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

Understand

We present a lattice QCD calculation of the $\Delta I=1/2$, $K\to\pi\pi$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\to\pi\pi$ decay, improving our 2015 calculation of these quantities.

• Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV.
• However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the $\pi\pi$ ground-state and more accurately relate the lattice operators to those defined in the Standard Model.
• We find ${\rm Re}(A_0)=2.99(0.32)(0.59)\times 10^{-7}$ GeV and ${\rm Im}(A_0)=-6.98(0.62)(1.44)\times 10^{-11}$ GeV, where the errors are statistical and systematic, respectively.