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.

OriginalsprogEngelsk
Artikelnummer89
TidsskriftJournal of High Energy Physics
Vol/bind2023
Udgave nummer1
Antal sider39
ISSN1029-8479
DOI
StatusUdgivet - 17 jan. 2023

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