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

TL;DR

This paper calculates the complete two-loop electroweak corrections to the top-quark's contribution to the CP violation parameter epsilon_K, reducing theoretical uncertainties in the Standard Model predictions.

Contribution

It provides the first full two-loop electroweak correction calculation for the top-quark contribution to epsilon_K, including QED-QCD logarithm resummation.

Findings

Top-quark contribution shifted by -1% with new corrections

Reduction in theoretical uncertainty for epsilon_K

Analysis of different electroweak input parameter schemes

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 $-1\%$.