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arXiv · 2212.08908

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

Sebastian Pögel·Xing Wang·Stefan Weinzierl
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Abstract

We describe a systematic approach to cast the differential equation for the $l$-loop equal mass banana integral into an $\varepsilon$-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 $\varepsilon$ for any loop $l$. The approach is based on properties of Calabi-Yau operators, and in particular on self-duality.

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Sebastian Pögel, Xing Wang, Stefan Weinzierl. 2022-12-17. Bananas of equal mass: any loop, any order in the dimensional regularisation parameter. https://doi.org/10.1007/jhep04(2023)117

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