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

TL;DR

This paper compares the Gunion-Bertsch approximation to exact calculations of QCD radiation processes, identifies deviations, and proposes an improved matrix element that aligns closely with the exact results across all phase space regions.

Contribution

The authors derive an improved Gunion-Bertsch matrix element that accurately reproduces the exact QCD radiation results in all phase space regions.

Findings

The original Gunion-Bertsch approximation deviates in certain phase space regions.

The improved matrix element shows excellent agreement with exact results.

The new version enhances the reliability of perturbative QCD calculations.

Abstract

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.