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Experimental Study of the Nucleon Spin Structure

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Experimental Study of the Nucleon Spin Structure ^ i iiimii IIIII HI mil IIIII inii mil urn urn urn urn mi mi KSOO20SJ731 R: FI DE009052456 ,\,L Experimental study of the nucleon spin structure »DE009052456* ACADEMISCH PROEFSCHRIFT ^«- ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam, op gezag van de Rector Magnificus Prof. dr. P.W.M. de Meijer ten overstaan van een door het college van dekanen ingestelde commissie in het openbaar te verdedigen in de Aula der Universiteit op dinsdag 7 mei 1996 te 13.30 uur door Maarten Frederik Litmaath geboren te Apeldoorn \/l\ J, VOL -2 7 promotor: Prof. dr. J.J. Engelen co-promotor: Dr. R. van Dantzig The work described in this thesis is part o[ the research program of the National Institute for Nuclear and High Energy Physics (N1KHEF) in Amsterdam, with financial support from the Dutch Foundation for Fundamental Research on Matter (FOM) and the Dutcli National Organization for Scientific Research (NVVO). In the front cover illustration the behavior of the quarks and gluons in a nucleon is visualized by locally probing the virtual particle composition of the nucleon wave func- tion. The picture has most kindly been provided by Al'SciMed (Art, Science, Media), 100 rue du Faubourg Saint Antoine. 75012 Paris, France, tcl. (33) 1 - 44 73 90 00. To my parents. NEXT PA left BL Contents Introduction 11 1.1 Deep-inelastic scattering 13 1.1.1 Cross-section asymmetries 15 1.1.2 Towards the asymmetry measurement 16 1.2 The spin-dependent structure function </i 17 1.2.1 The small i behavior of g\ 20 1.2.2 The deuteron structure function flj1 21 1.3 Sum rules 22 1.3.1 The Björken sum rule 23 1.3.2 The Ellis-Jaffe sum rules 23 1.4 The spin puzzle 24 Experimental setup and methods 27 2.1 Asymmetry measurement design 27 2.2 The polarized target 30 2.3 The beam 34 2.4 The spectrometer 35 2.4.1 The trigger system 41 2.4.2 The data acquisition 42 2.5 The beam polarimeter 43 2.5.1 The decay method 43 2.5.2 The scattering method 44 Micro strip gas counters 49 3.1 The hardware 50 3.2 The read-out amplifiers 51 3.3 On-line processing 53 3.4 Calibration issues 55 3.5 Efficiencies and aging 61 3.6 Track reconstruction issues 62 CONTENTS 4 Data analysis 65 4.1 Phoenix 67 4.1.1 Alignment and calibration 67 4.1.2 Track reconstruction 68 4.2 Geometry 71 4.3 Snomux 71 4.4 Acceptance effects 72 4.5 Asymmetry determination 74 4.5.1 Event selection 75 4.5.2 Asymmetry calculation 76 4.5.3 Systematic studies SO 4.5.4 Radiative corrections 83 4.5.5 Systematic errors S3 5 Results 87 5.1 The spin-dependent cross section asymmetry A\(x,Q2) S7 5.2 The spin-dependent structure function gi{x,Q2) 94 5.3 The Björken and Ellis-Jaflc Sum Rules 97 5.4 Spin content of the nuclcon 103 5.5 Discussion 105 5.6 Conclusions and outlook 109 Bibliography 11 Summary 11 Samcnvatting 11 Acknowledgements 12 List of Figures 1.1 The one boson exchange diagram for deep-inelastic muon-nucleon scattering. 13 2.1 Target polarization configurations 29 2.2 The SMC polarized target 30 2.3 Electronic and nuclear Zeeman levels for hydrogen 33 2.4 Schematic overview of the SMC spectrometer detectors 36 2.5 Three-dimensional impression of the SMC setup 37 2.6 Top view of the SMC muon decay polarimeter 43 2.7 Calculated energy spectra of positrons originating from muon decay. ... 45 2.S Measured decay positron energy spectrum for a 100 GeV /J+ beam. ... 45 2.9 Monte Carlo simulation of the muon decay polarimeter response 45 2.10 Michel curve fit of the positron spectrum after acceptance corrections. 45 2.11 Top view of the SMC muon-elcctron scattering polarimeter 46 3.1 A section of an MSGC plane 50 3.2 The position of the MSGC stations in the main spectrometer 51 3.3 Schematic overview of the APC 52 3.4 APC signal evolution 53 3.5 Pedestals and noise for two planes read out serially by one Sirocco. ... 55 3.6 MSGC clement and multiplicity spectra 56 3.7 MSGC pulse heights observed at normal beam intensity 58 3.S The MSGC trigger delay curve 60 3.9 Average radial efficiencies for MSAB and MSCD GO 3.10 Efficiency and threshold of an MSCD plane versus run number 61 3.11 Average efficiency versus run number for MSAB and MSCD 62 3.12 Temperature dependent shifts of various detectors 63 3.13 Improvement of track precision by the MSGC 64 4.1 The SMC data reduction and analysis chain 66 4.2 Typical vertex distribution along the beam 72 4.3 Systematic study on the effect of aging 82 5.1 Q2 dependence of A\(x,Q2) SS LIST OF FIGURES 5.2 Q- dependence of .*}(*.. Q7) 89 5.1! The kinematic ranges covered by the nucleon spin experiments 90 Ö.-1 Tlie ])roton asymmetry A*(x) 92 5.5 Comparison of 1992 and 1994 measurements of /\f (x) 93 5.0 The dcuterou asymmetry A'}(x) 94 5.7 The neutron asymmetry A"(x) 95 5.8 f/'i'U') at the average Q2 of each x bin 97 5.9 y'\[x) <>»d ij\(x) <"vt the average Q~ of each x bin 9S 2 5.10 a?(r) at Ql = 5GcV 99 5.11 !,'>{x) and <(.r) at Ql = 5GeV2 100 5.12 Björken and Ellis-Jaffe sum rule predictions and measurements 104 5.13 Experimental values for AS vs. higher order QCD corrections 10S List of Tables 2.1 Overview of tracking detectors 38 1.1 Event .selection criteria 75 5.1 Results for A* and g» 89 5.2 Results for /I',' and gf 90 5.3 Results for gj1 91 5.4 Results for g» and gf, evaluated at Q% = lOGeV2 96 2 2 2 5.5 Sum rule results at Q 0 = lOGcV and Ql = 5GeV 101 5.6 Contributions to the error on Ff 102 5.7 Contributions to the error on F',1 102 5.8 Contributions of quark spins to the nucleon spin 105 10 LIST OF TABLES 11 Chapter 1 Introduction The atomic nucleus is built of protons and neutrons, spin | particles that are collectively called nucleons. In 1968 an experiment [1] was performed at the Stanford Linear Accel- erator (SLAC), in which electrons of 20 GeV energy were observed to scatter off pointlike objects within nucleons. These constituents were called partons and were subsequently shown to have the quantum numbers of quarks, which were proposed by Gell-Mann and Zweig [2] to explain the hadron spectrum. In the naive Quark Parton Model (QPM) a nucleon contains three spin | valence quarks. The proton is formed by two u (up) quarks, each with electric charge |, and one d (down) quark with charge — A. The neutron is an isospin mirror image of the proton: it has two d quarks and one u quark. The valence quarks in either nucleon arc surrounded by a sea of virtual quark-antiquark pairs. Besides the flavors u and d, the sea also contains s (strange) quarks with charge — i. The heavy quarks c (charm), 6 (bottom) and t (top) do not play a role in the present discussion. Quarks possess besides flavor, spin and charge another quantum number called color. This can take three different values (red, green, blue). Antiquarks have the corresponding anticolors (cyan, magenta, yellow). The nucleon and all other hadrons, bound systems of quarks and antiquarks, are colorless (white). In principle a complete dynamic description of the internal structure of the nuclcon could be provided by Quantum Chromodynamics (QCD). According to this very suc- cessful field theory the quarks are bound by gluons, the gauge bosons of the strong interaction. The quark colors are the charges associated with this interaction. As gluons carry color themselves, they can interact with other gluons. As a result the strong cou- pling constant turns out to grow as the distance between quarks increases. Free quarks have not been observed at large interquark distances: quarks are confined. When a quark is knocked out of a nucleon by means of deep-inelastic scattering at high energy, part of that energy is converted into quark-antiquark pairs, and a jet of hadrons is formed. At small intcrquark distances the strong coupling constant is small and the: quarks appear to be almost free. This phenomenon is called asymptotic freedom. It allows the use of 12 Chapter 1. Introduction perturbation theory within QCD at small distances, i.e. at high resolution. The cross section for deep-inelastic scattering displays a phenomenon called scaling, when the scattering centers are truly pointlike and free. If, on the other hand, binding effects are revealed by increasing the resolution of the scattering probe, the cross section displays scaling violations, i.e. a non-trivial dependence on the resolution. Scaling vio- lations arc observed as predicted by perturbative QCD (pQCD). What, appears to be a quark at a particular resolution, turns out to oe a collection of quarks, antiquarks and gluons at a higher resolution. Gluons are radiated by quarks (and antiquarks), occa- sionally splitting intu quark-antiquark pairs, thus generating the sea. Although pQCD describes these processes in detail, the momentum distributions of quarks, antiquarks and gluons cannot be calculated from first principles. Instead, pQCD describes the change of the apparent distributions when the nucleon is probed at a different resolution.
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