Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

TMD gluon distributions for multiparton processes

Marcin Bury, Piotr Kotko, Krzysztof Kutak

TL;DR

This work extends the operator definitions of TMD gluon distributions to multiparton processes (five and six colored partons) by deploying color-flow decomposition to systematically derive gauge-invariant TMD operators. It constructs a complete basis of TMD distributions and provides explicit Φ matrices for all relevant 5- and 6-parton channels, including new structures F^{(3)} and F^{(7)}. A large-Nc analysis reveals a simplification where only a pair of basis structures dominate diagonally, with off-diagonal contributions being numerically small, aligning with CGC universality arguments. The results have immediate phenomenological relevance for multi-jet production in the small-x regime and could be integrated with CGC evolution (e.g., BK/JIMWLK) to describe forward jet processes. The work also lays groundwork for future extensions to quark-containing multiparton processes and connects with existing approaches to TMD factorization in high-energy QCD.

Abstract

We derive gauge invariant operators entering definitions of the Transverse Momentum Dependent (TMD) gluon distributions, for all five and six parton processes. Our calculations utilize color decomposition of amplitudes in the color flow basis. In addition, we find the general result for multi-gluon process (with arbitrary number of gluons) at large $N_{c}$. On phenomenological ground our results may be used for multi-jet production in the small-$x$ regime, where the TMD gluon distributions can be derived from the Color Glass Condensate effective theory.

TMD gluon distributions for multiparton processes

TL;DR

This work extends the operator definitions of TMD gluon distributions to multiparton processes (five and six colored partons) by deploying color-flow decomposition to systematically derive gauge-invariant TMD operators. It constructs a complete basis of TMD distributions and provides explicit Φ matrices for all relevant 5- and 6-parton channels, including new structures F^{(3)} and F^{(7)}. A large-Nc analysis reveals a simplification where only a pair of basis structures dominate diagonally, with off-diagonal contributions being numerically small, aligning with CGC universality arguments. The results have immediate phenomenological relevance for multi-jet production in the small-x regime and could be integrated with CGC evolution (e.g., BK/JIMWLK) to describe forward jet processes. The work also lays groundwork for future extensions to quark-containing multiparton processes and connects with existing approaches to TMD factorization in high-energy QCD.

Abstract

We derive gauge invariant operators entering definitions of the Transverse Momentum Dependent (TMD) gluon distributions, for all five and six parton processes. Our calculations utilize color decomposition of amplitudes in the color flow basis. In addition, we find the general result for multi-gluon process (with arbitrary number of gluons) at large . On phenomenological ground our results may be used for multi-jet production in the small- regime, where the TMD gluon distributions can be derived from the Color Glass Condensate effective theory.

Paper Structure

This paper contains 21 sections, 139 equations, 16 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. TMD gluon distributions
  4. Color decomposition
  5. Color flow Feynman rules for TMD operators
  6. Examples
  7. The operator basis for arbitrary TMD gluon distribution
  8. Operator structures for 5 and 6 colored partons
  9. Outline of the method using 4 parton example
  10. Five partons
  11. Six partons
  12. Large $N_{c}$ analysis for arbitrary number of gluons
  13. Summary
  14. Amplitude vectors $\vec{\mathcal{A}}$ and matrices $\mathbf{M}$
  15. Block matrices for six parton processes
  16. ...and 6 more sections