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arXiv · 2212.09762

Bootstrapping elliptic Feynman integrals using Schubert analysis

Roger Morales·Anne Spiering·Matthias Wilhelm·Qinglin Yang·Chi Zhang
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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.

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Roger Morales, Anne Spiering, Matthias Wilhelm, Qinglin Yang, Chi Zhang. 2022-12-19. Bootstrapping elliptic Feynman integrals using Schubert analysis. https://doi.org/10.1103/physrevlett.131.041601

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