Analysis ofCP-Noninvariant Interactions and theK10,K20System

In order to explain the recent observation of $K_2^{}{}_{}{}^0\to {\pi }^{+}+{\pi }^{-}$ by Christenson et al., we assume that the relevant interaction Hamiltonian can be separated into two parts: $H_G+H_F$, where $H_G$ is the usual $\mathrm{CP}$ conserving and $T$-invariant weak interaction and $H_F$ is a new interaction which is not invariant under $\mathrm{CP}$. Depending on the selection rule of $H_F$ with respect to the strangeness quantum number $S$, this new interaction $H_F$ can be much stronger than $H_G$, or somewhat weaker than $H_G$, or very much weaker than $H_G$. The properties of these three different classes of possibilities are discussed and some possible experimental tests are suggested. The system of $K_1^{}{}_{}{}^0$ and $K_2^{}{}_{}{}^0$ is analyzed for these different possibilities without assuming the validity of $\mathrm{CPT}$ invariance. Efforts are made to separate out the various experimental consequences that follow from different symmetry requirements which may be satisfied by this new $\mathrm{CP}$-noninvariant interaction $H_F$.