Cyclic Mario Worlds -- Color-Decomposition for One-Loop QCD

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.

19 pages + refs, 1 figure, 2 tables; v2 fixing typos, adding clarifications, journal version

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Cited by in corpus (9)

• On the Double Copy for Spinning Matter
• Multi-Quark Colour Decompositions from Unitarity
• The role of colour flows in matrix element computations and Monte Carlo simulations
• Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
• KLT-type relations for QCD and bicolor amplitudes from color-factor symmetry
• On Positive Geometry and Scattering Forms for Matter Particles
• High-order corrections to inflationary perturbation spectra in quantum gravity
• Loop-level double-copy for massive fermions in the fundamental
• Group constraint relations for five-point amplitudes in gauge theories with SO(N) and Sp(2N) groups