Current status of $\varepsilon_K$ in lattice QCD

TL;DR

This paper reviews the current lattice QCD calculations of the parameter _K, highlighting recent updates and their impact on the consistency between standard model predictions and experimental measurements.

Contribution

It provides an updated assessment of _K using recent lattice QCD inputs and compares the implications of exclusive versus inclusive _{cb} determinations.

Findings

Standard model _K with exclusive _{cb} is 3.2 sigma lower than experiment.

Inclusive _{cb} results show no significant tension.

Recent lattice updates have refined key inputs for _K evaluation.

Abstract

We present the current status of $\varepsilon_K$ 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 $\varepsilon_K$ 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.