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
23 - The parton model in QCD
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
The operator product expansion plus renormalization group result (22.2.34) tells us how QCD controls the Q2 variation of the moments of the deep inelastic structure functions. But it does not give us the actual value of the moments, since they depend upon unknown, non-calculable, hadronic matrix elements ON,j of certain operators. In Section 22.2.5 we saw that the moment equations can be replaced by an equation controlling the Q2 variation of the structure functions themselves, and this could be interpreted [see (22.2.53)] as a Q2 variation of the parton densities. Again the equation does not give us the actual value of the parton distribution—only their Q2 evolution is calculable. Thus the rôle of the unknown ON,j in the moment equation is taken by the unknown in the evolution equation.
It should be clear that all the difficulty stems from the hadrons. They are a non-perturbative manifestation of QCD and the problem is to derive some consequences of QCD without being able to handle the genuinely non-perturbative aspect. One is seeking a blend of the perturbative and the non-perturbative and the boundary between them is subtle. If individual hadrons are not involved, for example, in the totally inclusive reaction e+e− → hadrons, we can use purely perturbative QCD and end up with a genuine calculation of the cross-section to some order in αs, with no unknown constants or functions appearing. This can be seen in (22.1.22).
In the present chapter we develop a well defined calculational scheme for handling reactions involving individual hadrons—the QCD-improved parton model.
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- An Introduction to Gauge Theories and Modern Particle Physics , pp. 155 - 218Publisher: Cambridge University PressPrint publication year: 1996