Tree-level Split Helicity Amplitudes in Ambitwistor Space

TL;DR

This paper derives explicit formulas for all tree-level split helicity gluon amplitudes using BCFW recursion and Hodges diagrams in ambitwistor space, simplifying their structure into triangular components.

Contribution

It introduces a novel approach to compute split helicity gluon amplitudes by combining BCFW recursion with Hodges diagrams in ambitwistor space, revealing their triangular decomposition.

Findings

Explicit expressions for all split helicity amplitudes

Reproduction of six gluon split NMHV amplitudes

Amplitudes can be decomposed into triangles

Abstract

We study all tree-level split helicity gluon amplitudes by using the recently proposed BCFW recursion relation and Hodges diagrams in ambitwistor space. We pick out the contributing diagrams and find that all of them can be divided into triangles in a suitable way. We give the explicit expressions for all of these amplitudes. As an example, we reproduce the six gluon split NMHV amplitudes in momentum space.