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Elliptic Feynman integrals and pure functions. (English) Zbl 1409.81162

Summary: We propose a variant of elliptic multiple polylogarithms that have at most logarithmic singularities in all variables and satisfy a differential equation without homogeneous term. We investigate several non-trivial elliptic two-loop Feynman integrals with up to three external legs and express them in terms of our functions. We observe that in all cases they evaluate to pure combinations of elliptic multiple polylogarithms of uniform weight. This is the first time that a notion of uniform weight is observed in the context of Feynman integrals that evaluate to elliptic polylogarithms.

MSC:

81V05 Strong interaction, including quantum chromodynamics
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
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References:

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