A rare decay $K_L ¥to ¥mu^+ ¥mu^-$ has been measured precisely, while a similar rare decay $K_S ¥to ¥mu^+ ¥mu^-$ has not been seen yet, which will be measured by an upgrade of the LHCb experiment. Although both processes are almost CP conserving, I will point out that an interference contribution between $K_L$ and $K_S$ in a neutral kaon beam emerges from a genuine direct CP violation. It will be shown that the interference contribution can be a comparable size to the standard-model prediction of BR$(K_S ¥to ¥mu^+ ¥mu^-)$. I will also introduce several new physics effects in $K ¥to ¥mu^+ ¥mu^-$, and a connection with $¥epsilon’/¥epsilon$, which is a direct CP violation in $K ¥to ¥pi ¥pi$.
References:
arXiv:1707.06999, Phys.Rev.Lett. 119 (2017) 20, 201802
arXiv:1711.11030, JHEP 05 (2018) 024
arXiv:1712.04959, JHEP 04 (2018) 019