Four-loop QCD mixing of current–current operators

We calculate the anomalous dimension of the |Δ S| = 1 | Δ S | = 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 ε K ϵ K , 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.