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High-energy particles traversing the Quark-Gluon plasma experience modified(massive) dispersion, although their vacuum mass is negligible compared to thekinetic energy. Due to poor convergence of the perturbative series in theregime of soft loop momenta, a more precise determination of this effectivemass is needed. This paper continues our investigation on the factorisationbetween strongly-coupled infrared classical and perturbative ultravioletbehavior. The former has been studied non-perturbatively within EQCD bydetermining a non-local operator on the lattice. By computing thetemperature-scale contribution to the same operator in 4D QCD atnext-to-leading order (NLO), we remove the ultraviolet divergence of the EQCDcalculation with an opposite infrared divergence from the hard thermal scale.The result is a consistent, regulator-independent determination of theclassical contribution where the emergence of new divergences signalssensitivities to new regions of phase space. We address the numerical impact ofthe classical and NLO thermal corrections on the convergence of the factorisedapproach and on the partial applicability of our results to calculations oftransport coefficients.

The force-force correlator at the hard thermal scale of hot QCD