch as Supersymmetry or a “Grand Unified Theory” (GUT)

Whether these ambitious goals will finally be achieved by the CMS collaboration andexperiment, the next years will show. The detector itself is equipped to be sensitive to awide variety of physical processes in order to allow the simultaneous study of the theoriesand effects mentioned above.

3 EXPERIMENTAL FACILITIES 7

The main (and name-giving) part of the detector is a 4T superconducting solenoid,providing sufficient bending power to allow a high momentum resolution on ultra-highenergy particles. The bore of the magnet coil is with a diameter of 2.6m large enough tocontain the inner detector, consisting of ten layers of silicon microstrip detectors and threelayers of silicon pixel detectors close to the interaction point as well as a lead tungstatecrystal electromagnetic calorimeter and a brass/scintillator hadronic calorimeter. Outsidethe magnet coil, the muon chambers are located, which play a central role in the detectorconcept and also contributed to the detector’s name.

With a total length of 21.6m, a diameter of 14.6m, a total weight of approximately12 500 t and a collaboration with over 3 600 participants from 183 different institutes in 38countries, the CMS experiment is one of CERN’s main research facilities for the search fornew physics and tests of the Standard Model. More information on the CMS experimentand further technical descriptions of the detector (and its concept) can be found in [11].

3.5 ATLAS

The ATLAS (A Toroidal LHC ApparatuS) experiment is the second omni-purpose de-tector experiment at the LHC. Since the ATLAS detector is subject to the work of thisthesis, we will discuss the technical details of it to some extent. For any further informa-tion, however, the reader may refer to [12].

As the two experiments ATLAS and CMS were designed in a complementary manner,their agenda and research purposes are equal to a large extent. Hence, the reader mayrefer to Section 3.4 for a brief discussion of the physical phenomena which are subjectto the research performed by the ATLAS collaboration. Approximately 2 000 scientistsfrom 165 institutes in 35 countries participate in this research.

The ATLAS detector, as depicted in Figure 2, has a cylindrical layout and is nom-inally forward-backward-symmetric. Among the main (and name-giving) design featuresare the three large superconducting toroid magnets, arranged in an eight-fold azimuthalsymmetry, surrounding the calorimeters (one barrel and two end caps).

The inner detector of ATLAS is contained within a 2T solenoid magnet and is com-posed of three detector-subsystems. The innermost layer of detector material is the siliconpixel detector, consisting of three layers of silicon pixel cells, close to the central interac-tion vertex. Proceeding outward, four double-layers of silicon microstrip (SCT) detectorsfollow, completing the semiconductor tracker. The third component of the inner detectorright before the solenoid is the transition radiation tracker (TRT), a thick layer of poly-mide drift (straw) tubes.

The ATLAS calorimeters are located outside the inner detector. The inner, electro-

8 3 EXPERIMENTAL FACILITIES2008 JINST 3 S08003

Figure 1.1: Cut-away view of the ATLAS detector. The dimensions of the detector are 25 m inheight and 44 m in length. The overall weight of the detector is approximately 7000 tonnes.

The ATLAS detector is nominally forward-backward symmetric with respect to the interac-tion point. The magnet configuration comprises a thin superconducting solenoid surrounding theinner-detector cavity, and three large superconducting toroids (one barrel and two end-caps) ar-ranged with an eight-fold azimuthal symmetry around the calorimeters. This fundamental choicehas driven the design of the rest of the detector.

The inner detector is immersed in a 2 T solenoidal field. Pattern recognition, momentumand vertex measurements, and electron identification are achieved with a combination of discrete,high-resolution semiconductor pixel and strip detectors in the inner part of the tracking volume,and straw-tube tracking detectors with the capability to generate and detect transition radiation inits outer part.

High granularity liquid-argon (LAr) electromagnetic sampling calorimeters, with excellentperformance in terms of energy and position resolution, cover the pseudorapidity range |η | < 3.2.The hadronic calorimetry in the range |η | < 1.7 is provided by a scintillator-tile calorimeter, whichis separated into a large barrel and two smaller extended barrel cylinders, one on either side ofthe central barrel. In the end-caps (|η | > 1.5), LAr technology is also used for the hadroniccalorimeters, matching the outer |η | limits of end-cap electromagnetic calorimeters. The LArforward calorimeters provide both electromagnetic and hadronic energy measurements, and extendthe pseudorapidity coverage to |η | = 4.9.

The calorimeter is surrounded by the muon spectrometer. The air-core toroid system, with along barrel and two inserted end-cap magnets, generates strong bending power in a large volumewithin a light and open structure. Multiple-scattering effects are thereby minimised, and excellentmuon momentum resolution is achieved with three layers of high precision tracking chambers.

– 4 –

Figure 2: ATLAS Detector, length 44m, radial dim. 25m, weight approx. 7 000 t.Reproduced from [12] with kind permission from IOP Publishing.

magnetic calorimeter is divided into a barrel part as well as two end-caps and is designedas a sampling calorimeter with lead as the absorber and liquid argon as the active mater-ial. The electrodes as well as the absorber plates offer a unique, accordion-shaped designin order to provide full azimuthal symmetry without interrupting cracks.

The next layer is the hadronic calorimeter, using steel absorbers and scintillating tilesin the barrel region and again liquid argon with plates of copper as absorber materialin the end cap. The ATLAS calorimeter system will be discussed in further detail inSection 4.2.

The outermost detection layer is the muon chamber system, which mainly consists ofmonitored drift tubes and is based on the magnetic deflection of muon tracks in the largesuperconducting toroid magnets.

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4 Measuring jets

The LHC is a proton-proton collider. The actual collisions, however, happen between theconstituents of the protons, that is quarks of different flavours and gluons. As opposedto lepton colliders, processes at hadron colliders are therefore dominated by the stronginteraction. In high energy collisions, a large number of strongly interacting particles isproduced in every collision. These objects travel away from the interaction vertex withhigh velocity, possessing enough energy to overcome the confinement barrier and createnew particles to form composite objects, a process usually referred to as hadronization[14, 15]. Large numbers of hadrons emerge from the primary vertex, their momentumbeing almost aligned with respect to the momentum of the original particle produced in thecollision. The angular range under which these objects emerge is usually small due to thehigh momentum of the original product and relativistic effects. Jet production processesare not only subject to direct research, but also contribute as a major background tomany other measurements. Therefore, a high precision in the measurement of jets is ofgreat interest.

4.1 How do particles interact with matter

In this section, we briefly discuss the different ways of particles to interact with matter,such as the material of the calorimeter. We will especially focus on the interaction ofhigh energy particles with the electromagnetic calorimeter of ATLAS, which is subjectto our investigation, and we will also briefly discuss the physical effects arising in thedetection of jets. A full coverage of the mentioned effects, however, vastly exceeds thescope of this thesis. For a comprehensive and detailed description of all effects related tothe calorimetric measurement of particles, the reader may refer to [13].

Apart from weak interactions, which play a minor role for calorimetric purposes, thepossible interactions of particles with matter can roughly be divided into two categories:electromagnetic interactions and strong interactions. While the former play a role for allcharged particles and photons, the latter are only important for hadrons, such as baryonsand long-living mesons.

Some important examples for electromagnetic interactions are listed below.

• Charged particles traversing matter interact with the electromagnetic field generatedby the nuclei of the surrounding material, losing their energy by the emission ofphotons. This process called bremsstrahlung is by far the dominant process for lightparticles with very high energy. In practice, bremsstrahlung only plays a role for themeasurement of electrons.

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• Photons of sufficiently high energy may interact with the electromagnetic field ofthe nuclei generating electron-positron-pairs. This process is called pair production.Photons with an energy lower than twice the electron mass cannot undergo thisprocess.

• Any particle participating in the electromagnetic interaction may interact with theelectrons of the material by undergoing elastic scattering, exciting the interactionpartner to a higher energy level or depositing enough energy to ionize the atom withwhich it interacted.

Clearly, these processes result in the multiplication of the number of free particles,setting free electrons or producing electron-positron pairs, or photons through a variety ofdifferent processes. For particles of sufficient energy, where the former two processes play asignificant role, one therefore typically speaks of particle showers induced by the originalparticle, through which the energy is finally deposited in the detector material. Sinceelectrons (or positrons) and photons may undergo subsequent alternating conversions,the electromagnetic shower profiles of these particles are fairly similar.

Comparing this to processes of the strong interaction, such as

• scattering with associated production of mesons

• spallation of nuclei

• excitation of nuclei with subsequent radiation of nucleons or photons

it is clear that one will also find shower development here. It has to be noted though, thatwhile the development of electromagnetic showers can be understood in a relatively simplemanner, the details of the hadronic shower development are complex. This is mainly dueto the following reasons:

• Some mesons such as neutral pions will almost immediately decay into photons, thusinducing electromagnetic showers superimposed to the hadronic shower. Chargedmesons on the other hand will typically travel long distances before undergoing afurther hadronic interaction. These two factors together make hadronic showershighly irregular and inhomogeneous.

• Depending on the details of the shower development, a large number of relatively soft(i.e. low-energy) neutrons will be produced. The dominant (if not only) interactionprocess for such neutrons with the detector material is elastic scattering, which will(because of the mass difference between single soft neutrons and atomic nuclei) onlyaccount for low energy losses in every single interaction. This will cause the energy

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to spread widely over the detector, the deposition taking a considerable amount oftime. Hence, this energy will be practically lost for detection purposes.

Obviously, the relative importance as well as the total outcome of these effects dependon the material as well as on the concept of the detector, and also on the type andthe energy of the particle inducing the shower. In order to be able to quantify theproperties of calorimeters in a (relatively) material-independent way, one chooses to definethe radiation length X0 (for electromagnetic interaction) and the interaction length λ0 (forstrong interaction). Although a precise definition of these quantities (as found in [13])is beyond the scope of this thesis, both can be described in an approximate manner asthe typical length scale over which a particle taking part in the associate interaction willdeposit two thirds of its energy in the detector material because of radiation processes ornuclear interactions only, respectively.

From a phenomenological point of view, the main difference between hadronic showersand purely electromagnetic showers is that the former are much larger in the lateral aswell as in the longitudinal dimension. Therefore, electromagnetic calorimeters typicallyneed less material for a sufficient shower coverage, or from another point of view: theelectromagnetic radiation length of a material is typically much shorter than the hadronicinteraction length of the same material.

Due to the different ways of interaction, the transformation of energy from the hadronicto the electromagnetic sector of the deposition during the shower development and theinvisible energy deposition through detachment of nucleons from the nuclei of the detectormaterial, the calorimeter response to incoming hadrons is non-linear with the hadronenergy (and is in particular lower than that of an electron of equivalent energy). Somecalorimeters are thus designed to be compensating, that is, in a way such that a linearhadron response is recovered. This is typically achieved by doping the calorimeter materialwith radioactive materials that emit neutrons (e.g. 238U). This is, however, not the casefor the calorimeter system of ATLAS.

Especially problematic is the calorimetric measurement of jets. A jet consists of anumber of hadrons, typically mesons, a large fraction of which might be neutral pions,almost immediately decaying into photons. The measurement of jets is difficult, as theyare not single but composite objects, and will be discussed in further detail.

4.2 The calorimeter system of ATLAS

The calorimeter system of ATLAS, of which an overview was already given in Section 3.5in the course of a short presentation of the ATLAS detector, will be explained in furtherdetail here. We will, however, concentrate on the more central detector regions, devoted

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to precision physics. All of this information and further details on the calorimeter systemfor all detector regions may be found in [12].

Figure 3: The ATLAS Calorimeter System.Reproduced from [12] with kind permission from IOP Publishing.

The calorimeter system closer to the central vertex is the electromagnetic calorimeter,which will also be the main focus of this thesis. It is divided into a barrel part (for|η| < 1.475)1 and two end-cap components (for 1.375 < |η| < 3.2). The barrel calorimeterconsists of two identical half-barrels with inner and outer radii of 2.8m and 4m respect-ively and a length of 3.2m as well as a weight of 57 t each, separated by a small gap of4mm. Each end-cap calorimeter is divided into two wheels, the outer of which is coveringa more central pseudorapidity region (1.375 < |η| < 2.5), whilst the inner wheel coversthe more forward and backward regions (2.5 < |η| < 3.2).

All parts of the electromagnetic calorimeter use lead as the absorber material andliquid Argon as the active medium. The lead absorber plates (thickness varies between1.13mm and 2.2mm as a function of η) are folded in a special, accordion-shaped designin order to provide full and completely symmetric azimuthal coverage. Additional, thin(approximately 0.2mm) sheets of stainless steel to both sides of each lead plate provideadditional mechanical strength of the construction. For the region of |η| < 2.5, thecalorimeter is divided into three lateral sections. In the region of |η| < 1.8 an additionalliquid argon layer of 11mm depth acts as a presampler detector, used to correct for the

1The ATLAS coordinate system and the definition of the pseudorapidity η is given and explained tosome extent in appendix A.

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energy lost by electrons and photons upstream of the calorimeter. The first layer ofthe calorimeter is read out from the front, whereas the second and third layers are readout from the back. The total thickness of the absorber material in the electromagneticcalorimeter varies in the range of (22− 33)X0 (radiation lengths) as a function of η forthe more central detector regions.

The second calorimeter system of ATLAS is the hadronic tile-calorimeter. It coversthe region of |η| < 1.7 and is subdivided into a central barrel (for |η| < 1.0) and twoextended barrels (for 0.8 < |η| < 1.7), with a length of 5.8m and 2.6m each, respectively.Here, the absorber material is steel, while the active medium is plastic scintillator. Eachbarrel consists of 64 modules or wedges, made of steel plates and scintillating tiles. Thetotal depth of the tile calorimeter is approximately 7.4λ0 (interaction lengths).

The hadronic end cap calorimeter is again a sampling calorimeter, using liquid argonas the active medium and plates of copper as absorber material, covering the forwardand backward regions of the detector (1.5 < |η| < 3.2). Each of the end cap calorimetersis subdivided into two wheels, a front wheel and a rear wheel, each of which consistsof 32 identical wedge-shaped modules. The modules of the front wheels are made of 24copper plates, each 25mm thick, plus a 12.5mm thick front plate. In the rear wheels, thesampling fraction is coarser with modules made of 16 copper plates, each 50mm thick,plus a 25mm thick front plate.

4.3 Jet Energy Scale

As mentioned in Section 4, the ability to measure jets with high precision is crucialespecially at hadron colliders such as the LHC. A quantity called Jet Energy Scale (in thefollowing JES [1]) is therefore defined and used as a correction factor in order to correctthe calorimeter response to jets.

The importance of a precise knowledge of the JES factor is especially due to the factthat the JES uncertainty is the dominant experimental error on a number of importantmeasurements, such as

• the di-jet cross section

• the top quark mass measurements

• new physics searches with jets in the final state

The JES, typically defined as

RJES =pEM-meas.T

ptrueT

. (1)

14 4 MEASURING JETS

is usually calculated from Monte Carlo simulations, since the true energy of a jet isa priori unknown. Here, ptrue

T denotes the true transverse momentum of the jet andpEM-meas.T denotes the energy (or momentum) measured by the detector on reconstructed

information level.

However, any inaccuracy in the details of the simulation will directly affect the JetEnergy Scale. This applies to the simulation of the jet itself on truth level, e.g. thecomposition of the jet of different hadron types, as well as to the detector simulation,e.g. modelling of the single hadron response of the detector. The latter includes effectssuch as

• calorimeter non-compensation, i.e. the different (lower) response of the ATLAScalorimeter to hadrons.

• energy losses in inactive (dead) material regions of the calorimeter, such as supplyshafts or electronic material

• leakage, i.e. particles (jets) not fully contained in the calorimeter

• inefficiencies of the clustering algorithm or the calorimeter jet reconstruction

Clearly, one cannot expect the simulation to model all those effects with absolute ac-curacy. A precise in-situ measurement of the JES based on real collision data is thereforesubject to intense physical research (see, e.g., [1, 2, 3, 4]). One possible approach for ameasurement of the JES relies on the E/p-measurement. These measurements will bediscussed in the next section.

4.4 E/p measurements

The ratio between the energy E deposited by an isolated track in the calorimeter and itsmomentum p is an observable that can be used to assess the quality of the Monte Carlosimulation of calorimeter energy deposits.

The E/p measurements make use of the excellent resolution of the inner detectorsilicon tracker (especially for low energy charged particles). For calibration purposes, itis useful to define a quantity usually reffered to as E/p and defined as

E/p =Emeas.

pmeas.ID

where pmeas.ID denotes the track momentum information measured by the inner detector

silicon tracker. The quantity Emeas. is calculated from the sum of all the energy recon-structed making use of a topological clustering algorithm and associated with the track.

4 MEASURING JETS 15

The purpose of the topological clustering algorithm is to identify areas of connectedenergy deposits in the calorimeter, based on the significance of the energy deposits in cellswith respect to the expected noise level. A topological cluster is initiated by cells withan energy deposit |Ecell| > 4σnoise , where σnoise is the root mean square deviation of theelectronic noise in the cell. Then, iteratively, the cluster expands adding all neighboringcells with |Ecell| > 2σnoise . Finally, the cells surrounding the resulting cluster are added,regardless of their energy [2].

The association of the cluster to an isolated track is based on the energy weightedcluster position in the calorimeter layer and a geometrical extrapolation of the track tothis layer. A more detailed explanation can be found in [2]. A track is considered isolatedin this context, if its impact point in the electromagnetic calorimeter has a distance of

∆R ≥ 0.4

from the closest other track impact point (see also [3]) where R is defined in terms of angleφ in the transverse plain and pseudorapidity η. A proper definition of these quantitiesand further details on the ATLAS coordinate system can be found in the appendix A.

The value of the other quantity Emeas. involved in the definition of the E/p observableis given as the sum of all topoclusters within a distance of

∆R ≤ 0.2

from the track hit in the calorimeter. Plots from E/p measurements as performed in [3],showing the dependency of 〈E/p〉 as a function of track momentum p for all pseudorapidityregions can be found in appendix C.6.

The energy within this cone around the charged track can in principle be contaminatedby the showers induced by close-by particles produced in the proton-proton collision,although the track isolation requirement suppresses possible shower contamination fromcharged particles. There is, however, no obvious way to suppress shower contaminationfrom photons, mostly produced in π0 → γγ decays, and neutral hadrons [3].

In the following (see Sections 6.1 and 6.2), we will develop and discuss a procedure ofimproving these measurements by the development of an improved method for the estim-ation of these neutral contributions to the total energy deposition, based on a comparisonof LHC data and Monte Carlo samples generated with PYTHIA [5], on reconstructed aswell as on (GEANT 4 [7] hits) truth information level.

4.5 Background subtraction

As stated before, the subtraction of the background from neutral particles to the calor-imeter response requires further investigation. The background subtraction procedure

16 4 MEASURING JETS

applied in the past will briefly be discussed here, the improvements made within thescope of this thesis explained and discussed in the following sections (see 6.1, 6.2).

The background subtraction method is based on the idea that the energy depositedin the electromagnetic calorimeter by contaminating photons and hadrons accompanyingthe track subject to the investigation is independent of the details of the hadronic showerinduced by the track. Therefore, one can select events where the charged track hadronbehaves like a minimum ionizing particle (in the following short MIP), that is, selecttracks that induce a late hadronic shower, in the following referred to as MIP-tracks. Atrack is considered a MIP track if

• the energy deposited in the electromagnetic calorimeter within a cone of r < 0.1 issmaller than 1.1GeV

• the fraction of energy deposited in the hadronic calorimeter with respect to the trackmomentum is between 0.3 and 0.9

Excluding a small region around the MIP track itself, all of the energy released in theelectromagnetic calorimeter in the periphery of the track will (due to the track isolationrequirement explained in Section 4.4) originate from showers of neutral particles. Thebackground can therefore be measured in a halo around the MIP track itself, and itsmean value over many events in a given pseudorapidity and momentum bin can thus beused as an estimate for the background energy deposition in all hadronic events.

This procedure, as proposed in [3], however, has a substancial weakness: while thebackground estimate for halo region around the MIP track leads to satisfying results,the background in the central cone of r = 0.1, e.g. the innermost cone used for the MIPselection criterium itself, cannot be estimated directly. Instead, a correction factor R0.2

0.1

was used to correct the result of the background estimate. This correction factor wasdefined as

R0.20.1 =

E0.2EM

E0.2EM − E0.1

EM(2)

≈ A0.2

A0.2 − A0.1(3)

where Ar corresponds to the base surface of a cone with radius r. In the special caseconsidered above, the correction factor can be evaluated directly to yield the value of 4/3.

Clearly, this approximation is equal to the assumption of a “flat” distribution of thebackground energy deposition density ρ (r) around the charged hadron track, such thatρ (r) at a distance r from the track has a constant value ρ0, only depending on the track

4 MEASURING JETS 17

momentum p and the pseudorapidity bin (or detector region), hence

ρ (r) ≈ ρ0. (4)

This approximation might hold for low momenta of the charged hadron track, butis questionable especially when a jet-like structure starts to evolve, i.e. for high trackmomenta. This can also be seen from the plots in the appendix C.5. Therefore, we willelaborate on finding a better approximation (see 6.1, 6.2).

18 5 IMPROVING THE BACKGROUND SUBTRACTION

5 Improving the background subtraction

As discussed in the previous sections, a precise measurement of the JES is crucial formany applications. For an E/p measurement, the ratio between the track momentummeasured by the inner detector and the corresponding signal from the electromagneticcalorimeter is calculated. Contamination of the calorimeter signal from charged particlesis avoided by imposing a track isolation requirement onto the considered tracks. However,contamination originating from neutral particles such as photons (e.g. from neutral piondecays) cannot be avoided and must be estimated. Hence, tracks considered as MIPtracks are taken into account. For these tracks, the energy deposition from the chargedtrack considered is sharply localized to an area close to the track itself. Therefore, suchevents can be considered in order to extrapolate from the measured energy density in ahalo cone around the track to a background estimate for the full cone area. The correctionfactor as defined in Section 4.5 is naturally the ratio of the energy deposition in the fullcone of r = 0.2 with respect to a halo cone with 0.1 < r < 0.2, and is denoted by R0.2

0.1 inthe following.

5.1 Definition of the terminology

In order to achieve an explicit expression for R0.20.1 or, alternatively, the average elec-

tromagnetic background energy E0.2 as a function of the track momentum p directly,large samples of Monte Carlo data on reconstructed information level, passed through aGEANT 4 simulation of the detector response (see also appendix B), including noise anddigitization of the signal, as well as on truth information level as predicted by GEANT 4,and of LHC ATLAS data, both containing detailed information about the shower con-tainment in cone halos of increasing sizes (see Figure 4) were processed, binning the eventsin terms of energy deposition for each cone size, the track momentum and pseudorapidityat which the track was measured. The resulting energy deposition density was plotted asa function of the cone radius r for different selections and observables, all of which willbe explained in the following paragraphs.

The energy deposition density ρ (r) for the discrete set of radii ri is hereby defined asthe sum of all energy depositions of topoclusters in the electromagnetic calorimeter, thegravitational centers of which are contained within a cone of radius ri, minus the sum ofall energy depositions that are already contained in a cone of radius ri−1, divided by thebase area of the halo cone, i.e.

ρ (ri) =Eri − Eri−1

Ai − Ai−1. (5)

These (differential) energy deposition densities are plotted for different data sets. The

5 IMPROVING THE BACKGROUND SUBTRACTION 19

data set displayed with black markers and referred to as “DATA” contains real collisionevents, whereas the green data set referred to as “MC Reconstructed” contains samplesof PYTHIA Monte Carlo on reconstructed information level.

There are also several data sets of samples of PYTHIA Monte Carlo on GEANT 4hits truth information level, which are split up into the different contributions. Theactual background of neutral particles we want to measure (and estimate) is depicted inlight/dark red and referred to as “MC Truth EM cont.” in the plots, denoting that theenergy density contributing to this data set is originating from all particles interactingin the electromagnetic calorimeter except for the charged hadron track itself. The othercontribution, namely “MC Truth MIP”, is depicted in blue and denotes the deposition ofthe charged hadron (or, in this terminology, “MIP”) itself.

Some data sets are depicted in two slightly different colors, depending on whether theMIP selection was applied (light colors) or whether the sample was generated from allavailable events without applying the MIP selection (dark colors).

0.05

0.1

0.075

0.125

0.15

0.175

0.2

0.225

0.25

0.3

0.4

track

Figure 4: Radii of the used cones, example MIP track energy deposition in blue.

5.2 Discussion of the central detector region

A sample pair of plots for the lowest momentum bin 1.5GeV < p < 1.8GeV in the centraldetector region can be seen in Figures 5 and 6. The full set of plots can be viewed inappendix C.1. Here, however, a couple of notable features are visible.

First of all the agreement between the forward and backward aligned pseudorapiditybin can be noted. The two distributions are consistent one with the other within statisticalfluctuations.

The MIP selected reconstructed Monte Carlo sample (green), however, does not showfull agreement with the data. In fact, the deposition for the simulated data seems toexceed the measured deposition slightly. This disagreement is a consequence of a nonperfect phenomenological description of the soft QCD interactions in the Monte Carlo.The general shape of the distribution is, however, very similar for data and Monte Carloin all momentum and pseudorapidity bins.

Note also that the sum of the MIP track contribution itself (blue) is sharply decreasingoutside r ≈ 0.1. This provides a justification of the choice of the background estimationregion as the region outside a cone with r = 0.1.

This plot also shows that the contribution from particles not associated with theprimary track is a flat function of r. Thus, the approximation explained in Section 4.5 (2)and [3] seems to be justified, at least for low track momenta.

Furthermore, the background contribution in MIP selected tracks (light red) and intracks without the MIP track requirement (dark red) is in fact quite similar, justifying theapproach described in Section 4.5 and [3] that the background is independent of detailsof the hadronic showering process.

One might note, however, that there is not only an offset between the reconstructedMonte Carlo data and the experimental data, but also between the Monte Carlo data onreconstructed and on truth level, i.e. that the sum of the MIP track contribution (blue)and the background contribution (light red) for MIP selected events is not always equal tothe reconstructed curve (green). This effect is an artifact of the topoclustering algorithm.A further investigation of this offset is ongoing, but exceeds the scope of this work.

Comparing these results to the corresponding plots in a higher momentum bin (seeFigures 7 and 8), one might draw quite similar conclusions. Again, a sharp decrease ofthe MIP deposition curve for r > 0.1 is visible, and again one finds the Monte Carlo dataat a significantly higher energy deposition than the experimental data. Note, however, afew major differences. At first, a hard drop-off of the Monte Carlo truth level backgroundfor MIP selected events (light red) can be seen with respect to the corresponding curvefor tracks without the selection requirement. This is an artifact of the bias introduced

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ATLAS work in progress

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Figure 6: Differential energy deposition for 1.5GeV < p < 1.8GeV & −0.6 < η < 0.

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Figure 8: Differential energy deposition for 4.6GeV < p < 6.0GeV & −0.6 < η < 0.


by imposing the MIP track requirement and therefore has no physical meaning. Therequirement of a low deposition in the central cone for the reconstructed informationnaturally gives preference to events with an underfluctuation of the background insidethis cone.

The most notable feature of this plot is probably the increase of the true backgroundenergy deposition density for tracks without the MIP track requirement (dark red) closeto the cone center with respect to the flat distribution for a comparably low momentum(compare to Figures 5 and 6). The slow increase of the slope of the energy density depos-ition as a function of the track momentum can be viewed in more detail in appendix C.1.This, however, gives rise to the conclusion that the estimation of a flat background doesnot hold any longer for higher track momenta.

5.3 Discussion of the forward and backward detector regions

Comparable results can be obtained – although not with the same amount of clarity – forthe more forward (or backward) detector regions (see Figures 11 and 12), correspondingto higher values of pseudorapidity. Note that the momentum bins chosen here differfrom the ones chosen above. Although this might be irritating at first sight, a choiceof the same momentum bin would not be of greater physical meaning, since a similarabsolute momentum does not imply a similar transverse momentum for different regionsof pseudorapidity. This manifests in the fact that, of course, pT ≤ p. Therefore, some plotsin appendix C.1 – especially those for low momenta and high values of pseudorapidity –will be found missing due to lack of statistics in these bins.

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Figure 10: Differential energy deposition for 3.6GeV < p < 4.6GeV &−1.4 < η < −1.1

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Figure 12: Differential energy deposition for 6.0GeV < p < 10.0GeV &−1.4 < η < −1.1

26 6 THE PARAMETRIC APPROACH

6 The parametric approach

In this section, we will develop, apply and investigate a method to parametrize the back-ground from neutral particles in a linear way. First, we will derive an extrapolationmethod, making simple assumptions about the shape of the background energy depos-ition density distribution. Then, in the second part, we will apply this extrapolationmethod and discuss the results obtained.

6.1 Derivation

We consider the energy deposition Ei in a cone of radius ri (i = 0, . . . , n). In the following,we will consider the base area Ai = πr2i of the cone.

To avoid biasing the result with the a priori unknown contribution from the trackitself, we concentrate on the energy deposition in the annuli, which is given as

∆Ei = Ei − Ei−1

with i = 1, . . . n. For r ' r0, we expect this deposition to be free from contaminationfrom the central track energy deposition, where r0 is the typical radial dimension of thecentral track, which is also a priori unknown, but can be estimated to be r0 ≈ 0.1 fromthe plots shown in Section 5.

We also need to deal with the increasing area of the annuli. Therefore, we will in thefollowing consider the differential energy deposition density ρ, which we will define as

ρ =∂E

∂A

such that for the finite difference ∆i between the cones number (i) and (i− 1) respectively,we find

ρi =∆Ei∆Ai

.

We are interested in the correction factor Rts (p) (see also (2) in Section 4.5), which

we define as the ratio between the total background energy deposition in a cone of r = t

with respect to the deposition in the annulus with s < r < t, the latter being equal to thedifference between the deposition in the cone of r = t and in the cone of r = s, such that

Rts (p) =

E (p, r = t)

E (p, r = t)− E (p, r = s)(6)

=

[1− E (p, s)

E (p, t)

]−1. (7)

6 THE PARAMETRIC APPROACH 27

Therefore, we seek to find an expression for the total background energy depositionE (p, r). Using the above definition of the energy deposition density ρ, we can use thisquantity to express E in the form

E =

∫A

ρdA,

suppressing the dependency of the momentum p in the notation for the sake of simplicity.We can then write

E (r) =

∫ 2π

0

dϕ

∫ r

0

r′dr′ρ

which can be simplified by the assumption that the deposition density ρ = ρ (r) is inde-pendent of the angle ϕ to hold

E (r) = 2π

∫ r

0

ρ (r′) r′dr′. (8)

If we now assume that ρ (r) is a linear function of r such that

ρ (r) = ar + b (9)

we can carry out the integral to yield an expression for the total energy deposition, thatis

E (r) =2πa

3r3 + bπr2. (10)

Considering now that the values of a and b are obtained through a fit, the result ofthis calculation can be improved by choosing the fit parameters in a way such that thecorrelation between them is as small as possible. This can be done by parametrizing thelinear function in terms of two points, which are preferredly located at the limits of thefit interval I = [r1, r2] with r1 < r2, such that the new fit parameters are ρ1 and ρ2, thevalues of the energy deposition density at the fit range limits.

Since we now wish to express the old fit parameters in terms of the new ones, weconsider the linear function

ρ (r) =ρ2 − ρ1r2 − r1

· (r − r1) + ρ1 (11)

which passes through (r1, ρ1) and (r2, ρ2) (and is, of course, unique). By slightly rewritingthis equation to

ρ (r) =ρ2 − ρ1r2 − r1

· r + ρ1 −ρ2 − ρ1r2 − r1

· r1


and comparing to (9), we can easily identify

ρ2 − ρ1r2 − r1

= a (12)

ρ1 −ρ2 − ρ1r2 − r1

· r1 = b. (13)

Hence, (10) yields

E (r) =2π

3

[ρ2 − ρ1r2 − r1

]r3 +

[ρ1 −

ρ2 − ρ1r2 − r1

· r1]πr2. (14)

Remembering that the total energy deposition is a function of the track momentump, i.e., E = E (p, r), we now see that the fit parameters must depend on p, such that theρi = ρi (p) are also functions of p. Hence, the question arises whether what the resultingfunctional dependency of E (p, r) of the track momentum is, or – more precisely – howthe functional dependency of ρi (p) propagates to E (p, r). This question can easily beanswered by rewriting (14) in the form

E (r) =2π

3

[r3

r2 − r1

]ρ2 −

2π

3

[r3

r2 − r1

]ρ1 −

[πr2r1r2 − r1

]ρ2 +

[πr2r1r2 − r1

]ρ1 + πr2ρ1

=

[(2r

3− r1

)1

r2 − r1

]ρ2πr

2 −[(

2r

3− r1

)1

r2 − r1+ 1

]ρ1πr

2

yielding that the dependency of E is linear in both parameters ρi. Therefore, any func-tional dependency ρi (p) will directly translate in a linear way to the functional depend-ency of E (p). Physically speaking, we just calculated that if the energy deposition densityshows a particular functional dependency as a function of the momentum, then the totalenergy deposition will show the exact same dependency, which also meets intuition.

Recalling that the ρi are nothing else than the measured (or extrapolated) energydeposition densities at the fit range limits ri, the simplest assumption is that the ρi (p)are themselves linear functions of p, i.e.

ρi (p) =ρ2i − ρ1ip2 − p1

· (p− p1) + ρ1i (15)

where pj denotes the average track momentum corresponding to ρji . Inserting (15) fori = 1, 2 into (12) and (13) yields

a (p) =ρ21 − ρ11 − ρ22 + ρ12(p2 − p1) (r2 − r1)

· (p− p1) +ρ11 − ρ12

(r2 − r1)= α1p+ α2

b (p) =

[ρ21 − ρ11

(p2 − p1)− ρ21 − ρ11 − ρ22 + ρ12

(p2 − p1) (r2 − r1)· r1]· (p− p1) + ρ11 −

ρ11 − ρ12(r2 − r1)

· r1

= β1p+ β2


which allows us to calculate E (p, r) in terms of αk and βk, such that

E (p, r) =2π

3a (p) r3 + πb (p) r2

=

(2π

3α1r

3 + πβ1r2

)p+

(2π

3α2r

3 + πβ2r2

)= pc1 (r) + c2 (r) .

Recalling that the quantity we are interested in is the correction factor Rts (p), which is

given by (7) and is only dependent on the value of the total background energy depositionE (p, r) at two specific values r = s, t, we can treat the crk as parameters (instead offunctions) and obtain their values for r = s, t performing a fit of the form

E (p; r) = pcr1 + cr2

or, equivalently,

E (p; r) =Er

2 − Er1

p2 − p1(p− p1) + Er

1

to some values of E (p; r), calculated via (14) for r = s, t, making use of values for ρipreviously obtained. Here, the crk (or the Er

k respectively) are fit parameters (for k = 1, 2)for both r-values of our interest (namely for r = s, t), such that we can calculate Rt

s (p)

from (7) as a function of p via

Rts (p) =

[1− E (p, s)

E (p, t)

]−1=

[1− pcs1 + cs2

pct1 + ct2

]−1or, again equivalent to that,

Rts (p) =

[1− (Es

2 − Es1) (p− p1) + Es

1 (p2 − p1)(Et

2 − Et1) (p− p1) + Et

1 (p2 − p1)

]−1=

[1− (Es

2 − Es1) p+ Es

1p2 − Es2p1

(Et2 − Et

1) p+ Et1p2 − Et

2p1

]−1. (16)

6.2 Discussion

As discussed in the Section 5, a clearly visible increase of the background for the areadirectly around the MIP track could be observed. In proposing the parametric approachwe suggested a linear approximation of the energy deposition density distribution as afunction of the distance r from the charged track. This approximation was done byperforming a linear fit to the measured energy deposition density in the interval [0.1, 0.26].The fitting interval was chosen such that we are safely contained between inner regionof r < 0.1 which is biased by the MIP track requirement (as discussed in Section 5) andthe outer region r > 0.4 which might be biased by the track isolation requirement (seeSection 4.5).

The result of this approximation, again for the same pseudorapidity regions discussedin the previous sections, is shown in Figures 13, 14, 15 and 16 for the central detectorregions and in Figures 19, 20, 21 and 22 for the more forward and backward detectorregions.

Note how the slopes of the ATLAS data and the PYTHIA Monte Carlo on recon-structed as well as on truth information level agree. All fit results can again be viewedin appendix C.2. Note also that the Monte Carlo data for the background on truth in-formation level is represented in good approximation by the linear function for the dataset without the MIP track requirement (dark red).

In order to exclude that the result is biased by possibly different typical cluster sizesfor clusters associated with the central track for data and Monte Carlo simulated data, thedistributions for the Monte Carlo data on truth information level were plotted separatelyfor large (large root mean square deviation (RMS) of the energy density distributionwithin the cluster) and small (small RMS) clusters (see Figures 17 and 18). Althoughthere is a difference in the region close to the central track, as one would expect, theseplots show that the two distributions agree within statistical fluctuations in the rangeused for the fitting, indicated by the vertical lines. The corresponding distributions forother momentum and pseudorapidity bins can also be found in appendix C.4.

For the more forward and backward detector regions, one finds that the agreementbetween the slopes of data and Monte Carlo decreases. This is, however, not a problem.Even a disagreement of the slopes (as seen in Figures 21 and 22) where the parametriz-ation predicts a flat behaviour of the background in the central cone is only equal to theold approximation method (explained in Section 4.5, [3]) which assumed the backgroundto be a flat function regardless of track momentum and pseudorapidity.

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Figure 14: Linear approximation to differential energy depositionfor 1.5GeV < p < 1.8GeV & −0.6 < η < 0.

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5







>1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV < p < 6.0 GeV

< 0.0η0.6 <

Figure 16: Linear approximation to differential energy depositionfor 4.6GeV < p < 6.0GeV & −0.6 < η < 0.

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/Ge

Vρ

0

0.5

1

1.5

2

2.5

3

MC Truth EM cont. (low RMS, 29691 tracks)

MC Truth EM cont. (high RMS, 9755 tracks)ATLAS work in progress

>1.5 GeVT

all tracks with p

3.6 GeV < p < 4.6 GeV

< 0.6η0.0 <

Figure 17: Comparison of differential energy deposition for 3.6GeV 1.5 GeVT

all tracks with p

3.6 GeV < p < 4.6 GeV

< 0.0η0.6 <

Figure 18: Comparison of differential energy deposition for 3.6GeV < p < 4.6GeV& −0.6 < η < 0.0 for wide (high RMS) and narrow (low RMS) clusters.

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/Ge

Vρ

0

1

2

3

4

5

6

7

8

9

10







>1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV < p < 4.6 GeV

< 1.1η1.4 <

Figure 20: Linear approximation to differential energy depositionfor 3.6GeV < p < 4.6GeV & −1.4 < η < −1.1.

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/Ge

Vρ

0

1

2

3

4

5

6

7

8

9

10







>1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV < p < 10.0 GeV

< 1.1η1.4 <

Figure 22: Linear approximation to differential energy depositionfor 6.0GeV < p < 10.0GeV & −1.4 < η < −1.1.


Based on the successful linear parametrization of the data set, we can now try toexpress the total energy deposition in a cone of any desired size as a function of the trackmomentum. Hence, the mean track momentum of all tracks contributing to each data setin a given bin was computed respectively, as well as the integral over the parametrizationfrom r = 0 to the radius of the desired cone expressed as a function of this (average)track momentum. As explained in the previous section, this is also expected to behavelike a linear function in the same approximation as above. This can in fact be seen to bein reasonable agreement with the data (see Figures 23, 24, 25 and 26).

From this result, we can calculate the desired correction factor R0.20.1 directly. Note,

however, that the quantity needed for the estimation of the E/p background is actually theneutral background in a cone of r = 0.2, which is precisely the result obtained for E0.2 (p).Thus, one could equivalently also use the result already obtained.

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

MC Reconstructed (MIP tracks)

MC Truth EM (all tracks)

DATA (MIP tracks)

ATLAS work in progress(p) for tracks

0.1

1E>1.5 GeV

Twith p

< 0.6η0.0 <

Figure 23: Total background energy deposition in a cone of r = 0.1

for 0.0 < η < 0.6 as a function of the track momentum p.

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 0.0η0.6 <

Figure 24: Total energy deposition in a cone of r = 0.1 for −0.6 < η < 0.0 as afunction of the track momentum p.

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 0.6η0.0 <

Figure 25: Total energy deposition in a cone of r = 0.2 for 0.0 < η < 0.6 as afunction of the track momentum p.

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 0.0η0.6 <

Figure 26: Total background energy deposition in a cone of r = 0.2

for −0.6 < η < 0.0 as a function of track momentum p.

7 RESULTS 39

7 Results

In this section, we will briefly review the results obtained in Section 6.2 in the context ofthe considerations made previously (see Sections 4.4 and 4.5).

7.1 Results on E/p measurements

Making use of the results for the total background energy deposition Er (p) in cones ofr = 0.1 and r = 0.2 as functions of the track momentum p for all pseudorapidity binsrespectively obtained in Section 6.2, we can use equation 16 as derived in Section 6.1to calculate a momentum-based correction factor for the background subtracted in thecontext of E/p measurements (see Sections 4.4 and 4.5).

A new analysis of the considered 2010 data at√s = 7TeV was performed, using the

momentum-based correction factor R0.20.1 (p) as defined in Section 6.1 (see equation 6) and

the fit results obtained and discussed in Section 6.2.

The resulting E/p distributions can be found in appendix C.7 and compared withthe corresponding results for the previously used correction factor of R = 4/3, found inappendix C.6. The difference is, however, small.

As can be seen in Figures 27 and 28, the old background estimation method yieldsa backgorund estimate which is of the order of 10% lower than the new backgroundestimation method. This might be surprising at first sight when comparing to the plotsin Section 6.2, which clearly show that the background energy density deposition as afunction of the distance from the charged track is not constant, especially close to thetrack itself. But, since the difference occurs mainly in the cone centers, and since the totalarea in which the background contribution is significantly higher than estimated previouslyis comparably small, the total error arising from the “flat” background estimation is alsosmall. This shows that, although the discussion in Section 6.2 came to the conclusion thatthe assumption of a “flat” background in the innermost cone is not completely justified,the formerly applied procedure based on this assumption does not suffer from a largesystematic error. As a matter of optimization, however, the improved, parametric andmomentum-based correction method proposed in this thesis should be used for futuremeasurements.

40 7 RESULTS

p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1

< 0.6η0.0 < Monte Carlo background estimate with R=3/4

(p)η

Monte Carlo background estimate with R=R(p)

ηData background estimate with R=RData background estimate with R=3/4


Figure 27: E/p background distributions for 0.0 < η < 0.6 for the different correctionfactors respectively.

p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1


(p)η




Figure 28: E/p background distributions for −0.6 < η < 0.0 for the differentcorrection factors respectively.

7 RESULTS 41

7.2 Conclusions

The background estimation method for E/p measurements of the single hadron responseof the ATLAS calorimeter system was reviewed. The results obtained in Section 5 clearlyshow that the assumption of a “flat” background distribution does not hold in the regionclose to the track, especially for high track momenta. The solution proposed in Section 6.1was a parametric approach, trying to parametrize the differential energy deposition as afunction of distance from the charged track with a linear function. The results obtainedfrom this calculation have led to a new method to estimate the background correctionfactor based on the track momentum, see Section 6.2.

The impact of this new correction method on the E/p measurements is, however,small. Although the difference between the estimated “flat” background and the actualbackground energy deposition is large close to the track, the resulting integrated totalenergy deposition does not differ by much because of the decreasing weight given to theenergy deposition density for small radii. The underestimate of the background resultingfrom the previously made assumption does barely exceed 10%, leading to the comfortingconclusion that the results obtained by previous measurements are already accurate toa high degree, although the accuracy could be pushed further making use of the resultsobtained in this thesis.

7.3 Outlook

Although the corrections calculated on top of the background estimate were already small,a precise investigation of some of the plots shown in the appendix C.2 demonstrates thatthe assumption of a linear dependency of the energy deposition density as a functionof distance from the track is also not completely justified in some cases. However, anyassumption of a parametric model without clear physical motivation will impose a bias.While the assumption of simple models can often be motivated by their simplicity, morecomplex models always impose the danger of overfitting, especially if the number of datapoints accessible is low. One way of overcoming this danger is the consideration of largersets of data, which is expensive, though. Another possibility would be the use of non-parametric models, such as bayesian modelling techniques. Approaches to estimate thebackground with such models, using approved non-parametric algorithms such as krieging(see, e.g., [16]) have been made, but did not yet lead to significantly improved resultscompared to the simple parametric model proposed here. A further investigation of thesemodels would, however, be interesting.

42 PAGE 42

REFERENCES v

References

[1] ATLAS Collaboration. Jet energy scale and its systematic uncertainty for jets pro-duced in proton-proton collisions at

√s = 7 TeV and measured with the ATLAS

detector. ATLAS-CONF, 2010-056:23, July 22 2010. 13, 14

[2] ATLAS Collaboration. Response of the ATLAS calorimeters to single isolated had-rons produced in proton–proton collisions at a center–of–mass energy of

√s = 900

GeV. ATLAS-CONF, 2010-017:11, April 8 2010. 14, 15

[3] ATLAS Collaboration. ATLAS calorimeter response to single isolated hadrons andestimation of the calorimeter jet scale uncertainty. ATLAS-CONF, 2010-052:23, July16 2010. 14, 15, 16, 20, 30

[4] ATLAS Collaboration. ATLAS calorimeter response to single isolated hadrons and es-timation of the calorimeter jet scale uncertainty. ATLAS-CONF, 2011-028:16, March22 2011. 14

[5] Torbjörn Sjöstrand, Stephen Mrennab, and Peter Skandsc. PYTHIA 6.4 physics andmanual. Journal of High Energy Physics, 026:583, 2006. 15, 45

[6] ATLAS Collaboration. Charged-particle multiplicities in pp interactions measuredwith the ATLAS detector at the LHC. CERN-PH-EP, 2010-079:70, February 9 2011.45

[7] S. Agostinelli et al. Geant4 – a simulation toolkit. Nuclear Instruments and Methodsin Physics Research Section A: Accelerators, Spectrometers, Detectors and AssociatedEquipment, 506:issue 3, 250–303, 2003. 15, 45

[8] Lyndon Evans and Philip Bryant. The LHC machine. Journal of Instrumentation,The CERN Large Hadron Collider: Accelerator and Experiments:164, August 2008.http://jinst.sissa.it/LHC/LHCmachine/2008_JINST_3_S08001.pdf. 5

[9] ALICE Collaboration. The ALICE experiment at the CERN LHC. Journal of In-strumentation, The CERN Large Hadron Collider: Accelerator and Experiments:259,August 2008. http://jinst.sissa.it/LHC/ALICE/2008_JINST_3_S08002.pdf. 5

[10] LHCb Collaboration. The LHCb detector at the LHC. Journal of Instrumentation,The CERN Large Hadron Collider: Accelerator and Experiments:217, August 2008.http://jinst.sissa.it/LHC/LHCb/2008_JINST_3_S08005.pdf. 6

[11] CMS Collaboration. The CMS experiment at the CERN LHC. Journal of Instru-mentation, The CERN Large Hadron Collider: Accelerator and Experiments:361,August 2008. http://jinst.sissa.it/LHC/CMS/2008_JINST_3_S08004.pdf. 7

http://jinst.sissa.it/LHC/LHCmachine/2008_JINST_3_S08001.pdf

http://jinst.sissa.it/LHC/ALICE/2008_JINST_3_S08002.pdf

http://jinst.sissa.it/LHC/LHCb/2008_JINST_3_S08005.pdf

http://jinst.sissa.it/LHC/CMS/2008_JINST_3_S08004.pdf

vi REFERENCES

[12] ATLAS Collaboration. The ATLAS experiment at the CERN LHC. Journal of In-strumentation, The CERN Large Hadron Collider: Accelerator and Experiments:437,August 2008. http://jinst.sissa.it/LHC/ATLAS/2008_JINST_3_S08003.pdf. 7, 8, 12, vii

[13] Richard Wigmans. Calorimetry – Energy Measurement in Particle Physics. Number107 in International Series of Monographs on Physics. Oxford University Press, TexasTech University, 2000. ISBN 978-0-198-50296-6. 9, 11

[14] David Griffiths. Introduction to Elementary Particles. Wiley-VCH, 2004. ISBN978-0-471-60386-3. 6, 9, 43

[15] Francis Halzen and Alan D. Martin. Quarks and Leptons – An Introductory Coursein Modern Particle Physics. John Wiley & Sons, 1984. ISBN 978-0-471-88741-2. 6,9, 43

[16] Carl Edward Rasmussen and Christopher K. I. Williams. Gaussian Processes forMachine Learning. The MIT Press, 2006. ISBN 978-0-262-18253-X, http://www.

GaussianProcess.org/gpml. 41

http://jinst.sissa.it/LHC/ATLAS/2008_JINST_3_S08003.pdf

http://www.GaussianProcess.org/gpml

http://www.GaussianProcess.org/gpml

LIST OF FIGURES vii

List of Figures

1 CERN overview and LHC tunnelhttp://lhcb.web.cern.ch/lhcb-public/Objects/Detector/CERNMap.pdf . . . . . 4

2 The ATLAS Detector. Reproduced from [12] with kind permission from IOP Pub-

lishing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 The ATLAS Calorimeter system. Reproduced from [12] with kind permission from

IOP Publishing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Cone Radii and example MIP track energy deposition . . . . . . . . . . . . 19

5 Differential energy deposition for 1.5GeV < p < 1.8GeV & 0 < η < 0.6. . 21

6 Differential energy deposition for 1.5GeV < p < 1.8GeV & −0.6 < η < 0. 21

7 Differential energy deposition for 4.6GeV < p < 6.0GeV & 0 < η < 0.6. . 22

8 Differential energy deposition for 4.6GeV < p < 6.0GeV & −0.6 < η < 0. 22

9 Differential energy deposition for 3.6GeV < p < 4.6GeV & 1.1 < η < 1.4 . 24

10 Differential energy deposition for 3.6GeV < p < 4.6GeV & −1.4 < η <

−1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

11 Differential energy deposition for 6.0GeV < p < 10.0GeV & 1.1 < η < 1.4 25

12 Differential energy deposition for 6.0GeV < p < 10.0GeV & −1.4 < η <

−1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

13 Linear approximation to differential energy deposition for 1.5GeV < p < 1.8GeV& 0.0 < η < 0.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

14 Linear approximation to differential energy deposition for 1.5GeV < p < 1.8GeV& −0.6 < η < 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31


16 Linear approximation to differential energy deposition for 4.6GeV < p < 6.0GeV& −0.6 < η < 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

17 Comparison of differential energy deposition for 3.6GeV < p < 4.6GeV& 0.0 < η < 0.6 for wide (high RMS) and narrow (low RMS) clusters. . 33

18 Comparison of differential energy deposition for 3.6GeV < p < 4.6GeV& −0.6 < η < 0.0 for wide (high RMS) and narrow (low RMS) clusters. 33


http://lhcb.web.cern.ch/lhcb-public/Objects/Detector/CERNMap.pdf

viii LIST OF FIGURES

20 Linear approximation to differential energy deposition for 3.6GeV < p < 4.6GeV& −1.4 < η < −1.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34


22 Linear approximation to differential energy deposition for 6.0GeV < p < 10.0GeV& −1.4 < η < −1.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

23 Total background energy deposition in a cone of r = 0.1 for 0.0 < η < 0.6

as a function of the track momentum p. . . . . . . . . . . . . . . . . . . . . 37

24 Total energy deposition in a cone of r = 0.1 for −0.6 < η < 0.0 as afunction of the track momentum p. . . . . . . . . . . . . . . . . . . . . . . 37

25 Total energy deposition in a cone of r = 0.2 for 0.0 < η < 0.6 as afunction of the track momentum p. . . . . . . . . . . . . . . . . . . . . . . 38

26 Total background energy deposition in a cone of r = 0.2 for−0.6 < η < 0.0

as a function of track momentum p. . . . . . . . . . . . . . . . . . . . . . . 38

27 E/p background distributions for 0.0 < η < 0.6 for the different correctionfactors respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

28 E/p background distributions for −0.6 < η < 0.0 for the different correc-tion factors respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

29 Plot of η vs. polar angle θhttp://upload.wikimedia.org/wikipedia/commons/3/30/Pseudorapidity2.png . . 44

http://upload.wikimedia.org/wikipedia/commons/3/30/Pseudorapidity2.png

ACKNOWLEDGEMENTS ix

Acknowledgements

First of all, I want to thank my advisor Dr. Iacopo Vivarelli for his continuous support,including constructive and always polite criticism regarding my results and the way Ipresent them, and nearly infinite amounts of time for answering questions and makingsuggestions. I especially want to thank him for the possibility to join him on a visit toCERN, a truly inspiring opportunity. Thanks for numerous suggestions and constructivecriticism also go to Dr. Michael Duehrssen.

I also want to thank Prof. Dr. Karl Jakobs for the opportunity to write my thesis inhis group, and to participate in a such a fascinating project as the ATLAS collaboration.I also want to thank the other members of his group for welcoming me during the threemonths I spent writing my thesis.

Special thanks go to Dr. Cyrill Stachniss and Axel Rottman for a short introductionto krieging, although the work related to this did not make it to the final version of thisthesis.

Great thanks go to my parents for their continuous support, and favours beyondthinking. Special thanks also go to Freya for understanding I had little time for the sunnysides of life while working on my thesis. The latter, of course, also extends to many ofmy other friends, to whom I want to apologize for this and whom I also want to thankfor their understanding.

Carsten Burgard

x ACKNOWLEDGEMENTS

A THE ATLAS COORDINATE SYSTEM 43

A The ATLAS coordinate system

The coordinate system of ATLAS is a right-handed one, with the x axis pointing inradial direction towards the center of circle which the LHC tunnel describes, and thez-axis pointing along a tangent to the LHC tunnel tube center. The y-axis however isslightly tilted with respect to the vertical due to the general tilt of the tunnel, amountingto a total deviation from the vertical of approximately 1.5◦.

The usual coordinates are rT , η and φ, where rT is the distance from the beam axisitself (which is equal to the z-axis) and φ is the angle of the track in the transversal plain.The coordinate η denotes the pseudorapidity, usually defined as

η = − ln tanθ

2

where θ denotes the polar angle with respect to the beam (or z-) axis. This choice of ηas a suitable coordinate can easily be explained, considering that the LHC is a proton-proton collider. In the central interaction vertex, two partons collide, each carrying afraction x of the total momentum of the proton (which is sometimes denoted as xBj

and referred to as Bjorken- or Feynman-x [14, 15]). The precise value of x is of coursedifferent for both partners in every single interaction, and more or less random, followinga certain distribution given by the parton density functions, which in turn depend on themomentum transfer of the interaction. The relative velocity of the center-of-mass frameof the collision along the beam axis with respect to the detector is therefore a priori notknown.

Consequently, one wants to choose a coordinate system which is invariant underLorentz-transformations in the direction of the beam axis. This gives rise to the quantityη as defined above. Although η is not Lorentz-invariant (strictly speaking), the use ofη (instead of the polar angle θ against the beam axis) has some advantages. The pseu-dorapidity η is (as the name might suggest) very closely related to the rapidity y. Thiscan be shown very easily.

y = arc tanh(pzE

)def.=

1

2ln

(1 + pz

E

1− pzE

)=

1

2ln

(E + pzE − pz

)E�mc2≈ 1

2ln

(|~p|+ pL|~p| − pL

)= − ln

√|~p| − pL|~p|+ pL

= − ln

√1− cos θ

1 + cos θ

def.= − ln tan

θ

2

= η

44 A THE ATLAS COORDINATE SYSTEM

The rapidity y is indeed not Lorentz invariant either, but differences in rapidity are.Thus, any quantity ∆y will be Lorentz invariant – and therefore also differences in pseu-dorapidity in an approximate manner.

Since the pseudorapidity η can directly be calculated from the polar angle θ, theconsequent use of η as a coordinate with respect to the beam axis provides many practicaladvantages. The value η = 0 here corresponds to the transversal plain in the central regionof the detector, i.e. θ = π/2, whereas points along the beam axis correspond to infinitevalues of pseudorapidity. Although this might seem like a disadvantage, pseudorapidityvalues one has to deal with usually do not exceed η ≈ 5 due to the limited forward andbackward region coverage of the detector. Some examples for value pairs of η and θ arevisualized in figure 29.

Figure 29: Plot of η vs. polar angle θ

Since every track in an event is expressed in values of η and φ, all geometric quantitiesare defined based on these coordinates. Of particular importance for us is the distance∆R between two tracks, which is defined as

∆R =

√(∆η)2 + (∆φ)2

which is in an idealized view independent of the distance rT from the beam axis at whichit is measured. This is of course not true when taking into account changes in directionresulting from interaction with the detector material or with the magnetic field of theinner detector silicon tracker.

B MONTE CARLO SIMULATION 45

B Monte Carlo Simulation

The Monte Carlo samples used for this work correspond to a set of approximately 50million non diffractive minimum bias events. Approximately half of the simulated eventshave a filter selecting a 3.5GeV leading charged particle at generator level, in order toincrease the available number of events for high track momenta.

PYTHIA 6.4 [5] has been used for the generation of the events. The PYTHIA tuningcorresponds to AMBT1 (ATLAS Minimum Bias Tune 1) [6]. The detector response hasbeen simulated using GEANT 4 [7], with the Calibration Hits and ParticleID featuresenabled. The former keeps track of the energy deposited at GEANT 4 hit level andclassifies into different categories depending on whether the energy is visible or invisiblefor measurement purposes. The latter keeps track of the association of each hit to theparticle that generated it, therefore allowing (for the purposes of this work) for associationof the true energy deposit to the neutral background or the signal.

The MC simulated events have been reconstructed and analyzed using the same soft-ware used for real data.

46 C COLLECTION OF ALL PLOTS

C Collection of all plots

C.1 Energy deposition density

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< 0.0η0.6 <

C COLLECTION OF ALL PLOTS 47

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/GeV

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3.6 GeV < p < 4.6 GeV

< 1.4η1.5 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

2

4

6

8

10

12







>1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV < p < 4.6 GeV

< 1.5η1.8 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6







>1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV < p < 6.0 GeV

< 1.8η1.9 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6







>1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV < p < 10.0 GeV

< 1.9η2.3 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

5

10

15

20

25

30







>1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

1.5 GeV 1.5 GeVT

tracks with p

1.5 GeV 1.5 GeVT

tracks with p

1.8 GeV 1.5 GeVT

tracks with p

1.8 GeV < p < 2.2 GeV

< 0.0η0.6 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5







>1.5 GeVT

tracks with p

2.2 GeV 1.5 GeVT

tracks with p

2.2 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV < p < 6.0 GeV

< 0.0η0.6 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6







>1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

1.8 GeV 1.5 GeVT

tracks with p

1.8 GeV 1.5 GeVT

tracks with p

2.2 GeV 1.5 GeVT

tracks with p

2.2 GeV < p < 2.8 GeV

< 0.6η1.1 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6







>1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV < p < 10.0 GeV

< 0.6η1.1 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6

7

8

9

10







>1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

2.2 GeV 1.5 GeVT

tracks with p

2.2 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV < p < 4.6 GeV

< 1.1η1.4 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6







>1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

2.8 GeV < p < 3.6 GeV

< 1.4η1.5 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6

7

8

9

10







>1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV < p

< 1.4η1.5 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6







>1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV < p

< 1.5η1.8 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6







>1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV < p < 6.0 GeV

< 1.9η2.3 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6

7

8

9

10







>1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV < p

< 1.9η2.3 <

C.3 Linear approximation of the energy deposition as a functionof track momentum

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 0.6η0.0 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 0.0η0.6 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 1.1η0.6 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 0.6η1.1 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 1.4η1.1 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 1.1η1.4 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 1.5η1.4 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 1.4η1.5 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 1.8η1.5 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 1.5η1.8 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 1.9η1.8 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 1.8η1.9 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 2.3η1.9 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



DATA (MIP tracks)


0.1

1E>1.5 GeV

Twith p

< 1.9η2.3 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 0.6η0.0 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 0.0η0.6 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 1.1η0.6 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 0.6η1.1 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 1.4η1.1 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 1.1η1.4 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.2

0.4

0.6

0.8

1

1.2

1.4



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 1.5η1.4 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.2

0.4

0.6

0.8

1

1.2

1.4



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 1.4η1.5 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.2

0.4

0.6

0.8

1

1.2

1.4



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 1.8η1.5 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.2

0.4

0.6

0.8

1

1.2

1.4



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 1.5η1.8 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 1.9η1.8 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 1.8η1.9 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.2

0.4

0.6

0.8

1

1.2

1.4



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 2.3η1.9 <

p/MeV/c

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

E/G

eV

0

0.2

0.4

0.6

0.8

1

1.2

1.4



DATA (MIP tracks)


0.2

2E>1.5 GeV

Twith p

< 1.9η2.3 <

C.4 Comparison of jet energy deposition density for wide andnarrow clusters (radial RMS)

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2MC Truth EM cont. (low RMS, 5535 tracks)


>1.5 GeVT

all tracks with p

1.5 GeV 1.5 GeVT

all tracks with p

1.5 GeV 1.5 GeVT

all tracks with p

1.8 GeV 1.5 GeVT

all tracks with p

1.8 GeV < p < 2.2 GeV

< 0.0η0.6 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8



>1.5 GeVT

all tracks with p

2.2 GeV 1.5 GeVT

all tracks with p

2.2 GeV 1.5 GeVT

all tracks with p

2.8 GeV 1.5 GeVT

all tracks with p

2.8 GeV 1.5 GeVT

all tracks with p

3.6 GeV 1.5 GeVT

all tracks with p

3.6 GeV 1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

4.6 GeV < p < 6.0 GeV

< 0.0η0.6 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5



>1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV 1.5 GeVT

all tracks with p

1.8 GeV 1.5 GeVT

all tracks with p

1.8 GeV 1.5 GeVT

all tracks with p

2.2 GeV 1.5 GeVT

all tracks with p

2.2 GeV < p < 2.8 GeV

< 0.6η1.1 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8



>1.5 GeVT

all tracks with p

2.8 GeV 1.5 GeVT

all tracks with p

2.8 GeV 1.5 GeVT

all tracks with p

3.6 GeV 1.5 GeVT

all tracks with p

3.6 GeV 1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

6.0 GeV < p < 10.0 GeV

< 0.6η1.1 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6

7

8

9

10



>1.5 GeVT

all tracks with p

10.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV 1.5 GeVT

all tracks with p

2.2 GeV 1.5 GeVT

all tracks with p

2.2 GeV 1.5 GeVT

all tracks with p

2.8 GeV 1.5 GeVT

all tracks with p

2.8 GeV 1.5 GeVT

all tracks with p

3.6 GeV 1.5 GeVT

all tracks with p

3.6 GeV < p < 4.6 GeV

< 1.1η1.4 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.5

1

1.5

2

2.5

3



>1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV 1.5 GeVT

all tracks with p

2.8 GeV 1.5 GeVT

all tracks with p

2.8 GeV < p < 3.6 GeV

< 1.4η1.5 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.5

1

1.5

2

2.5

3



>1.5 GeVT

all tracks with p

3.6 GeV 1.5 GeVT

all tracks with p

3.6 GeV 1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV < p

< 1.4η1.5 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6



>1.5 GeVT

all tracks with p

2.8 GeV 1.5 GeVT

all tracks with p

2.8 GeV 1.5 GeVT

all tracks with p

3.6 GeV 1.5 GeVT

all tracks with p

3.6 GeV 1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

6.0 GeV < p < 10.0 GeV

< 1.5η1.8 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5



>1.5 GeVT

all tracks with p

10.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV 1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV < p

< 1.8η1.9 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5



>1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

4.6 GeV 1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

6.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV 1.5 GeVT

all tracks with p

10.0 GeV < p

< 1.9η2.3 <

C.5 Background estimation

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5


MC Truth EM cont. (7661 tracks, no MIP sel.)ATLAS work in progress

>1.5 GeVT

tracks with p

1.5 GeV 1.5 GeVT

tracks with p

1.5 GeV 1.5 GeVT

tracks with p

1.8 GeV 1.5 GeVT

tracks with p

1.8 GeV 1.5 GeVT

tracks with p

2.2 GeV 1.5 GeVT

tracks with p

2.2 GeV < p < 2.8 GeV

< 0.0η0.6 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5



>1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV < p < 10.0 GeV

< 0.0η0.6 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

2

4

6

8

10

12

14

16

18

20



>1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

1.8 GeV 1.5 GeVT

tracks with p

1.8 GeV 1.5 GeVT

tracks with p

2.2 GeV 1.5 GeVT

tracks with p

2.2 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

2.8 GeV < p < 3.6 GeV

< 0.6η1.1 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6



>1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV < p

< 0.6η1.1 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5



>1.5 GeVT

tracks with p

2.2 GeV 1.5 GeVT

tracks with p

2.2 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV < p < 6.0 GeV

< 1.1η1.4 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6

7

8

9

10



>1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

2.8 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV < p < 4.6 GeV

< 1.4η1.5 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

2

4

6

8

10

12



>1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

3.6 GeV 1.5 GeVT

tracks with p

3.6 GeV < p < 4.6 GeV

< 1.5η1.8 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5



>1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV < p < 6.0 GeV

< 1.8η1.9 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

1

2

3

4

5

6



>1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

4.6 GeV 1.5 GeVT

tracks with p

6.0 GeV 1.5 GeVT

tracks with p

6.0 GeV < p < 10.0 GeV

< 1.9η2.3 <

r0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

/GeV

ρ

0

5

10

15

20

25

30



>1.5 GeVT

tracks with p

10.0 GeV 1.5 GeVT

tracks with p

10.0 GeV < p

< 1.9η2.3 <

C.6 E/p plots, former correction factor

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

< 0.0η0.6 < Nondiffractive Minimum Bias MC

= 7 TeV)s2010 Data (

ATLAS work in progress = 4/30.2

0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.1R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.2

C.7 E/p plots, new correction factor

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9



ATLAS work in progress < 1.45 for Data0.2

0.11.40 < R

< 1.45 for MC0.2

0.11.39 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.41 < R

< 1.43 for MC0.2

0.11.38 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.45 < R

< 1.49 for MC0.2

0.11.36 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.45 < R

< 1.49 for MC0.2

0.11.41 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.54 < R

< 1.58 for MC0.2

0.11.54 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.51 < R

< 1.58 for MC0.2

0.11.46 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.58 < R

< 1.60 for MC0.2

0.11.54 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.58 < R

< 1.64 for MC0.2

0.11.34 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.61 < R

< 1.62 for MC0.2

0.11.54 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.49 < R

< 1.63 for MC0.2

0.11.39 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.47 < R

< 1.50 for MC0.2

0.11.44 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.47 < R

< 1.52 for MC0.2

0.11.47 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.2

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.56 < R

< 1.56 for MC0.2

0.11.52 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.20 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

<E

/p>

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9




0.11.52 < R

< 1.54 for MC0.2

0.11.52 < R

p/MeV0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

MC

/DA

TA

0.8

1

1.2

C.8 Comparison of background estimations for both correctionfactors

p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1

0.12


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1

0.12


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.05

0.1

0.15

0.2

0.25

0.3


(p)η

p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1

0.12


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1

0.12


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16


(p)η




p/MeV2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

bg

<E

/p>

0

0.02

0.04

0.06

0.08

0.1


(p)η

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