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Non-perturbative determination of the collisional broadening kernel and medium-induced radiation in QCD plasmas

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.