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On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals

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arxiv 2110.07968 v3 pith:TGLBVKFV submitted 2021-10-15 hep-th

classification hep-th
keywords methodfeynmanellipticintegralsbasisdemonstratedifferentialepsilon
verification ladder T0 review T1 audit T2 compute T3 formal
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In this paper we develop and demonstrate a method to obtain epsilon factorized differential equations for elliptic Feynman integrals. This method works by choosing an integral basis with the property that the period matrix obtained by integrating the basis over a complete set of integration cycles is diagonal. The method is a generalization of a similar method known to work for polylogarithmic Feynman integrals. We demonstrate the method explicitly for a number of Feynman integral families with an elliptic highest sector.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Bootstrapping form factor squared in ${\cal N}=4$ super-Yang-Mills

    hep-th 2025-06 conditional novelty 7.0 of 10

    A bootstrap using soft and collinear limits fixes the tree-level form factor squared in planar N=4 SYM up to N=6, unifying loop integrands from two-point master diagrams.

  2. Differential Equations for Energy Correlators in Any Angle

    hep-ph 2025-06 conditional novelty 7.0 of 10

    A first systematic differential equation framework for any-angle energy correlators in N=4 SYM, with four-point master integrals that include non-polylogarithmic elliptic and hyperelliptic sectors.

  3. First look at the evaluation of two-loop Feynman integrals for radiative return processes

    hep-ph 2026-07 accept novelty 6.0 of 10

    Planar two-loop four-point master integrals for massive radiative-return QED, including elliptic and nested-root sectors, are reduced to polynomial-in-ε differential equations that evaluate stably in the physical region.

  4. Electroweak double-box integrals for Moller scattering

    hep-ph 2024-12 conditional novelty 6.0 of 10

    Presents epsilon-factorised master integrals, boundary values, and numerical routines for the planar and non-planar electroweak double-box families relevant to NNLO Moller scattering.

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