Bootstrapping elliptic Feynman integrals using Schubert analysis

TL;DR

This paper extends the symbol bootstrap method to elliptic Feynman integrals, specifically computing the symbol of a twelve-point two-loop double-box integral using Schubert analysis, revealing its alphabet and coproduct structure.

Contribution

It introduces a novel approach to bootstrap elliptic Feynman integrals using Schubert analysis, providing explicit symbol and coproduct formulas for complex integrals.

Findings

Identified the symbol alphabet with 100 logarithms and 9 elliptic integrals.

Derived a compact formula for the (2,2)-coproduct of the integral.

Successfully extended bootstrap techniques to elliptic cases.

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.