Getting more flavour out of one-flavour QCD

Abstract

We argue that no notion of flavour is necessary when performing amplitude calculations in perturbative QCD with massless quarks. We show this explicitly at tree-level, using a flavour recursion relation to obtain multi-flavoured QCD from one-flavour QCD. The method relies on performing a colour decomposition, under which the one-flavour primitive amplitudes have a structure which is restricted by planarity and cyclic ordering. An understanding of SU(3)_c group theory relations between QCD primitive amplitudes and their organisation around the concept of a Dyck tree is also necessary. The one-flavour primitive amplitudes are effectively N=1 supersymmetric, and a simple consequence is that all of tree-level massless QCD can be obtained from Drummond and Henn's closed form solution to tree-level N=4 super Yang-Mills theory.

27 pages, 6 figures

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• Proof of a new colour decomposition for QCD amplitudes
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• The $L_{\infty }$ structure of gauge theories with matter
• Double copies of fermions as only gravitational interacting matter
• New relations for graviton-matter amplitudes
• All-multiplicity amplitudes with four massive quarks and identical-helicity gluons
• On Positive Geometry and Scattering Forms for Matter Particles
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• Scattering amplitudes in gauge theories with and without supersymmetry
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods