$\Delta I =1/2$ process of $K\to\pi\pi$ decay on multiple ensembles with periodic boundary conditions

TL;DR

This paper reports preliminary lattice QCD results for $K o\pi\pi$ decay and direct CP violation, using multiple ensembles with different lattice spacings, aiming to understand continuum limit behavior.

Contribution

The study introduces a new finer lattice ensemble and updates previous results with increased statistics, advancing the calculation of $K o\pi\pi$ decay matrix elements.

Findings

Preliminary results for $ ext{ extbackslash delta} I=1/2$ matrix elements.

Initial assessment of continuum limit with $O(a^2)$ scaling considerations.

Comparison between coarse and fine lattice results.

Abstract

We present our preliminary results for the $\Delta I = 1/2$ matrix elements of $K\to\pi\pi$ decay and $\varepsilon'$, the measure of direct $CP$ violation in $K\to\pi\pi$, computed on multiple ensembles with periodic boundary conditions (PBC) at the inverse lattice spacings of $a^{-1} \approx 1.0$~GeV and 1.4~GeV. The finer lattice ensemble is newly introduced as an extension to the first PBC calculation [1], while the calculation on the coarser ensemble is updated with the approximately doubled statistics. Our first attempt to take the continuum limit is also discussed with acknowledging potential significance of the $O(a^2)$ scaling violation on these coarse lattices.