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

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arxiv 2207.12893 v2 pith:LAWGHXIJ submitted 2022-07-26 hep-th hep-phmath-phmath.MP

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

classification hep-th hep-phmath-phmath.MP
keywords varepsilonfactorisedformformsintegralmeromorphicmodularbanana
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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Cited by 9 Pith papers

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