Bananas of equal mass: any loop, any order in the dimensional regularisation parameter

Abstract

We describe a systematic approach to cast the differential equation for the $l$-loop equal mass banana integral into an $\epsilon$-factorised form. With the known boundary value at a specific point we obtain systematically the term of order $j$ in the expansion in the dimensional regularisation parameter $\epsilon$ for any loop $l$. The approach is based on properties of Calabi-Yau operators, and in particular on self-duality.

34 pages, v2: version to be published

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