Improved opacity expansion at NNLO for medium induced gluon radiation

When an energetic parton propagates in a hot and dense QCD medium it loses energy by elastic scatterings or by medium-induced gluon radiation. The gluon radiation spectrum is suppressed at high frequency due to the LPM effect and encompasses two regimes that are known analytically: at high frequencies $$ \omega >{\omega}_c=\hat{q}{L}^2 $$ ω > ω c = q ̂ L 2 , where $$ \hat{q} $$ q ̂ is the jet quenching transport coefficient and L the length of the medium, the spectrum is dominated by a single hard scattering, whereas the regime ω < ωc is dominated by multiple low momentum transfers. In this paper, we extend a recent approach (dubbed the Improved Opacity Expansion (IOE)), which allows an analytic (and systematic) treatment beyond the multiple soft scattering approximation, matching this result with the single hard emission spectrum. We calculate in particular the NNLO correction analytically and numerically and show that it is strongly suppressed compared to the NLO indicating a fast convergence of the IOE scheme and thus, we conclude that it is sufficient to truncate the series at NLO. We also propose a prescription to compare the GW and the HTL potentials and relate their parameters for future phenomenological works.

Testing the Reliability of the Soft-Gluon Approximation for High p⊥ Particles

The soft-gluon approximation assumes that a high p ⊥ 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.