Abstract
We present a new color decomposition for QCD amplitudes at one-loop level as a generalization of the Del Duca-Dixon-Maltoni and Johansson-Ochirov decomposition at tree level. Starting from a minimal basis of planar primitive amplitudes we write down a color decomposition that is free of linear dependencies among appearing primitive amplitudes or color factors. The conjectured decomposition applies to any number of quark flavors and is independent of the choice of gauge group and matter representation. The results also hold for higher-dimensional or supersymmetric extensions of QCD. We provide expressions for any number of external quark-antiquark pairs and gluons.
Highlights
These relations have been utilized to find more compact color decompositions, first for the purely gluonic case by Del-Duca-Dixon-Maltoni (DDM) [57, 58] and later the generalization to any number of external quark-antiquark pairs by Johansson and Ochirov (JO) [59], which was proven by Melia [60] shortly thereafter
We present a new color decomposition for QCD amplitudes at one-loop level as a generalization of the Del Duca-Dixon-Maltoni and Johansson-Ochirov decomposition at tree level
We review the work by Johansson and Ochirov (JO) [59] about a new color decomposition for massless QCD at tree level and introduce the necessary notation
Summary
We review the work by Johansson and Ochirov (JO) [59] about a new color decomposition for massless QCD at tree level and introduce the necessary notation. The decomposition is written in terms of gauge group structure constants fabc and primitive (color-ordered) amplitudes as. Where we define the structure constants in terms of the gauge group generators T a (2.1). The primitive amplitudes A(1, 2, σ) are exactly the color-ordered amplitudes appearing in the trace-based color decomposition — and can be directly computed from planar diagrams with the given external ordering using color-ordered Feynman rules [66]. This decomposition is valid for any choice of gauge group since it only relies on defining properties of the Lie algebra
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