Interference between Neutral Kaons and Their Mass Difference

A $K^{+}$ beam of $990-\frac{\mathrm{MeV}}{c}$ momentum was used to produce a $K^0$ beam in charge-exchange collision with a copper target. By interposing an iron regenerator at a certain distance from the target and taking spark-chamber pictures of $2\pi$ decays behind the regenerator, we have observed the interference in the $2\pi$ decay mode between the $K_S$ state produced in the original charge exchange and the $K_S$ state ($K_{\mathrm{LS}}$) produced via regeneration. The difference in phase between these $K_S$ and $K_{\mathrm{LS}}$ states depends upon the proper time elapsed between production and regeneration (because of the mass difference between $K_S$ and $K_L$) and can therefore be changed at will by changing the corresponding distance. The shape of the curve with the observed minimum gives us the magnitude of the mass difference, and its sign as well if the phase of the regeneration amplitude is given. In a separate work we have determined that phase from scattering experiments with charged kaons on iron nuclei. Comparing that information with the present experiment, we obtain the following results: (1) The two-pion states into which $K_S$ and $K_{\mathrm{LS}}$ decay are quantum-mechanically identical. Since $\left|K_L〉 \mathrm{and} \right|K_{\mathrm{LS}}〉$ interference has already been observed, we must then expect that the time dependence of the $2\pi$ decay of $K^0$ will differ from that of ${\overline{K}}^0$ because of the $|K_S〉\to |2\mathrm{}\pi 〉$, $|K_L〉\to |2\mathrm{}\pi 〉$ interference. (2) The sign of the mass difference is such that $K_L$ is heavier than $K_S$ with a level of confidence that, barring unknown systematic errors, appears to be beyond question. (3) The value of the mass difference obtained by us is 0.42±0.04 in units of $\frac{\hslash }{{\tau }_S}$, where ${\tau }_S$ is the $K_S$ mean life. (4) We have also observed the effect of the constructive interference between the scattered amplitude $f_{11}|K_S〉$ and the diffraction-regenerated amplitude $f_{21}|K_S〉$. This effect confirms that $K_L$ is heavier than $K_S$.