2019 Update on $\varepsilon_K$ with lattice QCD inputs

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 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 $4.6\sigma \sim 4.2\sigma$ 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.