Notes on Fourier transform and its application to three-point momentum-space integrals

TL;DR

This paper explores the use of Fourier transforms to derive identities for three-point massless momentum-space Feynman integrals, aiding their calculation, especially for non-planar cases relevant in off-shell Sudakov form factors.

Contribution

It generalizes the Fourier transform approach from two-point to three-point integrals, establishing new identities to facilitate their computation, including non-planar configurations.

Findings

Derived identities for three-point integrals using Fourier transforms.

Applied identities to compute non-planar Feynman integrals.

Enhanced understanding of off-shell Sudakov form factors.

Abstract

The Fourier transform of two-point momentum-space Feynman integrals with massless propagators and two off-shell legs can be used to prove identities between their periods, exemplified by the glue-and-cut identity. We generalize this framework to massless momentum-space Feynman integrals with three off-shell legs and obtain a similar family of identities that can be used to calculate these integrals, especially for a non-planar subset of them, which naturally arise in the off-shell Sudakov form factors.