Electroweak Corrections to the Charm-Top-Quark Contribution to $\epsilon_K$

TL;DR

This paper calculates electroweak corrections to the charm-top-quark contribution in the effective $| riangle S|=2$ Lagrangian, refining the theoretical prediction of $ ext{epsilon}_K$ by reducing scheme ambiguities and quantifying a small correction.

Contribution

It provides the first calculation of electroweak corrections at leading and next-to-leading logs for $ ext{epsilon}_K$, fixing renormalization scheme ambiguities in the standard model prediction.

Findings

Electroweak corrections cause a -0.5% shift in the Wilson coefficient.

Calculation removes implicit scheme ambiguities in $ ext{epsilon}_K$ prediction.

Refines theoretical accuracy of $ ext{epsilon}_K$ in the standard model.

Abstract

We calculate the leading-logarithmic and next-to-leading-logarithmic electroweak corrections to the charm-top-quark contribution to the effective $|\Delta S| = 2$ Lagrangian, relevant for the parameter $\epsilon_K$. We find that these corrections lead to a $-0.5\%$ 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.