Direct CP violation and the $\Delta I=1/2$ rule in $K\to \pi \pi$ decay in the Standard Model

Abstract

We discuss the RBC & UKQCD collaborations' recent lattice calculation of $\epsilon'$, the measure of direct CP-violation in kaon decays. This result significantly improves on our previous 2015 calculation, with nearly 4$\times$ the statistics and more reliable systematic error estimates. We discuss how our results demonstrate the Standard Model origin of the $\Delta I=1/2$ rule, and present our plans for future calculations.