The dimension-shift conjecture for one-loop amplitudes

TL;DR

This paper proves a conjecture relating N=4 MHV and all-plus helicity amplitudes in pure Yang-Mills theory using unitarity cuts, providing a unified understanding of their one-loop structures across all dimensions.

Contribution

It provides a proof of the dimension-shifting conjecture for one-loop amplitudes in Yang-Mills theory to all orders in dimensional regularisation.

Findings

Confirmed the dimension-shifting relationship for all orders

Derived explicit forms of one-loop amplitudes for all multiplicities

Applied generalized D-dimensional unitarity to capture full amplitude structure

Abstract

A conjecture made by Bern, Dixon, Dunbar, and Kosower asserts a simple dimension-shifting relationship between the one-loop structure of N = 4 MHV amplitudes and all-plus helicity amplitudes in pure Yang-Mills theory. We prove this conjecture to all orders in dimensional regularisation using unitarity cuts, and evaluate the form of these simplest one-loop amplitudes using a generalised D-dimensional unitarity technique which captures the full amplitude to all multiplicities.