Journal of High Energy Physics (Jul 2023)

On a procedure to derive ϵ-factorised differential equations beyond polylogarithms

  • Lennard Görges,
  • Christoph Nega,
  • Lorenzo Tancredi,
  • Fabian J. Wagner

DOI
https://doi.org/10.1007/JHEP07(2023)206
Journal volume & issue
Vol. 2023, no. 7
pp. 1 – 52

Abstract

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Abstract In this manuscript, we elaborate on a procedure to derive ϵ-factorised differential equations for multi-scale, multi-loop classes of Feynman integrals that evaluate to special functions beyond multiple polylogarithms. We demonstrate the applicability of our approach to diverse classes of problems, by working out ϵ-factorised differential equations for single- and multi-scale problems of increasing complexity. To start we are reconsidering the well-studied equal-mass two-loop sunrise case, and move then to study other elliptic two-, three- and four-point problems depending on multiple different scales. Finally, we showcase how the same approach allows us to obtain ϵ-factorised differential equations also for Feynman integrals that involve geometries beyond a single elliptic curve.

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