entwicklungsarbeiten am cms spurdetektor und ...thesis/data/iekp-ka2006...entwicklungsarbeiten am...

Entwicklungsarbeiten am CMS Spurdetektor

und Rekonstruktion von Sekundärvertizes

von b- und c-Hadronen

Zur Erlangung des akademischen Grades einesDOKTORS DER NATURWISSENSCHAFTEN

von der Fakultät für Physik derUniversität Karlsruhe (TH)

genehmigte

DISSERTATION

von

Dipl.-Phys. Christian Piasecki

aus Karlsruhe

Tag der mündlichen Prüfung: 14.07.2006

Referent: Prof. Dr. Th. Müller, Institut für Experimentelle Kernphysik

Korreferent: Prof. Dr. G. Quast, Institut für Experimentelle Kernphysik

Deutsche Zusammenfassung

Das Standardmodell der Teilchenphysik ist eine der erfolgreichsten Theorien in dermodernen Wissenschaft. Es beschreibt die fundamentalen Teilchen und die zwischenihnen wirkende elektromagnetische, schwache und starke Kraft mit einer bemerkens-werten Präzision. Bis auf ein einziges Elementarteilchen wurden alle vom Standard-modell vorhergesagten Teilchen experimentell beobachtet. Das fehlende Teilchen, dasHiggsboson, wird benötigt um die Eichinvarianz trotz der massebehafteten Eichboso-nen der schwachen Wechselwirkung zu gewährleisten.

Mit Hilfe des Large Hadron Collider (LHC), einem Proton-Proton-Speicherringmit einer Schwerpunktsenergie von 14 TeV, und des Compact Muon Solenoid (CMS)Detektors, welche beide im Moment am CERN1 in Genf (Schweiz) gebaut werden,sollen das Higgsboson und so genannte ,,Physik jenseits des Standardmodell“ wie z.B.Supersymmetrie entdeckt werden. Zudem werden CMS und die drei anderen Detekto-ren des LHC Präzisionsmessungen einiger Größen des Standardmodells wie die Massedes W -Bosons und B0s -Oszillationen erlauben.

Um diese wissenschaftlichen Ziele zu erreichen, ist eine genaue Bestimmung derprimären und sekundären Vertizes eine wichtige Grundvoraussetzung.Der Primärvertex wird benötigt, um die primäre Kollision von weiteren Proton-Proton-Kollisionen zu unterscheiden. Des weiteren wird die genaue Position des Primärvertexfür die Analyse von Hadronen, die ein Bottom-Quark enthalten (B-Physik), und fürdie Identifizierung von Jets benötigt, die aus einem Bottom-Quark entstanden sind.Diese Identifizierung wird auch als b-tagging bezeichnet.Eine genaue Bestimmung der Sekundärvertexeigenschaften wird unter anderem für dieB-Physik und das b-tagging gebraucht.

Ein Spurdetektor, der sowohl den Abstand der Spuren geladener Teilchen zumStrahlrohr als auch die Krümmung und somit den Impuls der Spuren präzise undschnell vermessen kann, ist die Voraussetzung für die Vertexrekonstruktion.Beim LHC herrscht zudem eine hohe Strahlenbelastung, deshalb hat sich die CMS-Kollaboration für einen reinen Siliziumspurdetektor entschieden, wobei der innere Teilaus Silizium-Pixel- und der äußere aus Silizium-Streifen-Detektoren besteht.

Ein Teil dieser Doktorarbeit beschäftigt sich mit der Entwicklung und der Qua-

1Conseil Européen pour la Recherche Nucléaire

II

litätskontrolle der CMS-Silizium-Streifensensoren. Als Sensor bezeichnet man das Sili-ziumsubstrat ohne Ausleseelektronik und Energieversorgung. Um einen Siliziumstrei-fensensor zu charakterisieren wird er sowohl optisch als auch elektrisch vermessen.Dabei muss auf höchste Reinheit geachtet werden, zudem müssen Temperatur undLuftfeuchtigkeit genau geregelt und aufgezeichnet werden. Die Untersuchungen findendeshalb in klimatisierten Reinräumen statt und die Sensoren können auf bis zu -20◦Cabgekühlt werden.Im Rahmen dieser Arbeit wurden zwei Messstationen (so genannte ,,Probestations“)für Siliziumsensoren entwickelt und gebaut. Der elektrische Kontakt mit den Sensorenwird über Wolframnadeln (Probes) mit einem Durchmesser von 2 µm an der Spitze her-gestellt. Die Fixierung des Sensors erfolgt über Unterdruck durch eine Vakuumpumpe,die Wolframnadeln werden mit Hilfe von Mikromanipulatoren bewegt und fixiert. Umalle Messungen vollautomatisch durchführen zu können sind die Wolframnadeln unddie Messgeräte über ein komplexes computergesteuertes Relaisnetz miteinander ver-bunden. Die Messungen sowie die Aufzeichnung und die Verarbeitung der Messdatenwurde soweit automatisiert, dass auch Techniker und Studenten (auf HIWI-Job-Basis)die Messstationen nach einer kurzen Einarbeitungszeit bedienen konnten. Insgesamtwurden etwa 8000 Sensoren in Karlsruhe klassifiziert, außerdem wurden 35 Sensorenmit einem Zyklotron am Karlsruher Forschungszentrum mit Protonen bestrahlt undsowohl davor als auch danach vermessen, um die Strahlenhärte zu bestimmen.

Der Schwerpunkt dieser Dissertation ist die Entwicklung und Analyse von Se-kundärvertexrekonstruktionsalgorithmen. Das Kapitel über inklusive Sekundärvertex-rekonstruktion in Jets des ,,CMS Physics Technical Design Report, VolumeI“ und zweidazugehörige Noten basieren auf dieser Arbeit.Es wurden die Eigenschaften der Sekundär- und Tertiärvertizes von schwach zerfal-lenden b- und c-Hadronen in Abhängigkeit ihrer Energie, Flugstrecke und Positionim Detektor für verschiedene Sekundärvertexrekonstruktionsalgorithmen untersucht.Zudem wurde der Einfluss eines nicht perfekt ausgerichteten Spurdetektors auf dieVertexrekonstruktion ermittelt.

Die Analysen zeigten einen sehr starken Einfluss der Anzahl rekonstruierter Spurenauf die Vertexrekonstruktion. Es wurde zudem gezeigt, dass, falls ein Sekundärvertexrekonstruiert wird, ca. 10 Prozent der Spuren, die von einem schwach zerfallendenb- bzw. c-Hadron kommen, dem Primärvertex zugeordnet werden. Eine optimierteZuordnung der Spuren zu den Vertizes wird die Vertexrekonstruktion weiter verbessernkönnen.

Ein im Rahmen dieser Doktorarbeit speziell für das b-tagging entwickelter Vertex-rekonstruktionsalgorithmus, der so genannte “Tertiary Vertex Track Finder”, suchtspeziell nach Spuren aus der b-c-Zerfallskette, die nicht von den Standardvertexre-

III

konstruktionsalgorithmen einem Primär- oder Sekundärvertex zugeordnet wurden. Ernutzt die Eigenschaft dieser Spuren nahe an der Hadron-Fluglinie zu liegen, die durchden Primär- und Sekundärvertex bestimmt ist. Der Algorithmus zeigte sowohl in derVertexrekonstruktion als auch im darauf basierenden b-tagging deutlich bessere Resul-tate als der CMS Standardvertexrekonstruktionsalgorithmus. Bei gleicher Missidenti-fikationsrate von udsc-Quark- und Gluon-Jets konnte die b-tagging-Effizienz relativum bis zu 6 Prozent gesteigert werden, obwohl der b-tagging-Algorithmus noch aufden CMS Standardvertexrekonstruktionsalgorithmus optimiert war. Diese Steigerunglies sich auch mit einem nicht perfekt ausgerichteten Spurdetektor erreichen.

Die assoziierte Higgsbosonproduktion mit zwei Top-Quarks in dem Kanal tt̄H →bµνbqqbb gilt als Kandidat für eine Entdeckung eines leichten Higgsbosons am LHC.Die vier b-Jets im Endzustand erfordern eine sehr gute b-tagging-Güte. Die Signal-akkzeptanz in diesem Kanal lässt sich relativ bei Verwendung des Tertiary VertexTrack Finders um mehr als 10% steigern. Die Anzahl der akkzeptierten Untergrunder-eignisse bleibt konstant, so dass die Signifikanz S/

√B einer Entdeckung des Higgsbo-

sons auch um über 10% steigt.

Development of the CMS Tracker

and Reconstruction of Secondary Vertices

of b- and c-Hadrons

Zur Erlangung des akademischen Grades einesDOKTORS DER NATURWISSENSCHAFTEN

von der Fakultät für Physik der

Universität Karlsruhe (TH)

genehmigte

DISSERTATION

von

Dipl.-Phys. Christian Piasecki

aus Karlsruhe

Tag der mündlichen Prüfung: 14.07.2006

Referent: Prof. Dr. Th. Müller, Institut für Experimentelle Kernphysik

Korreferent: Prof. Dr. G. Quast, Institut für Experimentelle Kernphysik

Contents

Contents 3

1 Introduction 7

2 Theoretical Overview 9

2.1 The Standard Model of Particle Physics 9

2.1.1 Forces and Quantum Field Theory 9

2.1.2 Elementary Particles 10

2.1.3 Electroweak Interaction 10

2.1.4 Strong Interaction 11

2.1.5 Physics beyond the Standard Model 12

2.2 Lifetime of Particles 12

2.3 Properties of Primary, Secondary and Tertiary Vertices 15

3 The Large Hadron Collider and the CMS Detector 18

3.1 The Large Hadron Collider LHC 18

3.2 The Compact Muon Solenoid Detector 20

3.2.1 The Tracking System 22

3.2.2 The Electromagnetic Calorimeter ECAL 22

3

4 Contents

3.2.3 The Hadronic Calorimeter HCAL 22

3.2.4 The Magnet System 23

3.2.5 The Muon Chambers 23

3.2.6 Data Acquisition and Trigger 23

4 Quality Assurance of the CMS Tracking Detector SiliconStrip Sensors 25

4.1 The CMS Tracking Detector 25

4.2 Design and Properties of CMS Silicon Strip Sensors 26

4.3 Quality Assurance of CMS Silicon Strip Sensors 31

4.4 The Karlsruhe CMS Probing Laboratory 33

5 The CMS Simulation and Reconstruction Software 36

5.1 The Event Generation 36

5.2 The Detector Simulation 37

5.3 The Reconstruction Software 37

5.4 Grid and Computing Tools 37

6 Vertex Reconstruction 40

6.1 Track Reconstruction 40

6.2 Simulation of Tracker Misalignment 42

6.3 Fundamentals of Vertex Reconstruction 44

6.4 Primary Vertex Reconstruction 45

6.5 Secondary Vertex Reconstruction 45

6.5.1 Trimmed Kalman Vertex Finder TKVF 45

6.5.2 Filter for Secondary Vertices 46

Contents 5

6.5.3 Tertiary Vertex Track Finder TVTF 46

6.5.4 Further Secondary Vertex Reconstruction Algorithms 48

7 Performance of Secondary Vertex Reconstruction 52

7.1 Event Simulation and Reconstruction 52

7.2 Definition of Efficiency, Purity and Resolution ofSecondary Vertex Reconstruction 53

7.3 Reconstruction Efficiency and Purity of theTrimmed Kalman Vertex Finder (TKVF) 54

7.4 Vertex Resolution of the Trimmed Kalman Vertex Finder 57

7.5 Vertex Reconstruction Performance in Dependence of thenumber of Tracks and the Flight Distance of the Hadron 58

7.6 Reconstruction Performance of the Tertiary Vertex TrackFinder (TVTF) 64

8 Identification of b-jets at CMS 71

8.1 Basic Principles of b-tagging 71

8.2 b-tagging Methods at CMS 72

8.3 b-tagging Performance of CMS 75

8.4 tt̄H Reconstruction Performance in Dependence on differentSecondary Vertex Reconstruction Algorithms 83

9 Conclusions 86

A Relay Schematic of the Karlsruhe Probestations 89

B Calculation of the b-Flight-Line 92

6 Contents

C Production Chain of the Monte Carlo Data Samples 94

D CMKIN Card for bt03 b pt50-80 95

E b-Tagging Performance 97

List of Figures 101

List of Tables 104

Bibliography 107

Chapter 1

Introduction

The Standard Model of particle physics is one of the most successful theories in modernscience. It describes the fundamental particles and their electromagnetic, weak andstrong interactions with remarkable precision. All but one particle predicted by theStandard Model have been experimentally observed. The missing particle, the Higgsboson, is required to maintain gauge invariance in presence of the massive gauge bosonsof the weak interaction.

One of the main tasks of the Large Hadron Collider (LHC) and the Compact MuonSolenoid (CMS) detector, both currently under construction at CERN1 in Geneva(Switzerland), is the discovery of the Higgs Boson and physics beyond the StandardModel like Supersymmetry. Furthermore, CMS and the other three detectors of theLHC will allow precision measurements of some quantities of the Standard Model likethe W -boson mass and B0s -oscillations.

To reach these goals, a precise determination of primary and secondary vertices isa basic requirement. The primary vertex is required to find the primary collision inpresence of further proton-proton collisions in the same bunch crossing as well as inneighbourly bunch crossings. In addition, the precise position of the primary vertex isneeded for the analysis of b-hadrons (b-physics), the identification of b-jets (b-tagging),the determination of the beam profile and for the Higgs discovery channel H → γγ.A good estimation of secondary vertex parameters is important amongst others forb-tagging and b-physics.

For the vertex reconstruction a good tracking detector is essential. CMS has a fullsilicon tracking detector which consists of a silicon pixel and a silicon strip detector.

In this thesis one emphasis lies in the construction and the quality assurance of theCMS silicon tracking detector. For this, the optical and electrical properties of siliconstrip sensors have been investigated. Besides this work on the detector hardware, theother emphasis was the development and analysis of secondary vertex reconstruction

1Conseil Européen pour la Recherche Nucléaire

7

8 Chapter 1. Introduction

algorithms. The chapter on secondary vertex reconstruction in the CMS PhysicsTechnical Design Report Volume I [1] and the two corresponding notes [2, 3] base onthis work.

This thesis is structured as follows: In chapter 2, a brief theoretical overview of theorigin of primary, secondary and tertiary vertices is given, chapter 3 gives an overviewon the LHC and the CMS detector. Chapter 4 describes the construction and thequality assurance of the CMS silicon tracking detector. In chapter 5 the simulationand the reconstruction software of CMS are introduced and chapter 6 shows the modeof operation of the different vertex algorithms. In chapter 7 and 8 the performanceof the secondary vertex reconstruction and of the b-tagging is presented. Technicaldetails and additional information can be found in the appendices.

Chapter 2

Theoretical Overview

The Standard Model of particle physics describes the fundamental particles and theirinteractions with the exception of gravity. Because of its predictive power and itsremarkable agreement with precision experiments, it is one of the most successfultheories in modern science. This chapter gives a short overview of the StandardModel with emphasis on the lifetime of particles and the subsequent formation of thedifferent vertex types. An in-depth introduction to the Standard Model is given intextbooks like references [4, 5, 6].

2.1 The Standard Model of Particle Physics

2.1.1 Forces and Quantum Field Theory

In the Standard Model, all forces in nature except gravity can be described by thefollowing interactions:

• strong interaction

• electromagnetic interaction

• weak interaction

The concept of field quantisation, the description of interactions by exchange of parti-cles, was essential for the development of the theory of elementary particles and led tothe formulation of quantum electrodynamics (QED). In the sixties of the last centuryGlashow, Salam and Weinberg succeeded to unify the weak and the electromagneticinteraction to the electroweak force. Together with the quantum field theory of thestrong interaction, quantum chromodynamics (QCD), it forms the so called StandardModel of Particle Physics. The impact of gravity on space, time and matter is well

9

10 Chapter 2. Theoretical Overview

described by general relativity, a classical field theory. However, it was not possible toformulate gravity as a quantum field theory and so it is not part of the Standard Model.The strength of gravity is many orders of magnitude lower than the strength of theother three forces and can therefore be neglected at elementary particle experiments.

2.1.2 Elementary Particles

The elementary particles of the Standard Model are the twelve spin 12

fermions, whichare shown in table 2.1, and their antiparticles.

Generation 1 2 3

νe νµ ντLeptons

e− µ− τ−

u c tQuarks

d s b

Table 2.1: The quarks and leptons of the Standard Model

They appear in three generations, each generation consisting of one doublet of leptonsand one doublet of quarks. At present, the top-quark can only be produced at theTevatron, the pp–collider at Fermilab, which is operated at a centre of mass energy√

s = 1.96 TeV. The force carriers, which mediate the different interactions, are theSpin 1 bosons shown in table 2.2.

QED Weak Interaction QCD

photon Z- and W-bosons 8 gluons

γ Z0, W+, W− Gbr̄, Gbḡ, ...

Table 2.2: The force carriers of the Standard Model

2.1.3 Electroweak Interaction

The electromagnetic interaction is described by quantum electrodynamics (QED).Quantum electrodynamics is an abelian gauge theory, which can be described by aU(1) symmetry group. The gauge boson of QED is the massless photon, which couples

2.1. The Standard Model of Particle Physics 11

to all electrically charged particles. The coupling strength is proportional to the elec-tric charge. The electric charge of photons is 0, so they do not interact with each other.

The Glashow-Salam-Weinberg-model, a non-abelian gauge theory, unifies the QEDwith the weak interaction, which is described by a SU(2)L symmetry group. The indexL indicates that the weak interaction couples only to left handed particles. The resultof this unification is the symmetry group SU(2)L ⊗ U(1)Y and leads to a coupling ofisospin and charge. Thus results a new quantum number, the hypercharge Y:

Y = 2(Q − T3), (1)

where Q is the electric charge and T3 the third component of the weak isospin. Theweak interaction can only be described consistently in combination with the elec-tromagnetic one. The force carriers W+, W− and Z0 obtain their masses by the“Higgs mechanism”, which hides the local isospin symmetry (spontaneous symmetry-breaking). Their masses depend on the weak mixing angle θW :

mW± =

√

( πα√2GF

)

· 1sin θW

(2)

mZ0 = mW± ·1

cos θW(3)

Fermi coupling constant : GF = 1.16637(1) · 10−5GeV −2 (4)

The theory provides two other bosons: the massless photon and the Higgs boson,which gives elementary particles their masses. The Higgs boson is the only particle ofthe Standard Model that has not been discovered yet. The lower limit of the Higgsboson mass [7] is 114.4 GeV/c2 and is given by direct searches at the Large ElectronPositron Collider (LEP) at CERN. The upper limit is around 200 GeV/c2 and is givenby electroweak precision measurements [7] of the Standard Model.

2.1.4 Strong Interaction

The strong interaction is described by quantum chromodynamics (QCD) demandinglocal gauge invariance under transformations in the SU(3)colour space. Quarks have ared (r), green (g) or blue (b) colour charge. The force carriers of the strong interactionare eight massless gluons, which have a spin of 1 and an electric charge of 0:

rb̄, rḡ, bḡ, br̄, gr̄, gb̄,rr̄ − bb̄√

2,rr̄ + bb̄ − 2gḡ√

6

Gluons carry a combination of a colour–anticolour–state and so they interact witheach other. The interaction of gluons results in an increasing coupling constant αs


at higher distances and so inhibits free quarks, which is called confinement. On theother hand αs decreases at smaller distances, which is the reason for the asymptoticfreedom. The coupling constants αe of the electromagnetic force and αw of the weakforce show an oppositional behaviour and increase at smaller distances.

2.1.5 Physics beyond the Standard Model

Despite its achievements, the Standard Model leaves some questions unanswered:

• Why are there three independent symmetry groups for the strong, electromag-netic and weak interaction?

• Why are there so many free parameters (coupling constants, CKM matrix ele-ments and the masses of elementary particles)?

• Why are there three families of quarks and leptons?

• Why have protons and electrons exactly opposite electric charges?

• What is the origin of dark matter?

The attempt to answer these questions has led to theories that predict that at ener-gies greater than 1015 GeV the electroweak and the strong force unify. One of theseGrand Unified Theories (GUT) is the so-called Supersymmetry (SUSY), which pre-dicts amongst others, that every fundamental fermion has a bosonic superpartner andvice versa. Supersymmetry is favoured over other Grand Unified Theories becausesupersymmetric radiative corrections lead, in contradiction to the Standard Model, toan exact unification of the coupling constants [8]. Furthermore, the lightest supersym-metric particle is stable as a result of the R-parity1-conservation and would thereforebe an ideal candidate for cold dark matter.

2.2 Lifetime of Particles

The biggest experimental difference between strong, electromagnetic and weak decaysis the typical lifetime of the decaying particles. A typical strong decay involves alifetime around 10−23 s, a typical electromagnetic decay takes about 10−16 s and weakdecay times range from 3 · 10−25 s (for the W and Z bosons) up to 885.7 s (forthe neutron). The main reason for the wide range in the timescale of weak decays

1Multiplicative quantum number, SUSY-particles have R= -1,“normal”particles have R= 1

2.2. Lifetime of Particles 13

stems from its (∆m)5 dependency, where ∆m is the mass difference between thedecaying particle and its decay products. Another important reason for quarks is theCabibbo-Kobayashi-Maskawa (CKM) mechanism. The essential idea is that the quarkgenerations are skewed, for the purposes of weak interactions. Instead of

(

u

d

)

,

(

c

s

)

,

(

t

b

)

(5)

the weak force couples the pairs

(

u

d′

)

,

(

c

s′

)

,

(

t

b′

)

(6)

where d′, s′ and b′ are linear combinations of the physical quarks d, s and b:

d′

s′

b′

=

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

d

s

b

(7)

The Feynman graph for the transition of up- to down-type quarks is shown in figure 2.1.

�qup, charge = +

23

qdown, charge = -13

W+∼ |Vij|

Figure 2.1: Feynman graph for the transition of up- to down-type quarks.


The 90% confidence limits on the magnitudes of the elements of the CKM matrixare [9]

|Vij| =

0.9739 to 0.9751 0.221 to 0.227 0.0029 to 0.0045

0.221 to 0.227 0.9730 to 0.9744 0.039 to 0.044

0.0048 to 0.014 0.037 to 0.043 0.9990 to 0.9992

(8)

The quarks have the following masses, for the s, d, and u-quark the masses are esti-mates of so-called “current quark masses” in a mass-independent subtraction schemesuch as MS at a scale µ ≈ 2 GeV:

• top-quark: 174.3 ± 5.1 GeV/c2, direct observation of top events

• b-quark: 4.1 to 4.4 GeV/c2, “running” mass in the MS scheme

• c-quark: 1.15 to 1.35 GeV/c2, “running” mass in the MS scheme

• s-quark: 80 to 130 MeV/c2

• d-quark: 4 to 8 MeV/c2

• u-quark: 1.5 to 4 MeV/c2

The (∆m)5 dependency and the CKM mechanism cause the following lifetimes of theweakly decaying quarks and respectively of the corresponding hadrons:

• The top-quark has a lifetime of 4·10−25 s. This is shorter than the QCD timescaleof 3 ·10−24 s, therefore the top-quark decays before forming a hadron. The CKMmatrix element Vtb is nearly one, thus nearly all top-quarks decay into b-quarks.The great mass difference between the top-quark and its decay products and thematrix element cause the short lifetime of the top-quark.

• Weakly decaying b-hadrons like B± and B0 have a lifetime of around 1.5·10−12 s,whereas the b-quark mostly decays into a c-quark. The small value of Vcb and amass difference of about 3 GeV/c2 between b- and c-quark cause the relativelylong lifetime of weakly decaying b-hadrons.

• Weakly decaying c-hadrons like D± and D0 have a lifetime of at most 1 ·10−12 s,whereas the c-quark decays mostly into an s-quark. Although Vcs is nearly one,the small mass difference between c-hadrons and s-hadrons of about 1 GeV/c2

give rise to the comparatively long lifetime of weakly decaying c-hadrons.

2.3. Properties of Primary, Secondary and Tertiary Vertices 15

• Weakly decaying uds-hadrons like π±, K±, K◦l and K◦s have lifetimes between1 ·10−10 s and 5 ·10−8 s. The long lifetime is caused by the small mass differencebetween these hadrons and their decay products and this leads to a long flightdistance in modern collider detectors. These particles are normally stopped inthe calorimeters of the detector, only the K◦s naturally decays inside the tracker.

The particles, that are measured by a modern high energy collider detector, can inprinciple be classified into three types. First there are the stable and long-lived parti-cles like photons, electrons, positrons, protons, neutrinos, muons, π±, K± and so on.All these particles propagate through the inner parts of the detector, exceptions arehard interactions with the detector material and decays of the unstable particles, butthese decays so close to the beam line have a small probability.

The second type of particles are the very short living ones like W - and Z-bosons,gluons, top quarks and strongly and electromagnetically decaying hadrons. Theseparticles decay nearly at the same place where they are produced. As a consequencethe detector can not measure a flight distance.

The third type of particles are these, which have a significant flight distance, butdecay within the tracking detector. Weakly decaying b- and c-hadrons and tau leptonsbelong to this type, their signature is the existence of a secondary vertex.

2.3 Properties of Primary, Secondary and Tertiary

Vertices

A vertex in a collider detector is determined by the tracks of the stable and long-livedcharged particles that are produced at this vertex. The origin and the properties ofthe different vertex types in detectors is described below.

Primary Vertex

The primary vertex (PV) is the position of the initial proton-proton collision. Nearlyall particle physics processes like production, decay and hadronization of particlestake place at the primary vertex. The standard deviation of the LHC bunch crossingregion in x- and y-direction is 15 µm, so the primary vertex is close to the beamline. Furthermore, the tracks from the primary vertex have a small significance of thetransverse impact parameter. The transverse impact parameter is the distance in thetransverse (r-φ) plane between the beam line and the track. The significance of thetransverse impact parameter is defined as:

σ(ipT ) =ipT

∆ipT, (9)

whereas ∆ipT is the uncertainty of transverse impact parameter.


Secondary Vertex

The secondary vertex (SV) is the position of weakly decaying b- and c-hadrons and tauleptons, which are produced at the primary vertex. These particles have a significantlife time and therefore a significant flight distance of the order of millimetres. Theconsequence is, that the position of the secondary vertex is not equal to the positionof the primary vertex and that the secondary vertex has a significant distance to thebeam line. The mass and the significant life time of the decaying particles result inthat the tracks of the secondary vertex do not usually point exactly to the primaryvertex and have a large significance of the transverse impact parameter.

Another characteristic property of secondary vertices is their small charged invari-ant mass. For the charged invariant mass only charged particles are taken into accountand it is defined as

√

(E)2 − (px)2 − (py)2 − (pz)2. E is the sum of the energies, px,py and pz are the sums of the momenta in x-, y- and z-direction of the vertex tracks.The upper border for the charged invariant mass of a secondary vertex is the mass ofthe decaying particle, e.g. 6.4 GeV/c2 for the B±c and 1.87 GeV/c

2 for the D±, so thecharged invariant mass can be used to discriminate between b- and c-hadrons. Thereconstructed charged invariant mass is smaller than the mass of the decaying particlein most cases, because of neutral decay products and not reconstructed and wronglyassociated tracks.

Tertiary Vertex

A b-hadron decays into a c-hadron in most cases, this process is called b-c-decaychain. The c-hadron can create a further vertex at its decay position. This vertexis called tertiary vertex (TV) and has similar properties like the secondary vertex.The position of the tertiary vertex is not equal to the position of the primary vertexand the tertiary vertex has a significant distance to the beam line. Furthermore, thetracks of the tertiary vertex have a significance of the transverse impact parameter.The upper limit of the charged invariant mass is smaller than the one of secondaryvertices, because the mass of c-hadrons is smaller then the mass of b-hadrons. It isaround 2.7 GeV/c2 and is given by the mass of the Ω0c , which is the heaviest weaklydecaying c-baryon with one c-quark.

The boost of the b-hadron and the high mass of the c-hadron result in the proximityof the position of the tertiary vertex and the b-flight line, which is defined by theprimary and the secondary vertex. Figure 2.2 shows a typical b-c-decay chain in ab-jet. To get a better overview, the reconstructed tracks are not shown at full length.

2.3. Properties of Primary, Secondary and Tertiary Vertices 17

Figure 2.2: Schematic view of a b-c-decay chain.

Chapter 3

The Large Hadron Collider and theCMS Detector

The Compact Muon Solenoid (CMS) detector, currently under construction at theLarge Hadron Collider (LHC) at CERN (Geneva), is a multipurpose detector designedfor exploring new physics in proton-proton collisions at a centre-of-mass energy of14 TeV. This chapter gives an overview of the accelerator and the detector, which areexpected to start operation in summer 2007.

3.1 The Large Hadron Collider LHC

The Large Hadron Collider [10] is currently being installed in the 27 km long formerLarge Electron Positron Collider (LEP) tunnel at CERN. Located about 100 metresbelow the surface, this accelerator will provide proton-proton collisions with a centreof mass energy

√s = 14 TeV.

A total of 1232 superconducting niobium titanium dipole magnets, operating at atemperature of 1.9 Kelvin, are providing a magnetic field of 8.33 Tesla. Altogether2835 bunches of 1011 protons each are crossing with 25 ns time spacings in the in-teraction points. The design value of the luminosity at the interaction points is L =2 ·1033cm−2s−1 in the first three operating years of the LHC. The integrated luminos-ity of this “low luminosity phase” is 60 fb−1. After this initial phase, the LHC willoperate at the “high luminosity phase” with a luminosity of L = 1034cm−2s−1.

The major task of LHC will be to discover the Higgs Boson and potential physicsbeyond the Standard Model like Supersymmetry. Furthermore, it allows precisionmeasurements of the Standard Model, studies of CP violation of b-hadrons and theinvestigation of Heavy Ion Physics.

18

3.1. The Large Hadron Collider LHC 19

Figure 3.1: Schematic view of the LHC ring accelerator at CERN and its four detectorsALICE, ATLAS, CMS and LHCb.

To accomplish this goals, four detectors are built at the interaction points of the LHC:

• ATLAS1 [11] is a multipurpose detector with a toroidal magnetic field. It isdesigned to discover the Higgs Boson and physics beyond the Standard Model.

• CMS [12] is a multipurpose detector with a solenoid magnet and has the samemajor tasks as ATLAS. Because of its “compact” design CMS is nearly twice asheavy as ATLAS, but has only a quarter of its size.

• LHC-b2 [13] is designed for the study of b-physics and should e.g. investigatethe CP violation of b-hadrons.

• ALICE3 [14] is conceived for studying Heavy Ion Physics, because the LHCwill be operated in an alternative mode with heavy ion collisions. The Pb-Pbcollisions will have a centre-of-mass energy of more than 1100 TeV and producepotentially a Quark Gluon Plasma.

A schematic view of the LHC and its four detectors is given in figure 3.1.

1A Toroidal LHC ApparatuS

2LHC Beauty Experiment

3A Large Collider Experiment

20 Chapter 3. The Large Hadron Collider and the CMS Detector

3.2 The Compact Muon Solenoid Detector

With more than 2000 scientists and engineers, CMS is one of the largest internationalscientific collaborations in history. The CMS detector, which in total measures 15 m indiameter and 21.6 m in length, has a mass of 12500 t and will be located at the accesspoint 5 of the LHC ring. It allows to detect signatures of new physics by identifyingand measuring electrons, muons, photons, jets and missing energy with high spatialcoverage and over a large energy range. The detector has 16 millions readout channelsand is separated into a barrel section and two endcaps. Figure 3.2 shows schematiccuts through the detector, figure 3.3 gives an overview of the CMS detector and theparticipating countries.

Figure 3.2: Schematic cuts through the CMS detector across and along the beam pipe.

3.2. The Compact Muon Solenoid Detector 21

Figure 3.3: Overview of the CMS detector and participating countries.


3.2.1 The Tracking System

The high bunch crossing rate, the large number of underlying events and the radia-tion around the interaction points are a technological challenge for the CMS trackingsystem. Therefore, a full silicon approach was chosen for the tracker [15] [16]. It mea-sures the tracks coming from charged particles and quantifies their impact parameters.Furthermore, the tracker determines the momentum and the sign of the charge of theparticles by measuring the curvature of the tracks. The inner part of the tracker isa silicon pixel detector, the outer part a silicon strip detector. The tracker coverspseudorapidities4 up to |η| = 2.4. Chapter 4 gives an overview of the constructiondetails and the methods of the quality assurance of the CMS tracker components.

3.2.2 The Electromagnetic Calorimeter ECAL

The ECAL [17] encloses the tracker and covers pseudorapidities up to |η| = 3.0. Itis designed to measure the energies of electrons, positrons and photons with highprecision. The ECAL stops these relativistic particles in its absorber material andthe light produced during their passage through the ECAL is collected by avalanchediodes in the barrel and by vacuum phototriodes in the endcaps. The electromagneticcalorimeter is composed of 80,000 lead-tungstate (PbW04) crystals. Lead-tungstatewas chosen as absorber material because of its high density (8.28 g/cm3), its largenumber of electrons per atom and because it can be used simultaneously as scintillator.

3.2.3 The Hadronic Calorimeter HCAL

Hadrons will pass the ECAL without losing much of their energy as a result of theirlarger radiation length. These particles are stopped in the HCAL [18] where theycreate a hadronic shower by hadronic interactions with the calorimeter material nuclei.The HCAL plays an important role in the measurement of quarks, gluons and neutrinosby measuring the energy and direction of jets and missing transverse energy. TheHCAL is realised as a copper alloy calorimeter and covers pseudorapidities up to |η| =3.0. The 5 cm thick copper absorber plates are interleaved with plastic scintillators andwavelength shifting optical fibres. The very forward calorimeters (VFCAL) increasethe pseudorapidity coverage up to |η| = 5.0. They are located at both ends of thedetector and have a similar structure as the HCAL.

4The definition of the pseudorapidity is η = -ln(tanΘ2) .

3.2. The Compact Muon Solenoid Detector 23

3.2.4 The Magnet System

The magnet [19] of CMS, that surrounds the tracker and the calorimeters, is the worldslargest superconducting solenoid. It measures 13 m in length, has a diameter of 5.9 m,a mass of 500 t and provides a magnetic field of 4 Tesla. This strong magnetic field isneeded to bend the tracks of charged particles with a high momentum. The magneticflux is returned by a 1.5 m thick iron yoke weighing 7000 t.

3.2.5 The Muon Chambers

CMS was designed to offer an excellent muon identification. The sensors of the muonchambers [20], which surrounds the solenoid, are interleaved with the iron flux returnyoke plates of the magnet. These plates can only be traversed by muons and neutrinos.Furthermore, the magnetic field of 2 Tesla in the return yoke is used to determine themomentum of the muons. Three types of muon detectors will be used: Drift Tubes(DT) in the central barrel region, Cathode Strip Chambers (CSC) in the endcap regionand Resistive Parallel Plate Chambers (RPC) in both the barrel and the endcaps. TheRPC is very fast and will be used for the Level 1 Trigger and for the allocation tothe signal event. The DT and CSC provide a high precision of the momentum andposition measurement, furthermore tracker information is used to enhance the muonmeasurement. The muon detector covers pseudorapidities up to |η| = 2.4 for offlineanalyses and pseudorapidities up to |η| = 2.1 for triggering.

3.2.6 Data Acquisition and Trigger

The bunch crossing frequency at the interaction points will be 40 MHz and at eachcrossing there will be 25 proton-proton collisions in average in the high luminosityphase. This results in 109 interactions per second which have to be filtered by atrigger system to reduce the amount of data and to fit the capabilities of mass storagedevices and offline computing facilities. For this, a two level trigger system is used.

The Level 1 Trigger [21] consists of custom electronics and is part of the detectorhardware. It has to decide on the acceptability of an event within about 3 µs after acollision and reduces the data rate to 100 kHz. During this time period, the full datais kept in the memory buffers of the front-end electronics modules.

If accepted, the event data (about 1.5 MB after zero-suppression) is passed to theHigh Level Trigger system (HLT) [22]. The HLT, an on-line processor farm with a totalprocessing time of at most one second, reduces the event acceptance to a maximumrate of O(102)Hz.

A detailed overview of the CMS Trigger and Data Acquisition System (TriDAS)is given in figure 3.4.


Figure 3.4: Overview of the CMS Trigger and Data Acquisition System.

Chapter 4

Quality Assurance of the CMSTracking Detector Silicon StripSensors

The high bunch crossing rate, the large number of underlying events and especiallythe radiation from the interactions around the interaction point are a technologicalchallenge for the CMS tracking system. This chapter gives an overview of the construc-tion details and the methods of the quality assurance of the CMS tracker components.More details of the topics in this chapter can be found in [23] [24].

4.1 The CMS Tracking Detector

The CMS collaboration decided to use an all-silicon detector as tracker [15] [16] becauseit has a fast response and allows small pitches between the strips. The inner part ofthe tracker is a silicon pixel detector, the outer part a silicon strip detector. The siliconstrip detector consists of about 25000 silicon sensors and has an active area of about210 m2. For comparison, the CDF1 detector at Fermilab in Chicago(USA), which hasthe largest silicon tracker so far, has an active area of 7.5 m2.

Figure 4.1 illustrates the arrangement of the silicon pixel and silicon strip detectorsin the CMS tracker. One quarter of the tracker is shown, the other three quartersare located symmetrically around the interaction point of the proton beams which islocated at the bottom left of the figure.

The silicon pixel detector consists of three layers in the barrel region and two layersin the endcap regions. The total area of the pixel detector is ≈ 1 m2 and it comprises66 million pixels with an area of 100×150 µm2 each. It provides three-dimensional

1Collider Detector at Fermilab

25

26Chapter 4. Quality Assurance of the CMS Tracking Detector

Silicon Strip Sensors

Figure 4.1: Layout of the CMS silicon vertex detector.

space-points required for correct pattern recognition at small radii and allows a verygood track and corresponding vertex reconstruction.

The barrel silicon strip detector is made of 10 layers while the endcap part com-prises 9 disks on both sides. Additionally there are 3 small disks that fill the gapbetween the inner barrel and the endcaps. Some layers are made with double sidedmodules in order to provide a measurement in both r − φ and r − z coordinates. Astereo angle of 100 mrad has been chosen.

4.2 Design and Properties of CMS Silicon Strip

Sensors

CMS sensors are single sided n-doped sensors with p+-strip implants, poly crystallinebias resistors and AC coupled readout. The n-doped bulk and the p+-strip implantform a p-n junction which is reverse-biased. The width of the depletion region growslarger with higher voltage until the sensor is fully depleted. Charged particles thatpass the sensor create electron-hole pairs, the holes are drifting to the p+-strips andcreate a signal that is acquired by the readout electronics. The operation temperatureis below −10◦C to avoid annealing effects of irradiated silicon and to keep the totalleakage current low in order to drop the power consumption and to avoid a thermalrun away. Figure 4.2 shows the principle design of a CMS sensor, the most important

4.2. Design and Properties of CMS Silicon Strip Sensors 27

p+

Al

n -bulk

n -layer++

E-field

RInt

IInt

CInt

Passivation

Al

Bias resistor

Via

Shorts

Guard ring

Bias ring

AC-Pad DC-Pad

Marks for alignment

Strip number

AC Pad DC Pad

Bias resistor

Bias ring

Guard ring

Look on top

n+

SiO /Si N2 3 4

32

0-5

00

µm

Figure 4.2: Principle design of a CMS sensor, the mode of operation is given in thetext.



constituents are given in the following, for a detailed description see [25] [26]:

• BulkThe CMS sensors are produced on 6 inch n-doped silicon wafers. The inner fourlayers of the silicon strip tracker are made of sensors with a thickness of 320 µm,the outer layers consist of sensors with a thickness of 500 µm. The sensors inthe outer layers are larger and have longer strips which increases the signal tonoise ratio. This is compensated by the greater thickness of these sensors.The n-type silicon gets type inverted at a certain fluence. The full depletion volt-age of the silicon sensors decreases before type inversion and increases afterwards(see figure 4.3) which results in a longer operating time for the tracker.

• Bulk OrientationThe wafers are cut along the crystal plane. The advantage of this materialcompared to silicon in orientation is the lower number of dangling bounds(see figure 4.4). This results in less surface damage when charged particles passthe sensor.

• Strip implantsp+ strip implants (DC-strips) are implemented on one side of the sensors, theother side is not structured.

• Coupling capacitanceAn layer of SiO2/Si3N4 isolates the p

+-implants from the aluminium strips (AC-strips) above to get an AC coupling. These aluminium strips are connected tothe readout electronics. The resulting capacitances have to be as large as possiblein order to get a as low as possible resistance for the signal. For noise reasonsthe magnitude of the coupling capacitance has at least to be higher as the sumof the interstrip capacitances to the two neighbouring strips and the capacitanceto the backplane.

• Backside contactThe unstructured side of the sensors, named backplane, has a n++ layer with athickness up to 30 µm. The function of this layer is to realise an ohmic contactbetween bulk and the aluminium layer on the backplane which is put on highpotential.

• Bias ringThe p+-implants are connected with aluminium vias to the bias resistors, whichare connected to a common aluminium line named bias ring. This ring is con-nected to low potential and with aluminium vias to a p+-implant surroundingall strips. The function of this ring implant is to form an electric field around

4.2. Design and Properties of CMS Silicon Strip Sensors 29

Figure 4.3: Changes in the effective doping concentration with fluence: The effectivedoping concentration and therefore also the full depletion voltage changes with fluence.n-type silicon gets type inverted at a certain fluence by introduced acceptors andthe full depletion voltage is decreasing. With further introducing of acceptors byirradiation the full depletion voltages increases after type inversion [27].

the strip implants. Therefore the field distribution of the two outer strips is thesame as for the inner strips. Otherwise a different noise is expected for the outerstrips.

• Bias resistorsThe connection from the p+-implants to the bias ring is done with bias resistors.These ohmic resistors are made of heavily doped poly crystalline silicon. Theyare produced above the insulating layer and are connected to the strips withaluminium vias. These bias resistors have to be as homogeneous as possible sincethey define the potential on the p+-implants, which should be as homogeneousas possible.

• Guard ringOutside of the bias ring the guard ring surrounds the bias ring. Its inner sidehas to form the electric field around the bias ring. The outer side of the guard



BULK

Surface

Many dangling bonds

10 charges/cm²

Less dangling bonds

10 charges/cm²10

11

Figure 4.4: Silicon in and orientation.

P+

Guard ringStrip with metal overhang

Insulating layer

bulk

Electric field

Aluminium

Highest electric field density

Strip without metal overhang

Figure 4.5: Principle of the metal overhang design.

4.3. Quality Assurance of CMS Silicon Strip Sensors 31

ring has to adapt the electric field distribution to the borders of the sensors.Contrary to the bias ring the guard ring is operated in floating mode, i.e. it isnot connected to a certain potential.

• Metal overhangIn order to guarantee the high voltage stability, all aluminium structures have ametal overhang design which is shown in figure 4.5. The aluminium strips abovethe p+-implants and the bias ring are 4 µm wider than the implants below thedielectric layer. This moves the areas of highest electric field to be expectedaround the implants into the dielectric layer. Here a break through mechanismlike the avalanche or Zener effect is not possible since there are no free chargecarriers due to the higher band gap.

• Passivation layerOn top of the sensor a passivation layer protects the sensors surface. It is removedin the areas where contacts via micro bonding or probe needles are necessary.

4.3 Quality Assurance of CMS Silicon Strip Sen-

sors

To guarantee an operating time of so many CMS silicon strip sensors of more thanten years under LHC conditions a complex quality assurance is needed. The logisticof it is shown schematically in figure 4.6.

The sensors are produced by the two companies, Hamamatsu Photonics Company(HPK) in Hamamatsu-City (Japan) and ST Microelectronics (STM) in Sicilia (Italy).

All sensors are delivered to the Distribution Centre at CERN. This allocates thesensors equally to the four Quality Test Centres (QTC), Pisa, Perugia, Vienna andKarlsruhe. From these Centres a small amount of around 1% of the sensors and 5%of the standard test structures are sent to the two Irradiation Qualification Centres(IQC) Karlsruhe (protons) and Louvain-la-Neuve (neutrons) to control the radiationhardness. Another 5% of the test structures are sent to Pisa and Strasbourg forbonding tests and further 5% are sent to the Process Qualification Centres, Strasbourg,Vienna and Florence, where the homogeneity of the process parameters is controlled.In the PQC also some sensors are operated at operation voltage and the long termstability of the total leakage current is controlled for 72 h.

The geometrical properties and the surface of the sensors are checked during theoptical inspection in the Quality Test Centres. The electrical standard measurementsdone in the Quality Test Centres and Irradiation Qualification Centres are:

• Total leakage current voltage dependence (IV).



• Total capacitance voltage dependence (CV).

• Single DC-strip leakage currents (ILeak).

• Bias resistors (Rbias or Rpoly).

• Coupling capacitance between DC- and AC-strips (CC).

• Shorts between AC-strips.

• Shorts between implant (DC-strip) and aluminium (AC-strip) strip (Pinhole).

• Interstrip resistance (Rint, only done in IQC).

• Interstrip capacitance (Cint, only done in IQC).

The names in brackets are abbreviations used by the CMS collaboration.

PQC : Test of process control,

long term properties

BTC : Test of bondability

IQC : Test of radiation hardness

Control &

Distribution Center

CERN &

Production Committee

Quality

Test Center

Pisa

Quality

Test Center

Karlsruhe

Quality

Test Center

Perugia

Irradiation

QualificationCenters

Louvain, Karlsruhe

Process

Qualification &

Stability Centers

Strasbourg,

Vienna Florence

Quality

Test Center

Vienna

Module Assembly Centers

Sensor Fabrication

Center HPK

Sensor Fabrication

Center STM

25% 25%25% 25%

5% sensors

>5% test devices

1% sensors

~5% test devices

Bonding

TestCenters

Pisa, Strasbourg

~5% test

devices

QTC : Test of sensor properties

Inner barrel

Outer barrel

Outer barrel

Figure 4.6: Logistic of the CMS sensor quality assurance.

4.4. The Karlsruhe CMS Probing Laboratory 33

4.4 The Karlsruhe CMS Probing Laboratory

The Institut für Experimentelle Kernphysik of the Universität Karlsruhe (TH) oper-ates a Quality Test Centre and an Irradiation Qualification Centre. In the scope of thisthesis two full automated probestations have been designed and constructed. Withthese probestations all electrical QTC and IQC measurements mentioned in the lastsection can be executed on all sensor types and on teststructures that are producedon the free areas of the sensor wafers. The handling of the probestations has been sosimplified that assistant students and technicians can operate the probestations aftera short practise period.

To fulfil the strict purity conditions for silicon sensors the probestations are locatedin an air-conditioned grey room. Silicon sensors are sensitive to temperature and airhumidity, so these parameters have to be controlled and monitored.

Irradiated sensors are tested at the operating temperature of the CMS tracker, soone of the probestations can cool down the measured sensor to a temperature of -20◦C.The electrical contact between the different sensor components and the measurementdevices is done by special tungsten needles with a tip diameter of 2 µm. These needlesare fixed by micro manipulators. Figure 4.7 shows a probestation and the micromanipulators and needles contacted to a teststructure. The connections between theneedles that contact the sensor and the measurement devices are routed by a complexrelay circuit. The different switching states allow to toggle between all measurements.The relay schematic, the relay settings for the different measurements and the cablingof the probestations are shown in appendix A.

To verify the radiation hardness the silicon sensors are measured before and afterirradiation with 26 MeV protons at the Kompakt-Zyklotron (see figure 4.8) in theForschungszentrum Karlsruhe. The irradiation fluence corresponds to around 15 yearsof operation at the LHC. Overall 35 sensors and 60 teststructures have been irradiatedat the cyclotron and the radiation hardness of the sensors has been verified (see [26]).

Figure 4.9 shows a typical IV- and CV-curve of a non irradiated sensor. The kink inthe CV-curve at around 175 V corresponds to the full depletion voltage of the sensor.Altogether 8000 sensors have been investigated in Karlsruhe, the measurements havebeen mainly done by assistant students. The quality assurance showed problems inthe production phase of the ST-Microelectronics sensors while the Hamamatsu sensorsfulfilled all specifications. For this, the bigger part of the sensors was produced byHamamatsu.



Plastic

foil

Acrylic glass

Lock

TeststructureDry air

2µm

needles

Micro

manipulator

Figure 4.7: The Karlsruhe probestation.

Figure 4.8: The Kompakt-Zyklotron in Karlsruhe.

4.4. The Karlsruhe CMS Probing Laboratory 35

Bias-Voltage [V]0 100 200 300 400 500 600

Tot

al L

eaka

ge C

urre

nt [n

A]

0

50

100

150

200

250

300

Bias-Voltage [V]0 50 100 150 200 250 300 350

Tot

al C

apac

itanc

e [n

F]

2

4

6

8

10

12

Figure 4.9: An IV- (left) and CV-measurement (right) of a HPK W5B sensor.

Chapter 5

The CMS Simulation andReconstruction Software

Besides the development and construction of the CMS detector hardware, the physicsanalysis of the recorded data is another challenge. For this, large Monte Carlo datasamples are produced, according to the current knowledge of particle physics and thedesign of the detector. These Monte Carlo data samples are used to check the softwareframework, to test the ability to perform an analysis and to make estimations of theexpected sensitivities. This chapter gives an overview of the CMS simulation andreconstruction software and the Grid tools that provide the access to the decentralisedcomputing resources.

5.1 The Event Generation

The first step in the production chain of Monte Carlo data samples is the generation ofthe HEPEVT1 Ntuples which contain information about the requested particle physicsprocesses. Most of these data samples for CMS are produced by PYTHIA [28], aprogram for the generation of high-energy physics events, i.e. for the description ofcollisions of incident particles such as electrons, positrons, protons and antiprotons invarious combinations at high centre-of-mass energies. It contains theory and models fora number of physics aspects, including hard and soft interactions, parton distributions,initial and final state parton showers, multiple interactions, fragmentation and decay.PYTHIA calculations are in lowest order of perturbation theory and the fragmentationis based on the Lund String Model. The Monte Carlo data samples used in thisPhD thesis are produced with PYTHIA. Other event generators used in CMS are forexample ALPGEN [29], CompHEP [30], HERWIG [31] and MC@NLO [32].

1High-Energy Physics EVenT

36

5.2. The Detector Simulation 37

5.2 The Detector Simulation

The next step in the production chain is the simulation of the interaction of the parti-cles with the magnetic field of the solenoid and the detector material. The full detectorsimulation software for CMS are CMSIM [33] and its successor OSCAR [34], the fastdetector simulation framework is FAMOS [35]. CMSIM is based on GEANT3 [36]which is written in FORTRAN, OSCAR is based on GEANT4 which uses C++ asprogramming language. The interface between the event generators and the detectorsimulation software is CMKIN [37].

5.3 The Reconstruction Software

The Object Oriented Reconstruction for CMS Analysis (ORCA) [38] is the softwarefor the reconstruction of physics events detected with the CMS detector. It is dedicatedto the analysis of the detector data, final detector optimisations, trigger studies andglobal detector performance evaluation. Furthermore, it is used as final step in theproduction chain as it adds the underlying events to the signal process.

ORCA is based on CARF, the CMS Analysis and Reconstruction Framework.CARF implements two principles: event driven notification and action on demand.Event driven notification means that observers are notified of a new event arrivingand then start appropriate actions. Action on demand guarantees that objects areprocessed once and only if necessary.

The general framework of the CMS software is COBRA [39]. COBRA standsfor Coherent Object-Orientated Base for Reconstruction, Analysis and Simulation.An important subsystem of COBRA is the Detector Description Database DDD [40]which provides the infrastructure and services for detector geometry handling.

The final analysis is executed with ROOT [41] which is an object-oriented dataanalysis framework. Furthermore, the database for storing the Monte Carlo samplesand the reconstructed detector data is based on it.

5.4 Grid and Computing Tools

The huge data and Monte Carlo production rates of the four LHC experiments demandhigh computing power and large mass storages. Alone the CMS detector has a finalrecording rate after all trigger levels of 225 MB per second (see figure 5.1). To copewith these challenges the LHC experiments use grid technologies, namely the LHCComputing Grid (LCG) [42]. The key of the LHC offline computing system is amulti-tier hierarchical structure shown in figure 5.2. One central Tier-0 centre atCERN stores the raw data of each experiment. The Tier-0 centre also distributes raw

38 Chapter 5. The CMS Simulation and Reconstruction Software

and processed data to the Tier-1 centres, which are responsible for data archiving,reconstruction, reprocessing and other data-intensive analysis tasks. The next layerconsists of a numerous set of Tier-2 centres, which offer computing capacity for analysisand Monte Carlo simulation. At last, the Tier-3 centres offer resources that canbe used by local groups and provide small computing and storage capacities for thecollaboration. The workstation of the user is named Tier-4. More details on theCMS computing tools can be found in the CMS Computing Project Technical DesignReport [43].

Figure 5.1: Overview of the CMS online trigger system with the corresponding triggerrate and data flow.

5.4. Grid and Computing Tools 39

Figure 5.2: Schematic overview on the multi Tier hierarchical structure of the LHCComputing Grid.

Chapter 6

Vertex Reconstruction

This chapter describes the basic principles of the track and vertex reconstruction atCMS. Moreover, it gives details on the different algorithms that are used for thereconstruction of primary and secondary vertices.

6.1 Track Reconstruction

Track reconstruction [44, 45] in a dense environment needs an efficient search for hitsduring the pattern recognition stage and a fast propagation of trajectory candidates.In the CMS tracker, the first task is simplified by the arrangement of sensitive modulesin layers that are practically hermetic for a particle originating from the centre of thedetector.

The second task uses the fact that the magnetic field is almost constant in a largepart of the tracker volume and also that most of the support structure is concentratedon the layers, close to the sensors. During reconstruction the typical step length forpropagation of track parameters is on the order of the distance between two layers anda helical track model is adequate. For reconstruction purposes the detailed distributionof passive material as used in the simulation is replaced by an attribution of materialto layers. This model simplifies the estimation of energy loss and multiple scattering,which can be done at the position of the sensitive elements without requiring additionalpropagation steps.

Starting from the reconstructed hits (see figure 6.1), the track reconstruction isdecomposed into four logical parts:

• Seed generation

• Pattern recognition or trajectory building

• Ambiguity resolution

40

6.1. Track Reconstruction 41

• Track fitting and smoothing

Seed generation provides initial trajectory candidates for the full track reconstruc-tion. A seed must define initial trajectory parameters and errors. They can be ob-tained externally to the tracker, using inputs from other detectors, but the precisionof initial trajectory parameters obtained in such a way is, in general, poor. Anotherway is to construct seeds internally. In this case each seed is composed from the setof reconstructed hits that are supposed to come from 1 charged particle track. Since5 parameters are needed to start trajectory building, at least 3 hits, or 2 hits and abeam constraint, are necessary. If the beam constraint is used it is removed during thefinal fit. Hits that are seed constituents are provided by the dedicated reconstruction.

The pattern recognition is based on a combinatorial Kalman filter method. Thefilter proceeds iteratively from the seed layers, starting from a coarse estimate of thetrack parameters provided by the seed, and including the information of the successivedetection layers one by one. On each layer, i.e., with every new measurement, the trackparameters are known with a better precision, up to the last point, where they includethe full tracker information.

Figure 6.1: Number of hits in the tracking detector of pions with a pT of 10 GeV independence of η.

42 Chapter 6. Vertex Reconstruction

Ambiguities in track finding arise because a given track may be reconstructedstarting from different seeds, or because a given seed may result in more than onetrajectory candidate. These ambiguities, or mutually exclusive track candidates, mustbe resolved in order to avoid double counting of tracks.

For each trajectory, the building stage results in a collection of hits and in anestimate of the track parameters. However, the full information is only available atthe last hit of the trajectory and the estimate can be biased by constraints appliedduring the seeding stage. Therefore the trajectory is refitted using a least-squaresapproach, implemented as a combination of a standard Kalman filter and smoother.

Five parameters are chosen to describe a track: d0, z0, φ, cot θ, and the transversemomentum pT [44]. The track parameters are defined at the point of closest approachof the track to the beam axis (called the impact point); d0 and z0 hence measure thecoordinate of the impact point in the transverse and longitudinal plane (d0 = y0 cos φ−x0 sin φ, where x0 and y0 are the transverse coordinates of the impact point). Theazimuthal angle of the momentum vector of the track, φ, is taken at the impact point,and θ is the polar angle. Figure 6.2 shows the resolution of the 5 track parameters forsamples of single muons with pT of 1, 10, and 100 GeV/c.

6.2 Simulation of Tracker Misalignment

The large number of independent silicon sensors (about 15 000) and their excellentresolution of 10–50 µm make the alignment of the CMS strip and pixel trackers acomplex and challenging task. The displacement of silicon sensors from their expectedposition in the tracker is one of the largest potential sources of tracking uncertainties.To study the impact of tracker misalignment on track and vertex reconstruction inconcrete physics analysis channels, a realistic model of misalignment effects has beenimplemented within the standard CMS reconstruction software.

The displacement of detector modules is implemented after detector simulation atthe reconstruction level using a dedicated software tool, which is able to move androtate all tracker parts (individual modules as well as rods, layers, half-barrels, etc.).Hits on tracker sensors are generated according to the ideal detector geometry, andthe geometrical shifts and rotations of the sensors are introduced afterwards. Withinthe quoted uncertainties, the misalignments are applied using a flat distribution formechanical constraints, whereas a Gaussian distribution is used for laser and track-based alignment results. To achieve a reasonable χ2 distribution in the track fit, thehit position error is increased by adding an additional error in quadrature that reflectsthe size of the assumed misalignment (alignment position error).

Two different default misalignment scenarios have been developed, which can beeasily used but also modified if needed, as explained in [46]. The “First Data Taking”(or “Short Term”) scenario has an accuracy as expected from the mounting precision, a

6.2. Simulation of Tracker Misalignment 43

a) b)

c) d)

e)

Figure 6.2: Resolution of the 5 track parameters for single muons with transversemomenta of 1, 10 and 100 GeV/c : a) transverse momentum, b) φ, c) transverseimpact parameter, d) longitudinal impact parameter and e) cot θ [44].


laser system and some track based alignment for the pixel detectors after an integratedluminosity up to a few hundred pb−1. The “Long Term” scenario has a precisionas expected from the track based alignment after a period of data taking with anintegrated luminosity about 10 fb−1.

The effects on vertex reconstruction of both misalignment scenarios as well as ofthe scenario of a perfectly aligned tracking detector are studied in this thesis.

6.3 Fundamentals of Vertex Reconstruction

Vertex reconstruction usually involves two steps, vertex finding and vertex fitting.Vertex finding involves grouping tracks into vertex candidates. The vertex findingalgorithms can be very different depending on the physics case (primary or secondaryvertex finding, reconstruction of exclusive decays, etc.). Vertex fitting involves deter-mining the best estimate of the vertex parameters (position, covariance matrix, andtrack parameters constrained by the vertex position and their covariances) for a givenset of tracks, as well as indicators of the fit quality (total χ2, number of degrees offreedom, or track weights).

The most often used algorithm for vertex fitting is the well-known Kalman filter(KVF) [47]. It is mathematically equivalent to a global least-squares minimisation,which is the optimal estimator when the measurements are Gaussian and the fittedparameters depend linearly on those measurements. The filter can also compute animproved estimate of the track momenta, using both the vertex and the resultingtrack-to-track covariance matrices as constraints [48].

The Trimmed Kalman Fitter (TKF) is the conventional robust version of theKalman vertex fitter, where tracks that are incompatible with the vertex are removedone by one from the vertex, starting with the least compatible track. It is a hard-assignment, iterative fit. All vertex finding algorithms described below are using theTrimmed Kalman Fitter as vertex fitter.

At an exclusive reconstruction of vertices a set of tracks is fitted to a vertex andno vertex finding is needed. It is used for example for b-physics, where the tracks areexpected to belong to the b-hadron. In contrast to an inclusive reconstruction thealgorithm has to decide, which tracks belong to which vertex candidate. The recon-struction of the primary vertex or b-tagging are typical applications for an inclusivereconstruction. If all reconstructed tracks are given to the vertex finder it is calleda global reconstruction, if only a part of tracks like the tracks in a jet is given tothe vertex finder it is called a local reconstruction. For all studies in this work theprimary vertices have been reconstructed globally, while the secondary vertices havebeen reconstructed locally using the tracks in a jet.

In most cases b-hadrons produce a tertiary vertex because the decay chain proceedsvia charm production (the b-c-decay chain). The lifetime and the number of tracks

6.4. Primary Vertex Reconstruction 45

from the decay vertex are smaller for weakly decaying c- than for weakly decayingb-hadrons. For this reason the secondary and the tertiary vertices are merged into onevertex in most cases. If tracks coming from a tertiary vertex are also used to fit thesecondary vertex, the measured flight distance is shifted to a higher value.

6.4 Primary Vertex Reconstruction

The default primary vertex finder (PVF) of ORCA performs primary vertex recon-struction using all tracks reconstructed in the event. The four main steps are:

• Track preselection, based on their distance of closest approach to the beam (bydefault, the significance of the transverse impact parameter is required to be < 3)and their pT (pT > 1.5 GeV/c).

• Formation of clusters of tracks, based on the z-coordinate of their point of closestapproach with respect to the beam line (tracks closer than 1 mm are groupedtogether).

• A fit of a primary vertex candidate for each of these clusters, discarding tracksincompatible with the candidate vertex.

• The exclusion of poor fits (χ2 probability < 1%) and vertices incompatible withthe beam line (probability < 1%).

All the compatibility probabilities are computed assuming Gaussian resolutions. Thecompatibility with the beam axis is computed assuming a Gaussian beam spot witha width of 15 µm in x and y.

After vertex finding, the vertex candidates are sorted in decreasing order of thesum of the p2T of the associated tracks. A detailed description of the algorithm can befound in [49].

6.5 Secondary Vertex Reconstruction

6.5.1 Trimmed Kalman Vertex Finder TKVF

The Trimmed Kalman Vertex Finder [48] is the default secondary vertex finder ofORCA. It searches for vertex candidates among the input set of tracks, in an iterativeway. During the first iteration, a Trimmed Kalman Vertex Fitter is applied to thecomplete input set of tracks, yielding as outputs a vertex candidate and a set of trackswhich are incompatible with that vertex candidate. During the subsequent iterations,the same procedure is applied to the set of incompatible tracks identified at previousiterations.


6.5.2 Filter for Secondary Vertices

The Trimmed Kalman Vertex Finder is sensitive to primary and secondary vertices, soa vertex filter is used to select secondary vertex candidates. Furthermore, the vertexfilter rejects K0s candidates. The vertex filter uses the following cuts on the vertices:

• The distance from the vertex to the beam line has to exceed 100 µm but mustnot exceed 2.5 cm. The lower limit should reject primary vertices, the upperlimit photon conversions and nuclear interactions in the beampipe.

• The distance from the vertex to the beam line divided by its uncertainty has tobe greater than three: Lt

σLt> 3.

• The total invariant mass of the vertex must be smaller than 6.5 GeV/c2 todiscard primary vertices.

• If more than 65% of the tracks in a vertex are also used for the primary vertexthe vertex is rejected. The cut at 65% was chosen to reject vertices with threetracks that share two of this tracks with the primary vertex.

• Vertices with two oppositely charged tracks and an invariant mass of the K0smass (± 50 MeV) are rejected.

The 100 µm cut and the 3σ cut on the transverse flight distance are most important,because they reject most of the primary vertices. After these cuts the effect of the cutof 6.5 GeV/c2 on the total invariant mass of the vertex is very small. The cut on K0scandidates is important for b-tagging, because it highly reduces the mistagging rateof udsg-jets

6.5.3 Tertiary Vertex Track Finder TVTF

The Trimmed Kalman Vertex Finder has the following shortcoming: When a sec-ondary vertex is reconstructed, but the track reconstructor only finds one track fromthe tertiary vertex, this single track is not associated to the secondary vertex in manycases. This also happens when the tertiary vertex is reconstructed, but only onetrack from the secondary vertex is reconstructed. Therefore the Tertiary Vertex TrackFinder first uses the Trimmed Kalman Vertex Finder and the vertex filter describedin 6.5.2 and then tries to find these additional tracks coming from the b-c-decay chain.Because of the high momentum of the b-hadron the tertiary vertex of the c-hadronis close to the b-flight-line, which is given by the primary vertex and the secondaryvertex. So these additional tracks from the tertiary vertex are close to the b-flight-line,too.

6.5. Secondary Vertex Reconstruction 47

These additional tracks are not used to refit the vertex, but rather to get a morecomplete reconstruction of the vertex. This can be useful to discriminate between b-and c-jets. The b-c-decay chain of a typical b-jet and the relation between the flight-line of a b-hadron and the tertiary vertex is shown in Figure 6.3. To get a betteroverview, the reconstructed tracks are not shown at full length.

A similar algorithm to the Tertiary Vertex Track Finder has been already used in theDELPHI experiment [50]. The Tertiary Vertex Track Finder has been developed andoptimised for CMS within this thesis and the algorithm works as follows:

1. Reconstruction of the primary vertex using the Primary Vertex Finder.

2. Reconstruction of the secondary vertex using the Trimmed Kalman Vertex Finder.

3. Selection of secondary vertex candidates using the vertex filter described in 6.5.2.

4. Calculation of the b-flight line using the primary and the secondary vertex. De-tails of the calculation are given in appendix B.

5. If either no primary or no secondary vertex is found the filtered secondary ver-tices of the Trimmed Kalman Vertex Finder are used as result.

6. Adding of tracks with following properties to the secondary vertex:

(a) The track must not already be assigned to a primary or a secondary vertex.

(b) The transverse impact parameter1 significance of the track must be greaterthan 1.5 to reject tracks from the primary vertex

(c) The significance of the distance between the track and the b-flight-line mustbe smaller than 10 to get only tracks that are close to the b-flight line.

(d) The track’s point of closest approach to the b-flight-line, the so called“pseudo tertiary vertex”, must have a distance to the beam line between100 µm and 2.5 cm. The lower limit should reject tracks from the pri-mary vertices, the upper limit tracks from photon conversions and nuclearinteractions in the beampipe.

(e) The pseudo tertiary vertex must lie in the propagation direction of the jet.

The values of the cuts are motivated in 7.6.

1transverse distance between track and beam line


Figure 6.3: Schematic view of a b-c-decay chain and the principle of the TertiaryVertex Track Finder TVTF.

6.5.4 Further Secondary Vertex Reconstruction Algorithms

Two further secondary vertex reconstruction algorithms have been investigated in thisthesis: The D0Phi and the Combined Vertex Finder.

The method of the D0Phi described here is an adaptation to the CMS experiment ofan algorithm already used by the CDF Collaboration [51] for the top quark discovery.The algorithm is based on correlations between the track impact parameter (d0) andthe azimuthal angle (φ) in the transverse (r− φ) plane. The principle is illustrated inFig. 6.4.

Tracks are linearised at the point of closest approach to the primary vertex. If thetransverse impact parameter has the same sign of the track angular momentum, thefollowing relationship should hold:

d(i)0 ∼ l sin (φi − φB) ∼ l(φi − φB) (1)

where l is the vertex distance from the primary vertex in the transverse view and φBits azimuth.

For each track d(i)0 and φi are provided by the track reconstructor while l and φB

are unknown. It is important to notice that, according to eq.1, d(i)0 linearly depends on

φi and the slope (l) and the constant term (−lφB) are the same for tracks belonging


(1)d

d(2)

0

0 l

φ

φB

2

φ1

x

y

SecondaryVertex

Track 2

Track 1

Primary Vertex

Figure 6.4: Principle of the D0Phi Vertex Finder.

to the same vertex. Therefore, when each track is associated to a point in the d0 − φplane, tracks associated to the same secondary vertex and its corresponding tertiaryvertices are aligned with a positive slope, while primary tracks would be uncorrelated.An example is provided in Fig. 6.5: black dots are associated to tracks from a B-decaywhile open squares denote primary vertex tracks.

The basic requirement on tracks to be entered in the algorithm is that the absolutevalue of the transverse impact parameter significance should be larger than 2 to avoidthe use of tracks from the primary vertex. This results in a high purity but lowefficiency of finding secondary vertices. The definitions of purity and efficiency aregiven in 7.2. Besides the high vertex finding purity another benefit of the D0Phi VertexFinder is, that tracks from the tertiary vertex can be associated to the secondaryvertex, even when only one track from the tertiary vertex has been reconstructed.

To get a better use of the positive properties of the D0Phi Vertex Finder its results canbe combined with another vertex finder. This is done by the Combined Vertex Finder,which combines the results of two vertex reconstruction algorithms (sub-algorithms)and has been developed for CMS within the scope of this thesis. A good combinationfor the Combined Vertex Finder are the Trimmed Kalman and the D0Phi VertexFinder. This combination uses the high vertex finding efficiency of the TKVF and thehigh purity and the association of tertiary vertex tracks to the secondary vertex of theD0Phi Vertex Finder.


-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

-1.3 -1.25 -1.2 -1.15 -1.1 -1.05 -1 -0.95

B tracks

PV tracks

φ

d0

(cm

)

Figure 6.5: The D0 − φ plane with points corresponding to tracks in a b−jet. Blackdots correspond to tracks from a B-decay, while open squares correspond to primaryvertex tracks.

The Combined Vertex Finder works as follows:

1. Reconstruction of secondary vertex candidates using the Trimmed Kalman Ver-tex Finder.

2. Reconstruction of secondary vertex candidates using the D0Phi Vertex Finder.

3. Combination of the results of the sub-algorithms:

If only one sub-algorithm has found a secondary vertex candidate this candidateis taken as result. If both sub-algorithms have found a candidate, the positionand the position error of the first sub-algorithm plus the tracks of both sub-algorithms are taken as result.

Another mode of operation is to deliver only a result, when the first sub-algorithm has found a vertex candidate and only then use the extra tracks fromthe secondary sub-algorithm.

The main drawback of the D0Phi Vertex Reconstructor is that it is very slow, itsometimes needs more than a minute on a 2 GHz PC to reconstruct the vertices ina jet. The Combined Vertex Reconstructor uses the D0Phi Vertex Reconstructor as


default and so has the same drawback. The Tertiary Vertex Track Finder shows betterresults and is much faster than the D0Phi and the Combined Vertex Reconstructorand so these two vertex reconstructors are not used at CMS anymore.

Chapter 7

Performance of Secondary VertexReconstruction

This chapter shows the performance of the reconstruction of secondary vertices at CMSfor different vertex reconstruction algorithms and for different alignment scenarios ofthe tracker. The section on secondary vertex reconstruction in the CMS PhysicsTechnical Design Report Volume I [1] is based upon these studies.

7.1 Event Simulation and Reconstruction

For the studies in the chapters 7 and 8 Monte Carlo di-jet events are used. Theycontain at least one b-, c- or udsg-jets in the tracker pseudorapidity region |eta| < 2.4with transverse momenta pT between 30-50, 50-80, 80-120 and 120-170 GeV/c. Theyhave been simulated with pile-up events as expected at a luminosity of 2·1033cm−2s−1.The CMS term for these event samples is “bt03 di-jet events” and details of the eventgeneration and the simulation are given in appendices C and D.

For jet reconstruction an iterative cone algorithm with a cone size of 0.5 is utilised.The input used for the jet clustering are the towers from the electromagnetic andhadronic calorimeters. A calibration as deduced from the Monte Carlo simulation hasbeen applied to correct the raw jet energy. For the central part of the detector (barrel)only jets with |ηjet| < 1.4 are investigated, and in the forward parts (endcaps) only jetswith 1.4 < |ηjet| < (2.5− 23 ·0.5 ≈ 2.17) are used. The upper limit for the endcaps waschosen such that the jet is fully contained within the fiducial volume of the trackingdetector.

As far as not denoted the simulated distance of the vertex to the beam line mustbe between 100 µm and 2 cm. These cuts are demanded to get a simulated vertexthat lies in the acceptance of the used vertex reconstruction algorithms but anywaythe most simulated secondary vertices are in this range.

52

7.2. Definition of Efficiency, Purity and Resolution ofSecondary Vertex Reconstruction 53

For the reconstruction of tracks the combinatorial Kalman filter method describedin 6.1 is used and the following track selection cuts are applied:

• at least 8 reconstructed hits in total (pixel and silicon strip detectors);

• at least 2 reconstructed hits in the pixel detectors;

• transverse momentum pT > 1 GeV/c;

The association of tracks to jets is performed via a cone based ∆R =√

∆φ2 + ∆η2

distance criterion with ∆R(jet-track) = 0.3.

7.2 Definition of Efficiency, Purity and Resolution

of Secondary Vertex Reconstruction

The performance of the secondary vertex reconstruction is studied in terms of thefollowing variables:

Rate of secondary vertex finding: The number of jets with at least one recon-structed secondary vertex divided by the number of investigated jets.

Efficiency of secondary vertex finding: The number of jets with a reconstructedsecondary vertex with more than 50% tracks coming from the weakly decaying b- orc-hadron divided by the total number of investigated jets. The secondary and thetertiary vertices are merged into one vertex in most cases (see 6.3) and so tracks froma tertiary vertex are included in the efficiency and all other variables described hereas well.

Purity of secondary vertex finding: The number of jets with a reconstructedsecondary vertex with more than 50% tracks coming from the weakly decaying b- orc-hadron divided by the number of jets with a reconstructed secondary vertex. Thisdefinition is equivalent to efficiency divided by rate.

Track association efficiency: The number of reconstructed tracks associated to thevertex and coming from a weakly decaying b- or c-hadron divided by the number ofreconstructed tracks associated to the jet and coming from a weakly decaying b- orc-hadron.

Track association purity: The number of reconstructed tracks associated to thevertex and coming from a weakly decaying b- or c-hadron divided by the number ofall tracks in the vertex.

Flight distance: The reconstructed flight distance of a weakly decaying b- or c-hadron is defined as the distance between the simulated primary vertex and the

54 Chapter 7. Performance of Secondary Vertex Reconstruction

Figure 7.1: The definition of the flight distance and the 3D angle in space.

reconstructed secondary vertex. Only secondary vertices with a purity > 50% areconsidered.

3D angle in space: The 3D angle in space is defined as the angle between the linegiven by the simulated primary vertex to the simulated secondary vertex and the linegiven by the simulated primary vertex to the reconstructed secondary vertex. Onlysecondary vertices with a purity > 50% are considered. Figure 7.1 illustrates thedefinition of the flight distance and the 3D angle in space.

Pure b-hadrons: All tracks associated to the vertex must originate directly from theweakly decaying b-hadron.

7.3 Reconstruction Efficiency and Purity of the

Trimmed Kalman Vertex Finder (TKVF)

Tables 7.1 and 7.2 show the secondary vertex finding rate, efficiency and purity and thetrack allocation efficiency and purity determined using the Trimmed Kalman VertexFinder for weakly decaying b- and c-hadrons with a pT of 30-70 and 70-170 GeV/c. Thedegradation of the performance of the secondary vertex reconstruction in the forwardpart of the detector compared to the central part arises from the better track impactparameter resolution in the transverse (r-φ) plane compared to the longitudinal (r-z)

7.3. Reconstruction Efficiency and Purity of theTrimmed Kalman Vertex Finder (TKVF) 55

Tracker alignment perfect short term long term

Barrel Endcaps Barrel Barrel

b c b c b c b c

Secondary vertex finding

Rate [%] 69.6 28.5 62.5 23.6 66.1 21.2 66.7 23.1

Efficiency [%] 64.8 20.6 55.5 14.0 61.8 16.1 62.4 17.6

Purity [%] 93.1 72.4 88.7 59.3 93.5 76.1 93.5 76.2

Track association

Efficiency [%] 84.3 83.3 81.6 75.4 86.5 85.1 86.3 85.1

Purity [%] 92.1 79.7 88.3 69.6 92.3 81.8 92.3 82.1

Table 7.1: The vertex finding rate, efficiency and purity and the track efficiency andpurity from the TKVF for b- and c-hadrons which lie in the pT range 30–70 GeV/c.

Tracker alignment perfect short term long term

Barrel Endcaps Barrel Barrel

b c b c b c b c

Secondary vertex finding

Rate [%] 76.1 29.2 68.6 24.0 72.6 21.1 74.2 23.9

Efficiency [%] 70.2 20.9 59.7 13.9 67.7 15.8 69.1 18.0

Purity [%] 92.2 71.5 86.9 58.1 93.2 74.9 93.1 75.1

Track association

Efficiency [%] 77.6 78.9 72.5 71.1 80.5 80.1 80.1 81.1

Purity [%] 91.3 79.6 87.1 69.7 91.8 81.0 91.9 81.5

Table 7.2: The vertex finding rate, efficiency and purity and the track efficiency andpurity from the TKVF for b- and c-hadrons which lie in the pT range 70–170 GeV/c.

56 Chapter 7. Performance of Secondary Vertex Reconstruction

Entries 44107

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Efficiency0 0.2 0.4 0.6 0.8 1

rela

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io

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0.5

0.6

0.7

0.8Entries 44107

Mean 0.8431

Entries 44107

Mean 0.9206

Purity0 0.2 0.4 0.6 0.8 1

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