2021 Update on ${\epsilon }_K$ with lattice QCD inputs

Abstract

We present recent updates for ${\epsilon }_K$ 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 $|{\epsilon }_K|$ and does not explain its remaining 34\%, which leads to a strong tension in $|{\epsilon }_K|$ 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.

Comments: 10 pages, 5 figures, Lattice 2021 proceedings, arXiv admin note: text overlap with arXiv:1912.03024, the referee's suggestions incorporated