  Collisional broadening in QCD plasmas leads to the emission of medium induced
radiation, which governs the energy loss of highly energetic particles or jets.
While recent studies have obtained non-perturbative contributions to the
collisional broadening kernel $C(b_\bot)$ using lattice simulation of the
dimensionally reduced long-distance effective theory of QCD, Electrostatic QCD
(EQCD), so far all phenomenological calculations of jet quenching rely on
perturbative determinations of the collisional broadening kernel. By matching
the short-distance behavior of the lattice extracted EQCD broadening kernel, we
determine the fully matched QCD broadening kernel non-perturbatively. We
present results for the collisional broadening kernel in impact-parameter
($C_{\rm QCD}(b_\bot)$)) and momentum space ($C_{\rm QCD}(q_\bot)$) and employ
them to determine the rates of medium induced radiation in infinite and finite
size QCD plasmas. By contrasting our results with leading and next-to-leading
order perturbative determinations as well as various approximations of the
splitting rates employed in the literature, we investigate the effect of the
non-peturbative determination of CQCD($q_\bot$) on medium-induced radiation
rates.
