Update on $\varepsilon_K$ with lattice QCD inputs

TL;DR

This paper updates the calculation of the CP violation parameter in neutral kaons using lattice QCD inputs, revealing a significant tension with experimental data when using exclusive $|V_{cb}|$ values.

Contribution

It provides the latest lattice QCD-based evaluation of $oldsymbol{ ext{epsilon}_K}$, highlighting discrepancies with experimental results depending on the $|V_{cb}|$ determination method.

Findings

Exclusive $|V_{cb}|$ shows 4.0$\sigma$ tension with experiment.

Inclusive $|V_{cb}|$ shows no tension.

Updated lattice inputs improve the precision of $ ext{epsilon}_K$ evaluation.

Abstract

We report updated results for $\varepsilon_K$, 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 $\varepsilon_K$ 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.