Global Residues and Two-Loop Hepta-Cuts

Abstract

We examine maximal unitarity in the nonplanar case and derive remarkably compact analytic expressions for coefficients of master integrals with two-loop crossed box topology in massless four-point amplitudes in any gauge theory, thereby providing additional steps towards automated computation of the full amplitude. The coefficients are obtained by assembling residues extracted through integration on linear combinations of higher-dimensional tori encircling global poles of the loop integrand. We recover all salient features of two-loop maximal unitarity, such as the existence of unique projectors for each master integral. Several explicit calculations are provided. We also establish exact equivalence of our results and master integral coefficients recently obtained via integrand-level reduction in any renormalizable gauge theory.

38 pages, v2: minor changes, typos corrected, references added, journal version

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• Maximal Cuts in Arbitrary Dimension
• Direct Solution of Integration-by-Parts Systems
• Dual Conformal Symmetry, Integration-by-Parts Reduction, Differential Equations and the Nonplanar Sector
• Elliptic Functions and Maximal Unitarity
• Local integrands for two-loop all-plus Yang-Mills amplitudes
• Multivariate Residues and Maximal Unitarity
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• Maximal Unitarity for the Four-Mass Double Box
• Unitarity Cuts of Integrals with Doubled Propagators
• Cross-Order Integral Relations from Maximal Cuts
• Global Structure of Curves from Generalized Unitarity Cut of Three-loop Diagrams
• Massive Nonplanar Two-Loop Maximal Unitarity
• Multi-loop Integrand Reduction with Computational Algebraic Geometry
• Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves
• Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study