2018 Update on $\varepsilon_K$ with lattice QCD inputs

TL;DR

This paper updates the calculation of the CP-violation parameter _K in the standard model using lattice QCD inputs, revealing a significant tension with experimental measurements when using exclusive |, which disappears with inclusive | values.

Contribution

It provides the latest lattice QCD-based evaluation of _K and highlights the discrepancy between exclusive and inclusive | determinations.

Findings

Standard model with exclusive | explains only 70% of _K's experimental value.

A 4 tension exists between theory and experiment with exclusive |.

Tension disappears when using inclusive | values.

Abstract

We present updated results for $\varepsilon_K$ determined directly from the standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, $|V_{cb}|$, $|V_{us}|$, $\xi_0$, $\xi_2$, $\xi_\text{LD}$, $F_K$, and $m_c$. We find that the standard model with exclusive $|V_{cb}|$ and other lattice QCD inputs describes only 70% of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 30%, which leads to a strong tension in $|\varepsilon_K|$ at the $4\sigma$ level between the SM theory and experiment. We also find that this tension disappears when we use the inclusive value of $|V_{cb}|$ obtained using the heavy quark expansion based on QCD sum rules.