Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

TMD factorization and the gluon distribution in high energy QCD

Emil Avsar

TL;DR

This work provides a comprehensive, unified treatment of Transverse Momentum Dependent (TMD) factorization and the gluon distribution in high-energy QCD across hard-scattering, small-x, and CGC frameworks. It carefully distinguishes between various unintegrated gluon distributions (Weizsäcker-Williams, dipole) and clarifies the rapidity structure and gauge-link constructions required for consistent factorization. Through detailed analysis of single inclusive particle production at small x, the paper scrutinizes the validity and limitations of k_T-factorization, CGC factorization, and their hybrids, highlighting the importance of subtractions and gauge choices. The work emphasizes that, while CGC/Laplace-LLA pictures offer valuable insights, TMD-factorization grounded in rigorous all-order arguments remains essential for robust, predictive QCD phenomenology at high energies.

Abstract

This paper is a part of a series of works where we in detail examine the concept of Transverse Momentum Dependent (TMD), or k_T, factorization, which is frequently encountered in the literature and is widely used in the phenomenological applications of QCD at very high energies. We address the question of what exactly factorization is, as it is meant in different contexts and formalisms, and we compare the formalisms to each other. We clarify some basic concepts regarding factorization and how it exactly is applied in high energy QCD, and we make important notes on some key and fundamental points that are often overlooked. We offer an extensive analysis of single inclusive particle production, and we analyze the TMD gluon distribution that plays a pivotal role in high energy QCD.

TMD factorization and the gluon distribution in high energy QCD

TL;DR

This work provides a comprehensive, unified treatment of Transverse Momentum Dependent (TMD) factorization and the gluon distribution in high-energy QCD across hard-scattering, small-x, and CGC frameworks. It carefully distinguishes between various unintegrated gluon distributions (Weizsäcker-Williams, dipole) and clarifies the rapidity structure and gauge-link constructions required for consistent factorization. Through detailed analysis of single inclusive particle production at small x, the paper scrutinizes the validity and limitations of k_T-factorization, CGC factorization, and their hybrids, highlighting the importance of subtractions and gauge choices. The work emphasizes that, while CGC/Laplace-LLA pictures offer valuable insights, TMD-factorization grounded in rigorous all-order arguments remains essential for robust, predictive QCD phenomenology at high energies.

Abstract

This paper is a part of a series of works where we in detail examine the concept of Transverse Momentum Dependent (TMD), or k_T, factorization, which is frequently encountered in the literature and is widely used in the phenomenological applications of QCD at very high energies. We address the question of what exactly factorization is, as it is meant in different contexts and formalisms, and we compare the formalisms to each other. We clarify some basic concepts regarding factorization and how it exactly is applied in high energy QCD, and we make important notes on some key and fundamental points that are often overlooked. We offer an extensive analysis of single inclusive particle production, and we analyze the TMD gluon distribution that plays a pivotal role in high energy QCD.

Paper Structure

This paper contains 30 sections, 168 equations, 39 figures.

Table of Contents

  1. Introduction
  2. Unintegrated parton distributions
  3. The gluon "number density"
  4. The dipole gluon distribution
  5. On the rapidity variable in the gluon distribution
  6. Factorization
  7. Hard scattering factorization
  8. Basic parton model
  9. On the leading momentum regions in field theory
  10. Factorization in simple theory
  11. Including the gluons, and the Glauber region
  12. TMD factorization
  13. Factorization in BFKL
  14. Factorization in the CGC
  15. Basics of CGC
  16. ...and 15 more sections

Figures (39)

  • Figure 1: DIS in the simple parton model. Right: Factorized structure in the parton model.
  • Figure 2: Left: Reduced graphs for SIDIS where a hadron with momentum $p_B$ is detected. Right: Reduced graphs for the Drell-Yan process of lepton pair production in hadron-hadron scattering.
  • Figure 3: A two loop contribution to the Sudakov form factor.
  • Figure 4: Examples of reduced graphs for the two loop Sudakov form factor.
  • Figure 5: Generic contribution to inclusive DIS in simplified case.
  • ...and 34 more figures