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arXiv · 2207.12893

The three-loop equal-mass banana integral in $\varepsilon$-factorised form with meromorphic modular forms

Sebastian Pögel·Xing Wang·Stefan Weinzierl
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Abstract

We show that the differential equation for the three-loop equal-mass banana integral can be cast into an $\varepsilon$-factorised form with entries constructed from (meromorphic) modular forms and one special function, which can be given as an iterated integral of meromorphic modular forms. The $\varepsilon$-factorised form of the differential equation allows for a systematic solution to any order in the dimensional regularisation parameter $\varepsilon$. The alphabet of the iterated integrals contains six letters.

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Sebastian Pögel, Xing Wang, Stefan Weinzierl. 2022-07-26. The three-loop equal-mass banana integral in $\varepsilon$-factorised form with meromorphic modular forms. https://doi.org/10.1007/jhep09(2022)062

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