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.