Non-degenerate quark mass effect on $B_K$ with a mixed action

TL;DR

This paper studies how non-degenerate quark masses significantly influence the calculation of $B_K$, emphasizing the importance of including this effect for precise results, while also noting smaller impacts on related parameters.

Contribution

It demonstrates the sizable impact of non-degenerate quark masses on $B_K$ and improves fitting quality by incorporating these effects, advancing precision in lattice QCD calculations.

Findings

Non-degenerate quark effects on $B_K$ are significantly large.

Including non-degenerate effects improves fit quality for $B_K$.

Effects on $B_7^{(3/2)}$ and $B_8^{(3/2)}$ are relatively small.

Abstract

We investigate the effect of non-degenerate quarks on $B_K$. This effect is noticeably large for $B_K$ (significantly larger than statistical uncertainty). Hence, it is important to include this effect in order to determine $B_K$ with higher precision. We also observe that the quality of fitting for $B_K$ gets better when we include non-degenerate combinations to fit to the prediction by Van de Water and Sharpe. However, this effect on $B_7^{(3/2)}$ and $B_8^{(3/2)}$ turns out to be relatively small.