Infrared singularities of multileg amplitudes with a massive particle at three loops

Abstract

We determine the complete three-loop QCD soft anomalous dimension for multileg amplitudes involving a single massive coloured particle and any number of massless ones. This is achieved by applying a novel strategy based on a lightcone expansion of correlators of semi-infinite Wilson lines using the method of regions. The resulting region integrals depend exclusively on rescaling-invariant ratios that remain finite in the limit. We evaluate these integrals using differential equation techniques. The result is written in terms of uniform weight five generalised polylogarithms of a twelve letter alphabet in three variables, and is compatible with the massless limit as well as with two- and three-particle collinear factorization.

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