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Two-loop Electroweak Corrections to the Top-Quark Contribution to $\epsilon_K$
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abstract
The parameter $\epsilon_K$ measures $CP$ violation in the neutral kaon system. It is a sensitive probe of new physics and plays a prominent role in the global fit of the Cabibbo-Kobabyashi-Maskawa matrix. The perturbative theory uncertainty is currently dominated by the top-quark contribution. Here, we present the calculation of the full two-loop electroweak corrections to the top-quark contribution to $\epsilon_K$, including the resummation of QED-QCD logarithms. We discuss different renormalization prescriptions for the electroweak input parameters. In the traditional normalization of the weak Hamiltonian with two powers of the Fermi constant $G_F$, the top-quark contribution is shifted by $-1\%$.
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RI-(S)MOM to $\overline{\rm MS}$ conversion for $B_K$ at two-loop order
A two-loop scheme-conversion calculation shifts and tightens the world average of the kaon bag parameter to 0.7627(60), updating the Standard Model prediction for epsilon_K.
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