We calculate the anomalous dimension of the ∣ΔS∣=1 current-current operators of the weak effective Lagrangian at next-to-next-to-next-to-leading order (NNNLO) in QCD. This constitutes the first step towards a full four-loop calculation of the QCD correction to ϵK, the measure for indirect CP violation in the neutral kaon system. We present fully analytic results, together with the expressions necessary to transform our results to a basis with an arbitrary different definition of evanescent operators. As an application, we calculate the corresponding results in the ``standard'' operator basis used in B physics.
@article{arxiv.2604.16691,
title = {Four-loop QCD mixing of current-current operators},
author = {Joachim Brod and Emmanuel Stamou and Tom Steudtner},
journal= {arXiv preprint arXiv:2604.16691},
year = {2026}
}