One-loop same helicity YM amplitudes from BG currents

TL;DR

This paper introduces a new formula for one-loop all same helicity Yang-Mills amplitudes, expressing them as a sum of products of tree-level currents connected by an effective propagator, and proves its correctness and invariance.

Contribution

The paper presents a novel explicit formula for one-loop same helicity Yang-Mills amplitudes using Berends-Giele currents and region momenta, with a rigorous proof of its properties.

Findings

The formula correctly reproduces collinear limits.

It is invariant under shifts of region momenta.

The approach simplifies calculations of these amplitudes.

Abstract

We propose and prove a new formula for the one-loop all same helicity Yang-Mills amplitudes. These amplitudes are seen to arise as a sum of products of two tree-level Berends-Giele currents connected by an effective propagator. To make sense of the propagators one needs to introduce the so-called region, or dual momenta. The formula is proven by observing that it readily implies the correct collinear limit properties. The only non-trivial part of the proof is establishing that our formula for the amplitude is invariant under shifts of the region momenta.