Status report on ${\epsilon }_K$ with lattice QCD inputs

Abstract

We report the current status of ${\epsilon }_K$, 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 ${\epsilon }_K$ with exclusive $|V_{cb}|$ (lattice QCD inputs) has $3.2\sigma$ tension with the experimental value, while that of ${\epsilon }_K$ with inclusive $|V_{cb}|$ (heavy quark expansion) shows no tension.

7 pages, 6 figures, Lattice 2016 conference proceeding