On $\epsilon$-factorised bases and pure Feynman integrals

Abstract

We investigate $\epsilon$-factorised differential equations, uniform transcendental weight and purity for Feynman integrals. We are in particular interested in Feynman integrals beyond the ones which evaluate to multiple polylogarithms. We show that a $\epsilon$-factorised differential equation does not necessarily lead to Feynman integrals of uniform transcendental weight. We also point out that a proposed definition of purity works locally, but not globally.

25 pages, v2: text improvements

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• Three-loop banana integrals with four unequal masses
• On canonical differential equations for Calabi-Yau multi-scale Feynman integrals
• Canonical differential equations and intersection matrices
• Electroweak double-box integrals for Moller scattering