Simplicity in the Structure of QED and Gravity Amplitudes

TL;DR

This paper reveals that one-loop multi-photon amplitudes in QED with at least eight photons are composed solely of scalar box integrals, demonstrating a remarkable simplicity and cancellation pattern similar to supergravity theories.

Contribution

It establishes a 'no-triangle' property for QED amplitudes at one loop, derived through world-line and unitarity methods, highlighting the role of BCFW scaling behavior.

Findings

One-loop multi-photon QED amplitudes with ≥8 photons are only scalar box integrals.

The 'no-triangle' property in QED parallels that in N=8 supergravity.

The simple amplitude structure stems from excellent BCFW scaling of tree amplitudes.

Abstract

We investigate generic properties of one-loop amplitudes in unordered gauge theories in four dimensions. For such theories the organisation of amplitudes in manifestly crossing symmetric expressions poses restrictions on their structure and results in remarkable cancellations. We show that one-loop multi-photon amplitudes in QED with at least eight external photons are given only by scalar box integral functions. This QED `no-triangle' property is true for all helicity configurations and has similarities to the `no-triangle' property found in the case of maximal N = 8 supergravity. Results are derived both via a world-line formalism as well as using on-shell unitarity methods. We show that the simple structure of the loop amplitude originates from the extremely good BCFW scaling behaviour of the QED tree-amplitude.