Three-loop, five-particle integrals solved with a new factoring trick

Computing scattering amplitudes in maximally supersymmetric Yang-Mills theory requires master integrals that are extraordinarily difficult at three loops and five external legs. Working on the Coulomb branch — a slight deformation that regulates infrared divergences while preserving dual conformal symmetry — the authors introduce a technique that separates the kinematic cross-ratio dependence from individual integration regions, dramatically simplifying each piece. Of 82 regions in the most complex integral, 79 yield to this streamlined approach; the remaining three are handled via integration-by-parts reduction in parametric representation and the HyperInt package.