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Partons, Factorization and Resummation, TASI95

George Sterman

TL;DR

Sterman’s TASI95 lectures develop a coherent Minkowski-space framework for perturbative QCD centered on factorization and resummation. The work shows how short-distance hard parts decouple from long-distance jet and parton-distribution dynamics, enabling evolution via DGLAP and systematic resummation of Sudakov and small-x logarithms through Sudakov and BFKL formalisms. Unitarity arguments, IR safety criteria, and the light-cone expansion underpin the factorization structure, while the discussion of higher-order behavior highlights perturbative limitations and the need for nonperturbative input. Together, these ideas provide a robust, cross-process toolkit for predicting high-energy QCD observables across DIS, Drell–Yan, and e+e− annihilation, with broad implications for precision phenomenology and the understanding of two-scale problems in perturbative QCD.

Abstract

I review the treatment of high-energy QCD in Minkowski space, with an emphasis on factorization theorems as extensions of the operator product expansion. I discuss how the factorization properties of high-energy cross sections and amplitudes lead to evolution equations that resum large logarithms for two-scale problems.

Partons, Factorization and Resummation, TASI95

TL;DR

Sterman’s TASI95 lectures develop a coherent Minkowski-space framework for perturbative QCD centered on factorization and resummation. The work shows how short-distance hard parts decouple from long-distance jet and parton-distribution dynamics, enabling evolution via DGLAP and systematic resummation of Sudakov and small-x logarithms through Sudakov and BFKL formalisms. Unitarity arguments, IR safety criteria, and the light-cone expansion underpin the factorization structure, while the discussion of higher-order behavior highlights perturbative limitations and the need for nonperturbative input. Together, these ideas provide a robust, cross-process toolkit for predicting high-energy QCD observables across DIS, Drell–Yan, and e+e− annihilation, with broad implications for precision phenomenology and the understanding of two-scale problems in perturbative QCD.

Abstract

I review the treatment of high-energy QCD in Minkowski space, with an emphasis on factorization theorems as extensions of the operator product expansion. I discuss how the factorization properties of high-energy cross sections and amplitudes lead to evolution equations that resum large logarithms for two-scale problems.

Paper Structure

This paper contains 34 sections, 236 equations, 29 figures.

Table of Contents

  1. Introduction: Fundamental Issues and Problems
  2. A Prehistory of QCD
  3. Deeply inelastic scattering and the parton model
  4. QCD, asymptotic freedom and the running mass
  5. Wick rotation
  6. Infrared safety
  7. QCD in the $n$ plane
  8. Long and Short Distances in Minkowski Space
  9. Example: IR and CO divergences in the massless vertex function
  10. Analytic structure and IR divergences: Landau equations and physical pictures
  11. Power counting and pinch surfaces
  12. Pinch surfaces for the all-order EM form factor
  13. Short Distance Cross Sections and Unitarity
  14. Cut diagrams and generalized unitarity
  15. Infrared safety for inclusive annihilation and decay
  16. ...and 19 more sections

Figures (29)

  • Figure 1: Deeply inelastic scattering.
  • Figure 2: Deeply inelastic scattering in the parton model.
  • Figure 3: Heuristic picture of parton model DIS.
  • Figure 4: Scalar two-point function.
  • Figure 5: Wick rotation in the energy plane.
  • ...and 24 more figures