On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes

TL;DR

This paper investigates the factorisation properties of Yang-Mills amplitudes within the connected prescription framework, proposing a contour integration method that accurately captures multi-particle poles and verifying it across various gauge choices.

Contribution

It introduces a novel contour prescription for integration in the connected prescription of Yang-Mills amplitudes, ensuring correct factorisation results.

Findings

The new contour prescription correctly reproduces multi-particle poles.

Verification across multiple gauge-fixing conditions confirms robustness.

Provides a practical method for accurate amplitude computation.

Abstract

We examine factorisation in the connected prescription of Yang-Mills amplitudes. The multi-particle pole is interpreted as coming from representing delta functions as meromorphic functions. However, a naive evaluation does not give a correct result. We give a simple prescription for the integration contour which does give the correct result. We verify this prescription for a family of gauge-fixing conditions.