Structure of Infrared Singularities of Gauge-Theory Amplitudes at Three and Four Loops

Understand

The infrared divergences of massless n-parton scattering amplitudes can be derived from the anomalous dimension of n-jet operators in soft-collinear effective theory.

• Up to three-loop order, the latter has been shown to have a very simple structure: it contains pairwise color-dipole interactions among the external partons, governed by the cusp anomalous dimension and a logarithm of the kinematic invariants s_{ij}, plus a possible three-loop correlation involving four particles, which is described by a yet unknown function of conformal cross ratios of kinematic invariants.
• This function is constrained by two-particle collinear limits and by the known behavior of amplitudes in the high-energy limit.
• We construct a class of relatively simple functions satisfying these constraints.