Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Notational conventions
- Note added in proof: the discovery of the top quark (?)
- Note added in proof: the demise of the SSC
- 18 Determination of the Kobayashi–Maskawa matrix
- 19 Mixing and CP violation
- 20 Regularization, renormalization and introduction to the renormalization group
- 21 Gauge theories, QCD and the renormalization group
- 22 Applications of the QCD renormalization group
- 23 The parton model in QCD
- 24 Large pT phenomena and jets in hadronic reactions
- 25 Jets and hadrons in e+e− physics
- 26 Low pT or ‘soft’ hadronic physics
- 27 Some non-perturbative aspects of gauge theories
- 28 Beyond the standard model
- Appendix 1 Elements of field theory
- Appendix 2 Feynman rules for QED, QCD and the SM
- Appendix 3 Conserved vector currents and their charges
- Appendix 4 Operator form of Feynman amplitudes and effective Hamiltonians
- Appendix 5 S-matrix, T-matrix and Feynman amplitude
- Appendix 6 Consequences of CPT invariance for matrix elements
- Appendix 7 Formulae for the basic partonic 2 → 2 processes
- Appendix 8 Euclidean space conventions
- References
- Analytic subject index for vols. 1 and 2
21 - Gauge theories, QCD and the renormalization group
Published online by Cambridge University Press: 04 August 2010
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Notational conventions
- Note added in proof: the discovery of the top quark (?)
- Note added in proof: the demise of the SSC
- 18 Determination of the Kobayashi–Maskawa matrix
- 19 Mixing and CP violation
- 20 Regularization, renormalization and introduction to the renormalization group
- 21 Gauge theories, QCD and the renormalization group
- 22 Applications of the QCD renormalization group
- 23 The parton model in QCD
- 24 Large pT phenomena and jets in hadronic reactions
- 25 Jets and hadrons in e+e− physics
- 26 Low pT or ‘soft’ hadronic physics
- 27 Some non-perturbative aspects of gauge theories
- 28 Beyond the standard model
- Appendix 1 Elements of field theory
- Appendix 2 Feynman rules for QED, QCD and the SM
- Appendix 3 Conserved vector currents and their charges
- Appendix 4 Operator form of Feynman amplitudes and effective Hamiltonians
- Appendix 5 S-matrix, T-matrix and Feynman amplitude
- Appendix 6 Consequences of CPT invariance for matrix elements
- Appendix 7 Formulae for the basic partonic 2 → 2 processes
- Appendix 8 Euclidean space conventions
- References
- Analytic subject index for vols. 1 and 2
Summary
In the previous chapter we studied the general ideas of renormalization of a field theory, in particular, the freedom in the choice of a renormalization scheme and the consequences thereof as embodied in the renormalization group. For simplicity we talked mainly in terms of scalar φ4 theory. But we did illustrate the very important property of asymptotic freedom that emerges when these results are used in QCD.
In this chapter we show how to extend these ideas to the realistic case of gauge theories, and especially to QCD. We begin with a general outline of gauge theories and point out some of their subtleties, highlighting differences between QCD and QED. We then extend the renormalization group results of Chapter 20 to the case of QCD.
Introduction
In earlier chapters, and in those to follow, we constantly quote QCD corrections to naive quark–parton model estimates in various processes. It is felt at present that QCD is a serious candidate for the theory of strong interactions. QCD has many beautiful properties. It is a non-Abelian gauge theory describing the interaction of massless spin ½ objects, the ‘quarks’, which possess an internal degree of freedom called colour, and a set of massless gauge bosons (vector mesons), the ‘gluons’ which mediate the force between quarks in much the same way that photons do in QED. Loosely speaking, the quarks come in three colours and the gluons in eight.
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- Publisher: Cambridge University PressPrint publication year: 1996