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Splitting rates in QCD plasmas from a non-perturbative determination of the momentum broadening kernel $C(q_{\bot})$

We exploit a recent non-perturbative determination of the momentum broadening kernel $C(b_{\bot})$ in impact parameter space \cite{Moore:2021jwe}, to determine the momentum space broadening kernel $C(q_{\bot})$ in high-temperature QCD plasmas. We show how to use the non-pertubatively determined kernel $C(q_{\bot})$ to compute the medium-induced splitting rates in a QCD plasma of finite size. We compare the resulting in-medium splitting rates to the results obtained with leading-order and next-to-leading order perturbative determinations of $C(q_{\bot})$, as well as with various approximations of the splitting employed in the literature. Generally, we find that the differences in the splitting rates due to the momentum broadening kernel are larger than the errors associated with approximations of the splitting rate.