Bootstrapping elliptic Feynman integrals using Schubert analysis

Abstract

The symbol bootstrap has proven to be a powerful tool for calculating polylogarithmic Feynman integrals and scattering amplitudes. In this letter, we initiate the symbol bootstrap for elliptic Feynman integrals. Concretely, we bootstrap the symbol of the twelve-point two-loop double-box integral in four dimensions, which depends on nine dual-conformal cross ratios. We obtain the symbol alphabet, which contains 100 logarithms as well as 9 simple elliptic integrals, via a Schubert-type analysis, which we equally generalize to the elliptic case. In particular, we find a compact, one-line formula for the (2,2)-coproduct of the result.

arXiv comment5+6 pages, 4 figures

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• Classification of Feynman integral geometries for black-hole scattering at 5PM order
• Electroweak double-box integrals for Moller scattering
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• The spectrum of Feynman-integral geometries at two loops