2022 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 b|, but not with inclusive b|.

Contribution

It provides the latest lattice QCD-based evaluation of _K, highlighting the discrepancy between theory and experiment with exclusive b| values.

Findings

Standard model with exclusive b| explains only 65% of _K's experimental value.

Significant tension (_K discrepancy) at 3.9-5.1 sigma level with exclusive b|.

Tension disappears when using inclusive b|, but the small discrepancy persists and grows over time.

Abstract

We present recent updates 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 65% of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 35%, which leads to a strong tension in $|\varepsilon_K|$ at the $5.1\sigma \sim 3.9\sigma$ 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 the QCD sum rule approach, although this inclusive tension is small ($\approx 1.4\sigma$) but keeps increasing as time goes on.