The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms
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.
Keywords
Cite
@article{arxiv.1712.02785,
title = {The Elliptic Double-Box Integral: Massless Amplitudes Beyond Polylogarithms},
author = {Jacob L. Bourjaily and Andrew J. McLeod and Marcus Spradlin and Matt von Hippel and Matthias Wilhelm},
journal= {arXiv preprint arXiv:1712.02785},
year = {2018}
}
Comments
4+2 pages, 2 figures. Explicit results are included as ancillary files. v2: minor changes made for clarification; references added