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

2025/11/26 by Xuhang Jiang, Jiang, Xuhang
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical functions and polynomials #Particle physics theoretical and experimental studies

paper · pdf · doi:10.48550/arxiv.2511.21493

openalex publication_date 2025/11/26 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28

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.

Citations

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• Feynman integral relations from parametric annihilators
• Master Integrals for Four-Loop Massless Form Factors