Electroweak Corrections to the Charm-Top-Quark Contribution to ${\epsilon }_K$

We calculate the leading-logarithmic and next-to-leading-logarithmic electroweak corrections to the charm-top-quark contribution to the effective $\mathrm{\mid }\mathrm{\Delta }S\mathrm{\mid }=2$ Lagrangian, relevant for the parameter ${\epsilon }_K$. We find that these corrections lead to a $-0.5\mathrm{\%}$ shift in the corresponding Wilson coefficient. Moreover, our calculation removes an implicit ambiguity in the standard-model prediction of ${\epsilon }_K$, by fixing the renormalization scheme of the electroweak input parameters.