2023 Update of \(\varepsilon_K\) with lattice QCD inputs

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.