2023 Update of $\varepsilon_K$ with lattice QCD inputs

TL;DR

This paper updates the standard model prediction of _K using recent lattice QCD inputs, revealing a significant tension with experimental measurements when using exclusive |V_{cb}|, which disappears with inclusive |V_{cb}|.

Contribution

It provides the latest _K calculation with lattice QCD inputs and highlights the tension between theory and experiment based on different |V_{cb}| determinations.

Findings

Standard model with exclusive |V_{cb}| accounts for only 66% of _K experimental value.

Significant tension (.9.9) exists between SM prediction and experiment with exclusive |V_{cb}|.

Tension disappears when using inclusive |V_{cb}| from QCD sum rule approach.

Abstract

We report recent progress on $\varepsilon_K$ evaluated directly from the standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, $|V_{cb}|$, $|V_{us}|$, $|V_{ud}|$, $\xi_0$, $\xi_2$, $\xi_\text{LD}$, $f_K$, and $m_c$. We find that the standard model with exclusive $|V_{cb}|$ and lattice QCD inputs describes only 66\% of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 34\%, which corresponds to a strong tension in $|\varepsilon_K|$ at the $4.9\sigma \sim 3.9\sigma$ 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.