CPViolation and Coherent Decays of Kaon Pairs

The possible experimental use of correlations between two neutral-kaon decays is discussed. Kaon pairs produced either in proton-antiproton annihilation from an $s$ state or in $\varphi$ decay are in a $p$ wave, which is forbidden by Bose statistics for identical bosons. The observance of a particular decay mode, i.e., ${\pi }^{+}{\pi }^{-}$, for one kaon implies that the other kaon is forbidden to decay at the same time in this mode. Thus a kaon beam can be constructed that is just that coherent linear combination of $K_S$ and $K_L$ whose amplitudes for decay into this mode cancel one another. The existence of $\Delta I=\frac{3}{2}$ transitions leading to the $I=2\mathrm{}$ final state in $K^0$ decay can be tested by looking for double decays where one of the kaons decays into ${\pi }^{+}{\pi }^{-}$ and the other into ${\pi }^0{\pi }^0$. This double decay is allowed at the same time only if both $\Delta I=\frac{1}{2}$ and $\Delta I=\frac{3}{2}$ amplitudes are present in the kaon decay. Detailed calculations and experimental implications are discussed.