Infrared singularities and the collinear limits of multi-leg scattering amplitudes

Abstract

Scattering amplitudes admit a factorised structure in special kinematic limits, such as the soft and collinear limits. In this work, we investigate the multi-particle collinear limits of massless amplitudes at high perturbative orders, focusing on the exploration of the mechanisms via which strict collinear factorisation of $n$-particle scattering amplitudes is realised when $m$ particles become collinear. We show through four loops that the requirements on the structure of the massless soft anomalous dimension that are imposed by strict collinear factorisation in all two-particle collinear limits are enough to guarantee factorisation also in any multi-particle collinear limit. Demanding that strict collinear factorisation of massless partons is satisfied also for amplitudes that contain a massive coloured particle, we derive new constraints on the soft anomalous dimension by considering the collinear limit of three massless particles.