Proof of a new colour decomposition for QCD amplitudes

TL;DR

This paper proves a new colour decomposition for QCD tree-level amplitudes, using hierarchical Feynman diagrams that reveal a Dyck structure, advancing the understanding of colour factors in quantum chromodynamics.

Contribution

It provides a rigorous proof of Johansson and Ochirov's conjectured colour decomposition for QCD amplitudes, introducing the 'Mario World' diagram approach.

Findings

Proof of the conjectured colour decomposition

Introduction of 'Mario World' Feynman diagrams

Identification of Dyck structure in multi-quark amplitudes

Abstract

Recently, Johansson and Ochirov conjectured the form of a new colour decomposition for QCD tree-level amplitudes. This note provides a proof of that conjecture. The proof is based on "Mario World" Feynman diagrams, which exhibit the hierarchical Dyck structure previously found to be very useful when dealing with multi-quark amplitudes.