Current status of $\varepsilon_K$ with lattice QCD inputs

TL;DR

This paper evaluates the Standard Model prediction of the CP violation parameter epsilon_K using lattice QCD inputs and compares it with experimental data, revealing a tension with exclusive V_cb but not with inclusive V_cb.

Contribution

It provides a comprehensive analysis of epsilon_K using lattice QCD inputs and different V_cb determinations, highlighting the impact on SM predictions.

Findings

SM prediction of epsilon_K with exclusive V_cb is 3.6 sigma below experiment

Using inclusive V_cb, the discrepancy with experiment disappears

The analysis emphasizes the importance of V_cb determination method

Abstract

We present the Standard Model evaluation of the indirect CP violation parameter $\varepsilon_K$ using inputs determined from lattice QCD together with experiment: $|V_{us}|$, $|V_{cb}|$, $\xi_0$, and $\hat{B}_K$. We use the Wolfenstein parametrization ($|V_{cb}|$, $\lambda$, $\bar{\rho}$, $\bar{\eta}$) for the CKM matrix elements. For the central value, we take the angle-only fit of the UTfit collaboration, and use $|V_{us}|$ from the $K_{\ell 3}$ and $K_{\mu 2}$ decays as an independent input to fix $\lambda$. For the error estimate, we use results of the global unitarity triangle fits from the CKMfitter and UTfit collaborations. We find that the Standard Model (SM) prediction of $\varepsilon_K$ with exclusive $V_{cb}$ (lattice QCD results) is lower than the experimental value by $3.6(2)\sigma$. However, with inclusive $V_{cb}$ (results of the heavy quark expansion), the tension between the SM prediction of $\varepsilon_K$ and its experimental value disappears.