Abstract
We show that the differential equation for the three-loop equal-mass banana integral can be cast into an ε-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 ε-factorised form of the differential equation allows for a systematic solution to any order in the dimensional regularisation parameter ε. The alphabet of the iterated integrals contains six letters.
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Pögel, S., Wang, X. & Weinzierl, S. The three-loop equal-mass banana integral in ε-factorised form with meromorphic modular forms. J. High Energ. Phys. 2022, 62 (2022). https://doi.org/10.1007/JHEP09(2022)062
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DOI: https://doi.org/10.1007/JHEP09(2022)062