Status report on $\varepsilon_K$ with lattice QCD inputs

TL;DR

This paper reviews the current status of the CP violation parameter $oldsymbol{ ext{epsilon}_K}$ in the neutral kaon system, using lattice QCD inputs to evaluate the Standard Model prediction and compare it with experimental data.

Contribution

It updates the evaluation of $oldsymbol{ ext{epsilon}_K}$ using recent lattice QCD inputs and compares the tension between theory and experiment for different $|V_{cb}|$ determinations.

Findings

Standard Model $ ext{epsilon}_K$ with exclusive $|V_{cb}|$ shows 3.2$oldsymbol{\sigma}$ tension with experiment.

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

Updated lattice inputs have refined the theoretical prediction of $ ext{epsilon}_K$.

Abstract

We report the current status of $\varepsilon_K$, the indirect CP violation parameter in the neutral kaon system, evaluated using the lattice QCD inputs. We use lattice QCD to fix $\hat{B}_K$, $\xi_0$, $\xi_2$, $|V_{us}|$, $m_c(m_c)$, and $|V_{cb}|$. Since Lattice 2015, FLAG updated $\hat{B}_K$, exclusive $V_{cb}$ has been updated with new lattice data in the $\bar{B}\to D\ell\nu$ decay channel, and RBC-UKQCD has updated $\xi_0$ and $\xi_2$. Our preliminary results show that the standard model evaluation of $\varepsilon_K$ with exclusive $|V_{cb}|$ (lattice QCD inputs) has $3.2\sigma$ tension with the experimental value, while that of $\varepsilon_K$ with inclusive $|V_{cb}|$ (heavy quark expansion) shows no tension.