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arXiv · 1809.10698

Elliptic Feynman integrals and pure functions

Johannes Broedel·Claude Duhr·Falko Dulat·Brenda Penante·Lorenzo Tancredi
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Abstract

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.

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Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi. 2018-09-27. Elliptic Feynman integrals and pure functions. https://doi.org/10.1007/jhep01(2019)023

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