Climbing three-Reggeon ladders: four-loop amplitudes in the high-energy limit in full colour

TL;DR

This paper computes four-loop gauge theory amplitudes in the high-energy limit, revealing new quartic Casimir contributions to the soft anomalous dimension and providing detailed results for ${ m extbf{N}=4}$ super Yang-Mills.

Contribution

It presents the first four-loop calculations of partonic amplitudes in full colour at NNLL accuracy, including the soft anomalous dimension and finite hard function.

Findings

Four-loop amplitudes computed in full colour at NNLL.

Quartic Casimir contributions found in the soft anomalous dimension.

Finite hard function determined for ${ m extbf{N}=4}$ super Yang-Mills at four loops.

Abstract

Using an iterative solution of rapidity evolution equations, we compute partonic $2\to 2$ gauge theory amplitudes at four loops in full colour up to the Next-to-Next-to-Leading Logarithms (NNLL) in the Regge limit. By contrasting the resulting amplitude with the exponentiation properties of soft singularities we determine the four-loop correction to the soft anomalous dimension at this logarithmic accuracy, which universally holds in any gauge theory. We find that the latter features quartic Casimir contributions beyond those appearing in the cusp anomalous dimension. Finally, in the case of ${\cal N}=4$ super Yang-Mills, we also determine the finite hard function at four loops through NNLL in full colour.