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Eikonal gluon radiation at finite-Nc beyond 2-loops

We present first calculations of QCD matrix-elements in pert urbation theory at finite N c 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.