Current status of ${\epsilon }_K$ calculated with lattice QCD inputs

Abstract

We present results for ${\epsilon }_K$, the indirect CP violation parameter, calculated in the Standard Model using inputs from lattice QCD: the kaon bag parameter ${\hat{B}}_K$, and the CKM matrix element $V_{cb}$ from the axial current form factor for the exclusive decay $\bar{B}\to D^{\ast }\ell \bar{\nu }$ at zero-recoil. In addition, we take the coordinates of the unitarity triangle apex $(\bar{\rho },\bar{\eta })$ from the angle-only fit of the UTfit Collaboration and use $V_{us}$ to fix $\lambda$. In order to estimate the systematic error, we also use Wolfenstein parameters from the CKMfitter and UTfit. We find a $3.3(2)\sigma$ difference between ${\epsilon }_K$ and experiment with exclusive $V_{cb}$. We report details of this preliminary result.

Comments: 7 pages, 4 figures, Lattice 2014 proceeding; PoS (LATTICE 2014) 371