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The pion Form Factor from Lattice QCD
van der Heide, J.
Publication date
2004
Link to publication
Citation for published version (APA):
van der Heide, J. (2004). The pion Form Factor from Lattice QCD.
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Contents
Introduction 1 1. Quantum Chromodynamics 5
1.1. Continuum description 5 1.2. Feynman path integral 7 1.3. Running coupling constant 8
1.4. Chiral symmetry 8
2. Lattice Quantum Chromodynamics 1 1
2.1. Formalism 11 2.2. Lattice gauge action 12
2.3. Lattice fermion action 13 2.3.1. Wilson fermions 14 2.3.2. Improvement 16 2.4. Lattice path integral 18 2.5. The continuum limit 18 2.6. Errors in lattice QCD 20
3. Simulation techniques 23
3.1. Gauge section 23 3.1.1. Markov chains and Metropolis 24
3.1.2. Heat bath and overrelaxation 25 3.2. The quark propagator and pion n-point Green's functions 26
3.3. Pion two-point Green's function 27 3.3.1. Operator and gauge field smearing 28
3.4. Vector mesons 30 3.5. The three-point Green's function 30
3.6. Inversion of the fermion matrix 33
3.7. Simulation parameters 35
4. Analysis of the pion two-point function at T = 0 37
4.1. Parametrisation 37 4.2. Analysis techniques 38
4.2.1. Jackknife method 38 4.2.2. Fitting procedure 39
4.3. Operator smearing 41 4.4. Masses and energies 41
4.4.1. Fit strategy 41 4.4.2. Pion masses 43
4.4.3. Determination of KC 44
4.4.4. Rho masses 45 4.4.5. Energies and dispersion relation 46
4.5. 'Bethe-Salpeter amplitudes' and pion radius 49
4.5.1. Pion radius 50 4.5.2. Excited state wave function and radius 53
4.6. Conclusions 55
5. Analysis of the three-point function: extraction of the form factor at T = 0 57
5.1. Form factor of the free pion 57
5.2. Parametrisation 58 5.2.1. Current conservation and the second insertion 60
5.3. Simulation 62 5.4. Analysis methods 63
5.4.1. Q2 = 0: the second insertion test 65
5.5. Systematic uncertainties 67 5.6. Comparison of the currents 70 5.7. The form factor and vector meson dominance 73
5.8. Determination of the scale 76 5.9. Comparison to experiment 76 5.10. The pion charge radius 76
5.10.1. Extrapolation in m„ 78
5.11. Conclusions 79
6. Finite temperature 83
6.1. Spatial correlation functions 83
6.2. Dispersion relation 84
6.3. Simulation 86 6.4. Two-point function 86
6.4.1. Effective energy 86 6.4.2. Analysis techniques for screening energies and masses 87
6.4.3. Screening Masses 88 6.4.4. Screening energies and the dispersion relation 89
6.4.5. Spatial Bethe-Salpeter wave function and (T2)BS 91
6.5. Extraction of the form factor 91 6.5.1. Form factor at T ^ 0 93
6.5.2. Results 95 6.6. Conclusions 101
Contents
A. Additional figures and tables 103
A.l. Zero temperature 103 A.2. Finite temperature 105
Summary 117 Samenvatting 121 Dankwoord 125
