Angular Correlations inK0-Decay Processes

The reactions $K^0\to \{e^{\pm } or {\mu }^{\pm }\}+\nu +{\pi }^{\mp }$ afford a good opportunity to study fully the dynamics of decay processes involving leptons. It is shown that, under certain rather general assumptions customarily adopted in regard to weak lepton interactions, the distribution in angle between $\pi$ and $\nu$ has a simple, uniquely specified form, independent of the properties of the $K$ particle; namely, aside from a known, angle-dependent factor related to phase volume, the distribution is proportional to $A+Bcos\theta +C{cos}^2\theta$, where $A$, $B$, and $C$ may depend on the $\pi$ momentum. For any given momentum, the relative magnitudes of $A$, $B$, and $C$, when determined experimentally, can be expected to illuminate a second aspect of the problem; namely, the detailed nature of the lepton coupling. The situation is especially transparent for the $e-\nu -\pi$ mode in the case that the $K$ particle has zero spin. This is discussed in some detail.