Measurement of the Relative Phase of the $K_L\to {\pi }^{+}{\pi }^{-}$ AND $K_S\to {\pi }^{+}{\pi }^{-}$ Decay Amplitudes by "Vacuum Regeneration"

The nonexponential ${\pi }^{+}{\pi }^{-}$ decay of neutral $K\text{'}\mathrm{s}$, due to the interference of $K_S$ and $K_L$ in this common channel, has been quantitiatively studied using a beam which is preponderantly $K^0$ at $t=0\mathrm{}$. The value (40±5)° is obtained for $\arg {\eta }_{+-}$ (${\eta }_{+-}=\frac{〈{\pi }^{+}{\pi }^{-}\mathrm{}\left|T\right|\mathrm{}{K}_L〉}{〈{\pi }^{+}{\pi }^{-}|T\times |K_S〉}$), using $\frac{\Delta m}{h}=\frac{(M_L-M_S)}{h}=0.538\mathrm{}\times {10}^{10}$ ${\sec }^{-1\mathrm{}}$; allowing for the current uncertainty in $\Delta m$, the error in $\arg {\eta }_{+-}$ becomes ± 12.5°. This result agrees with the predictions of that class of theories which give $\arg {\eta }_{+-}\simeq invtan\left(\frac{2\Delta m}{h{\Gamma }_S}\right)$, in particular the "superweak" theory, for which this prediction is exact.