New Recursion Relations for Tree Amplitudes of Gluons

TL;DR

This paper introduces new recursion relations for calculating tree-level gluon amplitudes in gauge theory, resulting in more compact formulas and a new eight-gluon amplitude result, simplifying the computation process.

Contribution

The paper presents novel recursion relations that express any tree gluon amplitude as a sum over products of on-shell amplitudes, enabling more efficient calculations.

Findings

Recomputed all known tree-level amplitudes up to seven gluons.

Derived a new eight-gluon amplitude A(1+,2-,3+,4-,5+,6-,7+,8-).

Showed how to construct any amplitude using only three-gluon amplitudes.

Abstract

We present new recursion relations for tree amplitudes in gauge theory that give very compact formulas. Our relations give any tree amplitude as a sum over terms constructed from products of two amplitudes of fewer particles multiplied by a Feynman propagator. The two amplitudes in each term are physical, in the sense that all particles are on-shell and momentum conservation is preserved. This is striking, since it is just like adding certain factorization limits of the original amplitude to build up the full answer. As examples, we recompute all known tree-level amplitudes of up to seven gluons and show that our recursion relations naturally give their most compact forms. We give a new result for an eight-gluon amplitude, A(1+,2-,3+,4-,5+,6-,7+,8-). We show how to build any amplitude in terms of three-gluon amplitudes only.