An Overview of Maximal Unitarity at Two Loops
Henrik Johansson, David A. Kosower, Kasper J. Larsen
TL;DR
This work extends the maximal unitarity framework to two loops, focusing on the planar double-box, by reinterpreting maximal cuts as contour integrals around global poles. Contour choices are fixed by requiring that total-derivative integrals vanish and by exploiting IBP identities, yielding a projector-based method to extract master-integral coefficients. The approach produces an explicit contour-based coefficient formula and demonstrates how eight global poles govern the construction, with concrete weights provided for the one-mass case and full solutions available in MassiveTwoLoop. The methodology enables analytic and numerical computation of two-loop gauge-theory amplitudes, advancing NNLO precision and providing robust uncertainty estimates for LHC background processes.
Abstract
We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals of total derivatives vanish on it. The resulting formulae, like their one-loop counterparts, can be applied either analytically or numerically.