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Determination of the Semi-Leptonic Branching Fraction of Neutrino-Induced Charm Hadrons Using Nuclear Emulsion

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Determination of the Semi-Leptonic Branching Fraction of Neutrino-Induced Charm Hadrons Using Nuclear Emulsion Determination of the semi-leptonic branching fraction of neutrino-induced charm hadrons using nuclear emulsion Bart Van de Vyver Promotor: Prof. Jacques Lemonne Co-promotor: Dr. Pierre Vilain CERN-THESIS-2002-024 04/04/2002 April 4, 2002 Vakgroep Natuurkunde Faculteit van de Wetenschappen Vrije Universiteit Brussel Proefschrift ingediend met het oog op het behalen van de Wettelijke Graad van Doctor in de Wetenschappen CONTENTS Introduction ::::::::::::::::::::::::::::::::::::::::: 1 1. Neutrino-induced charm production ::::::::::::::::::::::::: 7 1.1 Introduction ...................................... 7 1.2 The inclusive cross section for neutrino scattering ................ 7 1.3 The parton model ................................... 11 1.4 Additional effects ................................... 15 1.4.1 Nuclear effects ................................ 15 1.4.2 Electroweak radiative corrections ..................... 16 1.5 QCD and the factorization theorem ......................... 17 1.6 The charm mass threshold and target mass effects ................ 22 1.7 Parton-level contributions to charm production .................. 26 1.8 Current experimental status ............................. 29 2. The CHORUS beam and detector ::::::::::::::::::::::::::: 33 2.1 Introduction ...................................... 33 2.2 The neutrino beam .................................. 35 2.3 Electronic components of the CHORUS detector ................. 37 2.3.1 Scintillating fibre trackers .......................... 37 2.3.2 Hexagonal magnet spectrometer ...................... 38 2.3.3 High resolution calorimeter ......................... 41 2.3.4 Muon spectrometer .............................. 43 2.3.5 Trigger and data acquisition ......................... 45 3. Nuclear emulsion and automatic scanning :::::::::::::::::::::: 47 3.1 Nuclear emulsion ................................... 49 3.1.1 Image formation and photographic development ............ 49 3.1.2 Composition of nuclear emulsion ..................... 52 3.1.3 Contents and characteristics of emulsion images ............. 53 3.1.4 Hybrid experiments ............................. 55 3.1.5 The CHORUS emulsion target ....................... 57 3.2 Microscope optics ................................... 61 3.2.1 Transverse resolution and numerical aperture .............. 61 3.2.2 Axial resolution and depth of focus .................... 62 3.2.3 Optical aberrations .............................. 66 3.2.4 Kohler¨ illumination .............................. 71 3.3 Digital signal processing ............................... 74 3.3.1 Digital filters ................................. 75 ii Contents 3.3.2 Hardware for digital signal processing .................. 75 3.4 The microscope hardware at CERN ......................... 77 3.4.1 Layout of the laboratory ........................... 78 3.4.2 Mechanics of the scanning table ...................... 78 3.4.3 The optical system .............................. 81 3.4.4 The digital camera .............................. 85 3.4.5 The DSP boards ................................ 87 3.5 Data acquisition and on-line analysis ........................ 88 3.5.1 Overview of the data flow .......................... 89 3.5.2 Real-time processing of single images ................... 92 3.5.3 On-line tracking for a tower of images ................... 94 3.5.4 Scanning procedure for thin sheets ..................... 100 3.5.5 Scanning procedure for thick sheets .................... 104 3.5.6 Alignment ................................... 105 3.5.7 Vertex analysis ................................ 108 4. Event reconstruction in emulsion ::::::::::::::::::::::::::: 111 4.1 The net scan procedure ................................ 111 4.2 Description of the measurement errors ....................... 114 4.3 The effect of multiple Coulomb scattering ..................... 119 4.4 Track fit ......................................... 122 4.5 Track matching to the electronic detectors ..................... 128 4.6 Vertex fit ........................................ 132 4.7 Distance of closest approach ............................. 138 4.7.1 Impact parameter between a track and a vertex ............. 139 4.7.2 Impact parameter between two tracks ................... 141 4.8 Event reconstruction ................................. 143 4.8.1 Track fitting and matching .......................... 144 4.8.2 Vertex fitting .................................. 144 4.8.3 The scanback track and vertex ....................... 145 4.8.4 Ambiguities .................................. 146 4.9 Selection of secondaries ............................... 147 4.9.1 Scanback vertex ................................ 148 4.9.2 Scanback track ................................ 150 5. The semi-leptonic branching fraction ::::::::::::::::::::::::: 153 5.1 The data sample .................................... 154 5.2 Manual checks ..................................... 159 5.3 Event simulation in emulsion ............................ 165 5.4 Comparison between data and simulation ..................... 168 5.4.1 Description of the measurement errors .................. 171 5.4.2 Description of the segment finding efficiency ............... 172 5.4.3 Migration of multiplicity between the true and reconstructed value .. 173 5.4.4 Contribution of quasi-elastic and diffractive processes ......... 174 5.5 The charm selection efficiency ............................ 178 5.6 Selection of muonic charm decays ......................... 182 5.7 Determination of the semi-leptonic branching ratio ............... 185 Contents iii 5.7.1 Comparison with other experiments .................... 188 5.7.2 The Cabibbo-Kobayashi-Maskawa matrix element Vcd ......... 189 j j Conclusions and outlook :::::::::::::::::::::::::::::::::: 191 Appendix 195 A. Digital signal processing: a primer :::::::::::::::::::::::::: 197 A.1 Definitions in DSP ................................... 197 A.2 The z-transform .................................... 199 A.3 The mathematics of digital filters .......................... 201 iv Contents LIST OF FIGURES 1.1 Kinematics of neutrino nucleon charged current scattering. ........... 8 1.2 Feynman diagram for neutrino nucleon charged current scattering. ...... 10 1.3 Possible helicity configurations in the scattering between neutrinos or an- tineutrinos and quarks or antiquarks. ....................... 13 1.4 Examples of electroweak radiative corrections to neutrino-quark scattering. 17 1.5 The fundamental vertices in QCD, the theory of strong interactions. ...... 17 1.6 The lowest order potential in any field theory. ................... 18 1.7 Corrections to the potential in abelian, as well as non-abelian, field theory. .. 19 1.8 Non-abelian corrections to the field theory potential. ............... 19 1.9 Some of the diagrams contributing to the LO splitting functions in the DGLAP equations. ....................................... 20 1.10 Some of the diagrams contributing to the NLO splitting functions in the DGLAP equations. ....................................... 20 1.11 The coordinate systems used in the helicity formalism. ............. 24 1.12 Tree-level Feynman diagram for neutrino-induced charm production. ..... 26 1.13 Feynman diagrams for the boson-gluon fusion process. ............. 27 1.14 Feynman diagrams for radiative gluon processes. ................ 27 2.1 Sketch of the CHORUS detector. .......................... 34 2.2 Sketch of the WANF neutrino beamline. ...................... 35 2.3 Neutrino beam composition and energy spectra. ................. 36 2.4 Geometry of the fibre trackers in the emulsion target region. .......... 38 2.5 The hexagonal air-core magnet and the resolution on the momentum mea- surement. ........................................ 39 2.6 Schematic view of the calorimeter and resolution on the energy measurement. 42 2.7 Schematic view of one of the six sections in the muon spectrometer and reso- lution on the muon momentum measurement. .................. 44 3.1 Automatic scanning of emulsion plates which have been exposed perpendic- ular to a particle beam. ................................ 48 3.2 Fading of the latent image in Fuji ET-7B emulsion depending on the storage and exposure conditions. ............................... 51 3.3 Emulsion distortion. ................................. 55 3.4 Schematic view of an X-ray gun between two interface emulsion sheets. ... 58 3.5 The reduction of edge distortions using a frame of dummy gel. ........ 59 3.6 Density of background tracks due to cosmic rays as a function of exposure time and shielding. .................................. 60 3.7 Airy diffraction pattern and intensity point spread function. .......... 63 3.8 Spherical aberration of a convergent lens. ..................... 67 vi List of Figures 3.9 Aplanatic front end of a homogeneous immersion objective. .......... 68 3.10 Inner coma aberration in the meridional plane. .................. 68 3.11 The effect of astigmatism on the image of a spoke wheel. ............ 69 3.12 The effect of deformation on the image of a centred square, for magnification increasing or decreasing as a function of the distance from the centre. ..... 70 3.13 Ray paths in a transmitted light microscope adjusted for Kohler¨ illumination. 72 3.14 Variables determining the image brightness in the case of Kohler¨ illumination. 73 3.15 Mounting of the emulsion plates on the scanning table. ............. 80 3.16 Schematic view of the imaging and illumination systems. ............ 83 3.17 Schematic view of the oil immersion
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