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.

Questo articolo esplora i giri e le loro implicazioni.

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