Dyck Words and Multi-Quark Primitive Amplitudes

Abstract

I study group theory (Kleiss-Kuijf) relations between purely multi-quark primitive amplitudes at tree level, and prove that they reduce the number of independent primitives to (n-2)!/(n/2)!, where n is the number of quarks plus antiquarks, in the case where quark lines have different flavours. I give an explicit example of an independent basis of primitives for any n which is of the form A(1,2,sigma), where sigma is a permutation based on a Dyck word.