Taming Calabi-Yau Feynman integrals: The four-loop equal-mass banana integral

Abstract

Certain Feynman integrals are associated to Calabi-Yau geometries. We demonstrate how these integrals can be computed with the method of differential equations. The four-loop equal-mass banana integral is the simplest Feynman integral whose geometry is a non-trivial Calabi-Yau manifold. We show that its differential equation can be cast into an $\epsilon$-factorised form. This allows us to obtain the solution to any desired order in the dimensional regularisation parameter $\epsilon$. The method generalises to other Calabi-Yau Feynman integrals. Our calculation also shows that the four-loop banana integral is only minimally more complicated than the corresponding Feynman integrals at two or three loops.

7 pages, v2: version to be published

References in corpus (2)

• The three-loop equal-mass banana integral in $\epsilon$-factorised form with meromorphic modular forms
• Symbology for elliptic multiple polylogarithms and the symbol prime

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