General Event Selection and Jet Energy Measurement

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B-hadron Production Rates

Production rates of the different weakly decaying B-hadron particles have been accurately determined using measurements from LEP and TeVatron experiments. These determinations use also results from B−B mixing obtained at b-factories and at the previous facilities. Several types of data have been combined. They comprise “direct” measurements as the production rates of B-hadrons decaying into a specific final state of known branching fraction (semileptonic decays or exclusive channel). A more inclusive approach was also followed by DELPHI using neural networks to separate charged from neutral b-hadrons. “Indirect” measurements have been used also as the mixing probability c. For b-hadron jets, produced at high energy, this probability corresponds to the average of the contributions from B0d and B0s mesons: c = fdcd + fscs (2.36) in which fq are the fractions of bq mesons in the jet and cd,s are the oscillation probabilities for B0d and B0s meson respectively.
These oscillation probabilities can be obtained by integrating the corresponding time distribution for mixed states. cq = 1 2 􀀀 DmqtBq2 1+ 􀀀 DmqtBq 2.

The Large Electron Positron Collider

The Large Electron Positron Collider LEP was a circular e+e− accelerator constructed at the CERN laboratory in Geneva (Switzerland). It operated from 1989 for 11 years and was, with a circumference of 27 km, the largest collider designed to that point. It consisted of eight 2.9 km long arcs and eight 0.43 km straight sections housing about 3400 dipole bending magnets, 820 quadrupoles, 500 sextupoles and 700 correcting magnets. Table 3.1 summarizes the main properties of the LEP collider. An extensive review can be found in [51].
At four points of the LEP circumference the e+ and e− beams crossed. In those interaction points the four experiments, namely ALEPH, DELPHI, L3 and OPAL, were placed to record the particles produced in the collisions. Figure 3.1 shows the LEP ring and the four experiments localization. The possibility of creating new heavy particles in a collider depends on the center of mass energy provided in the collision by the accelerated beams. For an e+e− symmetric machine like LEP, this is p s = 2E, where E is the beam energy. From 1989 to 1995 LEP operated at the energy of the Z resonance, p s = 91.2 GeV. This phase was named the LEP-I period and allowed for a wide study of Z production and decays. From 1995 onward, the energy of the beams was increased by progressively adding super-conducting cavities, reaching the maximum energy of about 210 GeV in the year 2000. This phase was aimed at studying W+W− pairs, produced above p s = 161 GeV, and to search for new particles such as the Higgs boson and supersymmetric particles. This phase was called the LEP-II period.
One of the main challenges in circular e+e− accelerators is to compensate for the energy loss due to the synchrotron radiation. Photons are emitted by electrons along their flight direction due to the transverse acceleration. Since the energy loss by synchrotron radiation is proportional to the beam energy raised at the fourth power, it can reach large values and has to be compensated for by the accelerating cavities. In addition, the dissipated power has to be absorbed by the ring components. At LEP, the synchrotron radiation was about 125MeV/turn when running at the Z energy and reached about 3400 MeV/turn in the LEP-II period.

The DELPHI Experiment

DELPHI (DEtector with Lepton, Photon and Hadron Identification) was designed and installed at LEP with the aim of providing high precision and granularity, and very effective particle identification, thanks to the implementation of a Ring Imaging Cherenkov detector. An advanced silicon detector also allowed very precise tracking and vertex determination.
The DELPHI detector is described in reference [52]. This section only seeks to summarize its main characteristics and sub-detectors. Furthermore, this document will refer only to the performance of DELPHI during the LEP-I period. It should be noted that many of these characteristics changed and improved during the years.
The DELPHI ensemble consisted of a cylindrical section in the central part called the “barrel” and two end-caps covering the “forward” regions. Figure 3.3 shows the layout of the barrel and of one end-cap. The DELPHI standard coordinate system is given by the z axis along the electron beam direction, the x axis pointing towards the center of LEP and the y axis upwards.
Cylindrical coordinates (R, q, f) usually are used, f and R being the azimuthal angle and radius in the x-y plane, respectively, and q the polar angle with respect to the z axis. The superconducting solenoid was 7.4m long with 5.2m inner diameter. It provided a highly uniform magnetic field of 1.23 T, corresponding to a current of 5000A, parallel to the z axis through the central part of the barrel. The super-conducting cable consisted of 17 wires made of 300 Nb-Ti filaments embedded in copper and cooled by liquid helium at 4.5 K. The main purpose of the super-conducting solenoid was to curve the trajectory of charged particles allowing their momentum measurement and identification (see Section 3.5.1).

Tracking Detectors

The tracking system provided the trajectories of the particles by evaluating their momenta and impact parameters. Detectors in this system were: the Vertex Detector (VD), the Inner Detector (ID), the Time Projection Chamber (TPC) and the Outer Detector (OD), in the barrel region; and the tracking chambers (FCA and FCB) in the forward region. They were the most important detectors for analyses involving B decays as we will see later.

The Vertex Detector

This detector provided a very precise measurement of the passage points of charged particles near the interaction point. This allowed for the determination of both primary and secondary vertices and the track impact parameter, providing a track reconstruction with a track resolution of about 300 μm. It is essential in the study of B hadrons coming from Z decays since their mean decay length is about 3mm from the primary vertex.
The VD detector consisted of three coaxial cylindrical layers of silicon strip detectors in the barrel region, at average radii of 6.3 cm, 9 cm, and 10.9 cm around the beam pipe. Each layer was formed by 24 overlapping (about 10 in f) modules of 23.6 cm length containing four detector plates each (see Figure 3.4). The polar angle coverage for charged particles hitting all three layers was 44 q 136. The readout pitch was 50 μm in the Rf plane perpendicular to the beam direction. In April 1994, the inner and outer layers were equipped with double-sided silicon detectors. The new detectors increased the polar angle coverage to 24 q 155.

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The Time Projection Chamber

The Time Projection Chamber, placed between the Inner and Outer Detectors, was the central tracking device in DELPHI. Along with the VD, it contributed to the track reconstruction, providing a precise measurement of the particle momenta. The TPC was a gas-filled (80% argon and 20% methane) cylinder, 340 cm long and with 120 cm radius, divided into 6 azimuthal sectors each with 192 sense wires and 16 circular pad rows (see Figures 3.6 and 3.7). Particles traversing the TPC ionized the gas. Free electrons drifted towards the end-caps by means of a 150 V/cm electric field parallel to the magnetic field of DELPHI. This electric field was created by a high tension plate (-20 kV) which separated the cylinder in two regions. The charge of the avalanche created by the drift electrons was collected on the two end plates of the TPC by means of anode wires and pad rows. This charge provided information on the charged particle energy loss per unit of length dE/dx. The z coordinate was calculated by measuring the drift time of the electrons and knowing their drift velocity. The TPC provided 16 space points per particle trajectory at 40 cm < R < 110 cm radii and between polar angles 39 q 141. The pad rows gave information about the ionization position in the Rf plane with a resolution of 250 μm per point. The z coordinate resolution was about 900 μm.

Table of contents :

La fonction de fragmentation du quark b, du LEP au TeVatron
Introduction
Théorie
Le cadre expérimental
Analyse de DELPHI
Extraction de la partie non perturbative
Fragmentation des quarks b mesurée dans CDF
Annexe : chapitres en Anglais
Abstract
1 Introduction 
2 Theory of Bottom Production, Fragmentation and Decay 
2.1 Overview: The Life Story of a Bottom Quark
2.2 Bottom Quark Production in The Hard Process
2.2.1 Bottom Quark Production at LEP
2.2.2 Bottom Quark Production at the TeVatron
2.3 Theoretical Aspects of b Fragmentation
2.3.1 Definitions of Fragmentation Functions
2.3.2 Perturbative and Non-perturbative Parts
2.3.3 Perturbative QCD
2.3.3.1 Theoretical QCD Calculations
2.3.3.2 Parton Showers in Monte Carlo Generators
2.3.4 Non-perturbative QCD
2.3.4.1 Hadronization in Monte Carlo Generators
Independent Hadronization
Cluster Hadronization
String Hadronization
Baryon Production
2.3.4.2 Phenomenological Hadronization Models
The Peterson Model
The Collins-Spiller Model
The Kartvelishvili Model
The Lund Symmetric Fragmentation Function
The Bowler Model
2.4 Excited States
2.5 B-hadron Production Rates
2.6 B Decays
3 Experimental Framework I- The LEP Collider and the DELPHI Experiment 
3.1 The Large Electron Positron Collider
3.2 The DELPHI Experiment
3.3 Tracking Detectors
3.3.1 The Vertex Detector
3.3.2 The Inner Detector
3.3.3 The Time Projection Chamber
3.3.4 The Outer Detector
3.4 Other Detectors
3.4.1 Ring Imaging Cherenkov Detectors
3.4.2 Electromagnetic and Hadron Calorimeters
3.4.3 Scintillators
3.4.4 Muon Chambers
3.5 Particle Identification and Reconstruction
3.5.1 Track Reconstruction
3.5.1.1 Primary Vertex Reconstruction
3.5.1.2 Impact Parameter Reconstruction
3.5.2 Hadron Identification
3.5.3 Lepton Identification
3.6 DELPHI Monte-Carlo Simulation
3.7 Data Reprocessing
4 Experimental Framework II- The TeVatron Collider and the CDF Experiment
4.1 TeVatron – the Source of pp Collisions
4.2 The CDF-II Detector
4.3 Standard Definitions in CDF-II
4.4 Tracking Systems
4.4.1 Silicon Tracking Detectors
4.4.2 Central Outer Tracker
4.4.3 Pattern Recognition Algorithms
4.4.4 Momentum Scale
4.5 Time of Flight
4.6 Calorimeters
4.7 Muon Systems
4.8 Triggering
4.8.1 Level 1 Trigger
4.8.2 Level 2 Trigger
4.8.3 Level 3 Trigger
4.9 Luminosity Measurement
5 B Fragmentation at DELPHI 
5.1 General Event Selection and Jet Energy Measurement
5.1.1 Data/Monte-Carlo comparison and adjustments
5.1.1.1 Accuracy of track reconstruction
5.1.1.2 Efficiency and track energy distribution
5.1.2 Jet energy reconstruction
5.2 B-Energy Reconstruction
5.3 Selection of B Candidates
5.4 Measurement of the B-Fragmentation Distribution
5.4.1 Fit Results on Real Data Events
5.4.2 Fit Results on Simulated Events
5.5 Systematic Uncertainties
5.5.1 Real Data and Simulation Tuning
5.5.1.1 Energy Calibration
5.5.1.2 Level of the Non-b Background
5.5.1.3 Track Energy and Multiplicity Tuning
5.5.1.4 Jet Multiplicity
5.5.1.5 Summary
5.5.2 Physics Parameters
5.5.2.1 b-Hadron Lifetimes
5.5.2.2 B Production Rate
5.5.2.3 b-Hadron Charged Multiplicity
5.5.2.4 g!bb Rate
5.5.2.5 Summary
5.5.3 Parameters Used in the Analysis
5.5.3.1 Parametrization of the Weight Function
5.5.3.2 b-Tagging Selection
5.5.3.3 Jet Clustering Parameter Value
5.5.3.4 Level of Ambiguous Energy
5.5.3.5 Secondary Vertex Charged Multiplicity
5.5.3.6 Summary
5.6 Comparison with Other Experiments
6 Extraction of the x-Dependence of the Non-perturbative QCD Component 
6.1 Introduction
6.2 Extracting the x-Dependence of the Non-perturbative QCD Component
6.3 x-Dependence Measurement of the Non-perturbative QCD Component
6.3.1 The Perturbative QCD Component is Provided by a Generator
6.3.2 The Perturbative QCD Component is Obtained by an Analytic Computation Based on QCD
6.4 Results Interpretation
6.4.1 Comparison with Models
6.4.2 Proposal for a New Parametrization
6.5 Checks
6.5.1 The Use of a Fitted Parametrization
8 Contents
6.5.2 The Effect of Parametrization
6.5.3 Number of Degrees of Freedom
6.5.4 Using a Different Tuning of the Monte Carlo
6.6 Combination of Fragmentation Distributions from All Experiments
6.7 Comparison of Results for All Experiments
6.8 Thoughts about Fitting Moments of Fragmentation Functions
6.9 Charm Fragmentation
6.10 Conclusions
7 B Fragmentation and Related Studies at CDF 
7.1 Introduction
7.2 Data Sample
7.2.1 Reconstruction of B± !J/yK±
7.2.2 Subtracting the Backgrounds in the Data
7.3 Monte Carlo Samples
7.3.1 General Description
7.3.2 PYTHIA Parameters
7.4 Outline of the Analysis Method
7.5 Preliminary Monte Carlo Studies
7.6 Data and Monte Carlo Comparisons
7.6.1 Comparisons with msel=5 Samples
7.6.2 Comparisons with an msel=1 Sample
7.7 A Method of Fitting the Fragmentation Function Parameters
7.8 An Estimate of the b Production Cross Section
7.8.1 Evaluation of Efficiency
7.8.2 The Inclusive b Quark Production Cross Section
7.8.3 Statistical Error Estimation
7.8.4 Systematic Error Estimation
7.8.4.1 Luminosity
7.8.4.2 Branching Ratios and Production Fraction
7.8.4.3 Trigger and Reconstruction Efficiencies
7.8.5 Comparison with Other Measurements and with Theoretical Predictions
8 Conclusion
A The Mellin Transformation 
B Fitting Histograms of Singular Error Matrices 
Bibliography 

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