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We report updated results for $varepsilon_K$, the indirect CP violation parameter in neutral kaons, which is evaluated directly from the standard model with lattice QCD inputs. We use lattice QCD inputs to fix $bar{B}_K$, $|V_{cb}|$, $xi_0$, $xi_2$, $|V_{us}|$, and $m_c(m_c)$. Since Lattice 2016, the UTfit group has updated the Wolfenstein parameters in the angle-only-fit method, and the HFLAV group has also updated $|V_{cb}|$. Our results show that the evaluation of $varepsilon_K$ with exclusive $|V_{cb}|$ (lattice QCD inputs) has $4.0sigma$ tension with the experimental value, while that with inclusive $|V_{cb}|$ (heavy quark expansion based on OPE and QCD sum rules) shows no tension.
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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 $4.6sigma sim 4.2sigma$ 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.
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 70% of the experimental value of $|varepsilon_K|$ and does not explain its remaining 30%, which leads to a strong tension in $|varepsilon_K|$ at the $4sigma$ 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.
We report a strong tension in $varepsilon_K$ at the $4sigma$ level between the experimental value and the theoretical value calculated directly from the standard model using lattice QCD inputs such as $hat{B}_K$, $|V_{cb}|$, $|V_{us}|$, $xi_0$, $xi_2$, $xi_text{LD}$, $F_K$, and $m_c$. The standard model with lattice QCD inputs describes only 70% of the experimental value of $varepsilon_K$, and does not explain its remaining 30%. We also find that this tension disappears when we use the inclusive value of $|V_{cb}|$ (results of the heavy quark expansion based on QCD sum rules) to determine $varepsilon_K$. This tension is highly correlated with the present discrepancy between the exclusive and inclusive values of $|V_{cb}|$. In order to resolve, in part, the issue with $|V_{cb}|$, it would be highly desirable to have a comprehensive re-analysis over the entire set of experimental data on the $bar{B} to D^* ell bar{ u}$ decays using an alternative parametrization of the form factors, such as the BGL parametrization, and a comparison with results of the CLN method.
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