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An algorithm towards $\varepsilon$-factorising Feynman Integrals

epsilon-collaboration, :, Iris Bree, Federico Gasparotto, Antonela Matijašić, Pouria Mazloumi, Dmytro Melnichenko, Sebastian Pögel, Toni Teschke, Xing Wang, Stefan Weinzierl, Konglong Wu, Xiaofeng Xu

Abstract

In this talk, we use several examples to elaborate on how a recently proposed algorithm can turn non-trivial Feynman integrals into an $\varepsilon $-factorised manner, regardless of their hidden geometric essence. In particular, some extra details about three-loop banana integrals with unequal-mass configuration are provided.

An algorithm towards $\varepsilon$-factorising Feynman Integrals

Abstract

In this talk, we use several examples to elaborate on how a recently proposed algorithm can turn non-trivial Feynman integrals into an -factorised manner, regardless of their hidden geometric essence. In particular, some extra details about three-loop banana integrals with unequal-mass configuration are provided.
Paper Structure (7 sections, 37 equations, 3 figures)

This paper contains 7 sections, 37 equations, 3 figures.

Table of Contents

  1. Introduction
  2. A Sketch of the Method
  3. Appetiser Example: Pentabox
  4. Three-loop Banana with Unequal masses
  5. Basis $J$
  6. Constraints
  7. Conclusion

Figures (3)

  • Figure 1: Massless onshell pentabox.
  • Figure 2: The banana integral (the leftmost sector 15) together with its relevant super-sectors.
  • Figure 3: The dimensions of decomposed subspaces within the top sector. The subscript "geom" means that the geometric filtration is used here.