Polarized target for the measurement of the gluon contribution to the nucleon spin in the COMPASS experiment Nagoya University Thesis for the degree Doctor of Philosophy in Physics by Naoki TAKABAYASHI 1 2002 1 Supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists. CONTENTS 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 2. Spin structure of the nucleon : : : : : : : : : : : : : : : : : : : : : 5 2.1 Deep inelastic scattering . 5 2.2 Cross section and structure functions in unpolarized DIS . 7 2.3 Cross section and structure functions in polarized DIS . 9 2.4 Structure functions and spin puzzle in Parton Model picture . 13 2.4.1 Parton distribution . 14 2.4.2 Spin puzzle in Parton Model picture . 16 2.5 Structure functions and spin puzzle in QCD evolved Parton Model . 18 2.5.1 Unpolarized structure functions . 18 2.5.2 Factorization schemes . 20 2.5.3 DGLAP equation and Scaling violation . 22 2.5.4 Spin-dependent structure functions and polarized DGLAP equation . 23 2.6 Interpretation of small ∆Σ. Is gluon contribution large? . 24 2.6.1 Sum rules . 25 2.6.2 Axial anomaly . 26 3. COMPASS experiment : : : : : : : : : : : : : : : : : : : : : : : : : 30 3.1 Open charm lepto-production via photon-gluon fusion . 30 3.2 Expectations . 35 3.2.1 Luminosity . 35 3.2.2 Reconstruction of the open charm events . 35 3.2.3 Statistical accuracy . 37 3.3 Comparison with the other experiments on ∆g . 40 3.3.1 High pT hadron pairs . 40 3.3.2 pp¯ collision . 41 3.3.3 Comparison of the expected precisions and the kine- matic ranges . 42 Contents ii 3.4 Experimental setup . 43 3.4.1 Polarized muon beam . 44 3.4.2 Polarized target . 47 3.4.3 COMPASS spectrometer . 49 4. Polarized Target : : : : : : : : : : : : : : : : : : : : : : : : : : : : 54 4.1 Dynamic nuclear polarization . 55 4.1.1 Definition of polarization . 55 4.1.2 Thermal equilibrium polarization . 56 4.1.3 Zeeman splitting . 57 4.1.4 Dipolar-dipolar interaction . 58 4.1.5 Macroscopic effects . 63 4.1.6 Hyperfine interaction . 64 4.1.7 Equal spin temperature . 70 4.2 The polarization measurement . 72 4.2.1 Nuclear magnetic resonance . 72 4.2.2 Detection of the absorption function . 73 4.2.3 Area method . 77 4.3 Polarized target apparatus . 79 4.3.1 Dilution refrigerator . 79 4.3.2 Superconducting magnet . 85 4.3.3 Microwave system . 88 4.3.4 Nuclear magnetic resonance system . 90 4.4 Target material 6LiD . 92 4.4.1 Choice of the material . 92 4.4.2 Preparation of 6LiD . 97 4.5 Results from polarized target . 99 4.5.1 TE calibration . 99 4.5.2 Deuteron polarization . 104 4.5.3 Paramagnetic resonance at high polarization . 108 4.5.4 Verification of equal spin temperature theory . 109 5. Superconducting magnet for the polarized target : : : : : : : : : : 112 5.1 Electromagnetics . 113 5.2 Cryogenics . 119 5.2.1 Normal continuous operation . 121 5.2.2 Cooling down phase . 122 5.3 Active protection system . 124 5.4 Anomalous cases . 127 Contents iii 6. Conclusions and Outlook : : : : : : : : : : : : : : : : : : : : : : : 131 Appendix 134 A. Parameters in Chapter 3 : : : : : : : : : : : : : : : : : : : : : : : : 135 B. Parameters in Chapter 4 : : : : : : : : : : : : : : : : : : : : : : : : 137 C. Parameters in Chapter 5 : : : : : : : : : : : : : : : : : : : : : : : : 139 LIST OF FIGURES 2.1 Feynman diagram of DIS . 6 2.2 DIS in the infinite momentum frame . 15 2.3 Amplitudes of DIS off a quark . 18 2.4 Squares of the Feynman diagram involving real gluon emission 19 2.5 Squares of the Feynman diagrams with a initial gluon . 19 2.6 Illustration of the QCD processes of the four splitting functions 21 2.7 Diagrams relevant to axial anomaly . 27 3.1 Example of the possible shapes of ∆g . 31 3.2 Feynman diagram of open charm leptoproduction via photo- gluon fusion . 32 3.3 Expected statistical accuracy . 38 3.4 Feynman diagram of the high pT jet pair . 40 3.5 Feynman diagram of the γ production in pp or pp¯ collisions . 42 3.6 Projected accuracies on Deltag=g . 43 3.7 M2 polarized muon beam line . 45 3.8 Spin configurations of in the COMPASS experiment . 48 3.9 COMPASS spectrometer in 2001 . 51 4.1 DNP mechanism via dipolar-dipolar interaction . 62 4.2 DNP mechanism via hyperfine interaction . 70 4.3 Series LRC resonance circuit . 74 4.4 Side view of the COMPASS polarized target apparatus . 80 4.5 Materials inside the particle detection acceptance . 81 4.6 Diagram of the dilution refrigerator . 82 4.7 Phase diagram of 3He-4He mixture . 84 4.8 Operation of the magnet system during the field rotation . 86 4.9 Magnetic field during the field rotation . 87 4.10 Microwave system . 88 4.11 Schematic outline of the NMR system . 91 4.12 Face centered cubic structure . 92 4.13 Simple illustration of the F-center . 98 List of Figures v 4.14 Paramagnetic resonance spectrum of the irradiated 6LiD . 99 4.15 NMR signal extraction . 100 4.16 Relaxation of the nuclear spin to the thermal equilibrium . 101 4.17 Build-up of the deuteron polarization . 105 4.18 Enhanced deuteron signals . 106 4.19 Paramagnetic resonance spectrum of 6LiD at high polarization108 4.20 Test of EST . 110 5.1 Illustration of the coils in Magnet . 113 5.2 Electric scheme of Solenoid and Corrections . 115 5.3 Electric scheme of Dipole . 116 5.4 Cryogenic scheme of Magnet . 120 LIST OF TABLES 3.1 Numerical presentation of the cross sections of open charm lepto-production . 36 3.2 Parameters of the polarized muon beam . 46 4.1 Thickness of the material in the polarized target apparatus . 89 4.2 Figure of merit of the target materials . 95 4.3 Measurements for TE calibration . 102 4.4 Errors in TE calibration . 103 4.5 Maximum deuteron polarization . 107 5.1 Electromagnetic characteristics of Solenoid . 114 5.2 Electromagnetic characteristics of Corrections . 117 5.3 Electromagnetic characteristics of Dipole . 118 5.4 DL (Slow discharge) . 125 5.5 DR (Rapid discharge) 1 . 126 5.6 DR (Rapid discharge) 2 . 127 5.7 Anomalous cases, AN1-AN3 . 128 5.8 Anomalous cases, AN4-AN6 . 129 5.9 Anomalous cases, AN7 . 130 A.1 Variables in Chapter 3 . 136 B.1 Constants in Chapter 4 . 138 B.2 Units for Chapter 4 . 138 B.3 Abbreviations for Chapter 4 . 138 C.1 Terms in Chapter 5 . 140 C.2 Abbreviations in Chapter 5 . 141 1. INTRODUCTION Scattering a beam of elementary particles such as leptons off a target of nucleons provides an experimental technique for investigating the structure of the nucleons. In low energy scattering, where the beam energy is less than the target mass, the nucleon looks like a point-like particle. However, as the energy of the incident lepton increases, the structure of nucleon be- gins to unveil. When the lepton energy increases above the nucleon mass, the charge distributions of the nucleons are probed. The deviation of the measured cross section from the known cross section for a point-like particle describes the charge distribution of the composite objects. The form factors, or charge distributions, of the nucleons were measured by this technique in the experiments during the 1970s at SLAC. If the lepton energy increases even higher, then the deep inelastic scat- tering (DIS) regime is reached. In DIS, the lepton has high enough energy to break apart the nucleons and therefore to probe the internal structure of the nucleons, namely the structure functions. Polarized DIS experiment, in which polarized leptons are scattered off a target of polarized nucleons, provides the information on the internal structure of the nucleon spin. The spin-dependent structure function of the nucleon was experimentally mea- sured first by the Yale-SLAC Collaboration E80 [1], and then by the E130 Collaboration [2] in 1970s and early 1980s, using 8 and 20 GeV electron beam. At CERN, the European Muon Collaboration (EMC) [3, 4] investi- gated the proton spin structure during the 1980s using 90 GeV muon beam. The EMC results reported in 1988 attracted the attentions of the re- searchers, which state that the quarks carry unexpectedly small fraction (0:128 0:013 (stat) 0:019 (sys)) of the nucleon spin. The EMC inter- preted its data in the framework of the naive Parton Model and found that the experimentally measured value of the Ellis-Jaffe Sum Rule [5] for the proton is too small compared to the theoretical prediction. Following the EMC results, extensive theoretical and experimental works were performed to understand the spin structure of the nucleon in 1990s. One of the the- oretical advances was to describe the spin dependent structure function in the framework of Quantum Chromodynamics (QCD), showing the Q2 evo- 1. Introduction 2 lution of the structure functions due to the interaction between quarks and gluons. Experimentally, precise measurements had been carried out by the Spin Muon Collaboration (SMC) at CERN using 100 and 190 GeV muon beam with proton and deuteron target, by a series of experiments at SLAC, E142, E143, E154 and E155 using 26-50 GeV electron beam with proton, deuteron, and 3He target, and by the HERMES collaboration at DESY using 28 GeV electron beam with proton and 3He target. These experi- mental data together with the QCD evolution analysis still show that the quarks carry unexpectedly small fraction, 20-30 %, of the nucleon spin at Q2 = 10 GeV2 and that the Ellis-Jaffe Sum Rule is violated. On the other hand, the Bjorken Sum Rule [6, 7], which is the difference of the first mo- ment of the spin-dependent structure function g1 between a proton and a neutron and which is a model independent result of QCD, was confirmed.