Double-Cut of Scattering Amplitudes and Stokes' Theorem

TL;DR

This paper introduces a novel method using Stokes' Theorem to analytically compute double-cut integrals in one-loop amplitudes, simplifying phase-space integrals through complex analysis techniques.

Contribution

It presents a new approach applying Stokes' Theorem to evaluate double-cut integrals, streamlining calculations in one-loop amplitude decompositions.

Findings

Simplifies phase-space integrals via indefinite and residue integrations.

Applicable to cut-construction of 2-point function coefficients.

Enhances analytical computation of one-loop amplitude components.

Abstract

We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions in two complex-conjugated variables, which are simply computed by an indefinite integration in a single variable, followed by Cauchy's Residue integration in the conjugated one. The method is suitable for the cut-construction of the coefficients of 2-point functions entering the decomposition of one-loop amplitudes in terms of scalar master integrals.