Book contents
- Frontmatter
- Contents
- Dedication
- Acknowledgments
- 1 Introduction
- 2 Why QCD?
- 3 Basics of QCD
- 4 Infra-red safety and non-safety
- 5 Libby-Sterman analysis and power-counting
- 6 Parton model to parton theory: simple model theories
- 7 Parton theory: further developments
- 8 Factorization for DIS, mostly in simple field theories
- 9 Corrections to the parton model in QCD
- 10 Factorization and subtractions
- 11 DIS and related processes in QCD
- 12 Fragmentation functions: e+e- annihilation to hadrons, and SIDIS
- 13 TMD factorization
- 14 Inclusive processes in hadron-hadron collisions
- 15 Introduction to more advanced topics
- Appendix A Notations, conventions, standard mathematical results
- Appendix B Light-front coordinates, rapidity, etc.
- Appendix C Summary of primary results
- References
- Index
10 - Factorization and subtractions
Published online by Cambridge University Press: 16 May 2011
- Frontmatter
- Contents
- Dedication
- Acknowledgments
- 1 Introduction
- 2 Why QCD?
- 3 Basics of QCD
- 4 Infra-red safety and non-safety
- 5 Libby-Sterman analysis and power-counting
- 6 Parton model to parton theory: simple model theories
- 7 Parton theory: further developments
- 8 Factorization for DIS, mostly in simple field theories
- 9 Corrections to the parton model in QCD
- 10 Factorization and subtractions
- 11 DIS and related processes in QCD
- 12 Fragmentation functions: e+e- annihilation to hadrons, and SIDIS
- 13 TMD factorization
- 14 Inclusive processes in hadron-hadron collisions
- 15 Introduction to more advanced topics
- Appendix A Notations, conventions, standard mathematical results
- Appendix B Light-front coordinates, rapidity, etc.
- Appendix C Summary of primary results
- References
- Index
Summary
In Sec. 9.13 we saw how factorization theorems give a lot of predictive power to QCD. They are essential in the analysis of data at high-energy colliders, not just for understanding the QCD aspects but also in searches for new physics, for example.
So far we have seen a genuine proof (Sec. 8.9) only for inclusive DIS, and only in a model theory without gauge fields. In this chapter we will formulate the principles that apply very generally, to other reactions, and when dealing with the full complications of a gauge theory.
The general class of problem concerns the extraction of the asymptotic behavior of amplitudes and cross sections as some external parameter, like a momentum, gets large. In general discussions, we denote the large parameter by Q. As well as factorization theorems in their broadest sense, such asymptotic problems also encompass simpler situations like renormalization, the operator product expansion (OPE), and the IR divergence issue in QED.
There is a common and general mathematical structure in these different problems that could undoubtedly use further codification. Perhaps methods based on Hopf algebras, or some generalization, would provide an appropriate mathematical structure. So far these methods have been applied to renormalization (e.g., Connes and Kreimer, 2000, 2002).
In this chapter, I interleave a general formal treatment with its application to the Sudakov form factor, including explicit calculations at one-loop order. The general treatment will underlie all further work in this book.
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- Foundations of Perturbative QCD , pp. 313 - 397Publisher: Cambridge University PressPrint publication year: 2011