The three-loop equal-mass banana integral in ε-factorised form with meromorphic modular forms
Sebastian Pögel (PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, Mainz, D — 55099, Germany); Xing Wang (PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, Mainz, D — 55099, Germany); Stefan Weinzierl (PRISMA Cluster of Excellence, Institut für Physik, Johannes Gutenberg-Universität Mainz, Mainz, D — 55099, Germany)
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.
