2021 Update on $\varepsilon_K$ with lattice QCD inputs

TL;DR

This paper updates the standard model prediction of psilon_K using recent lattice QCD inputs, revealing a significant tension with experimental measurements when using exclusive b|, which disappears with inclusive b| values.

Contribution

It provides the latest psilon_K calculation with lattice QCD inputs and compares the effects of exclusive versus inclusive b| on the SM-experiment tension.

Findings

Standard model with exclusive b| explains only 66% of psilon_K

Tension between theory and experiment is 3.7-4.5 sigma with exclusive b|

Tension disappears when using inclusive b| from QCD sum rule approach

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 66\% of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 34\%, which leads to a strong tension in $|\varepsilon_K|$ at the $4.5\sigma \sim 3.7\sigma$ 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.