One-loop Integrals from Volumes of Orthoschemes

2023/06/07 by Lecheng Ren, Marcus Spradlin, Ren, Lecheng +5 · 2 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2306.04630

openalex publication_date 2023/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Recently in arXiv:2012.05599 Rudenko presented a formula for the volume of hyperbolic orthoschemes in terms of alternating polylogarithms. We use this result to provide an explicit analytic result for the one-loop scalar n-gon Feynman integral in n dimensions, for even n, with massless or massive internal and external edges. Furthermore, we evaluate the general six-dimensional hexagon integral in terms of classical polylogarithms.

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• Analytic results for one-loop integrals in dimensional regularisation
• Multipoint conformal integrals in D dimensions. Part II: Polygons and basis functions

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