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An Analytic Computation of Three-Loop Five-Point Feynman Integrals

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arxiv 2411.18697 v2 pith:TSEZ5ELL submitted 2024-11-27 hep-ph hep-th

An Analytic Computation of Three-Loop Five-Point Feynman Integrals

Yuanche Liu , Antonela Matija\v{s}i\'c , Julian Miczajka , Yingxuan Xu , Yongqun Xu , Yang Zhang This is my paper
classification hep-ph hep-th
keywords differentialequationintegralsthree-loopanalyticcomputationfeynmanfive-point
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We evaluate the three-loop five-point pentagon-box-box massless integral family in the dimensional regularization scheme, via canonical differential equation. We use tools from computational algebraic geometry to enable the necessary integral reductions. The boundary values of the differential equation are determined analytically in the Euclidean region. To express the final result, we introduce a new representation of weight six functions in terms of one-fold integrals over the product of weight-three functions with weight-two kernels that are derived from the differential equation. Our work paves the way to the analytic computation of three-loop multi-leg Feynman integrals.

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Cited by 2 Pith papers

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  1. Pseudo-Evanescent Feynman Integrals from Local Subtraction

    hep-th 2026-05 conditional novelty 7.0

    Local subtraction reduces pseudo-evanescent Feynman integrals to products of one-loop integrals or one-fold integrals, with the finite part of the two-loop all-plus five-point amplitude arising solely from ultraviolet...

  2. AMFlow 2.0: significant algorithmic and software improvements for Feynman integral evaluation

    hep-ph 2026-07 accept novelty 5.0

    AMFlow 2.0 cuts symbolic and numerical cost of multi-loop Feynman integral evaluation via an FT recursion mode, a C++ DE solver, and modern IBP reducers, demonstrated on a three-loop five-point family.