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  • i

    Abstract

    Jefferson Lab Experiment E04-001 used the Rosenbluth technique to mea-

    sure R = σL/σT and F2 on nuclear targets. This experiment was part of

    a multilab effort to investigate quark-hadron duality and the electromagnetic

    and weak structure of the nuclei in the nucleon resonance region. In addition

    to the studies of quark-hadron duality in electron scattering on nuclear targets,

    these data will be used as input form factors in future analysis of neutrino data

    which investigate quark-hadron duality of the nucleon and nuclear axial struc-

    ture functions. An important goal of this experiment is to provide precise data

    which to allow a reduction in uncertainties in neutrino oscillation parameters

    for neutrino oscillation experiments (K2K, MINOS). This inclusive experiment

    was completed in July 2007 at Jefferson Lab where the Hall C High Momentum

    Spectrometer detected the scattered electron. Measurements were done in the

    nuclear resonance region (1 < W 2 < 4 GeV 2) spanning the four-momentum

    transfer range 0.5 < Q2 < 4.5 (GeV 2). Data was collected from four nuclear

    targets: C, Al, Fe and Cu.

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  • ii

    Acknowledgments

    I am heartily thankful to my supervisor, Prof. Donal Day, whose encouragement,

    guidance and support enabled me to develop an understanding of the subject.

    I thank the members of University of Virginia research group Dr. Oscar Rondon,

    Prof. Donald Crabb, Prof. Kent Paschke, and Prof. Mark Williams for carefully

    reviewing my thesis.

    I am grateful to Dr. Peter Bosted and Prof. Eric Christy for their continuous in-

    volvement and help in the analysis of this experiment. I am also thankful to graduate

    students Ibrahim Albayrak and Ya Li for their contribution to this analysis and Dr.

    Patricia Solvignon for organizing analysis meetings.

    It is a pleasure to thank those who made this thesis possible such as the authors

    of the E04-001 proposal, Prof. Arie Bodek and Prof. Cynthia Keppel.

  • iii

    Contents

    Introduction 1

    1. Nucleon Structure 7

    1.1 Inclusive Lepton-Nucleon Reactions . . . . . . . . . . . . 7

    1.1.1 Deep Inelastic Scattering and Quark Parton Model 13

    1.1.2 Scaling Violation in DIS . . . . . . . . . . . . . . 18

    1.2 F2 and R in the Nuclear Resonance Region . . . . . . . . 21

    1.3 Quark Hadron Duality . . . . . . . . . . . . . . . . . . . 24

    1.3.1 Bloom-Gilman Duality . . . . . . . . . . . . . . . 24

    1.3.2 Duality in Nuclei . . . . . . . . . . . . . . . . . . 27

    1.4 Theoretical Basis of Duality . . . . . . . . . . . . . . . . 29

    1.4.1 Moments of Structure Functions . . . . . . . . . . 29

    1.4.2 Operator Product Expansion . . . . . . . . . . . 30

    1.5 The Nuclear Dependence of R . . . . . . . . . . . . . . . 33

    1.6 Neutrino Scattering . . . . . . . . . . . . . . . . . . . . . 36

    1.6.1 Structure Functions in DIS . . . . . . . . . . . . . 37

    1.6.2 Neutrino Scattering in Resonance Region . . . . . 39

    2. Experimental Apparatus 43

  • iv

    2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

    2.2 The Thomas Jefferson Accelerator Facility . . . . . . . . 44

    2.3 Beam-line Apparatus . . . . . . . . . . . . . . . . . . . . 46

    2.3.1 Beam Position Monitors . . . . . . . . . . . . . . 46

    2.3.2 Beam Current Monitors . . . . . . . . . . . . . . 48

    2.3.3 Beam Raster . . . . . . . . . . . . . . . . . . . . 49

    2.4 Experimental Hall C . . . . . . . . . . . . . . . . . . . . 50

    2.5 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

    2.6 High Momentum Spectrometer . . . . . . . . . . . . . . 54

    2.6.1 HMS Optics Design . . . . . . . . . . . . . . . . . 54

    2.7 HMS Detector Package . . . . . . . . . . . . . . . . . . . 55

    2.7.1 Drift Chambers . . . . . . . . . . . . . . . . . . . 56

    2.7.2 Hodoscopes . . . . . . . . . . . . . . . . . . . . . 58

    2.7.3 Gas Čerenkov Detector . . . . . . . . . . . . . . . 60

    2.7.4 Electromagnetic Calorimeter . . . . . . . . . . . . 62

    2.8 Data Acquisition System . . . . . . . . . . . . . . . . . . 64

    2.8.1 Triggers . . . . . . . . . . . . . . . . . . . . . . . 65

    3. Data Analysis 68

    3.1 BCM Calibrations . . . . . . . . . . . . . . . . . . . . . . 68

  • v

    3.2 Detector Calibrations . . . . . . . . . . . . . . . . . . . . 71

    3.2.1 Drift Chamber Calibration . . . . . . . . . . . . . 71

    3.2.2 C̆erenkov Calibration . . . . . . . . . . . . . . . . 73

    3.2.3 Calorimeter Calibration . . . . . . . . . . . . . . 75

    3.3 Target Coordinate Reconstruction . . . . . . . . . . . . . 79

    3.4 Extraction of the Differential Cross Section . . . . . . . . 81

    3.4.1 Acceptance Cuts . . . . . . . . . . . . . . . . . . 81

    3.4.2 Particle Identification Cuts . . . . . . . . . . . . . 83

    3.4.3 Background from the target walls . . . . . . . . . 90

    3.4.4 Charge Symmetric Background . . . . . . . . . . 91

    3.4.5 Pion Contamination . . . . . . . . . . . . . . . . 94

    3.4.6 Electronic and Computer Dead Times . . . . . . 95

    3.4.7 Trigger Efficiency . . . . . . . . . . . . . . . . . . 98

    3.4.8 Tracking Efficiency . . . . . . . . . . . . . . . . . 100

    3.4.9 Acceptance Calculation . . . . . . . . . . . . . . . 103

    3.4.10 Bin Centering Corrections . . . . . . . . . . . . . 108

    3.4.11 Radiative Corrections . . . . . . . . . . . . . . . . 109

    3.4.12 Coulomb Correction . . . . . . . . . . . . . . . . 116

    3.5 Cross Section Model . . . . . . . . . . . . . . . . . . . . 119

    3.5.1 Quasi-elastic model . . . . . . . . . . . . . . . . . 120

  • vi

    3.5.2 Inelastic Model . . . . . . . . . . . . . . . . . . . 123

    3.6 Global Fit and Model Iteration . . . . . . . . . . . . . . 125

    3.7 Extraction of R and F2 . . . . . . . . . . . . . . . . . . . 128

    3.8 Systematic Uncertainties . . . . . . . . . . . . . . . . . . 131

    4. Results and Discussions 136

    4.1 Elastic Electron-Proton Cross Section . . . . . . . . . . . 136

    4.2 Differential Cross Sections . . . . . . . . . . . . . . . . . 138

    4.3 Cross Section Ratios and Extraction of RA −RD . . . . 149

    4.4 Rosenbluth Separated R . . . . . . . . . . . . . . . . . . 157

    4.5 F2 Structure Function and Duality in Nuclei . . . . . . . 165

    4.6 Structure Functions and Duality Studies . . . . . . . . . 173

    5. Summary and Conclusions 186

    References 188

    A APPENDIX 199

    1.1 Tables of Rosenbluth Separated R, F1, F2 and FL . . . . 199

    1.2 HMS Kinematic Settings . . . . . . . . . . . . . . . . . . 218

    1.3 Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . 222

  • 1

    Introduction

    The study of the strongly interacting particles of nature is the study of hadrons. The

    hadrons make up the atomic nucleus and the proton and neutron account for almost

    all the mass in the known universe. In contrast to their abundance our knowledge of

    the force which determines their interactions - the force responsible for both holding

    the nucleus together, limiting its maximum size as well as determining its dynamics,

    is the least well understood of the four fundamental forces of nature. This should

    not be surprising given the description of the strong interaction in terms of Quantum

    ChromoDynamics (QCD) wherein the nucleons are the lowest mass excitations of the

    complicated blend of quark and gluon condensates which form the QCD vacuum. The

    key features associated with the QCD Lagrangian are exhibited by the nucleon are:

    color confinement, asymptotic freedom and spontaneously broken chiral symmetry.

    A study of the nucleon is a study of the strong interaction and QCD. QCD is a

    renormalizable field theory based upon the principle of local gauge invariance under

    the exchange of color. QCD describes the strong force in terms of fermion fields of

    a given color charge, given the name quarks by Gell-Mann, interacting through the

    exchange of massless gauge bosons known as gluons. The distinctive feature of QCD

    which sets it apart from the electroweak theory is the fact that these gluons possess

    non-zero color charge (unlike the photons in electro-magnetism which carry no electric

    charge).

    Among the main consequences is the property of color confinement – quarks and

    gluons are not permitted to exist as isolated free particles, but must combine to form

    color-neutral singlets: the three-quark baryons, of which the nucleons are the most

    stable, and the quark/anti-quark mesons. To date, the quantum numbers of all known

  • 2

    strongly interacting particles have been accounted for using a model based upon the

    non-Abelian internal SU(3)c symmetry of QCD for elementary quarks of six different

    flavors (these are labeled in order of increasing mass as up, down, strange, charm,

    bottom and top). Though the static properties of the nucleon can be described in this

    manner, the extreme non-linear nature of the strong force means that the dynamical

    properties of its constituents

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