# Application of BCFW-recursion relations and the Feynman-tree theorem to the four gluon amplitude with all plus helicities

## TL;DR

This paper demonstrates a method combining BCFW recursion relations and the Feynman-tree theorem to compute the all-plus helicity four-gluon amplitude, simplifying traditional loop diagram calculations.

## Contribution

It introduces a novel approach that leverages on-shell amplitudes and factorization to efficiently calculate complex gluon scattering amplitudes.

## Key findings

- Successfully computes the four-gluon all-plus helicity amplitude.
- Shows the method reproduces known results with potentially less computational effort.
- Illustrates the approach with explicit example of one-loop box diagrams.

## Abstract

Recently it has been shown that in gauge theories amplitudes to any perturbation order can be obtained by glueing together simple three-point on-shell amplitudes. These three-point amplitudes in turn are fixed by locality and Lorentz invariance. This factorization into three-point on-shell amplitudes follows from the BCFW recursion relations and the Feynman-tree theorem. In an explicit example, that is, the four-gluon amplitude with all plus helicities, we illustrate the method. In conventional calculation this amplitude corresponds to one-loop box diagrams.