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

TL;DR

This paper computes the complete three-loop soft anomalous dimension in QCD for multileg amplitudes involving one massive particle, using a novel lightcone expansion and advanced integral techniques.

Contribution

It introduces a new method based on lightcone expansion and regions to evaluate three-loop soft anomalous dimensions with massive particles in QCD.

Findings

Derived the three-loop soft anomalous dimension for massive particles.

Expressed results in terms of weight five generalized polylogarithms.

Ensured compatibility with massless and collinear limits.

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.