CP Violation in \tau ->\nu\pi K_S and D->\pi K_S: The Importance of K_S-K_L Interference

Abstract

The $B$-factories have measured CP asymmetries in the $\tau\to\pi K_S\nu$ and $D\to K_S\pi$ modes. The $K_S$ state is identified by its decay to two pions at a time that is close to the $K_S$ lifetime. Within the Standard Model and many of its extensions, the asymmetries in these modes come from CP violation in $K^0-\bar{K}^0$ mixing. We emphasize that the interference between the amplitudes of intermediate $K_S$ and $K_L$ is as important as the pure $K_S$ amplitude. Consequently, the measured asymmetries depend on the times over which the relevant decay rates are integrated and on features of the experiment.