Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms

Jacob L. Bourjaily, Andrew J. McLeod, Marcus Spradlin, Matt Von Hippel, Matthias Wilhelm

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92 Scopus citations


We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a fourfold, rational (Feynman-)parametric representation for the integral, expressed directly in terms of dual-conformally invariant cross ratios; from this, the desired form is easily obtained. The essential features of this integral are illustrated by means of a simplified toy model, and we attach the relevant expressions for both integrals in ancillary files. We propose a normalization for such integrals that renders all of their polylogarithmic degenerations pure, and we discuss the need for a new "symbology" of mixed iterated elliptic and polylogarithmic integrals in order to bring them to a more canonical form.

Original languageEnglish (US)
Article number121603
JournalPhysical review letters
Issue number12
StatePublished - Mar 23 2018

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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