On Triple-Cut of Scattering Amplitudes

TL;DR

This paper introduces a novel method for analyzing the triple-cut of one-loop amplitudes in dimensional regularisation, simplifying phase-space integration and aiding in extracting coefficients of multi-point functions.

Contribution

It defines the triple-cut as a difference of two double-cuts with causal and anti-causal prescriptions, providing a new effective tool for amplitude analysis.

Findings

Simplified phase-space integration using residues theorem.

Applicable to arbitrary dimensions.

Effective extraction of coefficients for multi-point functions.

Abstract

It is analysed the triple-cut of one-loop amplitudes in dimensional regularisation within spinor-helicity representation. The triple-cut is defined as a difference of two double-cuts with the same particle content, and a same propagator carrying, respectively, causal and anti-causal prescription in each of the two cuts. That turns out into an effective tool for extracting the coefficients of the three-point functions (and higher-point ones) from one-loop-amplitudes. The phase-space integration is oversimplified by using residues theorem to perform the integration over the spinor variables, via the holomorphic anomaly, and a trivial integration on the Feynman parameter. The results are valid for arbitrary values of dimensions.