The tree world

TL;DR

This paper demonstrates that higher-order gauge and gravity amplitudes can be constructed from tree amplitudes with added particle pairs, simplifying complex calculations and exemplified through a four-gluon amplitude computation.

Contribution

It introduces a method to express all perturbative amplitudes as forward limits of tree amplitudes with extra particle pairs, extending the utility of BCFW recursion.

Findings

Higher-order amplitudes are given by tree amplitudes with added pairs in the forward limit.

Explicit computation of the four-gluon all-plus helicity amplitude at next-to-leading order.

The approach simplifies calculations of complex gauge and gravity amplitudes.

Abstract

Tree amplitudes of any gauge theory and gravity can be factorized into primitive three-particle amplitudes by the BCFW recursion relations. We show that the amplitudes at any perturbation order are given by tree amplitudes with additional pairs of particles in the forward limit. As an example we compute the four-gluon all-plus helicity amplitude at next-to-leading order.