Using colour conservation and rescaling symmetry, the two-particle collinear constraints are shown to imply multi-particle collinear factorisation through four loops, and a new triple-collinear constraint is derived for one-mass amplitudes.
Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
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abstract
The light-like cusp anomalous dimension is a universal function that controls infrared divergences in quite general quantum field theories. In the maximally supersymmetric Yang-Mills theory this function is fixed fully by integrability to the three-loop order. At four loops a non-planar correction appears which we obtain for the first time from a numerical computation of the Sudakov form factor. Key ingredients are widely applicable methods to control the number-theoretic aspects of the appearing integrals. Our result shows explicitly that quadratic Casimir scaling breaks down at four loops.
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Infrared singularities and the collinear limits of multi-leg scattering amplitudes
Using colour conservation and rescaling symmetry, the two-particle collinear constraints are shown to imply multi-particle collinear factorisation through four loops, and a new triple-collinear constraint is derived for one-mass amplitudes.