A Tale of Two Loops: Simplifying All-Plus Yang-Mills Amplitudes

TL;DR

This paper explores new methods to simplify all-plus Yang-Mills amplitudes, which are uniquely simple and related to supersymmetric theories, by analyzing their structure prior to integration.

Contribution

It introduces three novel approaches to analyze the structure of all-plus amplitudes before integration, enhancing understanding and simplification techniques.

Findings

Tree-level all-plus amplitudes vanish.

Loop-level all-plus amplitudes relate to $ ext{N}=4$ SYM amplitudes.

New methods improve the analysis of amplitude structures.

Abstract

Pure Yang-Mills amplitudes with all external gluons carrying positive helicity, known as all-plus amplitudes, have an especially simple structure. The tree amplitudes vanish and, up to at least two loops, the loop-level amplitudes are related to those of $\mathcal{N}=4$ super-Yang-Mills (SYM) theory. This makes all-plus amplitudes a useful testing ground for new methods of simplifying more general classes of amplitudes. In this thesis we consider three new approaches, focusing on the structure before integration.