Clean Prediction of \CP violating processes $\psi$, $\phi$ and $\Upsilon(1S)$ decay to KsKs and KLKL

Abstract

The ratio of $K_S K_S$ ($K_L K_L$) and $K_S K_L$ production rates is calculated by considering $K^0 - K^0bar$ oscillation in $J/\psi \to K^0K^0bar$ decay. The theoretical uncertainty due to strong interaction in $J/\psi$ decay is completely canceled in the ratio, therefore, the absolute branching fractions of the \CP violating processes of $J/\psi \to K_S K_S $ and $K_L K_L$ can be cleanly and model-independently determined in case that $J/\psi \to K_S K_L$ decay is precisely measured. In the future $\tau$-Charm factory, the expected \CP violating process of $J/\psi \to K_S K_S $ should be reached. It is important to measure $J/\psi$ to $K_S K_S$ and K_S K_L decays simultaneously, so that many systematic errors will be canceled. More precise measurements are suggested to examine the predicted isospin relation in $J/\psi \to KKbar$ decays. All results can be extended to decays of other vector quarkonia, $\phi$, $\psi(2S)$ and $\Upsilon(1S)$ and so on.