Eikonal gluon bremsstrahlung at finite N_c beyond two loops

TL;DR

This paper develops a formalism and computational tools for calculating soft gluon emissions in QCD beyond two loops at finite N_c, extending previous large-N_c results to more general cases.

Contribution

It introduces a general formalism and a Mathematica program for automated calculation of eikonal squared amplitudes at arbitrary loop orders in QCD.

Findings

Explicit eikonal squared amplitudes up to five loops provided.

Formalism valid at finite N_c and in the eikonal approximation.

Results match known large-N_c results in the appropriate limit.

Abstract

We present a general formalism for computing the matrix-element squared for the emission of soft energy-ordered gluons beyond two loops in QCD perturbation theory at finite $N_c$. Our formalism is valid in the eikonal approximation. A Mathematica program has been developed for the automated calculation of all real/virtual eikonal squared amplitudes needed at a given loop order. For the purpose of illustration we show the explicit forms of the eikonal squared amplitudes up to the fifth-loop order. In the large-$N_c$ limit our results coincide with those previously reported in literature.