Methods for Testing theCPTTheorem

The decay and interactions of the neutral $K$ mesons are shown to provide some direct tests of the validity of the $\mathrm{CPT}$ theorem for weak interactions of strange particles. The connection with related tests of $\mathrm{CP}$ and $T$ invariance is also discussed. It is found that the absence of a $2\pi$ decay mode of the $K_2$ is an indication of $\mathrm{CP}$ invariance of the nonleptonic interactions of the $K$ meson but not a proof thereof. Even if $\mathrm{CPT}$ invariance is assumed, the $2\pi$ mode does not provide an unambiguous test of $\mathrm{CP}$ invariance. It is shown that the absence of a detectable charge asymmetry in the leptonic decay of the $K_2$ indicates either $\mathrm{CPT}$ or $\mathrm{CP}$ invariance of the leptonic interactions if the nonleptonic interactions are assumed to be $\mathrm{CP}$ invariant. A direct test of $\mathrm{CP}$ invariance would be provided by a measurement of the interference term in the leptonic decay curve of the $K^0$, as noted by Sachs and Treiman. A direct test of $\mathrm{CPT}$ invariance would be provided by an accurate measurement of the interference term for each of the charge states in the leptonic decay of the $K^0$.