Update on ${\epsilon }_K$ with lattice QCD inputs

Abstract

We report updated results for ${\epsilon }_K$, 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 ${\epsilon }_K$ with exclusive $|V_{cb}|$ (lattice QCD inputs) has $4.0\sigma$ tension with the experimental value, while that with inclusive $|V_{cb}|$ (heavy quark expansion based on OPE and QCD sum rules) shows no tension.

Comments: 8 pages, 7 figures, Lattice 2017 proceeding, references updated