Clean Prediction of \CP violating processes $ψ$, $ϕ$ and $Υ(1S)$ 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 $J/ψ\to K^0K^0bar$ decay. The theoretical uncertainty due to strong interaction in $J/ψ$ decay is completely canceled in the ratio, therefore, the absolute branching fractions of the \CP violating processes of $J/ψ\to K_S K_S $ and $K_L K_L$ can be cleanly and model-independently determined in case that $J/ψ\to K_S K_L$ decay is precisely measured. In the future $τ$-Charm factory, the expected \CP violating process of $J/ψ\to K_S K_S $ should be reached. It is important to measure $J/ψ$ 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 $J/ψ\to KKbar$ decays. All results can be extended to decays of other vector quarkonia, $ϕ$, $ψ(2S)$ and $Υ(1S)$ and so on.