All Split Helicity Tree-Level Gluon Amplitudes

TL;DR

This paper derives explicit formulas for split helicity gluon amplitudes at tree level using a new recursion relation, providing a diagrammatic expansion and discussing potential generalizations.

Contribution

It introduces a closed-form solution for split helicity gluon amplitudes based on a new recursion relation, with a simple diagrammatic interpretation.

Findings

Explicit formulas for split helicity amplitudes derived

Diagrammatic zigzag expansion introduced

Potential generalizations discussed

Abstract

Recently a new recursion relation for tree-level gluon amplitudes in gauge theory has been discovered. We solve this recursion to obtain explicit formulas for the closed set of amplitudes with arbitrarily many positive and negative helicity gluons in a split helicity configuration. The solution admits a simple diagrammatic expansion in terms of zigzag diagrams. We comment on generalizations of this result.