Calculating hard probe radiative energy loss beyond soft-gluon approximation: Examining the approximation validity

TL;DR

This study relaxes the soft-gluon approximation in the DGLV formalism to evaluate its validity in calculating radiative energy loss of high-momentum partons in QGP, finding that the approximation remains surprisingly accurate.

Contribution

We analytically relax the soft-gluon approximation within DGLV formalism and compare results, demonstrating its validity in practical predictions of parton energy loss.

Findings

Small differences in energy loss predictions when relaxing the approximation

Opposite sign effects on gluon radiation and suppression, leading to similar overall results

Soft-gluon approximation remains valid in DGLV formalism despite relaxations

Abstract

The soft-gluon approximation, which implies that radiated gluon carries away a small fraction of initial parton's energy, is a commonly used assumption in calculating radiative energy loss of high momentum partons traversing QGP created at RHIC and LHC. While soft-gluon approximation is convenient, different theoretical approaches reported significant radiative energy loss of high $p_{\perp}$ partons, thereby questioning its validity. To address this issue, we relaxed the soft-gluon approximation within DGLV formalism. The obtained analytical expressions are quite distinct compared to the soft-gluon case. However, numerical results for the first order in opacity fractional energy loss lead to small differences in predictions for the two cases. The difference in the predicted number of radiated gluons is also small. Moreover, the effect on these two variables has an opposite sign, which when combined results in almost overlapping suppression predictions. Therefore, our results imply that, contrary to the commonly held doubts, the soft-gluon approximation in practice works surprisingly well in DGLV formalism. Finally, we also discuss generalizing this relaxation in the dynamical QCD medium, which suggests a more general applicability of the conclusions obtained here.