The soft-gluon approximation assumes that a high parton propagating through dense QCD matter loses only a small amount of its energy via gluon radiation. This assumption is made in many different jet quenching approaches, which nevertheless predicted a sizable radiative energy loss of such particles. This questions the reliability of this approximation, which must then be reconsidered. To address this issue, we relaxed the soft-gluon approximation within the DGLV formalism to the first order in opacity. The obtained analytical expressions are notably different from the soft-gluon case. Surprisingly the numerical effects that stem from waiving this assumption on fractional radiative energy loss and number of radiated gluons are small. Additionally, the effect on suppression is negligible, which can be intuitively understood by the cancellation of the opposite effects on the above mentioned variables. Consequently, our results surprisingly indicate that, contrary to the doubts mentioned above, the soft-gluon approximation remains well-founded within the DGLV formalism. We also investigate the effects of this assumption in the case of a dynamical medium, which suggests generality of the conclusions presented here.
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