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The parameter $\epsilon_K$ measures $CP$ violation in the neutral kaonsystem. It is a sensitive probe of new physics and plays a prominent role inthe global fit of the Cabibbo-Kobabyashi-Maskawa matrix. The perturbativetheory uncertainty is currently dominated by the top-quark contribution. Here,we present the calculation of the full two-loop electroweak corrections to thetop-quark contribution to $\epsilon_K$, including the resummation of QED-QCDlogarithms. We discuss different renormalization prescriptions for theelectroweak input parameters. In the traditional normalization of the weakHamiltonian with two powers of the Fermi constant $G_F$, the top-quarkcontribution is shifted by $-1\%$.

Two-loop Electroweak Corrections to the Top-Quark Contribution to $\epsilon_K$