Eikonal gluon radiation at finite-Nc beyond 2 loops

TL;DR

This paper computes finite-Nc corrections to eikonal gluon radiation beyond two loops in e+ e- annihilation, using a Mathematica-based approach to handle complex color and kinematic structures.

Contribution

It introduces the first calculations of finite-Nc effects at three loops and beyond in the eikonal approximation for e+ e- processes, extending previous large-Nc results.

Findings

Finite-Nc corrections are computed at higher loops.

The Mathematica code efficiently evaluates complex color traces.

Results agree with known large-Nc limits.

Abstract

We present first calculations of QCD matrix-elements in perturbation theory at finite Nc beyond 2 loops in the eikonal approximation for e+ e- annihilation processes. For the emission of n soft energy-ordered gluons we solve both the colour and kinematic structures at a given order in perturbation theory by means of a Mathematica program that relies solely on a recently developed Mathematica code, ColorMath, that evaluates the trace of products of colour matrices. At large Nc, our squared amplitudes reduce to those already known in the literature.