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On $\varepsilon$-factorised bases and pure Feynman integrals (2301.02264v2)
Published 5 Jan 2023 in hep-th, math-ph, and math.MP
Abstract: We investigate $\varepsilon$-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 $\varepsilon$-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.
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