Infrared singularities of scattering amplitudes and N3LL resummation for n-jet processes

Becher, Thomas; Neubert, Matthias (2020). Infrared singularities of scattering amplitudes and N3LL resummation for n-jet processes. Journal of High Energy Physics, 2020(1), 025. Springer 10.1007/JHEP01(2020)025

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We revisit the multi-loop structure of the anomalous-dimension matrix gov-
erning the infrared divergences of massless n-particle scattering amplitudes in non-abelian gauge theories. In particular, we derive its most general form at four-loop order, significantly simplifying corresponding expressions given previously. By carefully reevaluating the constraints imposed by two-particle collinear limits, we find that at four-loop order color structures involving dabcd, the symmetrized trace of four group generators, appear along R with cusp logarithms ln[μ2/(−sij)]. As a consequence, naive Casimir scaling of the cusp anomalous dimensions associated with the quark and gluon form factors is violated, while a generalized form of Casimir scaling still holds. Our results provide an important ingredient for resummations of large logarithms in n-jet cross sections with next-to-next-to-next-to leading logarithmic (N3LL) accuracy.

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