Combinatorial Factorization

The simplest integrands in the CHY formulation of scattering amplitudes are constructed using the so-called Parke-Taylor functions. Parke-Taylor functions also turn out to belong to a large class of rational functions known as MHV leading singularities. In fact, Parke-Taylor functions correspond to planar MHV leading singularities. In this note we study the behavior of CHY integrands constructed using non-planar MHV leading singularities under collinear and multi-particle factorization limits. General $n$-particle MHV leading singularities are completely characterized by a set of $(n-2)$ triples of particle labels. We give a simple operation on this combinatorial data which "factors" the list into two sets of triples defining two lower point MHV leading singularities. The fact that general MHV leading singularities form a closed set under "multi-particle factorizations" is surprising from their gauge theoretic origin.