Improved opacity expansion at NNLO for medium induced gluon radiation

Understand

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 $\omega >\omega_c = \hat q L^2$, where $\hat 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 $\omega <\omega_c$ 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.