Prescriptive Unitarity with Elliptic Leading Singularities

Abstract

We investigate the consequences of elliptic leading singularities for the unitarity-based representations of two-loop amplitudes in planar, maximally supersymmetric Yang-Mills theory. We show that diagonalizing with respect to these leading singularities ensures that the integrand basis is term-wise pure (suitably generalized, to the elliptic multiple polylogarithms, as necessary). We also investigate an alternative strategy based on diagonalizing a basis of integrands on differential forms; this strategy, while neither term-wise Yangian-invariant nor pure, offers several advantages in terms of complexity.

25 pages; 20 figures

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• Canonical Differential Equations Beyond Genus One
• Bootstrapping elliptic Feynman integrals using Schubert analysis
• Cutting the traintracks: Cauchy, Schubert and Calabi-Yau
• On $\epsilon$-factorised bases and pure Feynman integrals
• A double copy from twisted (co)homology at genus one
• Illustrations of Integrand-Basis Building at Two Loops
• All Two-Loop, Color-Dressed, Six-Point Amplitude Integrands in sYM
• Electroweak double-box integrals for Moller scattering
• The Stratification of Rigidity