Splitting rates in QCD plasmas from a nonperturbative determination of the momentum broadening kernel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>q</mml:mi><mml:mo>⊥</mml:mo></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math>
Sören Schlichting, Ismail Soudi
Abstract
We exploit a recent nonperturbative determination of the momentum broadening kernel $C({b}_{\ensuremath{\perp}})$ in impact parameter space [G. D. Moore, S. Schlichting, N. Schlusser, and I. Soudi, J. High Energy Phys. 10 (2021) 059], to determine the momentum space broadening kernel $C({q}_{\ensuremath{\perp}})$ in high-temperature QCD plasmas. We show how to use the nonperturbatively determined kernel $C({q}_{\ensuremath{\perp}})$ 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 $C({q}_{\ensuremath{\perp}})$, 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.