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arXiv · 1712.02785

The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms

Jacob L. Bourjaily·Andrew J. McLeod·Marcus Spradlin·Matt von Hippel·Matthias Wilhelm
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Abstract

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 four-fold, 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 iterated elliptic/polylogarithmic integrals in order to bring them to a more canonical form.

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Jacob L. Bourjaily, Andrew J. McLeod, Marcus Spradlin, Matt von Hippel, Matthias Wilhelm. 2017-12-07. The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms. https://doi.org/10.1103/physrevlett.120.121603

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