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Radiative parton processes in perturbative QCD - an improved version of the Gunion and Bertsch cross section from comparisons to the exact result

In this work we compare the Gunion-Bertsch approximation of the leading order perturbative QCD radiation matrix element to the exact result. To this end, we revisit the derivation of the Gunion-Bertsch approximation as well as perform extensive numerical comparisons of the Gunion-Bertsch and the exact result. We find that when employing the matrix elements to obtain rates or cross sections from phase space integration, the amplitude by Gunion and Bertsch deviates from the correct result in characteristic regions of the phase space. We propose an improved version of the Gunion-Bertsch matrix element which agrees very well with the exact result in all phase space regions.