Long-distance singularities in multi-leg scattering amplitudes

TL;DR

This paper reports the completion of a three-loop calculation of the soft anomalous dimension in massless gauge-theory scattering amplitudes, revealing novel non-dipole corrections and providing insights into long-distance singularities in multi-leg QCD processes.

Contribution

The work presents the first three-loop calculation showing non-dipole corrections in multi-leg scattering amplitudes, enhancing understanding of long-distance singularities in QCD.

Findings

Non-dipole corrections appear at three loops for four coloured partons.

Non-dipole corrections at three loops for three coloured partons are kinematics-independent.

The final result is expressed in single-valued harmonic polylogarithms and satisfies key theoretical constraints.

Abstract

We report on the recent completion of the three-loop calculation of the soft anomalous dimension in massless gauge-theory scattering amplitudes. This brings the state-of-the-art knowledge of long-distance singularities in multi-leg QCD amplitudes with any number of massless particles to three loops. The result displays some novel features: this is the first time non-dipole corrections appear, which directly correlate the colour and kinematic degrees of freedom of four coloured partons. We find that non-dipole corrections appear at three loops also for three coloured partons, but these are independent of the kinematics. The final result is remarkably simple when expressed in terms of single-valued harmonic polylogarithms, and it satisfies several non-trivial constraints. In particular, it is consistent with the high-energy limit behaviour and it satisfies the expected factorization properties in two-particle collinear limits.