Time Dependence ofKe30Decays

Abstract

An experiment was performed at the Brookhaven Cosmotron to detect the $\beta$ decay of the products of the reaction ${\pi }^{-}+p\to \Lambda +K^0$. We have obtained spark-chamber photographs of 116 $K^0\to {\pi }^{\mp }+e^{\pm }+\nu$ events, and have determined the proper decay time of each $K^0$. The time distribution should be of the form ${\mathrm{}|1+x|\mathrm{}}^2{e}^{-{\lambda }_{1}t}+{\mathrm{}|1-x|\mathrm{}}^2{e}^{-{\lambda }_{2}t}-4\mathrm{}\mathrm{Im}\mathrm{}\left(x\right)\mathrm{}sin\delta t{e}^{\frac{-({\lambda }_1+{\lambda }_2)t}{2}}$, where ${\lambda }_1$ and ${\lambda }_2$ are the $K_S$ and $K_L$ decay rates, $\delta =m\left(K_L\right)-m\left(K_S\right)$, and $x$ is the complex ratio of the $\Delta S=-\Delta Q$ amplitude to the $\Delta S=+\Delta Q$ amplitude. We find $\mathrm{Re}\mathrm{}\left(x\right)=0.17_{-0.35\mathrm{}}^{}{}_{}{}^{+0.16\mathrm{}}$, $\mathrm{Im}\mathrm{}\left(x\right)=0.0\mathrm{}\pm 0.25$, a result inconsistent with a "maximal" violation of $\mathrm{CP}$ invariance.