Color ordering in QCD

Abstract

We derive color decompositions of arbitrary tree and one-loop QCD amplitudes into color-ordered objects called primitive amplitudes. Furthermore, we derive general fermion flip and reversion identities spanning the null space among the primitive amplitudes and use them to prove that all color-ordered tree amplitudes of massless QCD can be written as linear combinations of color-ordered tree amplitudes of $\mathcal{N}=4$ super Yang-Mills theory.