Perturbative QCD and Partons

Short-distance QCD predictions combine perturbative scattering with long-distance hadron structure. The organizing question is which factorization theorem applies to a specified measurement and scale hierarchy. This chapter develops the required parameters, parton distributions, evolution, convolutions, and uncertainty estimates while keeping each approximation’s domain explicit.

Enter this chapter

Begin with QCD Fields, Scales, and the Perturbative Domain to identify the scales on which a QCD calculation is perturbative.

Topics

1. QCD Fields, Scales, and the Perturbative Domain — Defines QCD fields and tests the perturbative hierarchy.
2. Short-Distance QCD Parameters, Mass Schemes, and Thresholds — Tracks schemes, active flavors, and heavy thresholds.
3. Inclusive Annihilation and the Emergence of Jets — Uses inclusive annihilation to expose color and jets.
4. Deep-Inelastic Scattering and the Parton Model — Introduces structure functions and Bjorken scaling.
5. Collinear Factorization and Operator-Defined PDFs — Defines PDFs as renormalized hadron matrix elements.
6. DGLAP Evolution and Scaling Violation — Derives collinear scaling violations.
7. Fragmentation Functions and Timelike Evolution — Separates fragmentation from incoming-hadron structure.
8. High-Energy QCD and Small-x Evolution — Identifies logarithms enhanced by a large rapidity interval.
9. TMD Factorization, Rapidity Evolution, and Glauber Limits — Resolves small recoil and the limitations of transverse-momentum factorization.
10. Hadron-Collider Factorization and Parton Luminosities — Combines beam distributions with partonic cross sections.
11. QCD Radiation, Jets, and Event Shapes — Constructs infrared-safe measurements of radiation.
12. QCD Predictions and Uncertainty Budgets — Combines perturbative, hadronic, and input uncertainties.

How the ideas fit together

Factorization assigns short-distance coefficients and hadron matrix elements a common scale convention. Their separate scale dependences cancel in the observable through the calculated order; evolution moves logarithms between these factors without determining the nonperturbative input. A different measurement can require a different theorem: retaining small recoil needs information integrated out of a collinear PDF, while identified hadrons require fragmentation. Consequently, successful factorization for one inclusive process does not establish it for every less-inclusive observable. Collins, Soper, and Sterman 1989, §§ 2–6.

Where to go next

Continue to Confinement and Chiral QCD to distinguish QCD confinement from an unbreakable flux-tube criterion.

References

• Collins, John C., Davison E. Soper, and George Sterman. “Factorization of Hard Processes in QCD.” In Perturbative Quantum Chromodynamics, edited by A. H. Mueller, 1–91. World Scientific, 1989. DOI. Open PDF.