Status report on $\varepsilon_K$ with lattice QCD inputs

Abstract

We report the current status of $\varepsilon_K$, the indirect CP violation parameter in the neutral kaon system, evaluated using the lattice QCD inputs. We use lattice QCD to fix $\hat{B}_K$, $\xi_0$, $\xi_2$, $|V_{us}|$, $m_c(m_c)$, and $|V_{cb}|$. Since Lattice 2015, FLAG updated $\hat{B}_K$, exclusive $V_{cb}$ has been updated with new lattice data in the $\bar{B}\to D\ell\nu$ decay channel, and RBC-UKQCD has updated $\xi_0$ and $\xi_2$. Our preliminary results show that the standard model evaluation of $\varepsilon_K$ with exclusive $|V_{cb}|$ (lattice QCD inputs) has $3.2\sigma$ tension with the experimental value, while that of $\varepsilon_K$ with inclusive $|V_{cb}|$ (heavy quark expansion) shows no tension.