Lectures on QED and QCD: practical renormalization of one- and two-loop diagrams

Andrey Grozin9812569146, 9789812569141, 9789812706751

The increasing precision of experimental data in many areas of elementary particle physics requires an equally precise theoretical description. In particular, radiative corrections (described by one- and multi-loop Feynman diagrams) have to be considered. Although a growing number of physicists are involved in such projects, multi-loop calculation methods can only be studied from original publications. With its coverage of multi-loop calculations, this book serves as an excellent supplement to the standard textbooks on quantum field theory. Based around postgraduate-level lectures given by the author, the material is suitable for both beginners and graduate students.

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Table of contents :
1.1 Divergences, regularization and renormalization……Page 10
Preface……Page 6
Part 1. QED and QCD……Page 14
1. One-loop diagrams 3……Page 16
1.2 Massive vacuum diagram……Page 19
1.3 Integrals in d dimensions……Page 22
1.4 Feynman parametrization……Page 26
1.5 Massless propagator diagram……Page 27
1.6 Tensors and y-matrices in d dimensions……Page 30
2.1 Lagrangian and Feynman rules……Page 34
2.2 Photon propagator……Page 36
2.3 Wardidentity……Page 38
2.4 Photon self-energy……Page 40
2.5 Photon field renormalization …….Page 41
2.6 Electron propagator……Page 43
2.7 Vertex and charge renormalization . . . …….Page 46
2.8 Electron mass……Page 52
3.1 Lagrangian and Feynman rules……Page 56
3.2 Quark propagator……Page 61
3.3 Gluon propagator……Page 62
3.4 Ghost propagator……Page 65
3.5 Quark-gluon vertex……Page 66
3.6 Coupling constant renormalization……Page 67
3.7 Ghost-gluon vertex……Page 69
3.8 Three-gluon vertex……Page 71
3.9 Four-gluon vertex……Page 78
4.1 Massless propagator diagram……Page 86
4.2 Photon self-energy……Page 92
4.3 Photon field renormalization……Page 95
4.4 Charge renormalization……Page 100
4.5 Electron self-energy……Page 102
4.6 Electron field renormalization……Page 106
4.7 Two-loop corrections in QCD……Page 110
5.1 On-shell renormalization of photon field……Page 114
5.2 One-loop massive on-shell propagator diagram……Page 116
5.3 On-shell renormalization of electron mass and field……Page 119
5.4 On-shell charge……Page 122
5.5 Magnetic moment……Page 124
5.6 Two-loop massive vacuum diagram……Page 129
5.7 On-shell renormalization of photon field and charge at two loops . . . . . . . . . . . . . …….Page 131
5.8 On-shell renormalization in QCD……Page 132
6.1 Photon field……Page 134
6.2 Electron field……Page 137
6.3 Charge……Page 140
6.4 Electron mass……Page 142
6.5 Decoupling in QCD……Page 144
7. Conclusion: Effective field theories……Page 148
Appendix A Colour factors……Page 154
Bibliography……Page 168
Part 2. Multiloop calculations……Page 170
8.1 Introduction……Page 172
8.2 Oneloop……Page 173
8.3 Two loops……Page 175
8.4 Three loops……Page 181
8.5 G (1,1,1,1, n)……Page 184
8.6 Non-planar basis integral……Page 188
9.1 Crash course of HQET……Page 192
9.2 Oneloop……Page 194
9.3 Two loops……Page 195
9.4 Three loops……Page 200
9.5 J(1,1,n,1,1)……Page 202
9.6 I(l,1,1,1,n)……Page 204
10.1 One loop……Page 210
10.2 Two loops……Page 212
10.3 Two loops, two masses……Page 215
10.4 Three loops……Page 218
11.1 Multiple values……Page 222
11.2 Expanding hypergeometric functions in E: an example……Page 228
11.3 Expanding hypergeometric functions in E: the algorithm……Page 231
Bibliography……Page 234
Index……Page 236