Current status of ${\epsilon }_K$ in lattice QCD

Abstract

We present the current status of ${\epsilon }_K$ evaluated directly from the standard model using lattice QCD inputs. The lattice QCD inputs include ${\hat{B}}_K$, ${\xi }_0$, ${\xi }_2$, $|V_{us}|$, $m_c(m_c)$, and $|V_{cb}|$. Recently, FLAG has updated ${\hat{B}}_K$, exclusive $|V_{cb}|$ has been updated with new lattice data in the $\bar{B}\to D\ell \bar{\nu }$ decay mode, and RBC-UKQCD has updated ${\xi }_0$ and ${\xi }_2$. We find that the standard model evaluation of ${\epsilon }_K$ with exclusive $|V_{cb}|$ (lattice QCD inputs) is $3.2\sigma$ lower than the experimental value, while that with inclusive $|V_{cb}|$ (heavy quark expansion) shows no tension.

Comments: 6 pages, 6 figures, KAON 2016 proceeding, the same contents are also reported in ICHEP 2016 (PoS (ICHEP2016) 565). arXiv admin note: text overlap with arXiv:1611.00503