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 quark-gluon plasma created at the Relativistic Heavy Ion Collider and the Large Hadron Collider. While the soft-gluon approximation is convenient, different theoretical approaches have reported significant radiative energy loss of high-p perpendicular to partons, thereby questioning its validity. To address this issue, we relaxed the soft-gluon approximation within Djordjevic-Gyulassy-Levai-Vitev (DGLV) formalism. The obtained analytical expressions are quite distinct from 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.
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