Title: 2024 Update on $\varepsilon_K$ with lattice QCD inputs Show Chinese title

Title: 2024年$\varepsilon_K$的更新与格点QCD输入

Abstract: We report recent progress on $\varepsilon_K$ evaluated directly from the standard model (SM) with lattice QCD inputs such as $\hat{B}_K$, exclusive $|V_{cb}|$, $|V_{us}|$, $|V_{ud}|$, $\xi_0$, $\xi_2$, $\xi_\text{LD}$, $f_K$, and $m_c$. We find that the standard model with exclusive $|V_{cb}|$ and lattice QCD inputs describes only $2/3 \cong 65\%$ of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 35\%, which represents a strong tension in $|\varepsilon_K|$ at the $5.1\sigma \sim 4.1\sigma$ 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. We also report results for $|\varepsilon_K|$ obtained using the Brod-Gorbahn-Stamou (BGS) method for $\eta_i$ of $u-t$ unitarity, which leads to even a stronger tension of $5.7\sigma \sim 4.2\sigma$ with lattice QCD inputs. Show Chinese abstract

Abstract: 我们报告了近期关于从标准模型（SM）直接评估的$\varepsilon_K$的进展，使用如$\hat{B}_K$、独家$|V_{cb}|$、$|V_{us}|$、$|V_{ud}|$、$\xi_0$、$\xi_2$、$\xi_\text{LD}$、$f_K$和$m_c$等格点 QCD 输入。 We find that the standard model with exclusive $|V_{cb}|$ and lattice QCD inputs describes only $2/3 \cong 65\%$ of the experimental value of $|\varepsilon_K|$ and does not explain its remaining 35%, which represents a strong tension in $|\varepsilon_K|$ at the $5.1\sigma \sim 4.1\sigma$ 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. 我们还报告了使用Brod-Gorbahn-Stamou（BGS）方法得到的 $|\varepsilon_K|$ 的结果， $\eta_i$ 的 $u-t$ 单位性，这导致与格点QCD输入的 $5.7\sigma \sim 4.2\sigma$ 更强的矛盾。