On canonical differential equations for Calabi-Yau multi-scale Feynman integrals

Abstract

We generalise a method recently introduced in the literature, that derives canonical differential equations, to multi-scale Feynman integrals with an underlying Calabi-Yau geometry. We start by recomputing a canonical form for the sunrise integral with all unequal masses. Additionally, we compute for the first time a canonical form for the three-loop banana integral with two unequal masses and for a four-loop banana integral with two unequal masses. For the integrals we compute, we find an $\epsilon$-form whose connection has at most simple poles. We motivate our construction by studying the Picard-Fuchs operators acting on the integrals considered. In the appendices, we give a constructive explanation for why our generalisation works.

40 pages plus appendices and ancillary files

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Cited by in corpus (4)

• Three-loop banana integrals with four unequal masses
• Canonical differential equations and intersection matrices
• The spectrum of Feynman-integral geometries at two loops
• A construction of single-valued elliptic polylogarithms