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

TL;DR

This paper uses a non-perturbative approach to determine the momentum broadening kernel in high-temperature QCD plasmas and applies it to compute medium-induced splitting rates, revealing significant differences from perturbative estimates.

Contribution

It introduces a non-perturbative method to calculate the momentum broadening kernel in QCD plasmas and applies it to improve the accuracy of splitting rate computations.

Findings

Non-perturbative kernel differs significantly from perturbative ones.

Splitting rates are sensitive to the choice of the broadening kernel.

Differences in splitting rates exceed approximation errors.

Abstract

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.