Since RBC/UKQCD’s latest publication of lattice result for direct CP violation and the Delta I = 1/2 rule in $K ¥to ¥pi¥pi$ decay, which was made with G-parity boundary conditions in 2020, we have been revisiting this problem with a different lattice setup with periodic boundary conditions and multiple lattice spacings to see the consistency with our previous result and to improve the precision. While there was an expectation that it could be difficult to extract physical kinematics of K to pipi decay with periodic boundary conditions, we overcome it through the variational method. Also periodic boundary conditions provide a relatively easy way to introduce electromagnetic and isospin breaking corrections, which is desired to be implemented in near future.
In this talk, we show our preliminary result and discuss prospect of high-precision calculation of $K ¥to ¥pi¥pi$ decay with periodic boundary conditions.