Current status of $\varepsilon_K$ with lattice QCD inputs

Abstract

We present the Standard Model evaluation of the indirect CP violation parameter $\varepsilon_K$ using inputs determined from lattice QCD together with experiment: $|V_{us}|$, $|V_{cb}|$, $\xi_0$, and $\hat{B}_K$. We use the Wolfenstein parametrization ($|V_{cb}|$, $\lambda$, $\bar{\rho}$, $\bar{\eta}$) for the CKM matrix elements. For the central value, we take the angle-only fit of the UTfit collaboration, and use $|V_{us}|$ from the $K_{\ell 3}$ and $K_{\mu 2}$ decays as an independent input to fix $\lambda$. For the error estimate, we use results of the global unitarity triangle fits from the CKMfitter and UTfit collaborations. We find that the Standard Model (SM) prediction of $\varepsilon_K$ with exclusive $V_{cb}$ (lattice QCD results) is lower than the experimental value by $3.6(2)\sigma$. However, with inclusive $V_{cb}$ (results of the heavy quark expansion), the tension between the SM prediction of $\varepsilon_K$ and its experimental value disappears.