Massive Nonplanar Two-Loop Maximal Unitarity

Abstract

We explore maximal unitarity for nonplanar two-loop integrals with up to four massive external legs. In this framework, the amplitude is reduced to a basis of master integrals whose coefficients are extracted from maximal cuts. The hepta-cut of the nonplanar double box defines a nodal algebraic curve associated with a multiply pinched genus-3 Riemann surface. All possible configurations of external masses are covered by two distinct topological pictures in which the curve decomposes into either six or eight Riemann spheres. The procedure relies on consistency equations based on vanishing of integrals of total derivatives and Levi-Civita contractions. Our analysis indicates that these constraints are governed by the global structure of the maximal cut. Lastly, we present an algorithm for computing generalized cuts of massive integrals with higher powers of propagators based on the Bezoutian matrix method.

54 pages, 9 figures, v2: journal version

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• Direct Solution of Integration-by-Parts Systems
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• Local integrands for two-loop all-plus Yang-Mills amplitudes
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• The Polynomial Form of the Scattering Equations is an H-Basis
• Cross-Order Integral Relations from Maximal Cuts
• Two-loop Integral Reduction from Elliptic and Hyperelliptic Curves
• Maximal transcendental weight contribution of scattering amplitudes