Symbology for elliptic multiple polylogarithms and the symbol prime

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Elliptic multiple polylogarithms occur in Feynman integrals and in particular in scattering amplitudes. They can be characterized by their symbol, a tensor product in the so-called symbol letters. In contrast to the non-elliptic case, the elliptic letters themselves satisfy highly non-trivial identities, which we discuss in this paper. Moreover, we introduce the symbol prime, an analog of the symbol for elliptic symbol letters, which makes these identities manifest. We demonstrate its use in two explicit examples at two-loop order: the unequal-mass sunrise integral in two dimensions and the ten-point double-box integral in four dimensions. Finally, we also report the result of the polylogarithmic nine-point double-box integral, which arises as the soft limit of the ten-point integral.

Original languageEnglish
Article number89
JournalJournal of High Energy Physics
Issue number1
Number of pages39
Publication statusPublished - 17 Jan 2023

    Research areas

  • Scattering Amplitudes, Differential and Algebraic Geometry, Supersymmetric Gauge Theory, FEYNMAN-INTEGRALS, SPECIAL VALUES, K3, GEOMETRY, GRAPH

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