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Foundations of Perturbative QCD

Book Description

The most non-trivial of the established microscopic theories of physics is QCD: the theory of the strong interaction. A critical link between theory and experiment is provided by the methods of perturbative QCD, notably the well-known factorization theorems. Giving an accurate account of the concepts, theorems and their justification, this book is a systematic treatment of perturbative QCD. As well as giving a mathematical treatment, the book relates the concepts to experimental data, giving strong motivations for the methods. It also examines in detail transverse-momentum-dependent parton densities, an increasingly important subject not normally treated in other books. Ideal for graduate students starting their work in high-energy physics, it will also interest experienced researchers wanting a clear account of the subject.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Acknowledgments
  6. 1 Introduction
    1. 1.1 Factorization and high-energy collisions
    2. 1.2 Why we trust QCD is correct
    3. 1.3 Notation
    4. 1.4 Problems and exercises
  7. 2 Why QCD?
    1. 2.1 QCD: statement of the theory
    2. 2.2 Development of QCD
    3. 2.3 Deeply inelastic scattering
    4. 2.4 Parton model
    5. 2.5 Asymptotic freedom
    6. 2.6 Justification of QCD
    7. 2.7 QCD in the full Standard Model
    8. 2.8 Beyond the Standard Model
    9. 2.9 Relation between fields and particles
    10. Exercises
  8. 3 Basics of QCD
    1. 3.1 Quantization
    2. 3.2 Renormalization
    3. 3.3 Renormalization counterterms of QCD
    4. 3.4 Meaning of unit of mass, renormalization scale
    5. 3.5 Renormalization group
    6. 3.6 Solution of RG equations
    7. 3.7 Values of RG coefficients
    8. 3.8 Symmetries and approximate symmetries of QCD
    9. 3.9 Dealing with quark masses
    10. 3.10 CWZ (ACOT) method for heavy quarks
    11. 3.11 Relating CWZ subschemes with different numbers of active quarks
    12. Exercises
  9. 4 Infra-red safety and non-safety
    1. 4.1 e+e− total cross section
    2. 4.2 Explicit calculations
    3. 4.3 Evolution of state
    4. 4.4 Dispersion relation and effective virtuality of final-state quarks and gluons
    5. 4.5 Generalizations
    6. Exercises
  10. 5 Libby-Sterman analysis and power-counting
    1. 5.1 High-energy asymptotics and mass singularities
    2. 5.2 Reduced graphs and space-time propagation
    3. 5.3 Examples of general reduced graphs
    4. 5.4 One-loop vertex graph
    5. 5.5 Power-counting for vertex graph
    6. 5.6 Which reactions have a pinch in the Glauber region?
    7. 5.7 Coordinates for a PSS
    8. 5.8 Power-counting
    9. 5.9 Catalog of leading regions
    10. 5.10 Power-counting with multiple regions
    11. 5.11 Determination of Glauber-like regions
    12. Exercises
  11. 6 Parton model to parton theory: simple model theories
    1. 6.1 Field theory formulation of parton model
    2. 6.2 When is the parton model valid?
    3. 6.3 Parton densities as operator matrix elements
    4. 6.4 Consequences of rotation and parity invariance: polarization dependence
    5. 6.5 Polarization and polarized parton densities in spin-1 target
    6. 6.6 Light-front quantization
    7. 6.7 Parton densities as number densities
    8. 6.8 Unintegrated parton densities
    9. 6.9 Properties of parton densities
    10. 6.10 Feynman rules for pdfs
    11. 6.11 Calculational examples
    12. Exercises
  12. 7 Parton theory: further developments
    1. 7.1 DIS with weak interactions, neutrino scattering, etc.
    2. 7.2 Light-front perturbation theory
    3. 7.3 Light-front wave functions
    4. 7.4 Light-front quantization in gauge theories
    5. 7.5 Parton densities in gauge theories
    6. 7.6 Feynman rules for gauge-invariant parton densities
    7. 7.7 Interpretation of Wilson lines within parton model
    8. Exercises
  13. 8 Factorization for DIS, mostly in simple field theories
    1. 8.1 Factorization: overall view
    2. 8.2 Elementary treatment of factorization
    3. 8.3 Renormalization of parton densities
    4. 8.4 Renormalization group, and DGLAP equation
    5. 8.5 Moments and Mellin transform
    6. 8.6 Sum rules for parton densities and DGLAP kernels, including in QCD
    7. 8.7 Renormalization calculations: model theory
    8. 8.8 Successive approximation method
    9. 8.9 Derivation of factorization by ladder method
    10. 8.10 Factorization formula for structure functions
    11. 8.11 Transverse-spin dependence at leading power?
    12. Exercises
  14. 9 Corrections to the parton model in QCD
    1. 9.1 Lowest order
    2. 9.2 Projections onto structure functions
    3. 9.3 Complications in QCD
    4. 9.4 One-loop renormalization calculations in QCD
    5. 9.5 One-loop renormalization by subtraction of asymptote
    6. 9.6 DIS on partonic target
    7. 9.7 Computation of NLO gluon coefficient function
    8. 9.8 Choice of renormalization scale μ
    9. 9.9 NLO quark coefficient
    10. 9.10 Hard scattering with quark masses
    11. 9.11 Critique of conventional treatments
    12. 9.12 Summary of known higher-order corrections
    13. 9.13 Phenomenology
    14. Exercises
  15. 10 Factorization and subtractions
    1. 10.1 Subtraction method
    2. 10.2 Simple example of subtraction method
    3. 10.3 Sudakov form factor
    4. 10.4 Region approximator TR for Sudakov form factor
    5. 10.5 One-loop Sudakov form factor
    6. 10.6 Rationale for definition of TR
    7. 10.7 General derivation of region decomposition
    8. 10.8 Sudakov form factor factorization: first version
    9. 10.9 Factorization in terms of unsubtracted factors
    10. 10.10 Evolution
    11. 10.11 Sudakov: redefinition of factors
    12. 10.12 Calculations for Sudakov problem
    13. 10.13 Deduction of some non-leading logarithms
    14. 10.14 Comparisons with other work
    15. Exercises
  16. 11 DIS and related processes in QCD
    1. 11.1 General principles
    2. 11.2 Regions and PSSs, with uncut hadronic amplitude
    3. 11.3 Factorization for DIS
    4. 11.4 Renormalization of parton densities, DGLAP evolution
    5. 11.5 DIS with weak interactions
    6. 11.6 Polarized DIS, especially transverse polarization
    7. 11.7 Quark masses
    8. 11.8 DVCSandDDVCS
    9. 11.9 Ward identities to convert K gluons to Wilson line
    10. Exercises
  17. 12 Fragmentation functions: e+e− annihilation to hadrons, and SIDIS
    1. 12.1 Structure-function analysis of one-particle inclusive cross section
    2. 12.2 Statement of factorization etc. for e+e− → h(p) + X
    3. 12.3 LO calculation
    4. 12.4 Introduction to fragmentation functions
    5. 12.5 Leading regions and issues in a gauge theory
    6. 12.6 Which gauge to use in a proof?
    7. 12.7 Unitarity sum over jets/sum over cuts
    8. 12.8 Factorization for e+e− → h(p) + X in gauge theory
    9. 12.9 Use of perturbative calculations
    10. 12.10 One-loop renormalization of fragmentation function
    11. 12.11 One-loop coefficient functions
    12. 12.12 Non-perturbative effects and factorization
    13. 12.13 Generalizations
    14. 12.14 Semi-inclusive deeply inelastic scattering
    15. 12.15 Target fragmentation region: fracture functions
    16. Exercises
  18. 13 TMD factorization
    1. 13.1 Overview of two-particle-inclusive e+e− annihilation
    2. 13.2 Kinematics, coordinate frames, and structure functions
    3. 13.3 Region analysis
    4. 13.4 Collinear factors
    5. 13.5 Initial version of factorization with TMD fragmentation
    6. 13.6 Factorization and transverse coordinate space
    7. 13.7 Final version of factorization for e+e− annihilation
    8. 13.8 Evolution equations for TMD fragmentation functions
    9. 13.9 Flavor dependence of CS and RG evolution
    10. 13.10 Analysis of CS kernel K: perturbative and non-perturbative
    11. 13.11 Relation of TMD to integrated fragmentation function
    12. 13.12 Correction term for large qhT
    13. 13.13 Using TMD factorization
    14. 13.14 NLO calculation of TMD fragmentation function at small bT and at large kT
    15. 13.15 SIDIS and TMD parton densities
    16. 13.16 Polarization issues
    17. 13.17 Implications of time-reversal invariance
    18. Exercises
  19. 14 Inclusive processes in hadron-hadron collisions
    1. 14.1 Overview
    2. 14.2 Drell-Yan process: kinematics etc.
    3. 14.3 Glauber region example
    4. 14.4 Factorization for Drell-Yan
    5. 14.5 TMD pdfs and Drell-Yan process
    6. 14.6 Calculations with initial-state partons
    7. 14.7 Production of hadrons
    8. Exercises
  20. 15 Introduction to more advanced topics
    1. 15.1 Light-front wave functions and exclusive scattering at large momentum transfer
    2. 15.2 Exclusive diffraction: generalized parton densities
    3. 15.3 Small-x, BFKL, perturbative Regge physics
    4. 15.4 Resummation, etc.
    5. 15.5 Methods for efficient high-order calculations
    6. 15.6 Monte-Carlo event generators
    7. 15.7 Heavy quarks
    8. 15.8 Large x
    9. 15.9 Soft-collinear effective theory (SCET)
    10. 15.10 Higher twist: power corrections
  21. Appendix A: Notations, conventions, standard mathematical results
    1. A.1 General notations
    2. A.2 Units, and conversion factors
    3. A.3 Acronyms and abbreviations
    4. A.4 Vectors, metric, etc.
    5. A.5 Renormalization group (RG)
    6. A.6 Lorentz, vector, color etc. sub- and superscripts
    7. A.7 Polarization and spin
    8. A.8 Structure functions
    9. A.9 States, cross sections, integrals over particle momentum
    10. A.10 Dirac, or gamma, matrices
    11. A.11 Group theory
    12. A.12 Dimensional regularization and MS: basics
    13. A.13 Dimensional regularization: standard integrals
    14. A.14 Properties of F function
    15. A.15 Plus distributions, etc.
    16. A.16 Feynman parameters
    17. A.17 Orders of magnitude, estimation, etc.
  22. Appendix B: Light-front coordinates, rapidity, etc.
    1. B.1 Definition
    2. B.2 Boosts
    3. B.3 Rapidity
    4. B.4 Pseudo-rapidity
    5. B.5 Rapidity distributions in high-energy collisions
  23. Appendix C: Summary of primary results
  24. References
  25. Index