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$\varepsilon$-factorized differential equations for two-loop non-planar triangle Feynman integrals with elliptic curves

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arxiv 2305.13951 v2 pith:YTRN7Z2F submitted 2023-05-23 hep-th hep-ph

Xuhang Jiang , Xing Wang , Li Lin Yang , Jingbang Zhao This is my paper · ORCID
classification hep-thhep-ph
keywords ellipticintegralscurvesfamiliestrianglebananadifferentialequations
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

In this paper, we investigate two-loop non-planar triangle Feynman integrals involving elliptic curves. In contrast to the Sunrise and Banana integral families, the triangle families involve non-trivial sub-sectors. We show that the methodology developed in the context of Banana integrals can also be extended to these cases and obtain $\varepsilon$-factorized differential equations for all sectors. The letters are combinations of modular forms on the corresponding elliptic curves and algebraic functions arising from the sub-sectors. With uniform transcendental boundary conditions, we express our results in terms of iterated integrals order-by-order in the dimensional regulator, which can be evaluated efficiently. Our method can be straightforwardly generalized to other elliptic integral families and have important applications to precision physics at current and future high-energy colliders.

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Cited by 3 Pith papers

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

  1. Calabi-Yau Feynman integrals in gravity: $\varepsilon$-factorized form for apparent singularities

    hep-th 2024-12 conditional novelty 7.0 of 10

    An extended ansatz for canonical differential equations handles epsilon-dependent apparent singularities and yields an epsilon-factorized form for the four-loop Calabi-Yau Feynman integral relevant to 5PM black-hole s...

  2. Analytic result of a three-loop integral family in the Higgs decay to four massive bottom quarks

    hep-ph 2026-07 accept novelty 6.5 of 10

    Analytic master-integral results through O(ε²) are obtained for a three-loop family containing elliptic and K3 geometries by building and solving a mixed-sector ε-factorized differential equation.

  3. 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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