Abstract
Contents
1. Introduction 1
2. Quantum Chromodynamics 3
2.1. QCD Lagrangian 3
2.2. Renormalization and runningcoupling in QCD 5
2.3. Colour-ordered matrix elements 9
2.4. Infrared behaviour of QCD amplitudes 10
2.4.1. One-loop singularities 11
2.4.2. Two-loop singularities 12
2.4.3. Real radiation divergences 13
2.5. Parton model and mass factorization 17
2.6. Jet algorithms 20
3. Antenna subtraction 23
3.1. Subtraction method 23
3.2. Antenna functions 25
3.3. Phase space mappings 28
3.3.1. Final-final mapping 29
3.3.2. Initial-final mapping 31
3.3.3. Initial-initial mapping 32
3.4. NNLOJET 34
4. Event shapes in DIS 35
4.1. Event shape variables 35
4.2. QCD corrections to event shapes 38
4.2.1. Event shape distributions 39
4.2.2. Mean values 41
4.3. Hadronization effects 44
4.4. Phenomenological results 46
4.4.1. Event shape distributions 46
4.4.2. Mean values 49
4.5. Outlook on strong couplingconstant fit 50
5. Dijets at NNLO in full colour 53
5.1. Jet production cross sections 54
5.2. LC and SLC contributions 55
5.3. Dijet matrix elements 55
5.3.1. A-type matrix elements 57
5.3.2. B-type matrix elements 62
5.3.3. C-type matrix elements 70
5.3.4. D-type matrix elements 78
5.3.5. E-type matrix elements 85
5.3.6. F-type matrix elements 86
5.3.7. G-type matrix elements 86
6. Antenna subtraction for dijets atNNLO 88
6.1. NLO part of NNLO subtraction 88
6.1.1. Real to virtual: B-type 88
6.1.2. Remainder interference terms of the B-type 91
6.1.3. Virtual to real: D-type 95
6.2. Double real subtraction 98
6.2.1. B-type matrix element with only abelian gluons 99
6.2.2. R-term 102
6.2.3. E-type 108
6.2.4. F-type 110
6.2.5. G-type 111
6.2.6. Tests of the RR subtraction term 112
6.3. Real-virtual subtraction 113
6.3.1. Most subleading B-type 115
6.3.2. Subsubleading C-type 116
6.3.3. First subleading B-type 119
6.4. Double virtual subtraction 121
6.4.1. Integrated dipole structure in B-typeprocessesas an example 123
7. Phenomenological results of FCdijets 126
7.1. Single jet inclusive cross section 127
7.1.1. Calculational setup 127
7.1.2. PDF differences 129
7.1.3. Results 129
7.1.4. Subleading colour contributions 129
7.1.5. Decomposition into different partonic initialstates 132
7.2. Dijet production 134
7.2.1. Calculational setup 135
7.2.2. Results and quantification of subleading colourcontributions 137
7.3. Triple differential dijet crosssection 138
7.3.1. PDF differences 140
7.3.2. Results 141
7.3.3. Decomposition into different partonic initialstates 144
7.4. SLC contribution discussion 147
8. Conclusion 149
Jonathan, Mo