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Quantum Chromodynamics

Book Description

Aimed at graduate students and researchers in theoretical physics, this book presents the modern theory of strong interaction: quantum chromodynamics (QCD). The book exposes various perturbative and nonperturbative approaches to the theory, including chiral effective theory, the problems of anomalies, vacuum tunnel transitions, and the problem of divergence of the perturbative series. The QCD sum rules approach is exposed in detail. A great variety of hadronic properties (masses of mesons and baryons, magnetic moments, form factors, quark distributions in hadrons, etc.) have been found using this method. The evolution of hadronic structure functions is presented in detail, together with polarization phenomena. The problem of jets in QCD is treated through theoretical description and experimental observation. The connection with Regge theory is emphasized. The book covers many aspects of theory which are not discussed in other books, such as CET, QCD sum rules, and BFKL.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface
  6. 1 General properties of QCD
    1. 1.1 QCD Lagrangian
    2. 1.2 Quantization of the QCD Lagrangian
    3. 1.3 The Gribov ambiguity
    4. 1.4 Feynman rules
    5. 1.5 Regularization
    6. 1.6 γ5 problem
    7. 1.7 Renormalization
    8. 1.8 One-loop calculations
    9. 1.9 Renormalization group
    10. 1.10 Asymptotic freedom in QCD
    11. 1.11 The renormalization scheme and scale ambiguity
    12. 1.12 Anomalous dimensions of twist-2 operators
    13. 1.13 Colour algebra
    14. References
  7. 2 Chiral symmetry and its spontaneous violation
    1. 2.1 The general properties of QCD at low energies
    2. 2.2 The masses of the light quarks
    3. 2.3 Spontaneous violation of chiral symmetry. Quark condensate
    4. 2.4 Goldstone theorem
    5. 2.5 Chiral effective theory (CET) at low energies
    6. 2.6 Low-energy sum rules in CET
    7. 2.7 The nucleon and pion-nucleon interaction in CET
    8. Problems
    9. References
  8. 3 Anomalies
    1. 3.1 Generalities
    2. 3.2 The axial anomaly
    3. 3.3 The axial anomaly and the scattering of polarized electron (muon)on polarized gluon
    4. 3.4 The scale anomaly
    5. 3.5 The infrared power-like singularities in photon-photon, photongluon, and gluon-gluon scattering in massless QED and QCD. Longitudinal gluons in QCD
    6. Problems
    7. References
  9. 4 Instantons and topological quantum numbers
    1. 4.1 Tunneling in quantum mechanics
    2. 4.2 Instantons and the topological current
    3. 4.3 Instantons in Minkowski space-time
    4. 4.4 Fermions in the instanton field. Atiyah-Singer theorem
    5. 4.5 The vacuum structure in QCD
    6. 4.6 The pre-exponential factor of the instanton action. The dilute gas instanton model
    7. 4.7 Quark propagator in the instanton field
    8. 4.8 Appendix
    9. Problems
    10. References
  10. 5 Divergence of perturbation series
    1. 5.1 Renormalization group approach to renormalons
    2. 5.2 High-order estimates in zero-dimensional models
    3. 5.3 Zero charge and asymptotic freedom in scalar models
    4. 5.4 Renormalized strongly nonlinear scalar model
    5. 5.5 Functional approach to the high-order estimates
    6. 5.6 Series divergence in models with gauge interactions
    7. 5.7 Asymptotic estimates in the pure Yang-Mills theory
    8. 5.8 Asymptotic estimates in quantum electrodymamics
    9. 5.9 Applications of high-order estimates
    10. References
  11. 6 QCD sum rules
    1. 6.1 Operator product expansion
    2. 6.2 Condensates
    3. 6.3 Condensates, induced by external fields
    4. 6.4 QCD sum rules method
    5. 6.5 Determination of αs (Q2) and the condensates from low-energy data
    6. 6.6 Calculations of light meson masses and coupling constants
    7. 6.7 Sum rules for baryon masses
    8. 6.8 Calculation technique
    9. 6.9 Static properties of hadrons
    10. 6.10 Three-point functions and formfactors at intermediate momentum transfers
    11. 6.11 Valence quark distributions in hadrons
    12. Problems
    13. References
  12. 7 Evolution equations
    1. 7.1 Introduction
    2. 7.2 Parton model in QCD
    3. 7.3 Evolution equations for parton distributions
    4. 7.4 Splitting kernels in the Born approximation
    5. 7.5 OPE on light cone and parton model
    6. 7.6 Evolution equations for fragmentation functions
    7. 7.7 Parton distributions in QCD in LLA
    8. 7.8 Hard processes beyond the LLA
    9. 7.9 Parton-number correlators
    10. 7.10 Deep inelastic electron scattering off the polarized proton
    11. 7.11 Parton distributions in polarized nucleon
    12. 7.12 Evolution equations for quasipartonic operators
    13. 7.13 Q2-dependence of the twist-3 structure functions for the polarized target
    14. 7.14 Infrared evolution equations at small x
    15. References
  13. 8 QCD jets
    1. 8.1 Total cross section of e+e−-annihilation into hadrons
    2. 8.2 Jet production
    3. 8.3 Two-jet events
    4. 8.4 Three-jet events
    5. 8.5 Event shape
    6. 8.6 Inclusive spectra
    7. 8.7 Colour coherence
    8. 8.8 Soft-gluon approximations
    9. 8.9 Soft-gluon distributions
    10. 8.10 Hump-backed shape of parton spectra
    11. 8.11 Multiplicity distributions and KNO scaling
    12. 8.12 Moments of fragmentation functions at small j — 1 438
    13. 8.13 Modified Leading Logarithmic Approximation (MLLA)
    14. References
  14. 9 BFKL approach
    1. 9.1 Introduction
    2. 9.2 Gluon reggeization
    3. 9.3 Reggeon vertices and trajectory
    4. 9.4 BFKL equation
    5. 9.5 BFKL pomeron
    6. 9.6 Bootstrap of the gluon reggeization
    7. 9.7 Next-to-leading order BFKL
    8. References
  15. 10 Further developments in high-energy QCD
    1. 10.1 Effective-action approach
    2. 10.2 BFKL dynamics and integrability
    3. 10.3 The odderon in QCD
    4. 10.4 Baxter-Sklyanin representation
    5. 10.5 Maximal transcendentality and anomalous dimensions
    6. 10.6 Discussion of obtained results
    7. References
  16. Notations
  17. Index