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Color evolution of 2 -> 3 processes

Malin Sjodahl

TL;DR

The paper develops a color-space framework for soft-gluon resummation in 2→3 QCD processes by constructing multiplet-inspired bases in the s-channel to simplify color evolution. It extends known 2→2 results to 2→3 by building complete orthogonal color bases for qq̄→qq̄g, gg→qq̄g, and gg→ggg, and deriving the corresponding soft anomalous dimension matrices. The matrices exhibit diagonal and block-diagonal structures reflecting color exchanges, with sizes 4×4, 11×11, and 22×22, and are validated for symmetry and completeness using computer algebra. These results enable more complete resummation for 2→3 processes and can be extended to more final-state partons, though the complexity requires further theoretical advances in the underlying group theory.

Abstract

The color structure needed for resummation of all colored 2 -> 3 processes is calculated using multiplet inspired s-channel bases. In this way the resulting matrices, describing the color structure, are guaranteed to obey simplifying symmetries.

Color evolution of 2 -> 3 processes

TL;DR

The paper develops a color-space framework for soft-gluon resummation in 2→3 QCD processes by constructing multiplet-inspired bases in the s-channel to simplify color evolution. It extends known 2→2 results to 2→3 by building complete orthogonal color bases for qq̄→qq̄g, gg→qq̄g, and gg→ggg, and deriving the corresponding soft anomalous dimension matrices. The matrices exhibit diagonal and block-diagonal structures reflecting color exchanges, with sizes 4×4, 11×11, and 22×22, and are validated for symmetry and completeness using computer algebra. These results enable more complete resummation for 2→3 processes and can be extended to more final-state partons, though the complexity requires further theoretical advances in the underlying group theory.

Abstract

The color structure needed for resummation of all colored 2 -> 3 processes is calculated using multiplet inspired s-channel bases. In this way the resulting matrices, describing the color structure, are guaranteed to obey simplifying symmetries.

Paper Structure

This paper contains 21 sections, 43 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Gluon resummation
  3. 2 $\rightarrow$ 2 processes
  4. A simple example, $qq \rightarrow qq$
  5. Color structure of $qg \rightarrow qg$
  6. Color structure of $gg \to gg$
  7. 2 $\to$ 3 processes
  8. Construction of complete orthogonal bases
  9. $q \overline{q} \to q \overline{q} g$
  10. $gg \to q \overline{q} g$
  11. $gg \to ggg$
  12. Results
  13. Conclusions
  14. Basis tensors and normalizations
  15. $q \overline{q} \to q \overline{q} g$
  16. ...and 6 more sections

Figures (6)

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  • ...and 1 more figures