Lattice calculation of K→ππ decay and ππ scattering

We discuss the recent status of our lattice calculation of $\Delta I = 1/2$ amplitudes of $K\to\pi\pi$ decay and $\varepsilon'$, the measure of direct $CP$ violation. One highlight is that we now have the results 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. We also present some improvements in calculation of the two-pion scattering lengths for the $I=0$ and $I=2$ channels.