Current status of $\varepsilon_K$ calculated with lattice QCD inputs

TL;DR

This paper calculates the Standard Model prediction of the CP violation parameter _K using lattice QCD inputs and compares it with experimental data, revealing a significant discrepancy.

Contribution

It provides a lattice QCD-based calculation of _K incorporating updated CKM inputs and systematic error estimates, highlighting a notable tension with experimental results.

Findings

A 3.3(2) discrepancy between theory and experiment with exclusive V_{cb}

Use of lattice QCD inputs for _K calculation

Systematic error estimation from different CKM parameter sources

Abstract

We present results for $\varepsilon_K$, 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 $\bar{B}\to D^*\ell\bar{\nu}$ 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 $\varepsilon_K$ and experiment with exclusive $V_{cb}$. We report details of this preliminary result.