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.
Cite
@article{arxiv.2207.12893,
title = {The three-loop equal-mass banana integral in $\varepsilon$-factorised form with meromorphic modular forms},
author = {Sebastian Pögel and Xing Wang and Stefan Weinzierl},
journal= {arXiv preprint arXiv:2207.12893},
year = {2022}
}